Calculation of moment invariants via hadamard transform

Abstract

The calculation of moment invariants via the Hadamard transform is proposed. First of all, the relationship between moments and coefficients of a Hadamard transformed image is established. Moments can then be calculated from these coefficients via addition and shift operations except for a negligible amount of multiplication operations. Furthermore, based on the relationship among moments, the higher order ones can be computed from the lower order ones. For the simply connected binary image regions, the amount of computation can be further reduced by projecting the original two-dimensional (2D) image to the x- and y-direction one-dimensional (1D) arrays and tracing the object's boundary to get the values. Simulation results indicate that the amount of computation required for the proposed algorithm is only about 50% of Li's algorithm.