NAMIC Wiki - User contributions [en]

Projects:LearningRegistrationCostFunctions

2009-09-10T22:49:25Z

Ythomas: /* (2b) Cross-validating In-vivo Subjects */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications.

= Motivation =
Image registration is ambiguous. For example, the figures below show two subjects with Brodmann areas overlaid on their cortical folding patterns. Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|300px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|300px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights of the wSSD (black). The optimal uniform weights of the wSSD are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|300px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|300px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered, as shown by the green outline in Fig(a). During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|250px|(a) Initial Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|250px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|250px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|300px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We use the ex-vivo MT template to predict MT+ in the 42 in-vivo subjects. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|300px]]

== (2b) Cross-validating In-vivo Subjects ==
We now perform cross-validation within the in-vivo data set. We consider 9, 19 or 29 training subjects for the task-optimal template. For FreeSurfer, there is no training, so there is only 1 data point. Like before, task-optimal template achieves lower localization errors.

<center>
<table>
<tr>
<td>
[[Image:To.LeftInvivoCrossValidation.png|thumb|center|250px|(a) Initial Template]]
</td>
<td>
[[Image:To.RightInvivoCrossValidation.png|thumb|center|250px|(b) Test Subject]]
</td>
</tr>
</table>
</center>

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T22:49:10Z

Ythomas:

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications.

= Motivation =
Image registration is ambiguous. For example, the figures below show two subjects with Brodmann areas overlaid on their cortical folding patterns. Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|300px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|300px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights of the wSSD (black). The optimal uniform weights of the wSSD are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|300px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|300px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered, as shown by the green outline in Fig(a). During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|250px|(a) Initial Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|250px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|250px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|300px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We use the ex-vivo MT template to predict MT+ in the 42 in-vivo subjects. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|300px]]

== (2b) Cross-validating In-vivo Subjects ==
We now perform cross-validation within the invivo data set. We consider 9, 19 or 29 training subjects for the task-optimal template. For FreeSurfer, there is no training, so there is only 1 data point. Like before, task-optimal template achieves lower localization errors.

<center>
<table>
<tr>
<td>
[[Image:To.LeftInvivoCrossValidation.png|thumb|center|250px|(a) Initial Template]]
</td>
<td>
[[Image:To.RightInvivoCrossValidation.png|thumb|center|250px|(b) Test Subject]]
</td>
</tr>
</table>
</center>

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T22:47:48Z

Ythomas: /* (2) Localizing fMRI-defined MT+ Using Cortical Folding */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications.

= Motivation =
Image registration is ambiguous. For example, the figures below show two subjects with Brodmann areas overlaid on their cortical folding patterns. Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|300px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|300px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights of the wSSD (black). The optimal uniform weights of the wSSD are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|300px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|300px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered, as shown by the green outline in Fig(a). During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|250px|(a) Initial Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|250px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|250px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|300px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We use the ex-vivo MT template to predict MT+ in the 42 in-vivo subjects. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|300px]]

== (2b) Cross-validating In-vivo Subjects ==
We now perform cross-validation within the invivo data set. We consider 9, 19 or 29 training subjects for the task-optimal template. For FreeSurfer, there is no training, so there is only 1 data point.

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

File:To.RightInvivoCrossValidation.png

2009-09-10T22:46:00Z

Ythomas:

File:To.LeftInvivoCrossValidation.png

2009-09-10T22:45:49Z

Ythomas:

Projects:LearningRegistrationCostFunctions

2009-09-10T22:44:07Z

Ythomas: /* (2) Localizing fMRI-defined MT+ Using Cortical Folding */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications.

= Motivation =
Image registration is ambiguous. For example, the figures below show two subjects with Brodmann areas overlaid on their cortical folding patterns. Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|300px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|300px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights of the wSSD (black). The optimal uniform weights of the wSSD are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|300px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|300px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered, as shown by the green outline in Fig(a). During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|250px|(a) Initial Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|250px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|250px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|300px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We use the ex-vivo MT template to predict MT+ in the 42 in-vivo subjects. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|300px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T22:39:27Z

Ythomas: /* (1b) Interpreting Task-Optimal Template Estimation */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications.

= Motivation =
Image registration is ambiguous. For example, the figures below show two subjects with Brodmann areas overlaid on their cortical folding patterns. Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|300px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|300px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights of the wSSD (black). The optimal uniform weights of the wSSD are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|300px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|300px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered, as shown by the green outline in Fig(a). During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|250px|(a) Initial Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|250px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|250px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|300px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We use the ex-vivo MT template to predict MT+ in the 42 in-vivo subjects. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T22:38:45Z

Ythomas: /* (1) Localizing Brodmann Areas Using Cortical Folding */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications.

= Motivation =
Image registration is ambiguous. For example, the figures below show two subjects with Brodmann areas overlaid on their cortical folding patterns. Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|300px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|300px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights of the wSSD (black). The optimal uniform weights of the wSSD are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|300px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|300px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered, as shown by the green outline in Fig(a). During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px|(a) Initial Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We use the ex-vivo MT template to predict MT+ in the 42 in-vivo subjects. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T22:38:31Z

Ythomas: /* Motivation */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications.

= Motivation =
Image registration is ambiguous. For example, the figures below show two subjects with Brodmann areas overlaid on their cortical folding patterns. Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|300px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|300px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights of the wSSD (black). The optimal uniform weights of the wSSD are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered, as shown by the green outline in Fig(a). During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px|(a) Initial Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We use the ex-vivo MT template to predict MT+ in the 42 in-vivo subjects. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T22:38:21Z

Ythomas: /* Motivation */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications.

= Motivation =
Image registration is ambiguous. For example, the figures below show two subjects with Brodmann areas overlaid on their cortical folding patterns. Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|300px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|300px]]
</td>
</tr>
</table>
</center>

Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights of the wSSD (black). The optimal uniform weights of the wSSD are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered, as shown by the green outline in Fig(a). During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px|(a) Initial Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We use the ex-vivo MT template to predict MT+ in the 42 in-vivo subjects. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:RegistrationRegularization

2009-09-10T22:37:46Z

Ythomas: /* Key Investigators */

Back to [[Algorithm:MIT|MIT Algorithms]]

We propose a unified framework for computing atlases from manually labeled data sets at various degrees of “sharpness” and the joint registration and segmentation of a new brain with these atlases. In non-rigid registration, the tradeoff between warp regularization and image fidelity is typically set empirically. In segmentation, this leads to a probabilistic atlas of arbitrary “sharpness”: weak regularization results in well-aligned training images, producing a “sharp” atlas; strong regularization yields a “blurry” atlas. We study the effects of this tradeoff in the context of cortical surface parcellation, but the framework applies to volume registration as well. This is an important question because of the increasingly availability of atlases in public databases and the development of registration algorithms separate from the atlas construction process.

= Description =
In image registration, one usually optimizes the objective function with two parts. The first term is the similarity between images. The second term regularizes the warp. The smoothness parameter that weights the second term determines the tradeoff between the similarity measure and the regularization. In Atlas-based segmentation, one is given a set of labeled training images. The training images are co-registered to a common space. An atlas that summarizes the information between the image features and the labels is computed in this common space. This atlas is used to segment and normalize a new image.

[[Image:RegSeg.png|center|400px|]]

We employ a generative model for the joint registration and segmentation of images (see figures below). The atlas construction process arises naturally as estimation of the model parameters. This framework allows the computation of unbiased atlases from manually labeled data at various degrees of "sharpness", as well as the joint registration and segmentation of a novel brain in a consistent manner.

<center>
<table>
<tr>
<td>
[[Image:JointRegSeg.png|thumb|center|420px| Joint Registration-Segmentation]]
</td>
<td>
[[Image:GraphicalModel.png|thumb|center|400px|"A" is an atlas used to generate the label map L' in some universal atlas space. The atlas A and label map L' generate image I'. S is the smoothness parameter that generates random warp field R. This warp is then applied to the label map L' and image I' to create the label map L and the image I. We assume the label map L is available for the training images, but not for the test image. The image I is observed in both training and test cases.]]
</td>
</tr>
</table>
</center>

We use the generative model to compute atlases from manually labeled data at various degrees of “sharpness” and the joint registration-segmentation of a new brain with these atlases. Using this framework, we investigate the tradeoff between warp regularization and image ﬁdelity, i.e. the smoothness of the new subject warp and the sharpness of the atlas. We compare three special cases of our framework, namely:

(1) Progressive registration of a new brain to increasingly “sharp” atlases using increasingly flexible warps, by initializing each registration stage with the optimal warps from a “blurrier” atlas. We call this multiple atlases, multiple warp scales (MAMS).

(2) Progressive registration to a single atlas with increasingly flexible warps. We call this single atlas, multiple warp scales (SAMS).

(3) Registration to a single atlas with fixed constrained warps. We call this single atlas, single warp scale (SASS).

== Experimental Results ==

We use dice as the measure of segmentation quality. From the graph below, we note that the optimal algorithms correspond to a unique balance between atlas “sharpness” and warp regularization. Our experiments show that the optimal parameter values that correspond to this balance can be determined using cross-validation. The optimal parameter values are robust across subjects, and the same for both co-registration of the training data and registration of a new subject. This suggests that a single atlas at an optimal sharpness is sufficient to achieve the best segmentation results. Furthermore, our experiments also suggest that segmentation accuracy is tolerant up to a small mismatch between atlas sharpness and warp smoothness.

[[Image:AvgResults.jpg|thumb|center|300px|Plot of Dice as a function of the warp smoothness S. Note that S is on a log scale. <math>\alpha</math> corresponds to the sharpness of the atlas used.]]

In the figure below, we display the percentage improvement of SASS over FreeSurfer [1,2]. For each of the 35 structures for each hemisphere, we perform a one-sided paired-sampled t-test between SASS and FreeSurfer, where each subject is considered a sample. We use the False Discovery Rate (FDR) to correct for multiple comparisons. In the left hemisphere, SASS achieves statistically significant improvement over FreeSurfer for 17 structures (FDR < 0.05), while the remaining structures yield no statistical difference. In the right hemisphere, SASS achieves improvement for 11 structures (FDR < 0.05), while the remaining structures yield no statistical difference. The p-values for the left and right hemispheres are pooled together for the False Discovery Rate analysis.

<center>
<table>
<tr>
<td>
[[Image:Lh.PercentImprove1.png|thumb|center|150px|Left Medial]]
</td>
<td>
[[Image:Lh.PercentImprove2.png|thumb|center|150px|Left Lateral]]
</td>
<td>
[[Image:Rh.PercentImprove2.png|thumb|center|150px|Right Lateral]]
</td>
<td>
[[Image:Rh.PercentImprove1.png|thumb|center|142px|Right Medial]]
</td>
</tr>
</table>
</center>

[1] Fischl, Sereno and Dale. High-resolution intersubject averaging and a coordinate system for the cortical surface. Human Brain Mapping, 8(4):272--284, 1999

[2] Fischl, van der Kouwe, Destrieux, Halgren, Segonne, Salat, Busa, Seidman, Goldstein, Kennedy, Caviness, Makris, Rosen and Dale. Automatically Parcellating the Human cerebral Cortex. Cerebral Cortex, 14:11--22, 2004

= Key Investigators =

* MIT : [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH : Rahul Desikan, Bruce Fischl

= Publications =
''In Print''

* [http://www.na-mic.org/publications/pages/display?search=Projects:RegistrationRegularization&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database]

[[Category: Registration]] [[Category:Segmentation]]

Projects:SphericalDemons

2009-09-10T22:36:58Z

Ythomas: /* Key Investigators */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline
interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently
approximated on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, the resulting registration is
diffeomorphic and fast -- registration of two cortical mesh models with more than 100k nodes takes less than 5 minutes, comparable to the fastest surface registration algorithms. Moreover, the accuracy of our method compares favorably to the popular FreeSurfer
registration algorithm. We validate the technique in two different settings: (1) parcellation in a set of in-vivo cortical surfaces and (2) Brodmann area localization in ex-vivo cortical surfaces.

= Description =
Motivated by the spherical representation of the cerebral cortex, this work deals with the problem of registering spherical images. Cortical folding patterns are correlated with both cytoarchitectural and functional regions. In group studies of cortical structure and function, determining corresponding folds across subjects is therefore important.

Unfortunately, many spherical warping algorithms are computationally expensive. One reason is the need for invertible deformations that preserve the topology of structural or functional regions across subjects. In this work, we take the approach, previously demonstrated in the Euclidean space [3], of restricting the deformation space to be a composition of diffeomorphisms, each of which is parameterized by a stationary velocity field. In each iteration, the algorithm greedily seeks the best diffeomorphism to be composed with the current transformation, resulting in much faster updates.

