A general approach to moment calculation for polygons and line segments

摘要

The calculation of moments from the boundary of a solid digital area is a quite useful technique used in pattern recognition. A straightforward way of doing the calculation that does not have any numerical instabilities is presented. All the symmetries available in moment calculations are preserved, and it is shown how different moment formulas are related to each other. This includes relations between different moments and the relationships among different methods for calculating moments. Finally a direct relation between the moment expansion of a polygonal area and a stick figure made from one-dimensional lines embedded in a two-dimensional plane is derived.