Error analysis and accurate calculation of rotational moments

The Orthogonal rotation invariant moments suffer from two major errors – the geometric error and the numerical integration error. As a consequence of this, their rotation and scale invariance properties are affected. In this paper, we study the behavior of these errors by analyzing their effect on rotational moments, also known as Fourier–Mellin moments and radial moments, as the former can be expressed as linear combinations of the later. We show that the existing approaches to minimize these errors are not very effective for practical applications. A computational framework based on numerical integration approach is developed which reduces the geometric error and the numerical integration error simultaneously. Two popular numerical integration methods, namely, the Simpson’s method and Gaussian numerical integration method are used and their relative performance on the accuracy of the moments are analyzed. It is shown that the proposed approach provides more accurate moments which results in the significant improvement in rotation and scale invariance properties of the moments.

► An accurate calculation of rotational moments is described which reduces geometric and numerical integration errors.
► Significant improvement in rotation and scale invariance is observed.
► It is shown that geometric and numerical integration errors can be removed simultaneously.
► The method is useful for accurate calculation of various orthogonal rotation invariant moments.