1. Ilias Theodorakopoulos PhD Candidate
Sparse Representations Applications on computer vision and pattern recognition
Computer Vision Group
Electronics Laboratory
Physics Department
University of Patras
Ilias Theodorakopoulos
PhD Candidate
November 2012

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

3. Sparse Representation Formulation

4. Sparse Representation Formulation
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 OR the 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 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

7. Dictionary Learning D  X A

8. Dictionary Learning Different approaches
Dictionary Initialization
Sparse Coding
Using MP or BP approaches
Dictionary Update
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) ]

9. Applications
Image Processing
Computer Vision
Pattern Recognition

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

11. Denoising Source Result 30.829dB Dictionary Noisy image
[M. Elad, Springer 2010]
[J. Wright, Yi Ma, J. Mairal, G. Sapiro, T.S. Huang, Y. Shuicheng, 2010]

12. Compression 550 bytes per image 9.44 15.81 14.67 15.30 13.89 12.41
12.57
10.66
10.27
6.60
5.49
6.36
Original
JPEG
JPEG 2000
PCA
K-SVD
Bottom: RMSE values
[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 the Local 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. 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]

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

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

22. Joint Sparsity Multiple 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 , 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/
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 , 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
C. Hong, et al., "Sparsity induced similarity measure for label propagation," in Computer Vision, 2009 IEEE 12th International Conference on, 2009, pp
Z. Lei, et al., "A linear subspace learning approach via sparse coding," in Computer Vision (ICCV), 2011 IEEE International Conference on, 2011, pp
G. H. Sebastian Klenk, "A Sparse Coding Based Similarity Measure," DMIN 2009, pp , 2009.
I. Theodorakopoulos, et al., "Face recognition via local sparse coding," in Computer Vision (ICCV), 2011 IEEE International Conference on, 2011, pp
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 , 2009.
J. Wright, et al., "Sparse Representation for Computer Vision and Pattern Recognition," Proceedings of the IEEE, vol. 98, pp , 2010.
Y. Xiao-Tong and Y. Shuicheng, "Visual classification with multi-task joint sparse representation," in Computer Vision and Pattern Recognition (CVPR), IEEE Conference on, 2010, pp

24. Thank You
Questions