Upload
satish-naidu
View
216
Download
0
Embed Size (px)
Citation preview
7/29/2019 Theodorakopoulos Sparse 11 2012
1/24
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
7/29/2019 Theodorakopoulos Sparse 11 2012
2/24
Sparse Representation - Formulation
Sparse Coding
Matching Pursuits (MPs)
Basis Pursuits (BPs)
Dictionary Learning
Applications
7/29/2019 Theodorakopoulos Sparse 11 2012
3/24
Sparse RepresentationFormulation
0. .Min s t x
D
x D
7/29/2019 Theodorakopoulos Sparse 11 2012
4/24
Sparse RepresentationFormulation
Dictionary LearningProblem
Sparse CodingProblem
x D
7/29/2019 Theodorakopoulos Sparse 11 2012
5/24
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)
7/29/2019 Theodorakopoulos Sparse 11 2012
6/24
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
7/29/2019 Theodorakopoulos Sparse 11 2012
7/24
Dictionary Learning
D
X A
2
0,. . , jF s t j L D A
DA XMin
7/29/2019 Theodorakopoulos Sparse 11 2012
8/24
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) ]
7/29/2019 Theodorakopoulos Sparse 11 2012
9/24
Image Processing
Computer Vision
Pattern Recognition
Applications
7/29/2019 Theodorakopoulos Sparse 11 2012
10/24
Image Restoration
20%
50%
80%
[M. Elad, Springer 2010]
7/29/2019 Theodorakopoulos Sparse 11 2012
11/24
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]
7/29/2019 Theodorakopoulos Sparse 11 2012
12/24
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
7/29/2019 Theodorakopoulos Sparse 11 2012
13/24
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
7/29/2019 Theodorakopoulos Sparse 11 2012
14/24
7/29/2019 Theodorakopoulos Sparse 11 2012
15/24
Classification
[J. Wright, A.Y. Yang, A. Ganesh, S.S. Sastry, Yi Ma, 2009 ]
7/29/2019 Theodorakopoulos Sparse 11 2012
16/24
Classification of Dissimilarity Data
[I. Theodorakopoulos, G. Economou, S. Fotopoulos, 2013]
7/29/2019 Theodorakopoulos Sparse 11 2012
17/24
Multi-Level Classification
[A. Castrodad, G. Sapiro, 2012]
7/29/2019 Theodorakopoulos Sparse 11 2012
18/24
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
7/29/2019 Theodorakopoulos Sparse 11 2012
19/24
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]
7/29/2019 Theodorakopoulos Sparse 11 2012
20/24
7/29/2019 Theodorakopoulos Sparse 11 2012
21/24
Joint SparsityMultiple Observations
[H.Zhang, N.M. Nasrabadi, mY. Zhang, T.S. Huang, 2011]
7/29/2019 Theodorakopoulos Sparse 11 2012
22/24
Joint SparsityMultiple Modalities
[X.T. Yuan, X. Liu, S. Yan, 2012]
7/29/2019 Theodorakopoulos Sparse 11 2012
23/24
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.
7/29/2019 Theodorakopoulos Sparse 11 2012
24/24
Questions
Thank You