Another challenge in registration is the tradeoff between the image similarity measure and the regularization in the objective function. Since most regularizations favor smooth deformations, the gradient computation is complicated by the need to take into account the deformation in neighboring regions. For Euclidean images, the demons objective function facilitates a fast two-step optimization where the second step handles the warp regularization via a single convolution with a smoothing filter [2,3]. Based on spherical vector spline interpolation theory and other differential geometric tools, we show that the two-stage optimization procedure of the demons algorithm can be efficiently applied on the sphere.

[[Image:CoordinateChart.png | center | 400px]]

= Experimental Results =
We use two sets of experiments to compare the accuracy of Spherical Demons and FreeSurfer [1]. The FreeSurfer registration algorithm uses the same similarity measure as Spherical Demons, but penalizes for metric and areal distortion. Its runtime is more than an hour while our runtime is less than 5 minutes.

== (1) Parcellation of In-Vivo Cortical Surfaces ==

We consider a set of 39 left and right cortical surface models extracted from in-vivo MRI. Each surface is spherically parameterized and represented as a spherical image with geometric features at each vertex (e.g., sulcal depth and curvature). Both hemispheres are manually parcellated by a neuroanatomist into 35 major sulci and gyri. We validate our algorithm in the context of automatic cortical parcellation.

We co-register all 39 spherical images of cortical geometry with Spherical Demons by iteratively building an atlas and registering
the surfaces to the atlas. The atlas consists of the mean and variance of cortical geometry. We then perform cross-validation parcellation 4 times, by leaving out subjects 1 to 10, training a classifier using the remaining subjects, and using it to classify subjects 1 to 10. We repeat with subjects 11-20, 21-30 and 31-39. We also perform registration and cross-validation with the FreeSurfer algorithm [1] using the same features and parcellation algorithm. Once again, the atlas consists of the mean and variance of cortical geometry.

The average Dice measure (defined as the ratio of cortical surface area with correct labels to the total surface area averaged over the test set) on the left hemisphere is 88.9 for FreeSurfer and 89.6 for Spherical Demons. While the improvement is not big, the
difference is statistically significant for a one-sided t-test with the Dice measure of each subject treated as an independent sample (p = 2e-6). On the right hemisphere, FreeSurfer obtains a Dice of 88.8 and Spherical Demons achieves 89.1. Here, the improvement is smaller, but still statistically significant (p = 0.01).

<center>
<table>
<tr>
<td>
[[Image:SD.Lh.PercentImprove.lat.png|thumb|center|150px|Left Medial]]
</td>
<td>
[[Image:SD.Lh.PercentImprove.med.png|thumb|center|150px|Left Lateral]]
</td>
<td>
[[Image:SD.Rh.PercentImprove.lat.png|thumb|center|150px|Right Lateral]]
</td>
<td>
[[Image:SD.Rh.PercentImprove.med.png|thumb|center|142px|Right Medial]]
</td>
</tr>
</table>
</center>

Because the average Dice can be deceiving by suppressing small structures, we analyze the segmentation accuracy per structure. On
the left (right) hemisphere, the segmentations of 16 (8) structures are statistically significantly improved by Spherical Demons with respect to FreeSurfer, while no structure got worse (FDR = 0.05). The above figure shows the percentage improvement
of individual structures. Parcellation results suggest that our registration is at least as accurate as FreeSurfer.

== (2) Brodmann Areas Localization on Ex-vivo Cortical Surfaces ==

In this experiment, we evaluate the registration accuracy on ten human brains analyzed histologically postmortem. The histological sections were aligned to postmortem MR with nonlinear warps to build a 3D volume. Eight manually labeled Brodmann areas from histology were sampled onto each hemispheric surface model and sampling errors were manually corrected. Brodmann areas are cyto-architectonically defined regions closely related to cortical function.

It has been shown that nonlinear surface registration of cortical folds can significantly improve Brodmann area overlap across
different subjects. Registering the ex-vivo surfaces is more difficult than in-vivo surfaces because the reconstructed volumes are extremely noisy, resulting in noisy geometric features.

We co-register the ten surfaces to each other by iteratively building an atlas and registering the surfaces to the atlas. We
compute the average distance between the boundaries of the Brodmann areas for each pair of registered subjects. We perform a permutation test to test for statistical significance. Spherical Demons improves the alignment of 5 (2) Brodmann areas on the left (right) hemisphere (FDR = 0.05) compared with FreeSurfer and no structure gets worse. These results suggest that the Spherical Demons algorithm is at least as accurate as FreeSurfer in aligning Brodmann areas.

= Code =

Matlab code is currently available at http://yeoyeo02.googlepages.com/sphericaldemonsrelease

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

[2] J. Thirion. Image Matching as a Diffusion Process: an Analogy with Maxwell’s Demons. Medical Image Analysis,
2(3):243–260, 1998.

[3] T. Vercauteren, X. Pennec, A. Perchant, and N. Ayache. Non-parametric Diffeomorphic Image Registration with the
Demons Registration. In Proceedings of the International Conference on Medical Image Computing and Computer Assisted
Intervention (MICCAI), volume 4792 of LNCS, pages 319–326, 2007.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl
* INRIA: Nicholas Ayache
* Mauna Kea Technologies: Tom Vercauteren
* Kitware: Luis Ibanez, Michel Audette

= Publications =
''In Print''

* [http://www.na-mic.org/publications/pages/display?search=Projects:SphericalDemons&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database]

[[Category: Registration]] [[Category:Segmentation]]

Projects:SphericalDemons

2009-09-10T22:35:57Z

Ythomas: /* Key Investigators */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline
interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently
approximated on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, the resulting registration is
diffeomorphic and fast -- registration of two cortical mesh models with more than 100k nodes takes less than 5 minutes, comparable to the fastest surface registration algorithms. Moreover, the accuracy of our method compares favorably to the popular FreeSurfer
registration algorithm. We validate the technique in two different settings: (1) parcellation in a set of in-vivo cortical surfaces and (2) Brodmann area localization in ex-vivo cortical surfaces.

= Description =
Motivated by the spherical representation of the cerebral cortex, this work deals with the problem of registering spherical images. Cortical folding patterns are correlated with both cytoarchitectural and functional regions. In group studies of cortical structure and function, determining corresponding folds across subjects is therefore important.

Unfortunately, many spherical warping algorithms are computationally expensive. One reason is the need for invertible deformations that preserve the topology of structural or functional regions across subjects. In this work, we take the approach, previously demonstrated in the Euclidean space [3], of restricting the deformation space to be a composition of diffeomorphisms, each of which is parameterized by a stationary velocity field. In each iteration, the algorithm greedily seeks the best diffeomorphism to be composed with the current transformation, resulting in much faster updates.

Another challenge in registration is the tradeoff between the image similarity measure and the regularization in the objective function. Since most regularizations favor smooth deformations, the gradient computation is complicated by the need to take into account the deformation in neighboring regions. For Euclidean images, the demons objective function facilitates a fast two-step optimization where the second step handles the warp regularization via a single convolution with a smoothing filter [2,3]. Based on spherical vector spline interpolation theory and other differential geometric tools, we show that the two-stage optimization procedure of the demons algorithm can be efficiently applied on the sphere.

[[Image:CoordinateChart.png | center | 400px]]

= Experimental Results =
We use two sets of experiments to compare the accuracy of Spherical Demons and FreeSurfer [1]. The FreeSurfer registration algorithm uses the same similarity measure as Spherical Demons, but penalizes for metric and areal distortion. Its runtime is more than an hour while our runtime is less than 5 minutes.

== (1) Parcellation of In-Vivo Cortical Surfaces ==

We consider a set of 39 left and right cortical surface models extracted from in-vivo MRI. Each surface is spherically parameterized and represented as a spherical image with geometric features at each vertex (e.g., sulcal depth and curvature). Both hemispheres are manually parcellated by a neuroanatomist into 35 major sulci and gyri. We validate our algorithm in the context of automatic cortical parcellation.

We co-register all 39 spherical images of cortical geometry with Spherical Demons by iteratively building an atlas and registering
the surfaces to the atlas. The atlas consists of the mean and variance of cortical geometry. We then perform cross-validation parcellation 4 times, by leaving out subjects 1 to 10, training a classifier using the remaining subjects, and using it to classify subjects 1 to 10. We repeat with subjects 11-20, 21-30 and 31-39. We also perform registration and cross-validation with the FreeSurfer algorithm [1] using the same features and parcellation algorithm. Once again, the atlas consists of the mean and variance of cortical geometry.

The average Dice measure (defined as the ratio of cortical surface area with correct labels to the total surface area averaged over the test set) on the left hemisphere is 88.9 for FreeSurfer and 89.6 for Spherical Demons. While the improvement is not big, the
difference is statistically significant for a one-sided t-test with the Dice measure of each subject treated as an independent sample (p = 2e-6). On the right hemisphere, FreeSurfer obtains a Dice of 88.8 and Spherical Demons achieves 89.1. Here, the improvement is smaller, but still statistically significant (p = 0.01).

<center>
<table>
<tr>
<td>
[[Image:SD.Lh.PercentImprove.lat.png|thumb|center|150px|Left Medial]]
</td>
<td>
[[Image:SD.Lh.PercentImprove.med.png|thumb|center|150px|Left Lateral]]
</td>
<td>
[[Image:SD.Rh.PercentImprove.lat.png|thumb|center|150px|Right Lateral]]
</td>
<td>
[[Image:SD.Rh.PercentImprove.med.png|thumb|center|142px|Right Medial]]
</td>
</tr>
</table>
</center>

Because the average Dice can be deceiving by suppressing small structures, we analyze the segmentation accuracy per structure. On
the left (right) hemisphere, the segmentations of 16 (8) structures are statistically significantly improved by Spherical Demons with respect to FreeSurfer, while no structure got worse (FDR = 0.05). The above figure shows the percentage improvement
of individual structures. Parcellation results suggest that our registration is at least as accurate as FreeSurfer.

== (2) Brodmann Areas Localization on Ex-vivo Cortical Surfaces ==

In this experiment, we evaluate the registration accuracy on ten human brains analyzed histologically postmortem. The histological sections were aligned to postmortem MR with nonlinear warps to build a 3D volume. Eight manually labeled Brodmann areas from histology were sampled onto each hemispheric surface model and sampling errors were manually corrected. Brodmann areas are cyto-architectonically defined regions closely related to cortical function.

It has been shown that nonlinear surface registration of cortical folds can significantly improve Brodmann area overlap across
different subjects. Registering the ex-vivo surfaces is more difficult than in-vivo surfaces because the reconstructed volumes are extremely noisy, resulting in noisy geometric features.

We co-register the ten surfaces to each other by iteratively building an atlas and registering the surfaces to the atlas. We
compute the average distance between the boundaries of the Brodmann areas for each pair of registered subjects. We perform a permutation test to test for statistical significance. Spherical Demons improves the alignment of 5 (2) Brodmann areas on the left (right) hemisphere (FDR = 0.05) compared with FreeSurfer and no structure gets worse. These results suggest that the Spherical Demons algorithm is at least as accurate as FreeSurfer in aligning Brodmann areas.

= Code =

Matlab code is currently available at http://yeoyeo02.googlepages.com/sphericaldemonsrelease

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

[2] J. Thirion. Image Matching as a Diffusion Process: an Analogy with Maxwell’s Demons. Medical Image Analysis,
2(3):243–260, 1998.

[3] T. Vercauteren, X. Pennec, A. Perchant, and N. Ayache. Non-parametric Diffeomorphic Image Registration with the
Demons Registration. In Proceedings of the International Conference on Medical Image Computing and Computer Assisted
Intervention (MICCAI), volume 4792 of LNCS, pages 319–326, 2007.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl
* INRIA: Nicholas Ayache
* Mauna Kea Technologies: Tom Vercauteren

= Publications =
''In Print''

* [http://www.na-mic.org/publications/pages/display?search=Projects:SphericalDemons&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database]

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T22:34:28Z

Ythomas: /* (1) Localizing Brodmann Areas Using Cortical Folding */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications.

= Motivation =
Image registration is ambiguous. For example, the figures below show two subjects with Brodmann areas overlaid on their cortical folding patterns. Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|250px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|250px]]
</td>
</tr>
</table>
</center>

Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights of the wSSD (black). The optimal uniform weights of the wSSD are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered, as shown by the green outline in Fig(a). During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px|(a) Initial Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We use the ex-vivo MT template to predict MT+ in the 42 in-vivo subjects. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T22:33:42Z

Ythomas: /* (1b) Interpreting Task-Optimal Template Estimation */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications.

= Motivation =
Image registration is ambiguous. For example, the figures below show two subjects with Brodmann areas overlaid on their cortical folding patterns. Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|250px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|250px]]
</td>
</tr>
</table>
</center>

Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered, as shown by the green outline in Fig(a). During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px|(a) Initial Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We use the ex-vivo MT template to predict MT+ in the 42 in-vivo subjects. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T22:32:18Z

Ythomas: /* Motivation */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications.

