Computing a shape's moments from its boundary

Abstract

Moments have been among the most commonly used tools in the analysis of 2D shapes. Important information about a shape such as its size, center location and orientation are all moment-based attributes. There is also a number of very useful shape features such as maximum and minimum moments of inertia, moment invariants, shape spreadness and shape elongation which are also derived from moments. Traditionally, moments of a shape are computed from the occupancy array representation of the shape. That is, all the shape's pixels are involved in the computation. In this paper we propose a method which computes the same set of moments using only the corner pixels along a shape's boundary. The basic approach is to construct a set of triangles using the shape's corners and the origin of the coordinate system. The moments of these triangles are computed first. The moments of the shape are then derived from the triangles' moments. We have found the suggested method to be much more efficient than the traditional occupancy array based methods.