Presenter Yunhai@VCC

1. Co-Segmentation of 3D Shapes via Subspace Clustering Ruizhen Hu, Lubin Fan, Ligang Liu. Computer Graphics Forum (Proc. SGP), 2012 Presenter Yunhai@VCC

2. Background

3. Single-Shape Segmentation [Shalfman et al. 2002] [Katz et al. 05] [Attene et. al 2006] [Lai et al. 08] K-Means Core Extraction Fitting Primitives Random Walks [Golovinskiy and Funkhouser 08] [Shapira et al. 08] [Golovinskiy and Funkhouser 08] Normalized Cuts Shape Diameter Function Randomized Cuts

4. Supervised Co-Segmentation • Limitations • Prior knowledge of the category • Shape variation within each category shall be small [Kalogerakis et al.10, van Kaick et al. 11] Input Mesh Labeled Mesh Head Neck Torso Leg Tail Ear Training Meshes

5. Unsupervised Co-Segmentation [Huang et al. 11] [Sidi et al.11]

6. Problem • Each feature descriptor generally has its own advantages and limitations. • However, existing methods concatenate all features into a higher dimensional descriptor AGD SDF

7. Approach

8. Pipeline Gaussian curvature Shape diameter function Average geodesic distance Shape contexts Conformal factor Feature descriptors Subspace clustering Over-segmentation with normalized cuts

9. Subspace • Let be a given set of points drawn from an unknown union of linear or affine subspaces of unknown dimensions • The subspaces can be described as

10. An example

11. Subspace Sparse Representation • Each data point in a union of linear subspaces can always be represented as a linear combination of the points belonging to the same linear subspace. • To get a sparse linear combination>>minimizing the number of nonzero • In practice use:

12. Subspace Sparse Representation • Written in matrix form • To enforce the sparsity of the optimal solution

13. Sparse Subspace Clustering • Each entry of the matrix measures the linear correlation between two points in the dataset. We use this matrix to define a directed graph G = (V,E) • To make it balanced, we define the adjacency matrix • Cluster the graph with normalized cut

14. Sparse Subspace Clustering

15. An example Matrix of sparse coefficients Similarity graph Data drawn from 3 subspaces

16. Multi-feature co-segmentation • Multi-feature penalty

17. Multi-feature co-segmentation • Multi-feature: penalty W1 W2 Wn

18. Illustration of W

19. Clustering • Affinity matrix • Minimal curvature mc • Ncut clustering

20. Results

21. Result The algorithm vs supervised approach 92.6% vs 96.1%

22. Result Too many labels

23. Result The algorithm vs unsupervised approach 94.4% vs 88.2%

24. Compared to Sidi et al. • Do not require the input model to have the same topologies • Can generate the satisfactory co-segmentation results from only a few models ??

25. Limitation • Only use the geometric properties to distinguish patches and classify them.

26. Video

27. Q&A