= Motivation =
Image registration is ambiguous. For example, the figures below show two subjects with Brodmann areas overlaid on their cortical folding patterns. Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|250px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|250px]]
</td>
</tr>
</table>
</center>

Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered, as shown by the green outline in Fig(a). During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px|(a) Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We use the ex-vivo MT template to predict MT+ in the 42 in-vivo subjects. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T22:31:52Z

Ythomas: /* Motivation */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications.

= Motivation =
Image registration is ambiguous. For example, the figures below show two subjects with Brodmann areas overlaid on their cortical folding patterns. Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered, as shown by the green outline in Fig(a). During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px|(a) Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We use the ex-vivo MT template to predict MT+ in the 42 in-vivo subjects. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T22:31:32Z

Ythomas: /* Motivation */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications.

= Motivation =
Image registration is ambiguous. For example, the figures below show two subjects with Brodmann areas overlaid on the cortical folding patterns of two different subjects. Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered, as shown by the green outline in Fig(a). During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px|(a) Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We use the ex-vivo MT template to predict MT+ in the 42 in-vivo subjects. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Algorithm:MIT

2009-09-10T22:30:10Z

Ythomas: /* Learning Task-Optimal Registration Cost Functions */

Back to [[Algorithm:Main|NA-MIC Algorithms]]
__NOTOC__
= Overview of MIT Algorithms (PI: Polina Golland) =

Our group seeks to model statistical variability of anatomy and function across subjects and between populations and to utilize computational models of such variability to improve predictions for individual subjects, as well as characterize populations. Our long-term goal is to develop methods for joint modeling of anatomy and function and to apply them in clinical and scientific studies. We work primarily with anatomical, DTI and fMRI images. We actively contribute implementations of our algorithms to the NAMIC-kit.

= MIT Projects =

{| cellpadding="10" style="text-align:left;"
|| [[Image:Segmentation_example2.png|250px]]
||

== [[Projects:NonparametricSegmentation| Nonparametric Models for Supervised Image Segmentation]] ==

We propose a non-parametric, probabilistic model for the automatic segmentation of medical images,
given a training set of images and corresponding label maps. The resulting inference algorithms we
develop rely on pairwise registrations between the test image and individual training images. The
training labels are then transferred to the test image and fused to compute a final segmentation of
the test subject. [[Projects:NonparametricSegmentation|More...]]

<font color="red">'''New: '''</font> Supervised Nonparametric Image Parcellation, M.R. Sabuncu, B.T. Thomas Yeo, K. Van Leemput, B. Fischl, and P. Golland. To appear in Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009.

<font color="red">'''New: '''</font> Nonparametric Mixture Models for Supervised Image Parcellation, M.R. Sabuncu,
B.T.T. Yeo, K. Van Leemput, B. Fischl, and P. Golland. To be presented at PMMIA Workshop at MICCAI 2009.

|-

{| cellpadding="10" style="text-align:left;"
|| [[Image:lh.pm14686.BA2.gif|250px]]
||

== [[Projects:LearningRegistrationCostFunctions| Learning Task-Optimal Registration Cost Functions]] ==

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications. [[Projects:LearningRegistrationCostFunctions|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

|-

{| cellpadding="10" style="text-align:left;"
| style="width:15%" | [[Image:TetrahedralAtlasWarp.gif‎ |210px]]
| style="width:85%" |

== [[Projects:BayesianMRSegmentation| Bayesian Segmentation of MRI Images]] ==

The aim of this project is to develop, implement, and validate a generic method for segmenting MRI images that automatically adapts to different acquisition sequences. [[Projects:BayesianMRSegmentation|More...]]

<font color="red">'''New: '''</font> Automated Segmentation of Hippocampal Subﬁelds from Ultra-High Resolution In Vivo MRI, K. Van Leemput, A. Bakkour, T. Benner, G. Wiggins, L.L. Wald, J. Augustinack, B.C. Dickerson, P. Golland, and B. Fischl. Hippocampus, vol. 19, no. 6, pp. 549-557, June 2009

<font color="red">'''New: '''</font> Encoding Probabilistic Atlases Using Bayesian Inference, K. Van Leemput. IEEE Transactions on Medical Imaging, vol. 28, no. 6, pp. 822-837, June 2009

|-

| | [[Image:ICluster_templates.gif|200px]]
| |

== [[Projects:MultimodalAtlas|Multimodal Atlas]] ==

In this work, we propose and investigate an algorithm that jointly co-registers a collection of images while computing multiple templates. The algorithm, called '''iCluster''', is used to compute multiple atlases for a given population.
[[Projects:MultimodalAtlas|More...]]

<font color="red">'''New: '''</font> Image-driven Population Analysis through Mixture-Modeling, M.R. Sabuncu, S.K. Balci, M.E. Shenton and P. Golland. IEEE Transactions on Medical Imaging. Accepted for Publication, 2009.

|-

| | [[Image:CoordinateChart.png|250px]]
| |

== [[Projects:SphericalDemons|Spherical Demons: Fast Surface Registration]] ==

We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently approximated on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, [[Projects:SphericalDemons|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, M. Sabuncu, T. Vercauteren, N. Ayache, B. Fischl, P. Golland. Spherical Demons: Fast Surface Registration. MICCAI, volume 5241 of LNCS, 745--753, 2008.

<font color="red">'''New: '''</font> B.T.T. Yeo, M. Sabuncu, T. Vercauteren, N. Ayache, B. Fischl, P. Golland. Spherical Demons: Fast Surface Registration. IEEE TMI, In Press.

|-

| | [[Image:JointRegSeg.png|200px]]
| |

== [[Projects:RegistrationRegularization|Optimal Atlas Regularization in Image Segmentation]] ==

We propose a unified framework for computing atlases from manually labeled data sets at various degrees of “sharpness” and the joint registration and segmentation of a new brain with these atlases. Using this framework, we investigate the tradeoff between warp regularization and image ﬁdelity, i.e. the smoothness of the new subject warp and the sharpness of the atlas in a segmentation application.
[[Projects:RegistrationRegularization|More...]]

<font color="red">'''New:'''</font> B.T.T. Yeo, M.R. Sabuncu, R. Desikan, B. Fischl, P. Golland. Effects of Registration Regularization and Atlas Sharpness on Segmentation Accuracy. Medical Image Analysis, 12(5):603--615, 2008.

|-

| | [[Image:epi_correction_small.jpg|200px]]
| |

== [[Projects:FieldmapFreeDistortionCorrection|Fieldmap-Free EPI Distortion Correction]] ==

In this project we aim to improve the EPI distortion correction algorithms [[Projects:FieldmapFreeDistortionCorrection|More...]]

<font color="red">'''New: '''</font> Poynton C., Jenkinson M., Whalen S., Golby A.J., Wells III W. Fieldmap-Free Retrospective Registration and Distortion Correction for EPI-Based Functiona Imaging. MICCAI 2008.

|-

| | [[Image:mit_fmri_clustering_parcellation2_xsub.png|200px]]
| |

== [[Projects:fMRIClustering|fMRI clustering]] ==

In this project we study the application of model-based clustering algorithms in identification of functional connectivity in the brain. [[Projects:fMRIClustering|More...]]

<font color="red">'''New: '''</font> A. Venkataraman, K.R.A. Van Dijk, R.L. Buckner, P. Golland. Exploring Functional Connectivity in fMRI via Clustering. ICASSP 2009.

<font color="red">'''New: '''</font> D. Lashkari, E. Vul, N. Kanwisher, P. Golland. Discovering Structure in the Space of Activation
Profiles in fMRI. MICCAI 2008.

|-

| | [[Image:FoldingSpeedDetection.png|150px|]]
| |

== [[Projects:ShapeAnalysisWithOvercompleteWavelets|Shape Analysis With Overcomplete Wavelets]] ==

In this work, we extend the Euclidean wavelets to the sphere. The resulting over-complete spherical wavelets are invariant to the rotation of the spherical image parameterization. We apply the over-complete spherical wavelet to cortical folding development [[Projects:ShapeAnalysisWithOvercompleteWavelets|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, P. Yu, P.E. Grant, B. Fischl, P. Golland. Shape Analysis with Overcomplete Spherical Wavelets. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), volume 5241 of LNCS, 468--476, 2008

B.T.T. Yeo, W. Ou, P. Golland. On the Construction of Invertible Filter Banks on the 2-Sphere. Yeo, Ou and Golland. IEEE Transactions on Image Processing. 17(3):283--300. 2008.

|-

| | [[Image:Models.jpg|200px]]
| |

== [[Projects:DTIModeling|Fiber Tract Modeling, Clustering, and Quantitative Analysis]] ==

The goal of this work is to model the shape of the fiber bundles and use this model description in clustering and statistical analysis of fiber tracts. [[Projects:DTIModeling|More...]]

<font color="red">'''New:'''</font> Mahnaz Maddah, Marek Kubicki, William M. Wells, Carl-Fredrik Westin, Martha E. Shenton and W. Eric L. Grimson, Findings in Schizophrenia by Tract-Oriented DT-MRI Analysis. MICCAI 2008.

M. Maddah, L. Zollei, W. E. L. Grimson, W. M. Wells, Modeling of Anatomical Information in Clustering of White Matter Fiber Trajectories Using Dirichlet Distribution. MMBIA 2008.

M. Maddah, L. Zollei, W. E. L. Grimson, C-F Westin, W. M. Wells, A Mathematical Framework for Incorporating Anatomical Knowledge in DT-MRI Analysis. ISBI 2008.

|-

| | [[Image:TGIt.gif| 150px]]
| |

== [[Projects:LatentAtlasSegmentation|Joint Segmentation of Image Ensembles via Latent Atlases]] ==

Spatial priors, such as probabilistic atlases, play an important role in MRI segmentation. The atlases are typically generated by averaging manual labels of aligned brain regions across different subjects. However, the availability of comprehensive, reliable and suitable manual segmentations is limited. We therefore propose a joint segmentation of corresponding, aligned structures in the entire population that does not require a probability atlas.
[[Projects:LatentAtlasSegmentation|More...]]

<font color="red">'''New: '''</font> T. Riklin Raviv, K. Van Leemput, W.M. Wells III and P. Golland, Joint Segmentation of Image Ensembles via Latent Atlases, Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009

<font color="red">'''New: '''</font>
T. Riklin Raviv, B.H. Menze, K. Van Leemput, B. Stieltjes, M.A. Weber, N. Ayache, W. M. Wells III and P. Golland, Joint Segmentation using Patient specific Latent Anatomy Model
MICCAI workshop for Probabilistic Models on Medical Image Analysis (PMMIA) 2009

|-

| | [[Image:Progress_Registration_Segmentation_Shape.jpg|180px]]
| |

== [[Projects:ShapeBasedSegmentationAndRegistration|Shape Based Segmentation and Registration]] ==

This type of algorithm assigns a tissue type to each voxel in the volume. Incorporating prior shape information biases the label assignment towards contiguous regions that are consistent with the shape model. [[Projects:ShapeBasedSegmentationAndRegistration|More...]]

|-

| | [[Image:GroupwiseSummary.PNG|200px]]
| |

== [[Projects:GroupwiseRegistration|Groupwise Registration]] ==

We extend a previously demonstrated entropy based groupwise registration method to include a free-form deformation model based on B-splines. We provide an efficient implementation using stochastic gradient descents in a multi-resolution setting. We demonstrate the method in application to a set of 50 MRI brain scans and compare the results to a pairwise approach using segmentation labels to evaluate the quality of alignment.

In a related project, we develop a method that reconciles the practical advantages of symmetric registration with the asymmetric nature of image-template registration by adding a simple correction factor to the symmetric cost function. We instantiate our model within a log-domain diffeomorphic registration framework. Our experiments show exploiting the asymmetry in image-template registration improves alignment in the image coordinates.

