Image Description With Nonseparable Two-Dimensional Charlier and Meixner Moments

Abstract

This paper presents two new sets of nonseparable discrete orthogonal Charlier and Meixner moments describing the images with noise and that are noise-free. The basis functions used by the proposed nonseparable moments are bivariate Charlier or Meixner polynomials introduced by Tratnik et al. This study discusses the computational aspects of discrete orthogonal Charlier and Meixner polynomials, including the recurrence relations with respect to variable x and order n. The purpose is to avoid large variation in the dynamic range of polynomial values for higher order moments. The implementation of nonseparable Charlier and Meixner moments does not involve any numerical approximation, since the basis function of the proposed moments is orthogonal in the image coordinate space. The performances of Charlier and Meixner moments in describing images were investigated in terms of the image reconstruction error, and the results of the experiments on the noise sensitivity are given.Keywords : Bivariate discrete orthogonal polynomials; nonseparable discrete orthogonal moments; Charlier; Meixner; three-term recurrence relations; second order linear partial di®erence equations.