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Aleksey Golovinskiy and Thomas Funkhouser

Randomized Cuts for 3D Mesh Analysis. Aleksey Golovinskiy and Thomas Funkhouser. Motivation. Input Mesh. Segmentation. [http://www.aimatshape.net/research]. Motivation. Motivation. Motivation. Key Idea. Partition Function. Key Idea. Applications. Segmentation. Visualization.

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Aleksey Golovinskiy and Thomas Funkhouser

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  1. Randomized Cuts for 3D Mesh Analysis Aleksey Golovinskiy and Thomas Funkhouser

  2. Motivation Input Mesh Segmentation [http://www.aimatshape.net/research]

  3. Motivation

  4. Motivation

  5. Motivation

  6. Key Idea Partition Function

  7. Key Idea

  8. Applications Segmentation Visualization Registration Deformation

  9. Outline • Related Work • Method • Results • Applications

  10. Related Work – Shape Analysis • Local Shape Properties • Curvature • Global Shape Properties • Shape Diameter Function [Rusinkiewicz 2004] [Shapira et al. 2008]

  11. [Katz and Tal 2003] [Shlafman et al. 2002] [Shapira et al. 2008] Related Work – Mesh Segmentation • Shape Diameter Function • Fuzzy clustering and min cuts • K-means

  12. Related Work – Mesh Segmentation • Partition function needs a segmentation method • Segmentation methods benefit from partition function: • Which is easier to segment? Dihedral Angles Partition Function

  13. Related Work – Typical Cuts • [Gdalyahu et al. 2001]: image segmentation • Create many segmentations • Estimate likelihood of nodes in same segment • Extract connected components

  14. Outline • Related Work • Method • Results • Applications

  15. Method – Overview • Create randomized segmentations • Output: • Partition function • Cut consistency .5 .3 .01 …

  16. [Shapira et al. 2008] α= .1 β= 500 γ= 20 α= .05 β= 700 γ= 18 α= .07 β= 650 γ= 11 α= .12 β= 400 γ= 26 Method – Randomization • Vary algorithms • Vary parameters • Jitter mesh • Algorithm-specific choices [Katz and Tal 2003]

  17. Method – K-Means • Initialize K segment seeds, iterate: • Assign faces to closest seed • Move seed to cluster center • Randomization: random initial seeds

  18. Method – Hierarchical Clustering • Initialize with a segment per face • Iteratively merge segments • Randomization: choose merge randomly

  19. Method – Min Cut • Initialize with source + sink seed • Find min-cut (weighted towards middle) • Randomization: random source + sink

  20. Outline • Related Work • Method • Results • Applications

  21. Results – Examples

  22. Results – Articulation

  23. Results – Intra-Class Variation

  24. Results – Noise

  25. Results – Tessellation

  26. Results – Comparison to Alternatives

  27. Results – Timing • 4K models: 4 min per model • Not a problem: • 4K models capture salient parts • Computed once in model lifetime • Method-specific optimizations possible • Future work: recursive

  28. Outline • Related Work • Method • Results • Applications

  29. Applications – Visualization Dihedral Angles Shaded Surface Partition Function

  30. .5 .3 .01 … Applications – Segmentation • Compute cut consistency • Split among most consistent cut, recurse

  31. Applications – Segmentation

  32. X X PartitionFunctionSampling UniformSampling Applications – Surface Correspondence

  33. Applications – Deformation Input Mesh Partition Function Uniform Deformation Partition Function Deformation

  34. Conclusion Discrete Segmentation Partition Function Randomized Segmentations

  35. Future work • Other randomization methods • Other applications: saliency analysis, feature-preserving smoothing, skeleton embedding, feature detection, …

  36. Future work • Multi-dimensional partition function Scale

  37. Acknowledgements • Suggestions, code, feedback: • Adam Finkelstein, Szymon Rusinkiewicz, Philip Shilane, Yaron Lipman, Olga Sorkine and others • Models: • Aim@Shape, Stanford, Cyberware, Lior Shapira, Marco Attene, Daniela Giorgi, Ayellet Tal and others • Grants: • NSF (CNFS-0406415, IIS-0612231, and CCF-0702672) and Google

  38. Related Work – Shape Analysis • Local Shape Properties • Shape Diameter Function • Diffusion Distance [Rusinkiewicz 2004] [de Goes et al. 2008] [Shapira et al. 2008]

  39. Related Work – Random Cuts • [Karger and Stein 1996] • Randomized algorithm for finding min cut of a graph …

  40. Related Work – Random Cuts • Our method vs Typical Cuts: • 3D domain • Goal is partition function • Different segmentation algorithm

  41. Method – Dual Graph • Graph Nodes represent faces • Graph Arcs between adjacent faces • Lower cut cost at concave edges Input Model Graph Weights

  42. Method – Min Cuts • Initialize with source + sink seed • Find min-cut • Often trivial • Increase weight close to source + sink • Discourage cuts at relative distance < s • Randomization: random source + sink • Scale: s

  43. Results – Noise

  44. Results – Tessellation Reorder images

  45. Applications – Deformation Uniform Partition Function

  46. Method – Scale Multi-scale features?

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