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Efficient 3D Mesh Analysis with Randomized Cuts

This paper presents a method for 3D mesh analysis using randomized cuts, focusing on segmentation, visualization, registration, and deformation of meshes. The approach involves creating random segmentations, evaluating cut consistency, and exploring various applications. Results show improved articulation, noise reduction, and tessellation. The method proves to be efficient, with quick processing times and potential for optimizations. Future work includes exploring other randomization methods and applications like saliency analysis and feature detection. Acknowledgements to contributors and funding sources are also highlighted.

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Efficient 3D Mesh Analysis with Randomized Cuts

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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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