Fast computation of separable two-dimensional discrete invariant moments for image classification

In this paper, we present a new set of bivariate discrete orthogonal polynomials based on the product of Meixner׳s discrete orthogonal polynomials by Tchebichef׳s, Krawtchouk׳s and Hahn׳s discrete orthogonal polynomials. This set of bivariate discrete orthogonal polynomials is used to define three new types of discrete orthogonal moments as Meixner–Tchebichef moments, Meixner–Krawtchouk moments and Meixner–Hahn moments. We also present an approach to accelerate the computation of these moments by using the image block representation for binary images and image slice representation for gray-scale images. A novel set of Meixner–Tchebichef invariant moments, Meixner–Krawtchouk invariant moments and Meixner–Hahn invariant moments is also derived. These invariant moments are derived algebraically from the geometric invariant moments and their computation is accelerated using an image representation scheme. The proposed algorithms are tested using several well-known computer vision datasets including, moment׳s invariability and pattern recognition. The performance of these invariant moments used as pattern features for a pattern classification is compared with the shape descriptors of Hu, Legendre, Tchebichef–Krawtchouk, Krawtchouk–Hahn and Tchebichef–Hahn invariant moments, the texture descriptors and the color descriptors for four different databases.