<font color="red">'''New: '''</font> Asymmetric Image-Template Registration, M.R. Sabuncu, B.T. Thomas Yeo, T. Vercauteren, K. Van Leemput, P. Golland. To appear in Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009

[[Projects:GroupwiseRegistration|More...]]

|-

| | [[Image:MIT_DTI_JointSegReg_atlas3D.jpg|200px]]
| |

== [[Projects:DTIFiberRegistration|Joint Registration and Segmentation of DWI Fiber Tractography]] ==

The goal of this work is to jointly register and cluster DWI fiber tracts obtained from a group of subjects. [[Projects:DTIFiberRegistration|More...]]

|-

| | [[Image:brain.png|200px]]
| |

== [[Projects:DTIClustering|DTI Fiber Clustering and Fiber-Based Analysis]] ==

The goal of this project is to provide structural description of the white matter architecture as a partition into coherent fiber bundles and clusters, and to use these bundles for quantitative measurement. [[Projects:DTIClustering|More...]]

|-

| | [[Image:FMRIEvaluationchart.jpg|200px]]
| |

== [[Projects:fMRIDetection|fMRI Detection and Analysis]] ==

We are exploring algorithms for improved fMRI detection and interpretation by incorporting spatial priors and anatomical information to guide the detection. [[Projects:fMRIDetection|More...]]

|-

| | [[Image:Thalamus_algo_outline.png|200px]]
| |

== [[Projects:DTISegmentation|DTI-based Segmentation]] ==

Unlike conventional MRI, DTI provides adequate contrast to segment the thalamic nuclei, which are gray matter structures. [[Projects:DTISegmentation|More...]]

|-

| | [[Image:ConnectivityMap.png|200px]]
| |

== [[Projects:DTIStochasticTractography|Stochastic Tractography]] ==

This work calculates posterior distributions of white matter fiber tract parameters given diffusion observations in a DWI volume. [[Projects:DTIStochasticTractography|More...]]

|-

| | [[Image:HippocampalShapeDifferences.gif|200px]]
| |

== [[Projects:ShapeAnalysis|Population Analysis of Anatomical Variability]] ==

Our goal is to develop mathematical approaches to modeling anatomical variability within and across populations using tools like local shape descriptors of specific regions of interest and global constellation descriptors of multiple ROI's. [[Projects:ShapeAnalysis|More...]]

|}

Projects:LearningRegistrationCostFunctions

2009-09-10T22:29:48Z

Ythomas:

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered, as shown by the green outline in Fig(a). During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px|(a) Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We use the ex-vivo MT template to predict MT+ in the 42 in-vivo subjects. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Algorithm:MIT

2009-09-10T22:28:17Z

Ythomas: /* Learning Task-Optimal Registration Cost Functions */

Back to [[Algorithm:Main|NA-MIC Algorithms]]
__NOTOC__
= Overview of MIT Algorithms (PI: Polina Golland) =

Our group seeks to model statistical variability of anatomy and function across subjects and between populations and to utilize computational models of such variability to improve predictions for individual subjects, as well as characterize populations. Our long-term goal is to develop methods for joint modeling of anatomy and function and to apply them in clinical and scientific studies. We work primarily with anatomical, DTI and fMRI images. We actively contribute implementations of our algorithms to the NAMIC-kit.

= MIT Projects =

{| cellpadding="10" style="text-align:left;"
|| [[Image:Segmentation_example2.png|250px]]
||

== [[Projects:NonparametricSegmentation| Nonparametric Models for Supervised Image Segmentation]] ==

We propose a non-parametric, probabilistic model for the automatic segmentation of medical images,
given a training set of images and corresponding label maps. The resulting inference algorithms we
develop rely on pairwise registrations between the test image and individual training images. The
training labels are then transferred to the test image and fused to compute a final segmentation of
the test subject. [[Projects:NonparametricSegmentation|More...]]

<font color="red">'''New: '''</font> Supervised Nonparametric Image Parcellation, M.R. Sabuncu, B.T. Thomas Yeo, K. Van Leemput, B. Fischl, and P. Golland. To appear in Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009.

<font color="red">'''New: '''</font> Nonparametric Mixture Models for Supervised Image Parcellation, M.R. Sabuncu,
B.T.T. Yeo, K. Van Leemput, B. Fischl, and P. Golland. To be presented at PMMIA Workshop at MICCAI 2009.

|-

{| cellpadding="10" style="text-align:left;"
|| [[Image:lh.pm14686.BA2.gif|250px]]
||

== [[Projects:LearningRegistrationCostFunctions| Learning Task-Optimal Registration Cost Functions]] ==

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. [[Projects:LearningRegistrationCostFunctions|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

|-

{| cellpadding="10" style="text-align:left;"
| style="width:15%" | [[Image:TetrahedralAtlasWarp.gif‎ |210px]]
| style="width:85%" |

== [[Projects:BayesianMRSegmentation| Bayesian Segmentation of MRI Images]] ==

The aim of this project is to develop, implement, and validate a generic method for segmenting MRI images that automatically adapts to different acquisition sequences. [[Projects:BayesianMRSegmentation|More...]]

<font color="red">'''New: '''</font> Automated Segmentation of Hippocampal Subﬁelds from Ultra-High Resolution In Vivo MRI, K. Van Leemput, A. Bakkour, T. Benner, G. Wiggins, L.L. Wald, J. Augustinack, B.C. Dickerson, P. Golland, and B. Fischl. Hippocampus, vol. 19, no. 6, pp. 549-557, June 2009

<font color="red">'''New: '''</font> Encoding Probabilistic Atlases Using Bayesian Inference, K. Van Leemput. IEEE Transactions on Medical Imaging, vol. 28, no. 6, pp. 822-837, June 2009

|-

| | [[Image:ICluster_templates.gif|200px]]
| |

== [[Projects:MultimodalAtlas|Multimodal Atlas]] ==

In this work, we propose and investigate an algorithm that jointly co-registers a collection of images while computing multiple templates. The algorithm, called '''iCluster''', is used to compute multiple atlases for a given population.
[[Projects:MultimodalAtlas|More...]]

<font color="red">'''New: '''</font> Image-driven Population Analysis through Mixture-Modeling, M.R. Sabuncu, S.K. Balci, M.E. Shenton and P. Golland. IEEE Transactions on Medical Imaging. Accepted for Publication, 2009.

|-

| | [[Image:CoordinateChart.png|250px]]
| |

== [[Projects:SphericalDemons|Spherical Demons: Fast Surface Registration]] ==

We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently approximated on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, [[Projects:SphericalDemons|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, M. Sabuncu, T. Vercauteren, N. Ayache, B. Fischl, P. Golland. Spherical Demons: Fast Surface Registration. MICCAI, volume 5241 of LNCS, 745--753, 2008.

<font color="red">'''New: '''</font> B.T.T. Yeo, M. Sabuncu, T. Vercauteren, N. Ayache, B. Fischl, P. Golland. Spherical Demons: Fast Surface Registration. IEEE TMI, In Press.

|-

| | [[Image:JointRegSeg.png|200px]]
| |

== [[Projects:RegistrationRegularization|Optimal Atlas Regularization in Image Segmentation]] ==

We propose a unified framework for computing atlases from manually labeled data sets at various degrees of “sharpness” and the joint registration and segmentation of a new brain with these atlases. Using this framework, we investigate the tradeoff between warp regularization and image ﬁdelity, i.e. the smoothness of the new subject warp and the sharpness of the atlas in a segmentation application.
[[Projects:RegistrationRegularization|More...]]

<font color="red">'''New:'''</font> B.T.T. Yeo, M.R. Sabuncu, R. Desikan, B. Fischl, P. Golland. Effects of Registration Regularization and Atlas Sharpness on Segmentation Accuracy. Medical Image Analysis, 12(5):603--615, 2008.

|-

| | [[Image:epi_correction_small.jpg|200px]]
| |

== [[Projects:FieldmapFreeDistortionCorrection|Fieldmap-Free EPI Distortion Correction]] ==

In this project we aim to improve the EPI distortion correction algorithms [[Projects:FieldmapFreeDistortionCorrection|More...]]

<font color="red">'''New: '''</font> Poynton C., Jenkinson M., Whalen S., Golby A.J., Wells III W. Fieldmap-Free Retrospective Registration and Distortion Correction for EPI-Based Functiona Imaging. MICCAI 2008.

|-

| | [[Image:mit_fmri_clustering_parcellation2_xsub.png|200px]]
| |

== [[Projects:fMRIClustering|fMRI clustering]] ==

In this project we study the application of model-based clustering algorithms in identification of functional connectivity in the brain. [[Projects:fMRIClustering|More...]]

<font color="red">'''New: '''</font> A. Venkataraman, K.R.A. Van Dijk, R.L. Buckner, P. Golland. Exploring Functional Connectivity in fMRI via Clustering. ICASSP 2009.

<font color="red">'''New: '''</font> D. Lashkari, E. Vul, N. Kanwisher, P. Golland. Discovering Structure in the Space of Activation
Profiles in fMRI. MICCAI 2008.

|-

| | [[Image:FoldingSpeedDetection.png|150px|]]
| |

== [[Projects:ShapeAnalysisWithOvercompleteWavelets|Shape Analysis With Overcomplete Wavelets]] ==

In this work, we extend the Euclidean wavelets to the sphere. The resulting over-complete spherical wavelets are invariant to the rotation of the spherical image parameterization. We apply the over-complete spherical wavelet to cortical folding development [[Projects:ShapeAnalysisWithOvercompleteWavelets|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, P. Yu, P.E. Grant, B. Fischl, P. Golland. Shape Analysis with Overcomplete Spherical Wavelets. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), volume 5241 of LNCS, 468--476, 2008

B.T.T. Yeo, W. Ou, P. Golland. On the Construction of Invertible Filter Banks on the 2-Sphere. Yeo, Ou and Golland. IEEE Transactions on Image Processing. 17(3):283--300. 2008.

|-

| | [[Image:Models.jpg|200px]]
| |

== [[Projects:DTIModeling|Fiber Tract Modeling, Clustering, and Quantitative Analysis]] ==

The goal of this work is to model the shape of the fiber bundles and use this model description in clustering and statistical analysis of fiber tracts. [[Projects:DTIModeling|More...]]

<font color="red">'''New:'''</font> Mahnaz Maddah, Marek Kubicki, William M. Wells, Carl-Fredrik Westin, Martha E. Shenton and W. Eric L. Grimson, Findings in Schizophrenia by Tract-Oriented DT-MRI Analysis. MICCAI 2008.

M. Maddah, L. Zollei, W. E. L. Grimson, W. M. Wells, Modeling of Anatomical Information in Clustering of White Matter Fiber Trajectories Using Dirichlet Distribution. MMBIA 2008.

M. Maddah, L. Zollei, W. E. L. Grimson, C-F Westin, W. M. Wells, A Mathematical Framework for Incorporating Anatomical Knowledge in DT-MRI Analysis. ISBI 2008.

|-

| | [[Image:TGIt.gif| 150px]]
| |

== [[Projects:LatentAtlasSegmentation|Joint Segmentation of Image Ensembles via Latent Atlases]] ==

Spatial priors, such as probabilistic atlases, play an important role in MRI segmentation. The atlases are typically generated by averaging manual labels of aligned brain regions across different subjects. However, the availability of comprehensive, reliable and suitable manual segmentations is limited. We therefore propose a joint segmentation of corresponding, aligned structures in the entire population that does not require a probability atlas.
[[Projects:LatentAtlasSegmentation|More...]]

<font color="red">'''New: '''</font> T. Riklin Raviv, K. Van Leemput, W.M. Wells III and P. Golland, Joint Segmentation of Image Ensembles via Latent Atlases, Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009

<font color="red">'''New: '''</font>
T. Riklin Raviv, B.H. Menze, K. Van Leemput, B. Stieltjes, M.A. Weber, N. Ayache, W. M. Wells III and P. Golland, Joint Segmentation using Patient specific Latent Anatomy Model
MICCAI workshop for Probabilistic Models on Medical Image Analysis (PMMIA) 2009

|-

| | [[Image:Progress_Registration_Segmentation_Shape.jpg|180px]]
| |

== [[Projects:ShapeBasedSegmentationAndRegistration|Shape Based Segmentation and Registration]] ==

This type of algorithm assigns a tissue type to each voxel in the volume. Incorporating prior shape information biases the label assignment towards contiguous regions that are consistent with the shape model. [[Projects:ShapeBasedSegmentationAndRegistration|More...]]

|-

| | [[Image:GroupwiseSummary.PNG|200px]]
| |

== [[Projects:GroupwiseRegistration|Groupwise Registration]] ==

We extend a previously demonstrated entropy based groupwise registration method to include a free-form deformation model based on B-splines. We provide an efficient implementation using stochastic gradient descents in a multi-resolution setting. We demonstrate the method in application to a set of 50 MRI brain scans and compare the results to a pairwise approach using segmentation labels to evaluate the quality of alignment.

In a related project, we develop a method that reconciles the practical advantages of symmetric registration with the asymmetric nature of image-template registration by adding a simple correction factor to the symmetric cost function. We instantiate our model within a log-domain diffeomorphic registration framework. Our experiments show exploiting the asymmetry in image-template registration improves alignment in the image coordinates.

