Fast computation of orthogonal FourierMellin moments in polar coordinates
Fast, accurate and memory-efficient method is proposed for computing orthogonal FourierMellin moments. Since the basis polynomials are continuous orthogonal polynomials defined in polar coordinates over a unit disk, the proposed method is applied to polar coordinates where the unit disk is divided into a number of non-overlapping circular rings that are divided into circular sectors of the same area. Each sector is represented by one point in its center. The implementation of this method completely removes both approximation and geometrical errors produced by the conventional methods. Based on the symmetry property, a fast and memory-efficient algorithm is proposed to accelerate the moments computations. A comparison to conventional methods is performed. Numerical experiments are performed to ensure the efficiency of the proposed method.
fouriermellin moments polar coordinates symmetry property fast algorithm gray-level images