SPARSE REPRESENTATIONS APPLICATIONS ON COMPUTER VISION AND PATTERN RECOGNITION

Ilias TheodorakopoulosPhD Candidate

November 2012

Computer Vision GroupElectronics LaboratoryPhysics DepartmentUniversity of Patras

www.upcv.upatras.gr www.ellab.physics.upatras.gr

Περίληψη

Sparse Representation - Formulation Sparse Coding

Matching Pursuits (MPs) Basis Pursuits (BPs)

Dictionary Learning Applications

Sparse RepresentationFormulation

0. .Min s t x

D

x D

Sparse RepresentationFormulation

Dictionary Learning Problem

Sparse Coding Problem

x D

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

• When the solution of the initial problem is sparse enough, solving the linear problem is a good approximation

• Convex relaxation of the initial Sparse Representation problem

• Can be efficiently solved using linear programming

Instead of: Solve:

0. .Min s t x

D

1. .Min s t x

D

Dictionary Learning

DX A

2

0,. . , jFs t j L

D ADA XMin

Dictionary LearningDifferent approaches

Dictionary Initialization

Sparse CodingUsing 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) ]

• Image Processing• Computer Vision• Pattern Recognition

Applications

Image Restoration

20%

50%

80%

[M. Elad, Springer 2010]

Denoising

[M. Elad, Springer 2010]

Dictionary

Source

Result 30.829dB

Noisy image

PSNR 22.1dB

[J. Wright, Yi Ma, J. Mairal, G. Sapiro, T.S. Huang, Y. Shuicheng, 2010]

Compression

[O. Bryta, M. Elad, 2008]

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 JPEGJPEG 2000 PCA K-SVD

Bottom:RMSE

values

Compressive Sensing

[J. Wright, Yi Ma, J. Mairal, G. Sapiro, T.S. Huang, Y. Shuicheng, 2010]

Reconstruction based on classical techniques

Reconstruction based on simultaneous learning of Sparse dictionary and Sensing Matrix

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

[S. Yan, H. Wang, 2009]

• Related to the Local Linear Reconstruction Coefficients technique

• The structure and the weights of the graph are simultaneously generated

Applications: Spectral Clustering Label Propagation

L1 Graph – Label Propagation

[S. Yan, H. Wang, 2009]

Alternative Sparse-based Similarity Measures:

[H. Cheng, Z. Liu, J. Yang, 2009]

Compute the sparse representation of each sample using the C·D nearest samples as the dictionary

[S. Klenk, G. Heidemann, 2010]

Subspace Learning

Unsupervised Supervised

[L. Zhanga, P. Zhua, Q. Hub D. Zhanga, 2011]

Joint SparsityMultiple Observations

[H.Zhang, N.M. Nasrabadi, mY. Zhang, T.S. Huang, 2011]

Joint SparsityMultiple 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.

Questions

Thank You