<font color="red">'''New: '''</font> Asymmetric Image-Template Registration, M.R. Sabuncu, B.T. Thomas Yeo, T. Vercauteren, K. Van Leemput, P. Golland. To appear in Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009

[[Projects:GroupwiseRegistration|More...]]

|-

| | [[Image:MIT_DTI_JointSegReg_atlas3D.jpg|200px]]
| |

== [[Projects:DTIFiberRegistration|Joint Registration and Segmentation of DWI Fiber Tractography]] ==

The goal of this work is to jointly register and cluster DWI fiber tracts obtained from a group of subjects. [[Projects:DTIFiberRegistration|More...]]

|-

| | [[Image:brain.png|200px]]
| |

== [[Projects:DTIClustering|DTI Fiber Clustering and Fiber-Based Analysis]] ==

The goal of this project is to provide structural description of the white matter architecture as a partition into coherent fiber bundles and clusters, and to use these bundles for quantitative measurement. [[Projects:DTIClustering|More...]]

|-

| | [[Image:FMRIEvaluationchart.jpg|200px]]
| |

== [[Projects:fMRIDetection|fMRI Detection and Analysis]] ==

We are exploring algorithms for improved fMRI detection and interpretation by incorporting spatial priors and anatomical information to guide the detection. [[Projects:fMRIDetection|More...]]

|-

| | [[Image:Thalamus_algo_outline.png|200px]]
| |

== [[Projects:DTISegmentation|DTI-based Segmentation]] ==

Unlike conventional MRI, DTI provides adequate contrast to segment the thalamic nuclei, which are gray matter structures. [[Projects:DTISegmentation|More...]]

|-

| | [[Image:ConnectivityMap.png|200px]]
| |

== [[Projects:DTIStochasticTractography|Stochastic Tractography]] ==

This work calculates posterior distributions of white matter fiber tract parameters given diffusion observations in a DWI volume. [[Projects:DTIStochasticTractography|More...]]

|-

| | [[Image:HippocampalShapeDifferences.gif|200px]]
| |

== [[Projects:ShapeAnalysis|Population Analysis of Anatomical Variability]] ==

Our goal is to develop mathematical approaches to modeling anatomical variability within and across populations using tools like local shape descriptors of specific regions of interest and global constellation descriptors of multiple ROI's. [[Projects:ShapeAnalysis|More...]]

|}

Algorithm:MIT

2009-09-10T22:26:39Z

Ythomas: /* MIT Projects */

Back to [[Algorithm:Main|NA-MIC Algorithms]]
__NOTOC__
= Overview of MIT Algorithms (PI: Polina Golland) =

Our group seeks to model statistical variability of anatomy and function across subjects and between populations and to utilize computational models of such variability to improve predictions for individual subjects, as well as characterize populations. Our long-term goal is to develop methods for joint modeling of anatomy and function and to apply them in clinical and scientific studies. We work primarily with anatomical, DTI and fMRI images. We actively contribute implementations of our algorithms to the NAMIC-kit.

= MIT Projects =

{| cellpadding="10" style="text-align:left;"
|| [[Image:Segmentation_example2.png|250px]]
||

== [[Projects:NonparametricSegmentation| Nonparametric Models for Supervised Image Segmentation]] ==

We propose a non-parametric, probabilistic model for the automatic segmentation of medical images,
given a training set of images and corresponding label maps. The resulting inference algorithms we
develop rely on pairwise registrations between the test image and individual training images. The
training labels are then transferred to the test image and fused to compute a final segmentation of
the test subject. [[Projects:NonparametricSegmentation|More...]]

<font color="red">'''New: '''</font> Supervised Nonparametric Image Parcellation, M.R. Sabuncu, B.T. Thomas Yeo, K. Van Leemput, B. Fischl, and P. Golland. To appear in Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009.

<font color="red">'''New: '''</font> Nonparametric Mixture Models for Supervised Image Parcellation, M.R. Sabuncu,
B.T.T. Yeo, K. Van Leemput, B. Fischl, and P. Golland. To be presented at PMMIA Workshop at MICCAI 2009.

|-

{| cellpadding="10" style="text-align:left;"
|| [[Image:lh.pm14686.BA2.gif|250px]]
||

== [[Projects:LearningRegistrationCostFunctions| Learning Task-Optimal Registration Cost Functions]] ==

We propose a non-parametric, probabilistic model for the automatic segmentation of medical images,
given a training set of images and corresponding label maps. The resulting inference algorithms we
develop rely on pairwise registrations between the test image and individual training images. The
training labels are then transferred to the test image and fused to compute a final segmentation of
the test subject. [[Projects:NonparametricSegmentation|More...]]

<font color="red">'''New: '''</font> Supervised Nonparametric Image Parcellation, M.R. Sabuncu, B.T. Thomas Yeo, K. Van Leemput, B. Fischl, and P. Golland. To appear in Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009.

<font color="red">'''New: '''</font> Nonparametric Mixture Models for Supervised Image Parcellation, M.R. Sabuncu,
B.T.T. Yeo, K. Van Leemput, B. Fischl, and P. Golland. To be presented at PMMIA Workshop at MICCAI 2009.

|-

{| cellpadding="10" style="text-align:left;"
| style="width:15%" | [[Image:TetrahedralAtlasWarp.gif‎ |210px]]
| style="width:85%" |

== [[Projects:BayesianMRSegmentation| Bayesian Segmentation of MRI Images]] ==

The aim of this project is to develop, implement, and validate a generic method for segmenting MRI images that automatically adapts to different acquisition sequences. [[Projects:BayesianMRSegmentation|More...]]

<font color="red">'''New: '''</font> Automated Segmentation of Hippocampal Subﬁelds from Ultra-High Resolution In Vivo MRI, K. Van Leemput, A. Bakkour, T. Benner, G. Wiggins, L.L. Wald, J. Augustinack, B.C. Dickerson, P. Golland, and B. Fischl. Hippocampus, vol. 19, no. 6, pp. 549-557, June 2009

<font color="red">'''New: '''</font> Encoding Probabilistic Atlases Using Bayesian Inference, K. Van Leemput. IEEE Transactions on Medical Imaging, vol. 28, no. 6, pp. 822-837, June 2009

|-

| | [[Image:ICluster_templates.gif|200px]]
| |

== [[Projects:MultimodalAtlas|Multimodal Atlas]] ==

In this work, we propose and investigate an algorithm that jointly co-registers a collection of images while computing multiple templates. The algorithm, called '''iCluster''', is used to compute multiple atlases for a given population.
[[Projects:MultimodalAtlas|More...]]

<font color="red">'''New: '''</font> Image-driven Population Analysis through Mixture-Modeling, M.R. Sabuncu, S.K. Balci, M.E. Shenton and P. Golland. IEEE Transactions on Medical Imaging. Accepted for Publication, 2009.

|-

| | [[Image:CoordinateChart.png|250px]]
| |

== [[Projects:SphericalDemons|Spherical Demons: Fast Surface Registration]] ==

We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently approximated on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, [[Projects:SphericalDemons|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, M. Sabuncu, T. Vercauteren, N. Ayache, B. Fischl, P. Golland. Spherical Demons: Fast Surface Registration. MICCAI, volume 5241 of LNCS, 745--753, 2008.

<font color="red">'''New: '''</font> B.T.T. Yeo, M. Sabuncu, T. Vercauteren, N. Ayache, B. Fischl, P. Golland. Spherical Demons: Fast Surface Registration. IEEE TMI, In Press.

|-

| | [[Image:JointRegSeg.png|200px]]
| |

== [[Projects:RegistrationRegularization|Optimal Atlas Regularization in Image Segmentation]] ==

We propose a unified framework for computing atlases from manually labeled data sets at various degrees of “sharpness” and the joint registration and segmentation of a new brain with these atlases. Using this framework, we investigate the tradeoff between warp regularization and image ﬁdelity, i.e. the smoothness of the new subject warp and the sharpness of the atlas in a segmentation application.
[[Projects:RegistrationRegularization|More...]]

<font color="red">'''New:'''</font> B.T.T. Yeo, M.R. Sabuncu, R. Desikan, B. Fischl, P. Golland. Effects of Registration Regularization and Atlas Sharpness on Segmentation Accuracy. Medical Image Analysis, 12(5):603--615, 2008.

|-

| | [[Image:epi_correction_small.jpg|200px]]
| |

== [[Projects:FieldmapFreeDistortionCorrection|Fieldmap-Free EPI Distortion Correction]] ==

In this project we aim to improve the EPI distortion correction algorithms [[Projects:FieldmapFreeDistortionCorrection|More...]]

<font color="red">'''New: '''</font> Poynton C., Jenkinson M., Whalen S., Golby A.J., Wells III W. Fieldmap-Free Retrospective Registration and Distortion Correction for EPI-Based Functiona Imaging. MICCAI 2008.

|-

| | [[Image:mit_fmri_clustering_parcellation2_xsub.png|200px]]
| |

== [[Projects:fMRIClustering|fMRI clustering]] ==

In this project we study the application of model-based clustering algorithms in identification of functional connectivity in the brain. [[Projects:fMRIClustering|More...]]

<font color="red">'''New: '''</font> A. Venkataraman, K.R.A. Van Dijk, R.L. Buckner, P. Golland. Exploring Functional Connectivity in fMRI via Clustering. ICASSP 2009.

<font color="red">'''New: '''</font> D. Lashkari, E. Vul, N. Kanwisher, P. Golland. Discovering Structure in the Space of Activation
Profiles in fMRI. MICCAI 2008.

|-

| | [[Image:FoldingSpeedDetection.png|150px|]]
| |

== [[Projects:ShapeAnalysisWithOvercompleteWavelets|Shape Analysis With Overcomplete Wavelets]] ==

In this work, we extend the Euclidean wavelets to the sphere. The resulting over-complete spherical wavelets are invariant to the rotation of the spherical image parameterization. We apply the over-complete spherical wavelet to cortical folding development [[Projects:ShapeAnalysisWithOvercompleteWavelets|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, P. Yu, P.E. Grant, B. Fischl, P. Golland. Shape Analysis with Overcomplete Spherical Wavelets. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), volume 5241 of LNCS, 468--476, 2008

B.T.T. Yeo, W. Ou, P. Golland. On the Construction of Invertible Filter Banks on the 2-Sphere. Yeo, Ou and Golland. IEEE Transactions on Image Processing. 17(3):283--300. 2008.

|-

| | [[Image:Models.jpg|200px]]
| |

== [[Projects:DTIModeling|Fiber Tract Modeling, Clustering, and Quantitative Analysis]] ==

The goal of this work is to model the shape of the fiber bundles and use this model description in clustering and statistical analysis of fiber tracts. [[Projects:DTIModeling|More...]]

<font color="red">'''New:'''</font> Mahnaz Maddah, Marek Kubicki, William M. Wells, Carl-Fredrik Westin, Martha E. Shenton and W. Eric L. Grimson, Findings in Schizophrenia by Tract-Oriented DT-MRI Analysis. MICCAI 2008.

M. Maddah, L. Zollei, W. E. L. Grimson, W. M. Wells, Modeling of Anatomical Information in Clustering of White Matter Fiber Trajectories Using Dirichlet Distribution. MMBIA 2008.

M. Maddah, L. Zollei, W. E. L. Grimson, C-F Westin, W. M. Wells, A Mathematical Framework for Incorporating Anatomical Knowledge in DT-MRI Analysis. ISBI 2008.

|-

| | [[Image:TGIt.gif| 150px]]
| |

== [[Projects:LatentAtlasSegmentation|Joint Segmentation of Image Ensembles via Latent Atlases]] ==

Spatial priors, such as probabilistic atlases, play an important role in MRI segmentation. The atlases are typically generated by averaging manual labels of aligned brain regions across different subjects. However, the availability of comprehensive, reliable and suitable manual segmentations is limited. We therefore propose a joint segmentation of corresponding, aligned structures in the entire population that does not require a probability atlas.
[[Projects:LatentAtlasSegmentation|More...]]

<font color="red">'''New: '''</font> T. Riklin Raviv, K. Van Leemput, W.M. Wells III and P. Golland, Joint Segmentation of Image Ensembles via Latent Atlases, Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009

<font color="red">'''New: '''</font>
T. Riklin Raviv, B.H. Menze, K. Van Leemput, B. Stieltjes, M.A. Weber, N. Ayache, W. M. Wells III and P. Golland, Joint Segmentation using Patient specific Latent Anatomy Model
MICCAI workshop for Probabilistic Models on Medical Image Analysis (PMMIA) 2009

|-

| | [[Image:Progress_Registration_Segmentation_Shape.jpg|180px]]
| |

== [[Projects:ShapeBasedSegmentationAndRegistration|Shape Based Segmentation and Registration]] ==

This type of algorithm assigns a tissue type to each voxel in the volume. Incorporating prior shape information biases the label assignment towards contiguous regions that are consistent with the shape model. [[Projects:ShapeBasedSegmentationAndRegistration|More...]]

|-

| | [[Image:GroupwiseSummary.PNG|200px]]
| |

== [[Projects:GroupwiseRegistration|Groupwise Registration]] ==

We extend a previously demonstrated entropy based groupwise registration method to include a free-form deformation model based on B-splines. We provide an efficient implementation using stochastic gradient descents in a multi-resolution setting. We demonstrate the method in application to a set of 50 MRI brain scans and compare the results to a pairwise approach using segmentation labels to evaluate the quality of alignment.

In a related project, we develop a method that reconciles the practical advantages of symmetric registration with the asymmetric nature of image-template registration by adding a simple correction factor to the symmetric cost function. We instantiate our model within a log-domain diffeomorphic registration framework. Our experiments show exploiting the asymmetry in image-template registration improves alignment in the image coordinates.

