# ppt - University of Patras, Computer Vision Group

Τεχνίτη Νοημοσύνη και Ρομποτική

19 Οκτ 2013 (πριν από 4 χρόνια και 8 μήνες)

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SPARSE REPRESENTATIONS

APPLICATIONS ON COMPUTER VISION AND PATTERN
RECOGNITION

Ilias

Theodorakopoulos

PhD Candidate

November
2012

Computer Vision Group

Electronics Laboratory

Physics Department

University 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 Representation

Formulation

Sparse Representation

Formulation

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

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

:

Solve:

Dictionary Learning

D

X

A

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
,

&
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.
, Springer 2010]

Denoising

[M.
, Springer 2010]

Dictionary

Source

Result

30.829dB

Noisy

image

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

Compression

[O.
Bryta
, M.
, 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

JPEG

JPEG
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.
, G.
Sapiro
, 2012]

L
1
Graph

[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

L
1

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 Sparsity

Multiple Observations

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

Joint Sparsity

Multiple Modalities

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

References

O.
Bryt

and M.
, "Compression of facial images using the K
-
SVD algorithm," J. Vis.
Comun
. Image Represent., vol. 19, pp. 270
-
282, 2008.

A.

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.
, 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 I
nternational
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 C
onf
erence 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 Trans
act
ions 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.

10
31
-
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