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Stable Volumetric Features in Deformable-Shapes

Stable Volumetric Features in Deformable-Shapes . Roee Litman , Alex Bronstein, Michael Bronstein. The “Feature Approach” to Image Analysis. Video tracking Panorama alignment 3D reconstruction Content-based image retrieval. Non-rigid Shapes. Non-Rigid (preserve-volume).

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Stable Volumetric Features in Deformable-Shapes

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  1. Stable Volumetric Featuresin Deformable-Shapes Roee Litman, Alex Bronstein, Michael Bronstein

  2. The “Feature Approach”to Image Analysis • Video tracking • Panorama alignment • 3D reconstruction • Content-based image retrieval

  3. Non-rigid Shapes Non-Rigid(preserve-volume) Rigid(rotation + translation) Non-Rigid(change-volume)

  4. Problem formulation • Find a semi-local feature detector • High repeatability • Invariance to deformation • Robustness to noise, sampling, etc. • Sensitivity to volume changes. • Add informative descriptor

  5. The Goal “Head+Arm” take a shape Detect (stable) regions “Head” “Arm” “Upper Body” “Leg” “Leg”

  6. Repeatability (SHREC10 dataset)

  7. More Results (Taken from the TOSCA dataset) Horse regions + Human regions

  8. Partial matching How can we tell a centaur is part-humanand part-horse?

  9. Region Description Distance = 0.44 Distance = 0.34 Distance = 0.02 Distance = 0.08 Distance= 0.17 Distance = 0.25

  10. Region Matching Query 1st, 2nd, 4th, 10th, and 15th matches

  11. (The “how”) Methodology

  12. In a nutshell… The Feature Approach for Images Deformable Shape Analysis Shape MSER MSER Maximally Stable ExtremalRegion Diffusion Geometry

  13. Original MSER (Matas et-al)

  14. MSER – In a nutshell • Threshold image at consecutive gray-levels • Search regions whose area stay nearly the same through a wide range of thresholds

  15. MSER – In a nutshell

  16. Algorithm overview

  17. Algorithm overview • Represent as weighted graph • Component tree • Stable component detection

  18. Algorithm overview • Represent as weighted graph

  19. Weighting the graph In images • Illumination (Gray-scale) • Color (RGB) In Shapes • Mean Curvature (not deformation invariant) • Diffusion Geometry

  20. Weighting Option • For every point on the shape: • Calculate the prob. of a random walk to return to the same point. • Similar to Gaussian curvature • Intrinsic - i.e. deformation invariant

  21. Weight example Color-mapped Level-set animation

  22. Diffusion Geometry • Analysis of diffusion (random walk) processes • Governed by the heat equation • Solution is heat distributionat point at time

  23. Heat-Kernel • Given • Initial condition • Boundary condition, if these’s a boundary • Solve using: • i.e. - find the “heat-kernel”

  24. Probabilistic Interpretation The probability density for a transition by random walk of length , from to

  25. Spectral Interpretation • How to calculate ? • Heat kernel can be calculated directly from eigen-decomposition of the Laplacain • By spectral decomposition theorem:

  26. Laplace-Beltrami Eigenfunctions

  27. Deformation Invariance

  28. Auto-diffusivity • Special case - • The chance of returning to after time • Related to Gaussian curvature by • Now we can attach scalar value to shapes!

  29. Weight example Color-mapped Level-set animation

  30. Algorithm overview • Represent as weighted graph • Component tree • Stable component detection

  31. Region Hierarchy Nested Level-sets

  32. The Component Tree • Constructed as a pre-process of stable region detection. • Defined by level-set nesting relations. • Can be based on any weighted graph. • Allows to set “stability” value for all regions. • Only “Maximally-stable” regions are kept as features.

  33. Example(Partial tree – olny the stable regions)

  34. Performance

  35. Volume vs. Surface Original Volume & surface isometry Boundary isometry

  36. Volume vs. Surface Original Volume & surface isometry Boundary isometry

  37. Volumetric Shapes • Usually shapes are modeled as 2D boundary of a 3D shape. • Volumetric shape model better captures "natural" behavior of non-rigid deformations.(Raviv et-al) • Diffusion geometry terms can easily be applied to volumes • 2D Meshes can be voxelized

  38. Volumetric Regions Taken from the SCAPE dataset

  39. 3D Human Scans Taken from the SCAPE dataset

  40. Scanned Region Matching Query 1st, 2nd, 4th, 10th, and 15th matches

  41. Quantitative Results • Overlap ratio between a region R and its counterpart R’ is: • Repeatability is the percent of regions with overlap above a threshold

  42. Repeatability(on the SHREC’11 data-set)

  43. Conclusion • Extension of stable region detectionto volumetric models. • Allows comparison of scanned (SCAPE)and synthetic (TOSCA) shapes. • Better performance on SHREC’11.

  44. Thank You Any Questions?

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