A novel approach to the fast computation of Zernike moments

Abstract

This paper presents a novel approach to the fast computation of Zemike moments from a digital image. Most existing fast methods for computing Zemike moments have focused on the reduction of the computational complexity of the Zernike I-D radial polynomials by introducing their recurrence relations. Instead, in our proposed method, we focus on the reduction of the complexity of the computation of-the 2-D Zernike basis functions. As Zernike basis functions have specific symmetry or anti-symmetry about the x-axis, the y-axis, the origin, and the straight line y = x, we can generate the Zemike basis functions by only computing one of their octants. As a result, the proposed method makes the computation time eight times faster than existing methods. The proposed method is applicable to the computation of an individual Zemike moment as well as a set of Zemike moments. In addition, when computing a series of Zernike moments, the proposed method can be used with one of the existing fast methods for computing Zemike radial polynomials. This paper also presents an accurate form of Zernike moments for a discrete image function. In the experiments, results show the accuracy of the form for computing discrete Zernike moments and confirm that the proposed method for the fast computation of Zemike moments is much more efficient than existing fast methods in most cases.