Algorithms:Core1Visit May06:Shape

Martin Styner - Enhanced Correspondence and Statistics for Structural Shape Analysis

• spherical topology (vs star-shaped)
• spharm representation: can have self-intersections
• template-free alignment w/ first order ellipsoid
• works fine with all cortical structures
• approximation error for correspondence evaluation - distance on surface
  • are the curvature metrics independent? if not, should not be used for optimization (overfitting the model)
  • soln: you can use a separate training set and a testing set (not optimal)
  • you can recover the surface based on C and S (you can recompute both the mean and gaussian curvature) so this doesnt really solve the dependence problem
• robustness - several methods (spharm, mdl, even m-reps) give very similar results
• separating training and testing datasets
• bias could be introduced by the preprocessing (opening, closing, handle filling, smoothing, etc)
• application to namic data - results agree with different studies
• publications - Martha Shenton

Kilian Pohl - Building Shape Prior Models for Segmentation

• diffeomorphism
• two alternative ways for mapping
• adding two shapes in logodd space
• the black box: estimates the mean and variance
• data - schizophrenia group
• the size change we see can be not-growth but some other effects
• comparison to Martin's work: surface vs voxel sets
  • implicit assumption of closest point correspondence
  • preservation of topology

Ross Whitaker - A Nonparametric Approach to Shape Correspondence

• avoiding trivial solutions
• avoiding introducing extra information into the population (idea in mdl)
• choices about parametrization is arbitrary
• particles also used in fluid dynamics literature
• does initial particle configuration bias the results?
  • at the level detail, yes - but not the aggregation (not for the density etc, for example)
• correspondence is defined by labeling particles
• particles are trying to maximize entropy in a single surface
• shapes are interacting to minimize the entropy in the ensemble
• the need for splitting particles can be different in each shape
• sensitive to alignment - can be done together w/ procrustes
• can the particles reconfigure themselves?
  • 'triangle flipping' can happen - no guarantees
  • but that can be a good thing if you interpret it as a 'wrinkle'
• can compare a torus and a hippocampus
• neighborhood relations can be unpreserved
• two free parameters: particle density and threshold for very small modes (to regularize)
• local minima
• mdl results not good at 3 std dev away
• useful for topologically different structures
• what happens if the shape has disconnected parts
• so it can be used for multiple object correspondence
• can be extended to volumetric instead of surface
• swapping doesnt happen in 2D, but its not guaranteed it wont happen in 3D
• subdivision surfaces
• a shape representation vs a correspondence establishing technique
• comparing particle systems with each other
• the statistics are done on point data - the neighborhood info is not even used