An algorithm to minimize within-class scatter and to reduce common matrix dimension for image recognition

In this paper, a new algorithm using 2DPCA and Gram-Schmidt Orthogonalization Procedure for recognition of face images is proposed. The algorithm consists of two parts. In the first part, a common feature matrix is obtained; and in the second part, the dimension of the common feature matrix is reduced. Resulting common feature matrix with reduced dimension is used for face recognition. Column and row covariance matrices are obtained by applying 2DPCA on the column and row vectors of images, respectively. The algorithm then applies eigenvalue-eigenvector decomposition to each of these two covariance matrices. Total scatter maximization is achieved taking the projection of images onto d eigenvectors corresponding to the largest d eigenvalues of column covariance matrix, yielding the feature matrix. The each column of the feature matrix represents a feature vector. Minimization of within class scatter is achieved by reducing the redundancy of the corresponding feature vectors of the different images in the same class. A common feature vector for each dth eigenvector direction is obtained by applying Gram-Schmidt Orthogonalization Procedure. A common feature matrix is established by gathering d common feature vectors in a matrix form. Then, the dimension of common feature matrix is reduced to d \times d taking the projection of common feature matrix onto d eigenvectors which corresponds to the largest d eigenvalues of row covariance matrix. The performance of the proposed algorithm is evaluated experimentally by measuring the recognition rates. The developed algorithm produced better recognition rates compared to Eigenface, Fisherface and 2DPCA methods. Ar-Face and ORL face databases are used in the experimental evaluations.

Anahtar Kelimeler:

2DPCA, Gram-Schmidt orthogonalization, common feature matrix, face recognition, total scatter maximization, within-class scatter minimization

An algorithm to minimize within-class scatter and to reduce common matrix dimension for image recognition

Keywords:

2DPCA, Gram-Schmidt orthogonalization, common feature matrix, face recognition, total scatter maximization, within-class scatter minimization,

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[1] Zhao W., Chellappa R., Rosenfeld A. and Phillips P., Face Recognition,A Literature Survey, Technical Report (2000)
[2] Li J., Zhou S., and Shekhar C., A Comparison of Subspace Analysis for Face Recognition, ICASSP (2003)
[3] Zhao W., Chellappa R., Krishnaswamy A., Discriminant Analysis of Principle Components for Face Recognition, International Conference on Face and Gesture Recognition, fg, p.336, 3 rd. (1998)
[4] Turk M. and Petland A., Eigenfaces for Recognition, Journal of Cognitive Neutoscience, vol. 3, pp. 72–86 (1991)
[5] Belhumeur P., Hespanha J. and Kreigman D. J., Discriminant Eigenfeatures for Image Retreival, PAMI, 19 (7): 711–720 (1997)
[6] Sch¨olkopf B., Smola A. and Muller K., Nonlinear Component Analysis as a Kernel Eigenvalue Problem, Neural Computation, vol. 10, pp. 1299–1319 (1998)
[7] Mika S., Rotsch G., Wetson J., Sch¨olkopf B., and Mller K.-R., Fisher Discriminant Analysis with Kernels. In Neural Networks for Signal Processing IX, IEEE, Y.-H. Hu, J. Larsen, E. Wilson and S. Douglas, Eds., pp. 41–48 (1999)
[8] Yang J., Frangi A. F., Yang J., Zhang D., KPCA Plus LDA: A Complete Kernel Fisher Discriminant Framework for Feature Extraction and Recognition, IEEE Transactions on Pattern Analysis and Machine Intelligenc, vol. 27, No. 2 (2005)
[9] Kim K. I., Franz M. O. and Sch¨olkopf B. , Iterative Kernel Principal Component Analysis for Image Modelling, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, No. 9 (2005)
[10] Yang M., Kernel Eigenfaces v.s. Kernel Fisherfaces: Face Recognition Using Kernel Methods, Proceedings of the Fifth IEEE International Conference on Automatic Face and Gesture Recognition (2002)
[11] Yang J., David Z., Frangi A. F. and Yang J-Y., Two Dimensional PCA: A New Approach to Appearance-Based Face Representation and Recognition, Pattern Analysis and Machine Intelligence, IEEE Transactions on vol. 26, No. 1 (2004)
[12] Xu D., Yan S., Zhang L., Li M., Ma W., Liu Z., Zhang H., Parallel Image Matrix Compression for Face Recognition, mmm, 11.th International Multimedia Modelling Conference (MMM’05), pp. 232–238 (2005)
[13] Turhal U. C ¨ ¸., G¨ulmezoglu M. B., Barkana A., Face Recognition Using Common Matrix Approach, EUSIPCO, Antalya, on Sept: 4–8 (2005)
[14] G¨ulmezoglu M. B., Dzhafarov V., Keskin M. and Barkana A., A Novel Approach to Isolated Word Recognition, Speech and Audio Processing, IEEE Transactions on vol. 7, pp. 620–628 (1999)
[15] Turhal U. C ¨ ¸., Duysak A., G¨ulmezoglu M. B., A Two Stage Algorithm for Face Recognition: 2DPCA and WithinClass Scatter Minimization, (554) Signal Processing, Pattern Recognition, and Applications (2007)
[16] Cover T.M. and Hart P.E., Nearest Neighbor Pattern Classification, IEEE Trans. on Information Theory, pp. 21–27 (1967)
[17] Martinez A. M. and Benavante R., The Ar Face Database, CVC Tech. Report 24 (1998)
[18] ORL Face Recognition Database, http:www.cam-orl.co.uk