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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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Randomized Cuts for 3D Mesh Analysis Aleksey Golovinskiy and Thomas Funkhouser
Motivation Input Mesh Segmentation [http://www.aimatshape.net/research]
Key Idea Partition Function
Applications Segmentation Visualization Registration Deformation
Outline • Related Work • Method • Results • Applications
Related Work – Shape Analysis • Local Shape Properties • Curvature • Global Shape Properties • Shape Diameter Function [Rusinkiewicz 2004] [Shapira et al. 2008]
[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
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
Related Work – Typical Cuts • [Gdalyahu et al. 2001]: image segmentation • Create many segmentations • Estimate likelihood of nodes in same segment • Extract connected components
Outline • Related Work • Method • Results • Applications
Method – Overview • Create randomized segmentations • Output: • Partition function • Cut consistency .5 .3 .01 …
[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]
Method – K-Means • Initialize K segment seeds, iterate: • Assign faces to closest seed • Move seed to cluster center • Randomization: random initial seeds
Method – Hierarchical Clustering • Initialize with a segment per face • Iteratively merge segments • Randomization: choose merge randomly
Method – Min Cut • Initialize with source + sink seed • Find min-cut (weighted towards middle) • Randomization: random source + sink
Outline • Related Work • Method • Results • Applications
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
Outline • Related Work • Method • Results • Applications
Applications – Visualization Dihedral Angles Shaded Surface Partition Function
.5 .3 .01 … Applications – Segmentation • Compute cut consistency • Split among most consistent cut, recurse
X X PartitionFunctionSampling UniformSampling Applications – Surface Correspondence
Applications – Deformation Input Mesh Partition Function Uniform Deformation Partition Function Deformation
Conclusion Discrete Segmentation Partition Function Randomized Segmentations
Future work • Other randomization methods • Other applications: saliency analysis, feature-preserving smoothing, skeleton embedding, feature detection, …
Future work • Multi-dimensional partition function Scale
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
Related Work – Shape Analysis • Local Shape Properties • Shape Diameter Function • Diffusion Distance [Rusinkiewicz 2004] [de Goes et al. 2008] [Shapira et al. 2008]
Related Work – Random Cuts • [Karger and Stein 1996] • Randomized algorithm for finding min cut of a graph …
Related Work – Random Cuts • Our method vs Typical Cuts: • 3D domain • Goal is partition function • Different segmentation algorithm
Method – Dual Graph • Graph Nodes represent faces • Graph Arcs between adjacent faces • Lower cut cost at concave edges Input Model Graph Weights
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
Results – Tessellation Reorder images
Applications – Deformation Uniform Partition Function
Method – Scale Multi-scale features?