Orthogonal invariant Fourier-Mellin moments

Conventional image moment invariants suffer from information redundancy and are sensitive to noise. We propose new orthogonal image moments based on the function set {Q n (r)exp(jmθ)}, where (r,θ) are polar coordinates and the polynomial Q n (r) is obtained by orthogonalizing the powers {r0,r1,r2,…, r n }. The moments are rotation invariant because of the circular Fourier expansion. The scale invariance is obtained by normalizing separately the power terms r n . This behavior is similar to that of the Zernike moments, but the Zernike circle polynomials are obtained by orthogonalizing the powers {r |m |,r |m |+2,r |m |+4,…}. The new moments are based on the separable circular-Fourier and radial-Mellin transform with the power n of the r n completely independent on the m. That allows much lower order n than that used in the Zernike moment and the pseudo-Zernike moments. Thus, the new moments would be less sensitive to noise. The orthogonal Fourier-Mellin moments may be expressed and calculated in terms of the complex moments. Only the definition of the complex moments should be modified to allow real valued moment orders.