Transcript
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- Subspace Clustering Algorithms and Applications for Computer Vision Amir Adler
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- 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) 2
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- 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
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- The Subspace Clustering Problem 4 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
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- Subspace Clustering Challenges 5 Independent subspaces: Disjoint subspaces: Independent Disjoint However, disjoint subspaces are not necessarily independent, and considered more challenging to cluster.
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- Subspace Clustering Challenges 6 Intersecting subspaces: Corrupted data: Noise Outliers
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- 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) 7
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- Video Motion Segmentation 8 Input: video frames of a scene with multiple motions Output: Segmentation of tracked feature points into motions.
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- Video Motion Segmentation 9
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- Affine Camera Model 10
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- Video Motion Segmentation 11
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- Video Motion Segmentation 12
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- Temporal Video Segmentation 13 R. Vidal, Applications of GPCA for Computer Vision, CVPR 2008.
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- Face Clustering 14 Moghaddam & Pentland, Probabalistic Visual Learning for Object Recognition, IEEE PAMI 1997.
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- Face Clustering 15
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- 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) 16
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- The Spectral Clustering Approach 17
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- 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) 18
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- The Data Model 19
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- Sparse Subspace Clustering (SSC) 20
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- Self Expressive Data Single Subspace 21
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- Self Expressive Data Multiple Subspaces 22
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- Extension to Noisy Data 24
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- Performance Evaluation 25 Applied to the motion segmentation problem. Utilized the Hopkins-155 database:
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- Performance Evaluation 26
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- Paper Evaluation 27 Novelty Clarity Experiments Code availability Limitations High complexity: O(L^2)+O(L^3) Sensitivity to noise (data represented by itself)
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- 28 Low Rank Representation (LRR)
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- 29 Why Low Rank Representation(1/3)?
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- 30 Why Low Rank Representation(2/3)?
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- 31 Why Low Rank Representation(3/3)?
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- 32 Summary of the Algorithm
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- 33 Performance Face Clustering
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- Paper Evaluation 34 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
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- Closed Form Solutions 35 Favaro, Vidal & Ravichandran (CVPR 2011) Separation between clean and noisy data. Provides several relaxations to:
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- Case 1:Noiseless Data & Relaxed Constraint 36
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- Noiseless Data & Relaxed Constraint 37
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- Case 2: Noisy Data & Relaxed Constraints 38
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- Polynomial Shrinkage Operator 39
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- Performance Evaluation 40 The motion segmentation problem (Hopkins-155). Case 1 algorithm. Comparable to SSC, LRR. Processing time of 0.4 sec/sequence.
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- Paper Evaluation 41 Novelty Clarity Experiments Partial Complexity Analysis Spectral clustering remains O(L^3) Parameter setting unclear
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- Thank You! 42