Theodorakopoulos Sparse 11 2012

7/29/2019 Theodorakopoulos Sparse 11 2012

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SPARSE REPRESENTATIONSAPPLICATIONS ON COMPUTER VISION AND

PATTERN RECOGNITION

Ilias Theodorakopoulos

PhD CandidateNovember2012

Computer Vision GroupElectronics LaboratoryPhysics DepartmentUniversity of Patras

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


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Sparse Representation - Formulation

Sparse Coding

Matching Pursuits (MPs)

Basis Pursuits (BPs)

Dictionary Learning

Applications


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Sparse RepresentationFormulation

0. .Min s t x

D

x D


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Sparse RepresentationFormulation

Dictionary LearningProblem

Sparse CodingProblem

x D


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Sparse Coding (1/2)Matching Pursuits

Greedy approaches. One dictionary element isselected 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 representationerror becomes smaller than a threshold value ORthe

maximum number of dictionary elements are selected

Improved approaches: Orthogonal Matching Pursuit

(OMP), Optimized OMP (OOMP)


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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 initialSparse

Representationproblem

Can be efficiently solved using linearprogramming

Instead of: Solve:

0. .Min s t x

D1

. .Min s t x

D


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Dictionary Learning

D

X A

2

0,. . , jF s t j L D A

DA XMin


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Dictionary LearningDifferent approaches

Dictionary

Initialization

Sparse CodingUsing MP or BPapproaches

Dictionary Update

Hard Competitive

Only the selected dictionary

atoms are updated KSVD [Aharon, Elad &

Bruckstein (04) ]

Soft Competitive

All dictionary atoms areupdated based on a ranking

Sparse Coding Neural Gas

(SCNG) [ Labusch, Barth &

Martinetz (09) ]


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Image Processing

Computer Vision

Pattern Recognition

Applications


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Image Restoration

20%

50%

80%

[M. Elad, Springer 2010]


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Denoising

[M. Elad, Springer 2010]

Dictionary

Source

Result30.829dB

NoisyimagePSNR 22.1dB

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

Shuicheng, 2010]


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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


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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 andSensing Matrix


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Classification

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


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Classification of Dissimilarity Data

[I. Theodorakopoulos, G. Economou, S. Fotopoulos, 2013]


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Multi-Level Classification

[A. Castrodad, G. Sapiro, 2012]


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L1Graph

[S. Yan, H. Wang, 2009]

Related to theLocal Linear

Reconstruction Coefficients technique

The structure and the weights of the

graph are simultaneously generated

Applications:

Spectral Clustering

Label Propagation


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L1Graph Label Propagation

[S. Yan, H. Wang, 2009]

Alternative Sparse-based Similarity Measures:

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

Compute the sparserepresentation of each

sample using theCD nearest samples as the

dictionary

[S. Klenk, G. Heidemann, 2010]


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Joint SparsityMultiple Observations

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


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Joint SparsityMultiple Modalities

[X.T. Yuan, X. Liu, S. Yan, 2012]


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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. 792801, 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.


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Questions

Thank You

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Theodorakopoulos Sparse 11 2012