Abstract

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,…, rⁿ}. The moments are rotation invariant because of the circular Fourier expansion. The scale invariance is obtained by normalizing separately the power terms rⁿ. 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 rⁿ 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.

© 1991 Optical Society of America