A FEATURE EXTRACTION APPROACH USING OPTIMAL DISCRIMINANT TRANSFORM AND IMAGE RECOGNITION

In this paper important theories are developed based on the fact that the Fisher discriminant criterion function is a generalized Rayleigh quotient in essence. The extremum properties of generalized Rayleigh quotient are first analyzed and it is pointed out that it is rational to use conjugate orthogonal constraints instead of orthogonal constraints. Then the problem of finding the optimal discriminant vectors subjected to such constraints is solved using the property that there exist a set of conjugate orthogonal eigenvectors satisfying the generalized eigen-equation. Furthermore, it is pointed out that the theories in this paper is a progress of classical Fisher linear discriminant, and the optimal discriminant vectors presented are better than Foley-Sammons’ in a sense. Furthermore, how to calculate optimal discriminant vectors in case of the within-class scatter matrix being singular is discussed and a simple approximate algorithm is given. The results of experiments on Concordia University CENPARMI handwriting numeral database and Olivetti Research Laboratory （ORL） face database show that the algorithms presented are efficient and robust.