Computation of 2D Continuous Geometric Moments Through Inclusion–Exclusion

We propose a method for computing continuous (exact) geometric moments on 2D binary images, based on a decomposition into overlapping rectangles and on the inclusion-exclusion principle. The approach assumes that the input is given as a chain code describing the contour of the represented object (black pixels) and reduces the number of pixels where calculations are to be performed, especially when the contours have long axis-parallel sides.