High order multi-dimensional moment generating algorithm and the efficient computation of Zernike moments

The optimum computation of multi-dimensional (multi-D) image moments is presented in this paper. The developed algorithm is designed for the general case, specifically, to an arbitrary moment order R and to dimension d. The properties of the algorithm makes it best suited for obtaining the well known 2-D Zernike moments when they are computed through their relation to ordinary moments. A computational complexity model shows that the proposed algorithm takes only (NR+N)(N+R+1) additions with a negligible amount of multiplications, when an N-sized image is used to generate 2-D ordinary moments up to order R. While the speed improvement of obtaining Zernike moments is of the order O(R) with respect to direct computation through Zernike polynomials. The regular structure of the processing elements and the minimum number of operations of the algorithm makes it best suited for hardware and software implementations.