Post on 28-Dec-2015
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: mr_sriramesh@yahoo.com,{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
Artificial Neural Networks Lab IIT Madras
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
Artificial Neural Networks Lab IIT Madras
• 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
Artificial Neural Networks Lab IIT Madras
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
Artificial Neural Networks Lab IIT Madras
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)
Artificial Neural Networks Lab IIT Madras
1-D Processing
Input Image
Edginess
Image
Eigen Analysis
Eigenedginess:
1-D Processing
Input Image
Edginess
Image Eigen Analysis
Transformation Function
Transformed edginess:
Artificial Neural Networks Lab IIT Madras
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
Artificial Neural Networks Lab IIT Madras
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
Artificial Neural Networks Lab IIT Madras
Recognition performance due to variations in facial expression
Category %
Eigenface 94
Eigenedginess 93
Eigenhill 77
Eigenedge 47
Artificial Neural Networks Lab IIT Madras
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.
Artificial Neural Networks Lab IIT Madras
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.
Artificial Neural Networks Lab IIT Madras
Thank You
Artificial Neural Networks Lab IIT Madras