<font color="red">'''New: '''</font> Asymmetric Image-Template Registration, M.R. Sabuncu, B.T. Thomas Yeo, T. Vercauteren, K. Van Leemput, P. Golland. To appear in Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009

[[Projects:GroupwiseRegistration|More...]]

|-

| | [[Image:MIT_DTI_JointSegReg_atlas3D.jpg|200px]]
| |

== [[Projects:DTIFiberRegistration|Joint Registration and Segmentation of DWI Fiber Tractography]] ==

The goal of this work is to jointly register and cluster DWI fiber tracts obtained from a group of subjects. [[Projects:DTIFiberRegistration|More...]]

|-

| | [[Image:brain.png|200px]]
| |

== [[Projects:DTIClustering|DTI Fiber Clustering and Fiber-Based Analysis]] ==

The goal of this project is to provide structural description of the white matter architecture as a partition into coherent fiber bundles and clusters, and to use these bundles for quantitative measurement. [[Projects:DTIClustering|More...]]

|-

| | [[Image:FMRIEvaluationchart.jpg|200px]]
| |

== [[Projects:fMRIDetection|fMRI Detection and Analysis]] ==

We are exploring algorithms for improved fMRI detection and interpretation by incorporting spatial priors and anatomical information to guide the detection. [[Projects:fMRIDetection|More...]]

|-

| | [[Image:Thalamus_algo_outline.png|200px]]
| |

== [[Projects:DTISegmentation|DTI-based Segmentation]] ==

Unlike conventional MRI, DTI provides adequate contrast to segment the thalamic nuclei, which are gray matter structures. [[Projects:DTISegmentation|More...]]

|-

| | [[Image:ConnectivityMap.png|200px]]
| |

== [[Projects:DTIStochasticTractography|Stochastic Tractography]] ==

This work calculates posterior distributions of white matter fiber tract parameters given diffusion observations in a DWI volume. [[Projects:DTIStochasticTractography|More...]]

|-

| | [[Image:HippocampalShapeDifferences.gif|200px]]
| |

== [[Projects:ShapeAnalysis|Population Analysis of Anatomical Variability]] ==

Our goal is to develop mathematical approaches to modeling anatomical variability within and across populations using tools like local shape descriptors of specific regions of interest and global constellation descriptors of multiple ROI's. [[Projects:ShapeAnalysis|More...]]

|}

Algorithm:MIT

2009-09-10T22:24:11Z

Ythomas: /* Spherical Demons: Fast Surface Registration */

Back to [[Algorithm:Main|NA-MIC Algorithms]]
__NOTOC__
= Overview of MIT Algorithms (PI: Polina Golland) =

Our group seeks to model statistical variability of anatomy and function across subjects and between populations and to utilize computational models of such variability to improve predictions for individual subjects, as well as characterize populations. Our long-term goal is to develop methods for joint modeling of anatomy and function and to apply them in clinical and scientific studies. We work primarily with anatomical, DTI and fMRI images. We actively contribute implementations of our algorithms to the NAMIC-kit.

= MIT Projects =

{| cellpadding="10" style="text-align:left;"
|| [[Image:Segmentation_example2.png|250px]]
||

== [[Projects:NonparametricSegmentation| Nonparametric Models for Supervised Image Segmentation]] ==

We propose a non-parametric, probabilistic model for the automatic segmentation of medical images,
given a training set of images and corresponding label maps. The resulting inference algorithms we
develop rely on pairwise registrations between the test image and individual training images. The
training labels are then transferred to the test image and fused to compute a final segmentation of
the test subject. [[Projects:NonparametricSegmentation|More...]]

<font color="red">'''New: '''</font> Supervised Nonparametric Image Parcellation, M.R. Sabuncu, B.T. Thomas Yeo, K. Van Leemput, B. Fischl, and P. Golland. To appear in Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009.

<font color="red">'''New: '''</font> Nonparametric Mixture Models for Supervised Image Parcellation, M.R. Sabuncu,
B.T.T. Yeo, K. Van Leemput, B. Fischl, and P. Golland. To be presented at PMMIA Workshop at MICCAI 2009.

|-

{| cellpadding="10" style="text-align:left;"
| style="width:15%" | [[Image:TetrahedralAtlasWarp.gif‎ |210px]]
| style="width:85%" |

== [[Projects:BayesianMRSegmentation| Bayesian Segmentation of MRI Images]] ==

The aim of this project is to develop, implement, and validate a generic method for segmenting MRI images that automatically adapts to different acquisition sequences. [[Projects:BayesianMRSegmentation|More...]]

<font color="red">'''New: '''</font> Automated Segmentation of Hippocampal Subﬁelds from Ultra-High Resolution In Vivo MRI, K. Van Leemput, A. Bakkour, T. Benner, G. Wiggins, L.L. Wald, J. Augustinack, B.C. Dickerson, P. Golland, and B. Fischl. Hippocampus, vol. 19, no. 6, pp. 549-557, June 2009

<font color="red">'''New: '''</font> Encoding Probabilistic Atlases Using Bayesian Inference, K. Van Leemput. IEEE Transactions on Medical Imaging, vol. 28, no. 6, pp. 822-837, June 2009

|-

| | [[Image:ICluster_templates.gif|200px]]
| |

== [[Projects:MultimodalAtlas|Multimodal Atlas]] ==

In this work, we propose and investigate an algorithm that jointly co-registers a collection of images while computing multiple templates. The algorithm, called '''iCluster''', is used to compute multiple atlases for a given population.
[[Projects:MultimodalAtlas|More...]]

<font color="red">'''New: '''</font> Image-driven Population Analysis through Mixture-Modeling, M.R. Sabuncu, S.K. Balci, M.E. Shenton and P. Golland. IEEE Transactions on Medical Imaging. Accepted for Publication, 2009.

|-

| | [[Image:CoordinateChart.png|250px]]
| |

== [[Projects:SphericalDemons|Spherical Demons: Fast Surface Registration]] ==

We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently approximated on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, [[Projects:SphericalDemons|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, M. Sabuncu, T. Vercauteren, N. Ayache, B. Fischl, P. Golland. Spherical Demons: Fast Surface Registration. MICCAI, volume 5241 of LNCS, 745--753, 2008.

<font color="red">'''New: '''</font> B.T.T. Yeo, M. Sabuncu, T. Vercauteren, N. Ayache, B. Fischl, P. Golland. Spherical Demons: Fast Surface Registration. IEEE TMI, In Press.

|-

| | [[Image:JointRegSeg.png|200px]]
| |

== [[Projects:RegistrationRegularization|Optimal Atlas Regularization in Image Segmentation]] ==

We propose a unified framework for computing atlases from manually labeled data sets at various degrees of “sharpness” and the joint registration and segmentation of a new brain with these atlases. Using this framework, we investigate the tradeoff between warp regularization and image ﬁdelity, i.e. the smoothness of the new subject warp and the sharpness of the atlas in a segmentation application.
[[Projects:RegistrationRegularization|More...]]

<font color="red">'''New:'''</font> B.T.T. Yeo, M.R. Sabuncu, R. Desikan, B. Fischl, P. Golland. Effects of Registration Regularization and Atlas Sharpness on Segmentation Accuracy. Medical Image Analysis, 12(5):603--615, 2008.

|-

| | [[Image:epi_correction_small.jpg|200px]]
| |

== [[Projects:FieldmapFreeDistortionCorrection|Fieldmap-Free EPI Distortion Correction]] ==

In this project we aim to improve the EPI distortion correction algorithms [[Projects:FieldmapFreeDistortionCorrection|More...]]

<font color="red">'''New: '''</font> Poynton C., Jenkinson M., Whalen S., Golby A.J., Wells III W. Fieldmap-Free Retrospective Registration and Distortion Correction for EPI-Based Functiona Imaging. MICCAI 2008.

|-

| | [[Image:mit_fmri_clustering_parcellation2_xsub.png|200px]]
| |

== [[Projects:fMRIClustering|fMRI clustering]] ==

In this project we study the application of model-based clustering algorithms in identification of functional connectivity in the brain. [[Projects:fMRIClustering|More...]]

<font color="red">'''New: '''</font> A. Venkataraman, K.R.A. Van Dijk, R.L. Buckner, P. Golland. Exploring Functional Connectivity in fMRI via Clustering. ICASSP 2009.

<font color="red">'''New: '''</font> D. Lashkari, E. Vul, N. Kanwisher, P. Golland. Discovering Structure in the Space of Activation
Profiles in fMRI. MICCAI 2008.

|-

| | [[Image:FoldingSpeedDetection.png|150px|]]
| |

== [[Projects:ShapeAnalysisWithOvercompleteWavelets|Shape Analysis With Overcomplete Wavelets]] ==

In this work, we extend the Euclidean wavelets to the sphere. The resulting over-complete spherical wavelets are invariant to the rotation of the spherical image parameterization. We apply the over-complete spherical wavelet to cortical folding development [[Projects:ShapeAnalysisWithOvercompleteWavelets|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, P. Yu, P.E. Grant, B. Fischl, P. Golland. Shape Analysis with Overcomplete Spherical Wavelets. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), volume 5241 of LNCS, 468--476, 2008

B.T.T. Yeo, W. Ou, P. Golland. On the Construction of Invertible Filter Banks on the 2-Sphere. Yeo, Ou and Golland. IEEE Transactions on Image Processing. 17(3):283--300. 2008.

|-

| | [[Image:Models.jpg|200px]]
| |

== [[Projects:DTIModeling|Fiber Tract Modeling, Clustering, and Quantitative Analysis]] ==

The goal of this work is to model the shape of the fiber bundles and use this model description in clustering and statistical analysis of fiber tracts. [[Projects:DTIModeling|More...]]

<font color="red">'''New:'''</font> Mahnaz Maddah, Marek Kubicki, William M. Wells, Carl-Fredrik Westin, Martha E. Shenton and W. Eric L. Grimson, Findings in Schizophrenia by Tract-Oriented DT-MRI Analysis. MICCAI 2008.

M. Maddah, L. Zollei, W. E. L. Grimson, W. M. Wells, Modeling of Anatomical Information in Clustering of White Matter Fiber Trajectories Using Dirichlet Distribution. MMBIA 2008.

M. Maddah, L. Zollei, W. E. L. Grimson, C-F Westin, W. M. Wells, A Mathematical Framework for Incorporating Anatomical Knowledge in DT-MRI Analysis. ISBI 2008.

|-

| | [[Image:TGIt.gif| 150px]]
| |

== [[Projects:LatentAtlasSegmentation|Joint Segmentation of Image Ensembles via Latent Atlases]] ==

Spatial priors, such as probabilistic atlases, play an important role in MRI segmentation. The atlases are typically generated by averaging manual labels of aligned brain regions across different subjects. However, the availability of comprehensive, reliable and suitable manual segmentations is limited. We therefore propose a joint segmentation of corresponding, aligned structures in the entire population that does not require a probability atlas.
[[Projects:LatentAtlasSegmentation|More...]]

<font color="red">'''New: '''</font> T. Riklin Raviv, K. Van Leemput, W.M. Wells III and P. Golland, Joint Segmentation of Image Ensembles via Latent Atlases, Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009

<font color="red">'''New: '''</font>
T. Riklin Raviv, B.H. Menze, K. Van Leemput, B. Stieltjes, M.A. Weber, N. Ayache, W. M. Wells III and P. Golland, Joint Segmentation using Patient specific Latent Anatomy Model
MICCAI workshop for Probabilistic Models on Medical Image Analysis (PMMIA) 2009

|-

| | [[Image:Progress_Registration_Segmentation_Shape.jpg|180px]]
| |

== [[Projects:ShapeBasedSegmentationAndRegistration|Shape Based Segmentation and Registration]] ==

This type of algorithm assigns a tissue type to each voxel in the volume. Incorporating prior shape information biases the label assignment towards contiguous regions that are consistent with the shape model. [[Projects:ShapeBasedSegmentationAndRegistration|More...]]

|-

| | [[Image:GroupwiseSummary.PNG|200px]]
| |

== [[Projects:GroupwiseRegistration|Groupwise Registration]] ==

We extend a previously demonstrated entropy based groupwise registration method to include a free-form deformation model based on B-splines. We provide an efficient implementation using stochastic gradient descents in a multi-resolution setting. We demonstrate the method in application to a set of 50 MRI brain scans and compare the results to a pairwise approach using segmentation labels to evaluate the quality of alignment.

In a related project, we develop a method that reconciles the practical advantages of symmetric registration with the asymmetric nature of image-template registration by adding a simple correction factor to the symmetric cost function. We instantiate our model within a log-domain diffeomorphic registration framework. Our experiments show exploiting the asymmetry in image-template registration improves alignment in the image coordinates.

