Simple and fast computation of moments

Abstract In this paper we address the problem of efficient computation of moments from the boundary of a digital area. Boundary-based computation is superior to usual region-based approaches as the data dimension of boundary representations is substantially smaller than that of region representations. We investigate the inter-order relationship of moments. One of our results is that moments of higher order can be computed from moments of lower order. Based on this relationship a simple iterative algorithm is proposed for the computation of moments from a polygonal approximation of the boundary. In comparison with a direct computation method, our algorithm is simpler to program. The memory requirement is minimum. Simulation results show that a speed-up of factor 8 can be achieved using our algorithm. A special version of the algorithm can be utilized to compute moments from the run-length chain code of the boundary. Our algorithm can be applied to compute the most popular geometric moments as well as other types of moments like Legendre, Zernike, rotational and complex moments.