On the improvement of rotational invariance of Zernike moments

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.