On the fast computation of orthogonal Fourier–Mellin moments with improved numerical stability

Abstract

A fast and numerically stable recursive method for the computation of orthogonal Fourier–Mellin moments (OFMMs) is proposed. Fast recursive method is developed for the radial polynomials which occur in the kernel function of the OFMMs, thus enhancing the overall computation speed. The proposed method is free from any overflow situations as it does not consist of any factorial term. It is also free from underflow situations as no power terms are involved. The proposed recursive method is claimed to be fastest in comparison with the direct and other methods to compute OFMMs till date. The elimination of the computation of factorial terms makes the moments very stable even up to an order of 200, which become instable in conventional or in any other recursive methods proposed earlier wherein instability occurs at moment order ≥25. Experiments are performed on standard test images to prove the superiority of the proposed method on existing methods in terms of speed and numerical stability.