Exact Geometric Moment Computation for Gray Level Images

Geometric moments have been widely used in image processing and pattern recognition. However, there are still no algorithms to compute the exact geometric moments of gray level images. In this paper, a novel image presentation method, named overlapped rectangle image representation (ORIR), is firstly presented, and then, based on ORIR, an effective algorithm for computing the exact geometric moments is presented as well. The new algorithm replaces the double integrals on two-dimensional space with the single summation on ORIR list without introducing the discrete sampling error. The experimental results in this paper show that the moment values computed by the presented algorithm match the theoretical values very well.