<font color="red">'''New: '''</font> Asymmetric Image-Template Registration, M.R. Sabuncu, B.T. Thomas Yeo, T. Vercauteren, K. Van Leemput, P. Golland. To appear in Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009

[[Projects:GroupwiseRegistration|More...]]

|-

| | [[Image:MIT_DTI_JointSegReg_atlas3D.jpg|200px]]
| |

== [[Projects:DTIFiberRegistration|Joint Registration and Segmentation of DWI Fiber Tractography]] ==

The goal of this work is to jointly register and cluster DWI fiber tracts obtained from a group of subjects. [[Projects:DTIFiberRegistration|More...]]

|-

| | [[Image:brain.png|200px]]
| |

== [[Projects:DTIClustering|DTI Fiber Clustering and Fiber-Based Analysis]] ==

The goal of this project is to provide structural description of the white matter architecture as a partition into coherent fiber bundles and clusters, and to use these bundles for quantitative measurement. [[Projects:DTIClustering|More...]]

|-

| | [[Image:FMRIEvaluationchart.jpg|200px]]
| |

== [[Projects:fMRIDetection|fMRI Detection and Analysis]] ==

We are exploring algorithms for improved fMRI detection and interpretation by incorporting spatial priors and anatomical information to guide the detection. [[Projects:fMRIDetection|More...]]

|-

| | [[Image:Thalamus_algo_outline.png|200px]]
| |

== [[Projects:DTISegmentation|DTI-based Segmentation]] ==

Unlike conventional MRI, DTI provides adequate contrast to segment the thalamic nuclei, which are gray matter structures. [[Projects:DTISegmentation|More...]]

|-

| | [[Image:ConnectivityMap.png|200px]]
| |

== [[Projects:DTIStochasticTractography|Stochastic Tractography]] ==

This work calculates posterior distributions of white matter fiber tract parameters given diffusion observations in a DWI volume. [[Projects:DTIStochasticTractography|More...]]

|-

| | [[Image:HippocampalShapeDifferences.gif|200px]]
| |

== [[Projects:ShapeAnalysis|Population Analysis of Anatomical Variability]] ==

Our goal is to develop mathematical approaches to modeling anatomical variability within and across populations using tools like local shape descriptors of specific regions of interest and global constellation descriptors of multiple ROI's. [[Projects:ShapeAnalysis|More...]]

|}

Algorithm:MIT

2009-09-10T22:23:49Z

Ythomas: /* Spherical Demons: Fast Surface Registration */

Back to [[Algorithm:Main|NA-MIC Algorithms]]
__NOTOC__
= Overview of MIT Algorithms (PI: Polina Golland) =

Our group seeks to model statistical variability of anatomy and function across subjects and between populations and to utilize computational models of such variability to improve predictions for individual subjects, as well as characterize populations. Our long-term goal is to develop methods for joint modeling of anatomy and function and to apply them in clinical and scientific studies. We work primarily with anatomical, DTI and fMRI images. We actively contribute implementations of our algorithms to the NAMIC-kit.

= MIT Projects =

{| cellpadding="10" style="text-align:left;"
|| [[Image:Segmentation_example2.png|250px]]
||

== [[Projects:NonparametricSegmentation| Nonparametric Models for Supervised Image Segmentation]] ==

We propose a non-parametric, probabilistic model for the automatic segmentation of medical images,
given a training set of images and corresponding label maps. The resulting inference algorithms we
develop rely on pairwise registrations between the test image and individual training images. The
training labels are then transferred to the test image and fused to compute a final segmentation of
the test subject. [[Projects:NonparametricSegmentation|More...]]

<font color="red">'''New: '''</font> Supervised Nonparametric Image Parcellation, M.R. Sabuncu, B.T. Thomas Yeo, K. Van Leemput, B. Fischl, and P. Golland. To appear in Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009.

<font color="red">'''New: '''</font> Nonparametric Mixture Models for Supervised Image Parcellation, M.R. Sabuncu,
B.T.T. Yeo, K. Van Leemput, B. Fischl, and P. Golland. To be presented at PMMIA Workshop at MICCAI 2009.

|-

{| cellpadding="10" style="text-align:left;"
| style="width:15%" | [[Image:TetrahedralAtlasWarp.gif‎ |210px]]
| style="width:85%" |

== [[Projects:BayesianMRSegmentation| Bayesian Segmentation of MRI Images]] ==

The aim of this project is to develop, implement, and validate a generic method for segmenting MRI images that automatically adapts to different acquisition sequences. [[Projects:BayesianMRSegmentation|More...]]

<font color="red">'''New: '''</font> Automated Segmentation of Hippocampal Subﬁelds from Ultra-High Resolution In Vivo MRI, K. Van Leemput, A. Bakkour, T. Benner, G. Wiggins, L.L. Wald, J. Augustinack, B.C. Dickerson, P. Golland, and B. Fischl. Hippocampus, vol. 19, no. 6, pp. 549-557, June 2009

<font color="red">'''New: '''</font> Encoding Probabilistic Atlases Using Bayesian Inference, K. Van Leemput. IEEE Transactions on Medical Imaging, vol. 28, no. 6, pp. 822-837, June 2009

|-

| | [[Image:ICluster_templates.gif|200px]]
| |

== [[Projects:MultimodalAtlas|Multimodal Atlas]] ==

In this work, we propose and investigate an algorithm that jointly co-registers a collection of images while computing multiple templates. The algorithm, called '''iCluster''', is used to compute multiple atlases for a given population.
[[Projects:MultimodalAtlas|More...]]

<font color="red">'''New: '''</font> Image-driven Population Analysis through Mixture-Modeling, M.R. Sabuncu, S.K. Balci, M.E. Shenton and P. Golland. IEEE Transactions on Medical Imaging. Accepted for Publication, 2009.

|-

| | [[Image:CoordinateChart.png|250px]]
| |

== [[Projects:SphericalDemons|Spherical Demons: Fast Surface Registration]] ==

We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently approximated on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, [[Projects:SphericalDemons|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, M. Sabuncu, T. Vercauteren, N. Ayache, B. Fischl, P. Golland. Spherical Demons: Fast Surface Registration. MICCAI, volume 5241 of LNCS, 745--753, 2008.

B.T.T. Yeo, M. Sabuncu, T. Vercauteren, N. Ayache, B. Fischl, P. Golland. Spherical Demons: Fast Surface Registration. IEEE TMI, In Press.

|-

| | [[Image:JointRegSeg.png|200px]]
| |

== [[Projects:RegistrationRegularization|Optimal Atlas Regularization in Image Segmentation]] ==

We propose a unified framework for computing atlases from manually labeled data sets at various degrees of “sharpness” and the joint registration and segmentation of a new brain with these atlases. Using this framework, we investigate the tradeoff between warp regularization and image ﬁdelity, i.e. the smoothness of the new subject warp and the sharpness of the atlas in a segmentation application.
[[Projects:RegistrationRegularization|More...]]

<font color="red">'''New:'''</font> B.T.T. Yeo, M.R. Sabuncu, R. Desikan, B. Fischl, P. Golland. Effects of Registration Regularization and Atlas Sharpness on Segmentation Accuracy. Medical Image Analysis, 12(5):603--615, 2008.

|-

| | [[Image:epi_correction_small.jpg|200px]]
| |

== [[Projects:FieldmapFreeDistortionCorrection|Fieldmap-Free EPI Distortion Correction]] ==

In this project we aim to improve the EPI distortion correction algorithms [[Projects:FieldmapFreeDistortionCorrection|More...]]

<font color="red">'''New: '''</font> Poynton C., Jenkinson M., Whalen S., Golby A.J., Wells III W. Fieldmap-Free Retrospective Registration and Distortion Correction for EPI-Based Functiona Imaging. MICCAI 2008.

|-

| | [[Image:mit_fmri_clustering_parcellation2_xsub.png|200px]]
| |

== [[Projects:fMRIClustering|fMRI clustering]] ==

In this project we study the application of model-based clustering algorithms in identification of functional connectivity in the brain. [[Projects:fMRIClustering|More...]]

<font color="red">'''New: '''</font> A. Venkataraman, K.R.A. Van Dijk, R.L. Buckner, P. Golland. Exploring Functional Connectivity in fMRI via Clustering. ICASSP 2009.

<font color="red">'''New: '''</font> D. Lashkari, E. Vul, N. Kanwisher, P. Golland. Discovering Structure in the Space of Activation
Profiles in fMRI. MICCAI 2008.

|-

| | [[Image:FoldingSpeedDetection.png|150px|]]
| |

== [[Projects:ShapeAnalysisWithOvercompleteWavelets|Shape Analysis With Overcomplete Wavelets]] ==

In this work, we extend the Euclidean wavelets to the sphere. The resulting over-complete spherical wavelets are invariant to the rotation of the spherical image parameterization. We apply the over-complete spherical wavelet to cortical folding development [[Projects:ShapeAnalysisWithOvercompleteWavelets|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, P. Yu, P.E. Grant, B. Fischl, P. Golland. Shape Analysis with Overcomplete Spherical Wavelets. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), volume 5241 of LNCS, 468--476, 2008

B.T.T. Yeo, W. Ou, P. Golland. On the Construction of Invertible Filter Banks on the 2-Sphere. Yeo, Ou and Golland. IEEE Transactions on Image Processing. 17(3):283--300. 2008.

|-

| | [[Image:Models.jpg|200px]]
| |

== [[Projects:DTIModeling|Fiber Tract Modeling, Clustering, and Quantitative Analysis]] ==

The goal of this work is to model the shape of the fiber bundles and use this model description in clustering and statistical analysis of fiber tracts. [[Projects:DTIModeling|More...]]

<font color="red">'''New:'''</font> Mahnaz Maddah, Marek Kubicki, William M. Wells, Carl-Fredrik Westin, Martha E. Shenton and W. Eric L. Grimson, Findings in Schizophrenia by Tract-Oriented DT-MRI Analysis. MICCAI 2008.

M. Maddah, L. Zollei, W. E. L. Grimson, W. M. Wells, Modeling of Anatomical Information in Clustering of White Matter Fiber Trajectories Using Dirichlet Distribution. MMBIA 2008.

M. Maddah, L. Zollei, W. E. L. Grimson, C-F Westin, W. M. Wells, A Mathematical Framework for Incorporating Anatomical Knowledge in DT-MRI Analysis. ISBI 2008.

|-

| | [[Image:TGIt.gif| 150px]]
| |

== [[Projects:LatentAtlasSegmentation|Joint Segmentation of Image Ensembles via Latent Atlases]] ==

Spatial priors, such as probabilistic atlases, play an important role in MRI segmentation. The atlases are typically generated by averaging manual labels of aligned brain regions across different subjects. However, the availability of comprehensive, reliable and suitable manual segmentations is limited. We therefore propose a joint segmentation of corresponding, aligned structures in the entire population that does not require a probability atlas.
[[Projects:LatentAtlasSegmentation|More...]]

<font color="red">'''New: '''</font> T. Riklin Raviv, K. Van Leemput, W.M. Wells III and P. Golland, Joint Segmentation of Image Ensembles via Latent Atlases, Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009

<font color="red">'''New: '''</font>
T. Riklin Raviv, B.H. Menze, K. Van Leemput, B. Stieltjes, M.A. Weber, N. Ayache, W. M. Wells III and P. Golland, Joint Segmentation using Patient specific Latent Anatomy Model
MICCAI workshop for Probabilistic Models on Medical Image Analysis (PMMIA) 2009

|-

| | [[Image:Progress_Registration_Segmentation_Shape.jpg|180px]]
| |

== [[Projects:ShapeBasedSegmentationAndRegistration|Shape Based Segmentation and Registration]] ==

This type of algorithm assigns a tissue type to each voxel in the volume. Incorporating prior shape information biases the label assignment towards contiguous regions that are consistent with the shape model. [[Projects:ShapeBasedSegmentationAndRegistration|More...]]

|-

| | [[Image:GroupwiseSummary.PNG|200px]]
| |

== [[Projects:GroupwiseRegistration|Groupwise Registration]] ==

We extend a previously demonstrated entropy based groupwise registration method to include a free-form deformation model based on B-splines. We provide an efficient implementation using stochastic gradient descents in a multi-resolution setting. We demonstrate the method in application to a set of 50 MRI brain scans and compare the results to a pairwise approach using segmentation labels to evaluate the quality of alignment.

In a related project, we develop a method that reconciles the practical advantages of symmetric registration with the asymmetric nature of image-template registration by adding a simple correction factor to the symmetric cost function. We instantiate our model within a log-domain diffeomorphic registration framework. Our experiments show exploiting the asymmetry in image-template registration improves alignment in the image coordinates.

