Distortion invariant pattern recognition using the orthogonal Fourier–Mellin moments

Abstract

Scale and rotation by invariant pattern recognition is achieved using the orthogonal Fourier–Mellin moments, Q n (r)exp(jmθ), where Q n (r) are the polynomials on r and are generated by orthogonalizing the set of powers {r0,r1,…, r n }. The Q n (r) are in fact the modified Zernike radial polynomials without the restrictions that the radial moment orders must be even and greater than the circular moment orders |m|. The orthogonal Fourier–Mellin moments may be also calculated in the Cartesian coordinate system as the modified complex moments without the restriction that the moments order p and q must be positive integers. The Zernike moments have been shown to have the best overall performance among the various image moments. The performance of the new moments for pattern recognition is compared with that of the Zernike moments in terms of image representation, class separability, and noise sensitivity as functions of the number of the total moment features and of the radial orders of the moments. Experimental results show that for a given class of objects the orthogonal Fourier–Mellin moments use features of much lower radial orders for image classification, so it is then less sensitive to noise.