Accurate calculation of Zernike moments

Zernike moments (ZMs) are very effective global image descriptors which are used in many digital image processing applications. The digitization process compromises the accuracy of the moments and therefore, several of its properties are affected. There are two major discretization errors, namely, the geometric error and numerical integration error. In this paper we propose two new algorithms which eliminate these errors. The first algorithm performs the exact computation of geometric moments (GMs) over a unit disk and then uses GMs-to-ZMs relationship to compute the latter. This algorithm is computationally more expensive and it becomes numerically instable for higher order moments, therefore, we develop a second algorithm based on Gaussian quadrature numerical integration. The second algorithm reduces both the errors simultaneously and its accuracy increases as the degree of Gaussian quadrature numerical integration increases. The proposed algorithms are observed to provide very accurate ZMs which result in improved image reconstruction, reduction in reconstruction error and improvement in rotation and scale invariance. Exhaustive experiments are provided to support improved accuracy of ZMs and time complexity analysis is performed for the existing and the proposed methods.