Discrete Orthogonal Moment Features Using Chebyshev Polynomials R. Mukundan, 1 S.H.Ong 2 and P.A. Lee 3 1 Faculty of Information Science and Technology, Multimedia University 75450 Malacca, Malaysia. 2 Institute of Mathematical Sciences, University of Malaya 50603 Kuala Lumpur, Malaysia. 3 Faculty of Information Technology, Multimedia University 63100 Cyberjaya, Malaysia mukund@mmu.edu.my Abstract This paper introduces a new set of moment functions based on Chebyshev polynomials which are orthogonal in the discrete domain of the image coordinate space. Chebyshev moments eliminate the problems associated with conventional orthogonal image moments such as the Legendre moments and the Zernike moments. The theoretical framework of discrete orthogonal moments is given, and their superior feature representation capability is demonstrated. Keywords: Image Moment Functions, Orthogonal Moments, Chebyshev Polynomials 1 Introduction Moment functions are used in image analysis as feature descriptors, in a wide range of applications like object classification, invariant pattern recognition, object identification, robot vision, pose estimation and stereopsis. A general definition of moment functions Φ pq of order (p+q), of an image intensity function f(x, y) can be given as follows: Φ pq = Ψ ∫∫ xy pq (x,y) f(x, y) dx dy, p, q = 0,1,2,3.... (1) where Ψ pq (x,y) is a continuous function of (x, y) known as the moment weighting kernel or the basis set. The simplest of the moment functions, with Ψ pq (x,y) = x p y q (2) were introduced by Hu [1] to derive shape descriptors that are invariant with respect to image plane transformations. Legendre and Zernike moments were later introduced by Teague [2] with the corresponding orthogonal functions as kernels. These orthogonal moments have been proved to be less sensitive to image noise as compared to geometric moments, and possess far better feature representation capabilities. The information redundancy measure is minimum in an orthogonal moment set. The computation of orthogonal moments of images pose two major problems [3, 4, 6]: (i) The image coordinate space must be normalized to the range (typically, −1 to +1) where the orthogonal polynomial definitions are valid. (ii) The continuous integrals in (1) must be approximated by discrete summations without loosing the essential properties associated with orthogonality. This paper introduces a new set of moment functions based on Chebyshev (some times also written as “Tchebichef” [5]) polynomials that are orthogonal in the discrete domain of the image coordinate space. Chebyshev moments completely eliminate the two problems referred 20