eigenedginess vs. eigenhill, eigenface and eigenedge by s. ramesh, s. palanivel, sukhendu das and b....

Eigenedginess vs.

Eigenhill, Eigenface and Eigenedge

byS. Ramesh, S. Palanivel, Sukhendu Das and B. Yegnanarayana

Department of Computer Science and Engineering

IIT Madras, Chennai, INDIA

E-mail: [email protected],{spal@cs, sdas@, yegna@}.iitm.ernet.in

Artificial Neural Networks Lab IIT Madras

Different Representations of face• Grey level image

– Suffers illumination problem

• Edge map– Locality problem

• Spread edge profile (called hills)– Carries artificial edginess of the face

• Edginess image– Carries natural variations present in the face image


1-D Processing of images

for edge/edginess extraction

• Smoothing filter: 1-D Gaussian function

where 1 is the spatial spread of the Gaussian

• Differential Operator: First derivative of

Gaussian function

where 2 is the spatial spread of the Gaussian

22

2

2

322

)(

y

ey

yc

21

2

2

12

1)(

x

exg


• Method of 1-D processing

• Smoothing filter is applied along the horizontal scan lines of the image

• For the Smoothing filter output, the differential operator is applied along the vertical direction to extract the horizontal components of the edginess (strength of an edge)

• The process is repeated similarly in the orthogonal direction

• Finally the horizontal and vertical components of the edginess are combined to obtain the edginess map of the image

• Advantages of 1-D processing

• Better tolerance to noise than Canny’s operator

• Computational time reduced to 10% of 2D processing Artificial Neural Networks Lab IIT Madras

1-D Processing of images for edge/edginess extraction (contd.)

Grey level images

Edge images

Edginess images

Results


Eigenedginess

If x1, x2, ….., xP of N dimension are the input patterns, then the transformed lower dimension patterns (of M dimension) y1, y2, ….., yP are given by

yi = WT xi, i 1,2,....,P

W = [e1 e2 …. eM]N*M, where ei is the eigenvector associated with eigenvalues 1 2 …… M (M < N).

ei and i are eigenvectors and eigenvalues obtained by solving the eigenstructure equation:

C ei = i ei, where C = (xp - ) (xp - )T and = xp

Eigenvectors of the covariance matrix(C) of the edginess images are referred as eigenedginess

P

p 1

P

pP 1

1


Eigenvector 1

Eigenvector 2

Eigenedge EigenedginessEigenface Eigenhill Comparative illustration of the first three Eigenvectors

of faces, using all the four techniques

Eigenvector 3

Representation PerformanceEigenface 14

Eigenedge 24

Eigenhill 21

Eigenedginess 56

Face Recognition performance(Out of 80 faces)


1-D Processing

Input Image

Edginess

Image

Eigen Analysis

Eigenedginess:

1-D Processing

Input Image

Edginess

Image Eigen Analysis

Transformation Function

Transformed edginess:


Processing Stages

Transformed Edginess

Transformation functionArtificial Neural Networks Lab

IIT Madras

Results of eigenanalysis with Transformed edginess

x2 y2 y1 y4 No. of faces

recognized

(out of 80 faces)

No. of Principal

Components Used

0.1 0.6 0.1 0.8 33 53

0.2 0.6 0.1 0.8 48 61

0.3 0.6 0.1 0.8 48 48

0.4 0.6 0.1 0.8 53 48

0.5 0.6 0.1 0.8 56 44

0.6 0.6 0.1 0.8 56 54

0.7 0.6 0.1 0.8 57 52

0.8 0.6 0.1 0.8 57 52

0.9 0.6 0.1 0.8 56 52

1.0 1.0 0.0 1.0 56 (baseline) 52


The transformation function was used with: x1=0 and y3=0

No. of

eigenvectors

eliminated

Eigen

face

Eigen

edge

Eigen

Hill

Eigen

edginess

0 (baseline) 14 24 21 56

1 29 26 23 56

2 30 25 20 66

3 27 24 17 62

4 26 21 19 57

5 28 23 15 56

Effect of first few eigenvectors


Recognition performance due to variations in facial expression

Category %

Eigenface 94

Eigenedginess 93

Eigenhill 77

Eigenedge 47


Summary• Concept of edginess of an image is introduced for face

recognition, which is invariant to illumination and facial expression.

• Experimental results show that the performance of Eigenedginess representation is better than eigenhill, eigenface and eigenedge for face recognition.

• Performance of face recognition using transformed edginess image and the effect of first few eigenvectors are also discussed.


References• R. Brunelli and T. Poggio, “Face recognition: features versus

templates”, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.15, no.10, pp.1042-1052, October 1993.

• M. Turk and A. Pentland, “Eigenfaces for recognition”, Journal of Cognitive Neuro-Science, vol.3, pp. 71-86, 1991.

• Yilmaz, Alper and M.Gokmen, “Eigenhill vs. eigenface and eigenedge”, Pattern Recognition, vol.34, pp.181-184, 2001.

• P. Kiran Kumar, Sukhendu Das and B. Yegnanarayana, “One-Dimensional processing of images”,in International Conference on Multimedia Processing and Systems, IIT Chennai, India, pp. 181-185, August 13-15, 2000.


Thank You


eigenedginess vs. eigenhill, eigenface and eigenedge by s. ramesh, s. palanivel, sukhendu das and b....

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