Projects:RegistrationDocumentation:RegEval Anisotropy - Revision history

Meier: /* Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum */

2011-01-05T14:10:18Z

Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum

Meier: /* Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum */

2010-12-21T19:24:34Z

Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum

Meier: /* Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum */

2010-12-21T19:21:42Z

Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum

Meier: /* Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum */

2010-12-21T18:29:35Z

Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum

Meier: /* Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum */

2010-12-16T22:42:50Z

Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum

Meier: /* Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum */

2010-12-16T21:14:13Z

Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum

Meier: /* Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum */

2010-12-15T14:21:55Z

Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum

Meier: /* Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum */

2010-12-15T14:14:54Z

Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum

Meier: /* Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum */

2010-12-14T22:09:33Z

Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum

Meier: /* Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum */

2010-12-14T22:09:14Z

Experiment 1: Anisotropy degenerates Joint Histogram & Global Optimum

@@ Line 93: / Line 93: @@
 **we have a mix between many points with small distances from the axis, and few points with large distances, hence the original histogram appears "mixed in" in a summary of off-diagnoal energy. How to calibrate the two is best answered by how the registration algorithm evaluates the joint histogram shape into its cost function.
 **blurring for reference rotations and translations looks largely the same, so we use translation for ease of use (clearly defined residual RMS)
-**measuring off-diagnoal energy:
+**measuring off-diagnoal energy: Mattes MI as implemented in ITK:  extract code & compute as standalone
 == Experiment 2: Anisotropy most strongly affects rotation axes perpendicular to the largest voxel dimension ==

@@ Line 92: / Line 92: @@
 **the partial volume "bleed" works relative to the histogram mode/mean, i.e. low intensities are more likely to get brighter by PV, whereas higher intensities are more likely to be surrounded by lower ones and hence become darker by PV. Thus the joint histogram gets "squished" toward the middle from both ends (Fig.1), and ends up with a rotation relative to the 45 axis around a midpoint that's somewhere near the mode or mean intensity. We could measure this rotation as another metric. Most straightforward would be via principal axes.
 **we have a mix between many points with small distances from the axis, and few points with large distances, hence the original histogram appears "mixed in" in a summary of off-diagnoal energy. How to calibrate the two is best answered by how the registration algorithm evaluates the joint histogram shape into its cost function.
 == Experiment 2: Anisotropy most strongly affects rotation axes perpendicular to the largest voxel dimension ==

@@ Line 82: / Line 82: @@
 Image:RegEval_JHBlur_RotY_AGif.gif|Fig.6: for comparison: example joint histogram blurring effects from rotation around y (AP) axis 1-15 degrees
 Image:RegEval_JHBlur_RotZ_AGif.gif|Fig.7: for comparison: example joint histogram blurring effects from rotation around z (IS) axis 1-15 degrees
 </gallery>

@@ Line 88: / Line 88: @@
 **need an intuitive way or metric to interpret the blurring of the JH, what it means in terms of registration accuracy, robustness, capture range etc. One way would be to quantify the off-diagnoal amount of intensity, another more visual to compare to blurring from misalignment, i.e. find the misalignment that produces a similarly blurred JH.
 **the blurred histogram represents the new practically achievable global optimum, relative to the theoretical ideal of a 45-degree unity line
-**the partial volume "bleed" works relative to the histogram mode/mean, i.e. low intensities are more likely to get brighter by PV, whereas higher intensities are more likely to be surrounded by lower ones and hence become darker by PV. Thus the joint histogram has a rotation relative to the 45 axis around a midpoint that's somewhere near the mode or mean intensity. We could measure this rotation as another metric. Most straightforward would be via principal axes.
+**the partial volume "bleed" works relative to the histogram mode/mean, i.e. low intensities are more likely to get brighter by PV, whereas higher intensities are more likely to be surrounded by lower ones and hence become darker by PV. Thus the joint histogram gets "squished" toward the middle from both ends (Fig.1), and ends up with a rotation relative to the 45 axis around a midpoint that's somewhere near the mode or mean intensity. We could measure this rotation as another metric. Most straightforward would be via principal axes.
 **we have a mix between many points with small distances from the axis, and few points with large distances, hence the original histogram appears "mixed in" in a summary of off-diagnoal energy. How to calibrate the two is best answered by how the registration algorithm evaluates the joint histogram shape into its cost function.

