Orthogonal Polynomials with Two Discrete Variables and Their Applications in Image Reconstruction

The paper firstly discusses the properties of orthogonal polynomials with two discrete variables constructed on the triangle, including orthogonality and three orders recurrence relation of matrix form. And then, this paper proposes two new methods, respectively, for the computation of the orthogonal polynomials with two discrete variables and for the generation of orthogonal moments with two discrete variables by using its orthogonal polynomials as kernel function. The results show that the above methods are of better feasible and the Charlier orthogonal moments of two variables are of better performance than Zernike moments in image reconstruction.