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

Authors: ÜMİT ÇİĞDEM TURHAL, ALPASLAN DUYSAK

Abstract: 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 d^{th} 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.

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

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