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
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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.
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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