On the computational aspects of Zernike moments

The set of Zernike moments belongs to the class of continuous orthogonal moments which is defined over a unit disk in polar coordinate system. The approximation error of Zernike moments limits its applications in real discrete-space images. The approximation error of Zernike moments is divided into geometrical and numerical errors. In this paper, the geometrical and numerical errors of Zernike moments are explored and methods are proposed to minimize them. The geometrical error is minimized by mapping all the pixels of discrete image inside the unit disk. The numerical error is eliminated using the proposed exact Zernike moments where the Zernike polynomials are integrated mathematically over the corresponding intervals of the image pixels. The proposed methods also overcome the numerical instability problem for high order Zernike moments. Experimental results prove the superiority and reliability of the proposed methods in providing better image representation and reconstruction capabilities. The proposed methods are also not lacking in preserving the scale and translation invariant properties of Zernike moments.