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Subspace Clustering Algorithms and Applications for Computer Vision Amir Adler

Subspace Clustering Algorithms and Applications for Computer Vision Amir Adler. Agenda. The Subspace Clustering Problem Computer Vision Applications A Short Introduction to Spectral Clustering Algorithms Sparse Subspace Clustering (CVPR 2009) Low Rank Representation (ICML 2010)

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Subspace Clustering Algorithms and Applications for Computer Vision Amir Adler

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  1. Subspace ClusteringAlgorithms and Applications for Computer VisionAmir Adler

  2. Agenda • The Subspace Clustering Problem • Computer Vision Applications • A Short Introduction to Spectral Clustering • Algorithms • Sparse Subspace Clustering (CVPR 2009) • Low Rank Representation (ICML 2010) • Closed Form Solutions (CVPR 2011)

  3. Agenda • The Subspace Clustering Problem • Computer Vision Applications • A Short Introduction to Spectral Clustering • Algorithms • Sparse Subspace Clustering (CVPR 2009) • Low Rank Representation (ICML 2010) • Closed Form Solutions (CVPR 2011)

  4. The Subspace Clustering Problem • Given a set of points drawn from a union-of-subspaces, obtain the following: • 1) Clustering of the points • 2) Number of subspaces • 3) Bases of all subspaces • Challenges: • 1) Subspaces layout • 2) Corrupted data

  5. Subspace Clustering Challenges • Independent subspaces: • Disjoint subspaces: • Independent  Disjoint • However, disjoint subspaces arenot necessarily independent, and considered more challenging to cluster.

  6. Subspace Clustering Challenges • Intersecting subspaces: • Corrupted data: • Noise • Outliers

  7. Agenda • The Subspace Clustering Problem • Computer Vision Applications • A Short Introduction to Spectral Clustering • Algorithms • Sparse Subspace Clustering (CVPR 2009) • Low Rank Representation (ICML 2010) • Closed Form Solutions (CVPR 2011)

  8. Video Motion Segmentation • Input: video frames of a scene with multiple motions • Output: Segmentation of tracked feature points into motions.

  9. Video Motion Segmentation

  10. Affine Camera Model

  11. Video Motion Segmentation

  12. Video Motion Segmentation

  13. Temporal Video Segmentation R. Vidal, “Applications of GPCA for Computer Vision”, CVPR 2008.

  14. Face Clustering Moghaddam & Pentland, “Probabalistic Visual Learning for Object Recognition”, IEEE PAMI 1997.

  15. Face Clustering

  16. Agenda • The Subspace Clustering Problem • Computer Vision Applications • A Short Introduction to Spectral Clustering • Algorithms • Sparse Subspace Clustering (CVPR 2009) • Low Rank Representation (ICML 2010) • Closed Form Solutions (CVPR 2011)

  17. The Spectral Clustering Approach

  18. Agenda • The Subspace Clustering Problem • Computer Vision Applications • A Short Introduction to Spectral Clustering • Algorithms • Sparse Subspace Clustering (CVPR 2009) • Low Rank Representation (ICML 2010) • Closed Form Solutions (CVPR 2011)

  19. The Data Model

  20. Sparse Subspace Clustering (SSC)

  21. Self Expressive Data – Single Subspace

  22. Self Expressive Data –Multiple Subspaces

  23. Extension to Noisy Data

  24. Performance Evaluation • Applied to the motion segmentation problem. • Utilized the Hopkins-155 database:

  25. Performance Evaluation

  26. Paper Evaluation • Novelty • Clarity • Experiments • Code availability • Limitations • High complexity: O(L^2)+O(L^3) • Sensitivity to noise (data represented by itself)

  27. Low Rank Representation (LRR)

  28. Why Low Rank Representation(1/3)?

  29. Why Low Rank Representation(2/3)?

  30. Why Low Rank Representation(3/3)?

  31. Summary of the Algorithm

  32. Performance – Face Clustering

  33. Paper Evaluation • Novelty • Clarity • Experiments • Code availability • Limitations • High complexity: kO(L^3), k=200~300 • Sensitivity to noise (data represented by itself) • Parameter setting not discussed

  34. Closed Form Solutions • Favaro, Vidal & Ravichandran (CVPR 2011) • Separation between clean and noisy data. • Provides several relaxations to:

  35. Case 1:Noiseless Data & Relaxed Constraint =

  36. Noiseless Data & Relaxed Constraint

  37. Case 2: Noisy Data & Relaxed Constraints

  38. Polynomial Shrinkage Operator

  39. Performance Evaluation • The motion segmentation problem (Hopkins-155). • Case 1 algorithm. • Comparable to SSC, LRR. • Processing time of 0.4 sec/sequence.

  40. Paper Evaluation • Novelty • Clarity • Experiments • Partial Complexity Analysis • Spectral clustering remains O(L^3) • Parameter setting unclear

  41. Thank You!

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