Fast Computation of Orthogonal Fourier-Mellin Moments Using Modified Direct Method

A novel, modified direct method for Orthogonal Fourier-Mellin Moments (OFMMs) computation, which lacks of any factorial terms, is presented. The proposed algorithm is based on the substitution of the factorial terms by their approximate values, according to Stirling's Approximation formula. In this way, a new set of orthogonal moments, which are approximate versions of the original ones, are extracted. The approximation error introduced by the Stirling's Approximation formula is of low order and thus the resulted moments do not significantly differ from their original values. The resulted formulas are factorial free and therefore the time needed to compute the OFMMs is less than this of the conventional direct method.