Fast and accurate method for high order Zernike moments computation

Zernike moments (ZMs) which belong to a class of circularly orthogonal rotation invariant moments are very useful image descriptors for various image processing applications. They, however, suffer from various errors, such as discretization error, geometric error and numerical integration error. In this paper, we present an approach for their computation which reduces geometric error and numerical integration error. Geometric error is reduced by performing exact mapping of a square grid domain into a circular grid by using both the square and arc‐grids. Numerical integration error is reduced by resorting to Gaussian numerical integration over the square and arc‐grids. It is observed that the contribution of numerical integration error to the total error is much more than the geometric error. The effect of these two errors is more significant in small images as compared to large images. The use of numerical integration, however, enhances the time complexity. This problem is resolved by using recursive algorithms for the computation of radial polynomials, 8‐way symmetry of radial polynomials and 8‐way symmetry/anti‐symmetry of angular part of the kernel function. Exhaustive experiments on synthetic and real images are performed to demonstrate the effectiveness of the proposed approach.