Exact and fast computation of geometric moments for gray level images

Geometric moments are widely used in image processing and pattern recognition. While several methods have been proposed, exact geometric moment’s computation for gray level images is still unavailable. In this paper exact values of geometric moments are calculated using mathematical integration of the monomial terms over digital image pixels. This method removed the numerical approximation errors involved in conventional methods. A fast algorithm is proposed to accelerate the moment’s computations. The method is extended to compute the three-dimensional moments. A comparison with other conventional methods is performed. The obtained results explained the superiority of the proposed method.