Image Reconstruction with Polar Zernike Moments

Abstract

As an orthogonal moment, Zernike moment (ZM) is an attractive image feature in a number of application scenarios due to its distinguishing properties. However, we find that for digital images, the commonly used Cartesian method for ZM computation has compromised the advantages of ZMs because of their non-ideal accuracy stemming from two inherent sources of errors, i.e., the geometric error and the integral error. There exists considerable errors in image reconstruction using ZMs calculated with the Cartesian method. In this paper, we propose a polar coordinate based algorithm for the computation of ZMs, which avoids the two kinds of errors and greatly improves the accuracy of ZM computation. We present 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. As a result, ZM-based image reconstruction can be performed much more accurately.