An algorithm for high-precision numerical computation of Zernike moments is presented. The algorithm, based on the introduced polar pixel tiling scheme, does not exhibit the geometric error and numerical integration error which are inherent in conventional methods based on Cartesian coordinates. This yields a dramatic improvement of the Zernike moments accuracy in terms of their reconstruction and invariance properties. The introduced image tiling requires an interpolation algorithm which turns out to be of the second order importance compared to the discretization error. Various comparisons are made between the accuracy of the proposed method and that of commonly used techniques. The results reveal the great advantage of our approach.

Zernike moment (ZM) is a useful image feature because of its distinguishing properties such as the magnitude invariance to image rotation. However, we find that for digital images, the invariant property of ZMs is far from ideal when they are computed with the commonly used Cartesian method, which inevitably brings about geometric error and integral error. In this paper, we propose a polar coordinate based algorithm for the computation of ZMs, which avoids both kinds of errors. We provide solutions to the key issues in ZM computation under polar coordinate system, including the derivation of computation formulas, the polar pixel arrangement scheme, and the interpolation-based image conversion etc. Simulation results show that the proposed polar approach improves the rotational invariance of ZMs significantly.