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(New page: Back to Georgia Tech Algorithms __NOTOC__ = Label Space: A Coupled Multi-Shape Representation = Our Objective is to compare various shape representation techniques l...)
 
 
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  Back to [[Algorithm:GATech|Georgia Tech Algorithms]]
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  Back to [[Algorithm:Stony Brook|Stony Brook University Algorithms]]
 
__NOTOC__
 
__NOTOC__
 
= Label Space: A Coupled Multi-Shape Representation =
 
= Label Space: A Coupled Multi-Shape Representation =
  
Our Objective is to compare various shape representation techniques like linear PCA (LPCA), kernel PCA (KPCA), locally linear embedding (LLE) and
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Many techniques for multi-shape representation may often develop
kernel locally linear embedding (KLLE).
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inaccuracies stemming from either approximations or inherent variation.
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Label space is an implicit representation that offers unbiased algebraic
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manipulation and natural expression of label uncertainty.  We demonstrate
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smoothing and registration on multi-label brain MRI.
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= Description =
 
= Description =
  
The surfaces are represented as the zero level set of a signed distance function and shape learning is performed on the embeddings of these shapes. We carry out some experiments to see how well each of these methods can represent a shape, given the training set. We tested the performance of these methods on shapes of left caudate nucleus and left hippocampus. The training set of left caudate nucleus consisted of 26 data sets and the test set contained 3 volumes. Error between a particular shape representation and
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Two key aspects of coupled multi-object shape analysis are the choice of
ground truth was calculated by computing the number of mislabeled voxels using each of the methods. Figure 1 gives the error
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representation and subsequent registration to align the sample set.  Current
using each of the methods. Similar tests were done on a training set of 20 hippocampus data with 3 test volumes. Figure 2 gives the error table for each of the methods [1].
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techniques for such analysis tend to trade off performance between the two
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tasks, performing well for one task but developing problems when used for
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the other. We propose label space, a representation that is both flexible
 +
and well suited for both tasks.  Under this framework, object labels are
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mapped to vertices of a regular simplex, e.g. the unit interval for two
 +
labels, a triangle for three labels, a tetrahedron for four labels, etc.
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This forms a linear space with the property that all labels are equally
 +
spaced.  On examination, this representation has several desirable properties:
 +
algebraic operations may be done directly, label uncertainty is expressed as
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a weighted mixture of labels, interpolation is unbiased toward any label or
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the background, and registration may be performed directly.  To demonstrate these properties, we describe variational registration
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directly in this space.  Many registration methods fix one of the maps and
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align the rest of the set to this fixed map. To remove the bias induced by
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arbitrary selection of the fixed map, we align a set of label maps to their
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intrinsic mean map.
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[[Image:Table1.png|thumb|600px|Figure 1: Table gives the number of mislabelled voxels for each of the methods for left caudate nucleus]]
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[[Image:Label_space.png|thumb|Figure 1: The first three label space configurations: a unit interval for two labels, a triangle for three labels, and a tetrahedron for four labels (left to right). ]]
[[Image:Table2.png|thumb|600px|Figure 2: Figure 1: Table gives the number of mislabelled voxels for each of the methods for left hippocampus]]
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[[Image:Ls_original_aligned.png|thumb|Figure 2: Alignment of a set of 30 maps used in the study by Tsai et al. (2003).  The original and aligned sets are superimposed for visualization.]]
  
 
= Key Investigators =
 
= Key Investigators =
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= Publications =
 
= Publications =
  
''In Print''
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* [http://www.na-mic.org/publications/pages/display?search=LabelSpace&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&searchbytag=checked&sponsors=checked| NA-MIC Publications Database on Label Space: A Coupled Multi-Shape Representation]
* [http://www.na-mic.org/pages/Special:Publications?text=Projects%3AKPCA+LLE+KLLE+ShapeAnalysis&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database]
 
  
 
[[Category: Shape Analysis]]
 
[[Category: Shape Analysis]]

Latest revision as of 01:00, 16 November 2013

Home < Projects:LabelSpace
Back to Stony Brook University Algorithms

Label Space: A Coupled Multi-Shape Representation

Many techniques for multi-shape representation may often develop inaccuracies stemming from either approximations or inherent variation. Label space is an implicit representation that offers unbiased algebraic manipulation and natural expression of label uncertainty. We demonstrate smoothing and registration on multi-label brain MRI.


Description

Two key aspects of coupled multi-object shape analysis are the choice of representation and subsequent registration to align the sample set. Current techniques for such analysis tend to trade off performance between the two tasks, performing well for one task but developing problems when used for the other. We propose label space, a representation that is both flexible and well suited for both tasks. Under this framework, object labels are mapped to vertices of a regular simplex, e.g. the unit interval for two labels, a triangle for three labels, a tetrahedron for four labels, etc. This forms a linear space with the property that all labels are equally spaced. On examination, this representation has several desirable properties: algebraic operations may be done directly, label uncertainty is expressed as a weighted mixture of labels, interpolation is unbiased toward any label or the background, and registration may be performed directly. To demonstrate these properties, we describe variational registration directly in this space. Many registration methods fix one of the maps and align the rest of the set to this fixed map. To remove the bias induced by arbitrary selection of the fixed map, we align a set of label maps to their intrinsic mean map.


Figure 1: The first three label space configurations: a unit interval for two labels, a triangle for three labels, and a tetrahedron for four labels (left to right).
Figure 2: Alignment of a set of 30 maps used in the study by Tsai et al. (2003). The original and aligned sets are superimposed for visualization.

Key Investigators

  • Georgia Tech Algorithms: James Malcolm, Yogesh Rathi, Allen Tannenbaum

Publications