We propose a new set of bivariate discrete orthogonal polynomials, which are the product of Charlier’s discrete orthogonal polynomials with one variable by Tchebichef, Krawtchouk, and Hahn discrete orthogonal polynomials with one variable. This set of bivariate discrete orthogonal polynomials is used to define several new types of discrete orthogonal moments such as Charlier-Tchebichef moments (CTM), Charlier-Krawtchouk moments (CKM), and Charlier-Hahn moments (CHM). We also present an approach for fast computation of CTM, CKM, and CHM discrete orthogonal moments using the image block representation for binary images and image slice representation for grayscale images. A set of Charlier-Tchebichef invariant moments, Charlier-Krawtchouk invariant moments, and Charlier-Hahn invariant moments is also presented. These invariant moments are derived algebraically from the geometric invariant moments, and their computation is accelerated using an image representation scheme. The presented algorithms are tested in several well-known computer vision datasets including image reconstruction, computational time, moment’s invariability, and classification of objects. The performance of these invariant moments used as pattern features for a pattern classification is compared with Hu, Legendre, Tchebichef-Krawtchouk, Tchebichef-Hahn, and Krawtchouk-Hahn invariant moments.