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.

We consider the problem of estimating a function f (x, y) on the unit disk f {(x, y): x/sup 2/+y/sup 2//spl les/1}, given a discrete and noisy data recorded on a regular square grid. An estimate of f (x, y) based on a class of orthogonal and complete functions over the unit disk is proposed. This class of functions has a distinctive property of being invariant to rotation of axes about the origin of coordinates yielding therefore a rotationally invariant estimate. For-radial functions, the orthogonal set has a particularly simple form being related to the classical Legendre polynomials. We give the statistical accuracy analysis of the proposed estimate of f (x, y) in the sense of the L/sub 2/ metric. It is found that there is an inherent limitation in the precision of the estimate due to the geometric nature of a circular domain. This is explained by relating the accuracy issue to the celebrated problem in the analytic number theory called the lattice points of a circle. In fact, the obtained bounds for the mean integrated squared error are determined by the best known result so far on the problem of lattice points within the circular domain.

We give a detailed analysis of the accuracy of Zernike moments in terms of their discretization errors and the reconstruction power. It is found that there is an inherent limitation in the precision of computing the Zernike moments due to the geometric nature of a circular domain. This is explained by relating the accuracy issue to a celebrated problem in analytic number theory of evaluating the lattice points within a circle.

Moment descriptors have been developed as features in pattern recognition since the moment method was first introduced. In this paper, new moment features for Chinese character recognition are proposed. These provide significant improvements in terms of Chinese character recognition, especially for those characters that are very close in shapes.

Research has been performed investigating the use of moments for pattern recognition in recent years. The basic problem of the influence of discretization and noise on moment accuracy as object descriptors, has been barely investigated. In this paper, the detailed error analysis involved in the moment method is discussed. Several new techniques to increase the accuracy and efficiency of moment descriptor are proposed. We utilize these results for the problem of image reconstruction from the orthogonal Legendre moments computed from discrete and noisy data. The automatic selection of an optimal number of moments is also discussed.