A comparative analysis of algorithms for fast computation of Zernike moments

This paper details a comparative analysis on time taken by the present and proposed methods to compute the Zernike moments, Z_pq. The present method comprises of Direct, Belkasim's, Prata's, Kintner's and Coefficient methods. We propose a new technique, denoted as q-recursive method, specifically for fast computation of Zernike moments. It uses radial polynomials of fixed order p with a varying index q to compute Zernike moments. Fast computation is achieved because it uses polynomials of higher index q to derive the polynomials of lower index q and it does not use any factorial terms. Individual order of moments can be calculated independently without employing lower- or higher-order moments. This is especially useful in cases where only selected orders of Zernike moments are needed as pattern features. The performance of the present and proposed methods are experimentally analyzed by calculating Zernike moments of orders 0 to p and specific order p using binary and grayscale images. In both the cases, the q-recursive method takes the shortest time to compute Zernike moments.