Eigenedginess vs. Eigenhill, Eigenface and Eigenedge by S. 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 Artificial Neural Networks Lab IIT Madras

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

Artificial Neural Networks Lab IIT Madras Results Grey level images Edge images Edginess images Artificial Neural Networks Lab IIT Madras

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 Artificial Neural Networks Lab IIT Madras

Comparative illustration of the first three Eigenvectors Eigenface Eigenedge Eigenhill Eigenedginess Comparative illustration of the first three Eigenvectors of faces, using all the four techniques

Face Recognition performance (Out of 80 faces) Artificial Neural Networks Lab IIT Madras

Processing Stages 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

Artificial Neural Networks Lab IIT Madras Transformed Edginess Artificial Neural Networks Lab IIT Madras Transformation function

Results of eigenanalysis with Transformed edginess Artificial Neural Networks Lab IIT Madras The transformation function was used with: x1=0 and y3=0

Effect of first few eigenvectors Artificial Neural Networks Lab IIT Madras

Recognition performance due to variations in facial expression Artificial Neural Networks Lab IIT Madras

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

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

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