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Matching 3D Models With Shape Distributions

Matching 3D Models With Shape Distributions. Robert Osada, Tom Funkhouser Bernard Chazelle, and David Dobkin Princeton University. Shape Similarity. Determine similarity between 3D shapes. Computer Graphics. Computer Vision. Computational Biology. [Insulin, PDB]. [Caltech].

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Matching 3D Models With Shape Distributions

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  1. Matching 3D Models With Shape Distributions Robert Osada, Tom Funkhouser Bernard Chazelle, and David Dobkin Princeton University

  2. Shape Similarity • Determine similarity between 3D shapes ComputerGraphics ComputerVision Computational Biology [Insulin, PDB] [Caltech]

  3. Previous Work in 2D • Shape representations • Fourier analysis [Arbter90] • Turning function [Arkin91] • Size function [Uras95] • Metrics for comparing curves • Hausdorff • Fréchet • Bottleneck • etc.

  4. Previous Work in 3D • High-level representations • Generalized cylinders [Binford71] • Medial axis [Bardinet00] • Skeletons [Bloomenthal99] • Statistical • Moments [Reeves45, Prokop92] • Crease angle [Besl94] • Shells decomposition around centroid [Ankerst99] • Extended Gaussian Images [Horn84] • etc.

  5. Desired Properties • Match global properties of shape • Invariance • Rotation, translation, scale, mirror • Robustness • Noise, cracks, insertions and deletions • Practicality • Concise representation • Efficient comparison • Working with degenerate models

  6. Our Approach • Shape distributions • Concise shape descriptor • Common parameterization • Function of random points Random sampling Parameterization ShapeDistribution 3D Model

  7. Our Approach Parameterization Shape Function SimilarityMeasure Parameterization 3D Model Shape Distribution

  8. Issues • Which shape function? • How to compare shape distributions? Parameterization SimilarityMeasure Parameterization

  9. Issues • Which shape function? • How to compare shape distributions? Parameterization SimilarityMeasure Parameterization

  10. Which Shape Function? • Computationally simple options (~ 1s) • Based on random points • Angles, distances, areas, volumes   A3 D1 D2 D3 D4 [Ankerst99]

  11. Shape Function – D2 • Distance between two random points on surface Line Segment Circle Triangle Cube Cylinder Sphere Two adjacent spheres Two spheres moving apart

  12. Which Shape Function? • Sneak preview

  13. Shape Function – Key Questions • Invariant? • Rotation, translation, mirror (not scale) • Robust? • Noise, cracks, insertions and deletions • Descriptive?

  14. Issues • Which shape function? • How to compare shape distributions? Parameterization SimilarityMeasure Parameterization

  15. Comparison • Normalize for scale • Compare shape distributions  Parameterization Parameterization

  16. Normalization for Scale max mean search

  17. Compare shape distributions • Computationally simple options (~ .1ms) • Ln norms of densities (PDF) orcumulative densities (CDF) • More complex options • Earth mover’s distance, Bhattacharyaa distance. PDF CDF

  18. Experimental Results • Goal is to address the following: • Is the method robust? • How well does it classify? PDF L1 L2 L CDF L1 L2 L A3 D1 D2D3 D4 Max Mean Search

  19. Robustness Experiment • 10 Models Car Chair Human Missile Mug Phone Plane Skateboard Sub Table

  20. Robustness Experiment • 6 Transforms • Rotate, scale, mirror, noise, delete, insert • Total of 70 models 1% Noise 5% Deletion

  21. Robustness Results • Resulting distributions stable 7 Missiles 7 Mugs Probability Distance

  22. Classification Experiment • 133 Models categorized into25 Groups • Large variety • within a group • among groups 4 Mugs 6 Cars 3 Boats

  23. 5 Animals 4 Balls 2 Belts 3 Blimps 3 Boats 6 Cars 8 Chairs 3 Claws 4 Helicopters 11 Humans 3 Lamps 3 Lightnings 6 Missiles 4 Mugs 4 Openbooks Classification Results

  24. Classification Results Probability Distance

  25. Line Segment Circle 5 Animals 4 Balls 2 Belts 3 Blimps 3 Boats Triangle Cube 6 Cars 8 Chairs 3 Claws 4 Helicopters 11 Humans Cylinder Sphere Two adjacent spheres Two spheres moving apart 3 Lamps 3 Lightnings 6 Missiles 4 Mugs 4 Openbooks Classification Results

  26. Query NearestNeighbor 1stTier 2ndTier Results … Classification Results • Avoid bias due to varying group sizes

  27. Classification Results • Similarity matrix • Nearest Neighbor • 1st Tier • 2nd Tier • Blocks • Tanks • Mugs • Humans • Airplanes • Boats

  28. Classification Results

  29. Comparison to Moments • Method • Align 1st moments (translation) • Align 2nd moments (rotation and scale) • Compare using remaining moments (L2)

  30. Conclusion – Properties • Match global properties of shape • Invariance • Rotation, translation, scale, mirror • Robustness • Noise, cracks, insertions and deletions • Practicality • Concise representation • Efficient comparison • Works for degenerate models

  31. Conclusion – Key Ideas • Sampling gives common parameterization • Simplifies comparison • Comparing distributions is fast and easy • Avoids registration, correspondence, etc. • Simple shape functions are discriminating • Method suitable as preclassifier

  32. Future Work • Use a larger and more controlled database • Combine shape distributions with other classifiers into a working shape-based retrieval system

  33. Thank you • Sloan Foundation • NSF

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