<font color="red">'''New: '''</font> Asymmetric Image-Template Registration, M.R. Sabuncu, B.T. Thomas Yeo, T. Vercauteren, K. Van Leemput, P. Golland. To appear in Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009

[[Projects:GroupwiseRegistration|More...]]

|-

| | [[Image:MIT_DTI_JointSegReg_atlas3D.jpg|200px]]
| |

== [[Projects:DTIFiberRegistration|Joint Registration and Segmentation of DWI Fiber Tractography]] ==

The goal of this work is to jointly register and cluster DWI fiber tracts obtained from a group of subjects. [[Projects:DTIFiberRegistration|More...]]

|-

| | [[Image:brain.png|200px]]
| |

== [[Projects:DTIClustering|DTI Fiber Clustering and Fiber-Based Analysis]] ==

The goal of this project is to provide structural description of the white matter architecture as a partition into coherent fiber bundles and clusters, and to use these bundles for quantitative measurement. [[Projects:DTIClustering|More...]]

|-

| | [[Image:FMRIEvaluationchart.jpg|200px]]
| |

== [[Projects:fMRIDetection|fMRI Detection and Analysis]] ==

We are exploring algorithms for improved fMRI detection and interpretation by incorporting spatial priors and anatomical information to guide the detection. [[Projects:fMRIDetection|More...]]

|-

| | [[Image:Thalamus_algo_outline.png|200px]]
| |

== [[Projects:DTISegmentation|DTI-based Segmentation]] ==

Unlike conventional MRI, DTI provides adequate contrast to segment the thalamic nuclei, which are gray matter structures. [[Projects:DTISegmentation|More...]]

|-

| | [[Image:ConnectivityMap.png|200px]]
| |

== [[Projects:DTIStochasticTractography|Stochastic Tractography]] ==

This work calculates posterior distributions of white matter fiber tract parameters given diffusion observations in a DWI volume. [[Projects:DTIStochasticTractography|More...]]

|-

| | [[Image:HippocampalShapeDifferences.gif|200px]]
| |

== [[Projects:ShapeAnalysis|Population Analysis of Anatomical Variability]] ==

Our goal is to develop mathematical approaches to modeling anatomical variability within and across populations using tools like local shape descriptors of specific regions of interest and global constellation descriptors of multiple ROI's. [[Projects:ShapeAnalysis|More...]]

|}

Projects:LearningRegistrationCostFunctions

2009-09-10T22:21:19Z

Ythomas: /* (2) Localizing fMRI-defined MT+ Using Cortical Folding */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered, as shown by the green outline in Fig(a). During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px|(a) Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We use the ex-vivo MT template to predict MT+ in the 42 in-vivo subjects. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T22:17:45Z

Ythomas: /* (1b) Interpreting Task-Optimal Template Estimation */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered, as shown by the green outline in Fig(a). During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px|(a) Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T22:17:19Z

Ythomas: /* (1b) Interpreting Task-Optimal Template Estimation */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig.(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig.(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered, as shown by the green outline in Fig.(a). During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig.(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px|(a) Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T22:16:50Z

Ythomas: /* (1b) Interpreting Task-Optimal Template Estimation */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig.(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig.(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered: Fig.(a) shows the BA2 of the test subject (green) overlaid on the cortical geometry of the template subject after registration to the initial template geometry. During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig.(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px|(a) Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T22:16:05Z

Ythomas:

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig.(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig.(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered. Fig.(a) shows the BA2 of the test subject (green) overlaid on the cortical geometry of the template subject after registration to the initial template geometry. During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig.(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px|(a) Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T19:45:43Z

Ythomas: /* Experimental Results */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpreting Task-Optimal Template Estimation ==
Fig.(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig.(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered. Fig.(a) shows the BA2 of the test subject (green) overlaid on the cortical geometry of the template subject after registration to the initial template geometry. During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig.(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px|(a) Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T19:45:19Z

Ythomas: /* (1b) Interpretation */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpretation ==
Fig.(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig.(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered. Fig.(a) shows the BA2 of the test subject (green) overlaid on the cortical geometry of the template subject after registration to the initial template geometry. During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig.(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px|(a) Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The video below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T19:45:07Z

Ythomas: /* (1b) Interpretation */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpretation ==
Fig.(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the central sulcus. Fig.(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered. Fig.(a) shows the BA2 of the test subject (green) overlaid on the cortical geometry of the template subject after registration to the initial template geometry. During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training subjects. The ﬁnal template is shown in Fig.(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px|(a) Template]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px|(b) Test Subject]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px|(c) Final Template]]
</td>
</tr>
</table>
</center>

The figure below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T19:43:54Z

Ythomas: /* (1b) Interpretation */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpretation ==
The figure below illustrates an example of learninga task-optimal template for localizing BA2. Fig.(a) shows the initial cortical geometry of a template subject with its corresponding BA2 in black outline. In this particular subject, the postcentral sulcus is more prominent than the
central sulcus. Fig.(b) shows the cortical geometry of a test subject together with its BA2. In this subject, the central sulcus is more prominent than the postcentral sulcus. Consequently, in the uniform-weights method, the central sulcus of the test subject is wrongly mapped to the postcentral sulcus of the template, so that BA2 is misregistered. Fig.(a) shows the BA2 of the test subject (green) overlaid on the cortical geometry of the template subject after registration to the initial template geometry. During task-optimal training, our method interrupts the geometry of the postcentral sulcus in the template because the uninterrupted postcentral sulcus in the template is inconsistent with localizing BA2 in the training
subjects. The ﬁnal template is shown in Fig. 6(c). We see that the BA2 of the subject (green) and the task-optimal template (black) are well-aligned, although there still exists localization error in the superior end of BA2.

<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px|(a)]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px|(b)]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px|(c)]]
</td>
</tr>
</table>
</center>

The figure below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T19:40:48Z

Ythomas: /* (1b) Interpretation */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpretation ==
<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

The figure below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T19:40:30Z

Ythomas:

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpretation ==
<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px]]
</td>
<td>
[[Image:BA2_final_template.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

The figure below visualizes the template at each iteration of the optimization.
[[Image:lh.pm14686.BA2.gif]]

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

File:BA2 final template.png

2009-09-10T19:39:26Z

Ythomas:

Projects:LearningRegistrationCostFunctions

2009-09-10T19:38:27Z

Ythomas: /* (1b) Interpretation */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpretation ==
<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px]]
</td>
<td>
[[Image:lh.pm14686.BA2.gif|thumb|center|200px]]
</td>

</tr>
</table>
</center>

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

File:Lh.pm14686.BA2.gif

2009-09-10T19:37:35Z

Ythomas:

Projects:LearningRegistrationCostFunctions

2009-09-10T19:37:01Z

Ythomas: /* (1b) Interpretation */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpretation ==
<center>
<table>
<tr>
<td>
[[Image:BA2_template.png|thumb|center|200px]]
</td>
<td>
[[Image:BA2_subject.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T19:36:34Z

Ythomas:

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpretation ==
<center>
<table>
<tr>
<td>
[[Image:BA_template.png|thumb|center|200px]]
</td>
<td>
[[Image:BA_subject.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

File:BA2 template.png

2009-09-10T19:36:06Z

Ythomas:

File:BA2 subject.png

2009-09-10T19:35:31Z

Ythomas:

Projects:LearningRegistrationCostFunctions

2009-09-10T19:34:59Z

Ythomas:

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (1b) Interpretation ==

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T19:34:23Z

Ythomas:

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

=== (1a) Interpretation ===

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T19:33:44Z

Ythomas: /* Experimental Results */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

= (1a) Interpretation =

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T19:28:15Z

Ythomas: /* Publications */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Press''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T19:28:06Z

Ythomas: /* Publications */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Print''

* B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), In Press, 2009.

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T19:26:59Z

Ythomas: /* Publications */

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Print''

*

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T19:25:22Z

Ythomas:

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region. We see that once again, task-optimal template achieves better localization results than FreeSurfer.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Print''

* [http://www.na-mic.org/publications/pages/display?search=Projects:SphericalDemons&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database]

[[Category: Registration]] [[Category:Segmentation]]

Projects:LearningRegistrationCostFunctions

2009-09-10T19:24:29Z

Ythomas:

Back to [[NA-MIC_Internal_Collaborations:StructuralImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

We present a framework for learning registration cost functions. In medical image analysis, registration is rarely the final goal, but instead the resulting alignment is used in other tasks, such as image segmentation or group analysis. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. However, it is unclear that the same parameters are optimal for different applications. In this work, we propose a principled approach to leveraging the application context to effectively regularize the ill-posed problem of image registration. Our method learns the parameters of any smooth family of registration cost functions with respect to a specific task.

= Motivation =
Image registration is ambiguous. For example, Brodmann areas are parcellation of the cortex based on the cellular architecture of the cortex. The figures below show two subjects with Brodmann areas overlaid on the cortical folding pattern. Here, we see that perfectly aligning the inferior frontal sulcus will misalign the superior end of BA44 (Broca's language area). If our goal is segment sulci and gyri, perfectly alignment of the cortical folding pattern is ideal. But it is unclear whether perfectly aligning cortical folds is optimal for localizing Brodmann areas. Here, we show that by taking into account the end-goal of registration, we not only improve the application performance but also potentially eliminate ambiguities in image registration.

<center>
<table>
<tr>
<td>
[[Image:to.rh.pm1696.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
<td>
[[Image:to.rh.pm20784.BAsALL.lat.cropped.caption.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

= Description =
The key idea is to introduce a second layer of optimization over and above the usual registration. This second layer of optimization traverses the space of local minima, selecting registration parameters that result in good registration local minima as measured by the performance of the specific application in a training data set. The training data provides additional information not present in a test image, allowing the task-speciﬁc cost function to be evaluated during training. For example, if the task is segmentation, we assume the existence of a training data set with ground truth segmentation and a smooth cost function that evaluates segmentation accuracy. This segmentation accuracy is used as a proxy to evaluate registration accuracy.

If the registration cost function employs a single parameter, then the optimal parameter value can be found by exhaustive search. With multiple parameters, exhaustive search is not possible. Here, we demonstrate the optimization of thousands of parameters by gradient descent on the space of local minima, selecting registration parameters that result in good registration local minima as measured by the task-speciﬁc cost function in the training data set.

Our formulation is related to the use of continuation methods in computing the entire path of solutions of learning problems (e.g., SVM or Lasso) as a function of a single regularization parameter. Because we deal with multiple (thousands of) parameters, it is impossible for us to compute a solution manifold. Instead, we trace a path within the solution manifold that improves the task-speciﬁc cost function.

Another advantage of our approach is that we do not require ground truth deformations. As suggested in the example above, the concept of “ground truth deformations” may not always be well-deﬁned, since the optimal registration may depend on the application at hand. In contrast, our approach avoids the need for ground truth deformations by focusing on the application performance, where ground truth (e.g., via segmentation labels) is better deﬁned.

= Experimental Results =
We instantiate the framework for the alignment of hidden labels whose extents are not necessarily well-predicted by local image features. We consider the generic weighted Sum of Squared Differences (wSSD) cost function and estimate either (1) the optimal weights or (2) cortical folding template for localizing cytoarchitectural and functional regions based only on macroanatomical cortical folding information. We demonstrate state-of-the-art localization results in both histological and fMRI data sets.

== (1) Localizing Brodmann Areas Using Cortical Folding ==
In this experiment, we estimate the optimal template in the wSSD cost function for localizing Brodmann areas in 10 histologically-analyzed subjects. We compare 3 algorithms: task-optimal template (red), FreeSurfer (green) [1] and optimal uniform weights (black). Optimal uniform weights are found by setting all the weights to a single value and performing an exhaustive search of the weights. We see in the figure below, that task-optimal framework achieves the lowest localization errors.

<center>
<table>
<tr>
<td>
[[Image:to.Presentation.mean2.V1V2BA2.png|thumb|center|200px]]
</td>
<td>
[[Image:to.Presentation.mean2.BA44BA45MT.png|thumb|center|200px]]
</td>
</tr>
</table>
</center>

== (2) Localizing fMRI-defined MT+ Using Cortical Folding ==
In this experiment, we consider 42 subjects with fMRI-defined MT+ defined on the subject. MT+ is thought to include the cytoarchitectonically-defined MT, as well as, a small part of the medial superior temporal region.

[[Image:exvivoMTPredictsInvivoMT.png|thumb|center|200px]]

[1] B. Fischl, M. Sereno, R. Tootell, and A. Dale. High-resolution Intersubject Averaging and a Coordinate System for the
Cortical Surface. Human Brain Mapping, 8(4):272–284, 1999.

= Key Investigators =

* MIT: [[http://people.csail.mit.edu/ythomas/ | B.T. Thomas Yeo]], Mert Sabuncu, Polina Golland
* MGH: Bruce Fischl, Daphne Holt
* INRIA: Tom Vercauteren
* Aachen University: Katrin Amunts
* Research Center Juelich: Karl Zilles

= Publications =
''In Print''

* [http://www.na-mic.org/publications/pages/display?search=Projects:SphericalDemons&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database]

[[Category: Registration]] [[Category:Segmentation]]