Efficient Computation of Orthogonal Moments by Suppressing the Factorial Terms

Abstract

A Modified Direct Method for the computation of the Zernike moments is presented in this paper. The presence of many factorial terms, in the direct method for computing the Zernike moments, makes their computation process a very time consuming task. Although the computational power of the modern computers is impressively increasing, the calculation of the factorial of a big number is still an inaccurate numerical procedure. The main concept of the present paper is that, by using Stirling's Approximation formula for the factorial and by applying some suitable mathematical properties, a novel, factorial-free direct method can be developed. The resulted moments are not equal to those computed by the original direct method, but they are a sufficiently accurate approximation of them. The proposed methodology is generic and can be successfully applied to any orthogonal moments having kernel moment functions consisted of factorial terms. Keywords-Zernike moments, direct method, pattern classification, Stirling's approximation