@@ Line 79: / Line 79: @@
 Image:RegEval_JointHist_5mm.jpg| Fig.3:  same as Fig.2 for anisotropy ratio 5:1
 Image:RegEval_JointHist_AGif.gif|Fig.4: Example joint histogram blurring effects from anisotropic voxel size : 1x to 20x anisotropy
-Image:RegEval_JHBlur_RotZ_AGif.gif|Fig.5: for comparison: example joint histogram blurring effects from rotation around z (IS) axis 1-15 degrees
+Image:RegEval_JHBlur_RotX_AGif.gif|Fig.5: for comparison: example joint histogram blurring effects from rotation around x (LR) axis 1-15 degrees
 </gallery>

@@ Line 74: / Line 74: @@
 :#evaluate relative blurring: deviation from unity line
 *'''Results'''
-[[Image:RegEval_ImageHistory_3mm.png|400px|Example image processing pipeline]] Fig.1: Example processing pipeline simulating PV effects from anisotropic voxel size <br>
+<gallery widths="300px" perrow="3">
-[[Image:RegEval_JointHist_3mm.jpg|400px|Example joint histogram]] Fig.2: Example joint histogram blurring effects from anisotropic voxel size: '''leftmost''': reference blurring from interpolation blurring alone (no PV); middle: 3x1 anisotropy against original; '''right''': 3x1 anisotropy against blurred reference <br>
+Image:RegEval_ImageHistory_3mm.png| Fig.1: Example processing pipeline simulating PV effects from anisotropic voxel size
-[[Image:RegEval_JointHist_5mm.jpg|400px|Example joint histogram]] Fig.3:  Example joint histogram blurring effects from anisotropic voxel size: '''leftmost''': reference blurring from interpolation blurring alone (no PV); middle: 3x1 anisotropy against original; '''right''': 5x1 anisotropy against blurred reference <br><br>
+Image:RegEval_JointHist_3mm.jpg| Fig.2: Example joint histogram. left: reference blurring from interpolation blurring alone (no PV); middle: 3x1 anisotropy against original; '''right''': 3:1 anisotropy against blurred reference
 *'''Discussion'''
 **need an intuitive way or metric to interpret the blurring of the JH, what it means in terms of registration accuracy, robustness, capture range etc. One way would be to quantify the off-diagnoal amount of intensity, another more visual to compare to blurring from misalignment, i.e. find the misalignment that produces a similarly blurred JH.

@@ Line 76: / Line 76: @@
 [[Image:RegEval_ImageHistory_3mm.png|400px|Example image processing pipeline]] Example processing pipeline simulating PV effects from anisotropic voxel size <br>
 [[Image:RegEval_JointHist_3mm.jpg|400px|Example joint histogram]] Example joint histogram blurring effects from anisotropic voxel size: '''leftmost''': reference blurring from interpolation blurring alone (no PV); middle: 3x1 anisotropy against original; '''right''': 3x1 anisotropy against blurred reference <br>
-[[Image:RegEval_JointHist_5mm.jpg|400px|Example joint histogram]] Example joint histogram blurring effects from anisotropic voxel size: '''leftmost''': reference blurring from interpolation blurring alone (no PV); middle: 3x1 anisotropy against original; '''right''': 5x1 anisotropy against blurred reference
+[[Image:RegEval_JointHist_5mm.jpg|400px|Example joint histogram]] Example joint histogram blurring effects from anisotropic voxel size: '''leftmost''': reference blurring from interpolation blurring alone (no PV); middle: 3x1 anisotropy against original; '''right''': 5x1 anisotropy against blurred reference <br><br>
 [[Image:RegEval_JointHist_AGif.gif|400px|Example joint histogram blurring 1.1 to 20x anisotropy]] Example joint histogram blurring effects from anisotropic voxel size : 1.1 to 20x anisotropy
 *'''Discussion'''