Report

SPARSE REPRESENTATIONS APPLICATIONS 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 November 2012 Ilias Theodorakopoulos PhD Candidate Περίληψη Sparse Representation - Formulation Sparse Coding Matching Pursuits (MPs) Basis Pursuits (BPs) Dictionary Learning Applications Sparse Representation Formulation D x M in 0 s .t . x D Sparse Representation Formulation x D Dictionary Learning Problem Sparse Coding Problem 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 OR the maximum number of dictionary elements are selected Improved approaches: Orthogonal Matching Pursuit (OMP), Optimized OMP (OOMP) Sparse Coding (2/2) Basis Pursuits Instead of: M in 0 s .t . x D Solve: M in • Convex relaxation of the initial Sparse Representation problem • 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 1 s .t . x D Dictionary Learning X D M in D ,A DA X 2 F s .t . A j, j 0 L Dictionary Learning Different approaches Dictionary Initialization Hard Competitive Only the selected dictionary atoms are updated Sparse Coding Bruckstein (‘04) ] Using MP or BP approaches Soft Competitive Dictionary Update KSVD [ Aharon, Elad & All dictionary atoms are updated based on a ranking Sparse Coding Neural Gas (SCNG) [ Labusch, Barth & Martinetz (’09) ] Applications • • • Image Processing Computer Vision Pattern Recognition Image Restoration 20% 50% 80% [M. Elad, Springer 2010] Denoising Source Result 30.829dB Dictionary PSNR 22.1dB Noisy image [M. Elad, Springer 2010] [J. Wright, Yi Ma, J. Mairal, G. Sapiro, T.S. Huang, Y. Shuicheng, 2010] Compression Original JPEG JPEG 2000 PCA K-SVD 15.81 13.89 10.66 6.60 14.67 12.41 9.44 5.49 15.30 12.57 10.27 6.36 550 bytes per image Bottom: RMSE values [O. Bryta, M. Elad, 2008] 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] Face Recognition [I. Theodorakopoulos, I. Rigas, G. Economou, S. Fotopoulos, 2011] Classification [J. Wright, A.Y. Yang, A. Ganesh, S.S. Sastry, Yi Ma, 2009] Classification of Dissimilarity Data [I. Theodorakopoulos, G. Economou, S. Fotopoulos, 2013] Multi-Level Classification [A. Castrodad, G. Sapiro, 2012] L1Graph • • Related to the Local Linear Reconstruction Coefficients technique The structure and the weights of the graph are simultaneously generated [S. Yan, H. Wang, 2009] Applications: Spectral Clustering Label Propagation L1 Graph – Label Propagation [S. Yan, H. Wang, 2009] Alternative Sparse-based Similarity Measures: Compute the sparse representation of each sample using the C·D nearest samples as the dictionary [H. Cheng, Z. Liu, J. Yang, 2009] [S. Klenk, G. Heidemann, 2010] Subspace Learning Unsupervised [L. Zhanga, P. Zhua, Q. Hub D. Zhanga, 2011] Supervised Joint Sparsity Multiple Observations [H.Zhang, N.M. Nasrabadi, mY. Zhang, T.S. Huang, 2011] Joint Sparsity Multiple Modalities [X.T. Yuan, X. Liu, S. Yan, 2012] 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. Thank You Questions