Fast Computation of Geometric Moments and Invariants Using Schlick's Approximation

Geometric moments have been used in several applications in the field of Computer Vision. Many techniques for fast computation of geometric moments have therefore been proposed in the recent past, but these algorithms mainly rely on properties of the moment integral such as piecewise differentiability and separability. This paper explores an alternative approach to approximating the moment kernel itself in order to get a notable improvement in computational speed. Using Schlick’s approximation for the normalized kernel of geometric moments, the computational overhead could be significantly reduced and numerical stability increased. The paper also analyses the properties of the modified moment functions, and shows that the proposed method could be effectively used in all applications where normalized Cartesian moment kernels are used. Several experimental results showing the invariant characteristics of the modified moments are also presented.