Sparse Representations Applications on computer vision and pattern recognition

1. Sparse RepresentationsApplications on computer vision and pattern recognition Computer Vision Group Electronics Laboratory Physics Department University of Patras www.upcv.upatras.gr www.ellab.physics.upatras.gr IliasTheodorakopoulos PhD Candidate November 2012

2. Περίληψη • Sparse Representation - Formulation • Sparse Coding • Matching Pursuits (MPs) • Basis Pursuits (BPs) • Dictionary Learning • Applications

3. Sparse RepresentationFormulation

4. Sparse RepresentationFormulation Dictionary Learning Problem Sparse Coding Problem

5. Sparse Coding (1/2)Matching Pursuits • “Greedy” approaches. One dictionary element is selected in each iteration • Step 1: Find the element that best represents the input signal.. • Next Steps: Find the next element that best represents the input signal among the rest of dictionary elements… • The procedure is terminated when the representation error becomes smaller than a threshold value ORthe maximum number of dictionary elements are selected • Improved approaches: Orthogonal Matching Pursuit (OMP), Optimized OMP (OOMP)

6. Sparse Coding (2/2)Basis Pursuits Instead of: Solve: • Convex relaxation of the initialSparse Representationproblem • Can be efficiently solved using linear programming • When the solution of the initial problem is sparse enough, solving the linear problem is a good approximation

7. D X  A Dictionary Learning

8. Sparse Coding Using MP or BPapproaches Dictionary Update Dictionary LearningDifferent approaches • Hard Competitive • Only the selected dictionary atoms are updated • KSVD [ Aharon, Elad & Bruckstein (‘04) ] • Soft Competitive • All dictionary atoms are updated based on a ranking • Sparse Coding Neural Gas (SCNG) [ Labusch, Barth & Martinetz (’09) ] Dictionary Initialization

9. Applications Image Processing Computer Vision Pattern Recognition

10. 20% 50% 80% Image Restoration • [M. Elad, Springer 2010]

11. Source Result30.829dB Dictionary Denoising Noisyimage • [M. Elad, Springer 2010] • [J. Wright, Yi Ma, J. Mairal, G. Sapiro, T.S. Huang, Y. Shuicheng, 2010]

12. Compression JPEG 2000 Original JPEG PCA K-SVD 550bytes per image 15.81 13.89 10.66 6.60 14.67 12.41 9.44 5.49 Bottom:RMSE values 15.30 12.57 10.27 6.36 • [O. Bryta, M. Elad, 2008]

13. Compressive Sensing Reconstruction based on classical techniques Reconstruction based on simultaneous learning of Sparse dictionary and Sensing Matrix • [J. Wright, Yi Ma, J. Mairal, G. Sapiro, T.S. Huang, Y. Shuicheng, 2010]

14. Face Recognition • [I. Theodorakopoulos, I. Rigas, G. Economou, S. Fotopoulos, 2011]

15. Classification • [J. Wright, A.Y. Yang, A. Ganesh, S.S. Sastry, Yi Ma, 2009]

16. Classification of Dissimilarity Data • [I. Theodorakopoulos, G. Economou, S. Fotopoulos, 2013]

17. Multi-Level Classification • [A. Castrodad, G. Sapiro, 2012]

18. L1Graph • Related to theLocal Linear Reconstruction Coefficients technique • The structure and the weights of the graph are simultaneously generated • Applications: • Spectral Clustering • Label Propagation • [S. Yan, H. Wang, 2009]

19. L1Graph – Label Propagation • [S. Yan, H. Wang, 2009] Alternative Sparse-based Similarity Measures: • Compute the sparserepresentation of each sample using theC·D nearest samples as the dictionary • [H. Cheng, Z. Liu, J. Yang, 2009] • [S. Klenk, G. Heidemann, 2010]

20. Subspace Learning Unsupervised Supervised • [L. Zhanga, P. Zhua, Q. Hub D. Zhanga, 2011]

21. Joint SparsityMultiple Observations • [H.Zhang, N.M. Nasrabadi, mY. Zhang, T.S. Huang, 2011]

22. Joint SparsityMultiple Modalities • [X.T. Yuan, X. Liu, S. Yan, 2012]

23. References • O. Bryt and M. Elad, "Compression of facial images using the K-SVD algorithm," J. Vis. Comun. Image Represent., vol. 19, pp. 270-282, 2008. • A. Castrodad and G. Sapiro, "Sparse Modeling of Human Actions from Motion Imagery," International Journal of Computer Vision, vol. 100, pp. 1-15, 2012/10/01 2012. • J. M. Duarte-Carvajalino and G. Sapiro, "Learning to Sense Sparse Signals: Simultaneous Sensing Matrix and Sparsifying Dictionary Optimization," Image Processing, IEEE Transactions on, vol. 18, pp. 1395-1408, 2009. • M. Elad, Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing: Springer. • Z. Haichao, et al., "Multi-observation visual recognition via joint dynamic sparse representation," in Computer Vision (ICCV), 2011 IEEE International Conference on, 2011, pp. 595-602. • C. Hong, et al., "Sparsity induced similarity measure for label propagation," in Computer Vision, 2009 IEEE 12th International Conference on, 2009, pp. 317-324. • Z. Lei, et al., "A linear subspace learning approach via sparse coding," in Computer Vision (ICCV), 2011 IEEE International Conference on, 2011, pp. 755-761. • G. H. Sebastian Klenk, "A Sparse Coding Based Similarity Measure," DMIN 2009, pp. 512-516, 2009. • I. Theodorakopoulos, et al., "Face recognition via local sparse coding," in Computer Vision (ICCV), 2011 IEEE International Conference on, 2011, pp. 1647-1652. • E. G. Theodorakopoulos I., Fotopoulos S., "Classification of Dissimilarity Data via Sparse Representation," in ICPRAM 2013, 2013. • S. Y. a. H. Wang, "Semi-supervisedlearning by sparse representation," SIAM Int. Conf. Data Mining, pp. 792–801, 2009. • J. Wright, et al., "Robust Face Recognition via Sparse Representation," Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 31, pp. 210-227, 2009. • J. Wright, et al., "Sparse Representation for Computer Vision and Pattern Recognition," Proceedings of the IEEE, vol. 98, pp. 1031-1044, 2010. • Y. Xiao-Tong and Y. Shuicheng, "Visual classification with multi-task joint sparse representation," in Computer Vision and Pattern Recognition (CVPR), 2010 IEEE Conference on, 2010, pp. 3493-3500.

24. Thank You Questions