A characterization of discretized polygonal convex regions by discrete moments

Abstract

For a given planar region P its discretization on a discrete planar point set S consists of the points from S which fall into P. If P is bounded with a convex polygon having n vertices and the number of points from P ∩ S is finite, the obtained discretization of P will be called discrete convex n-gon. In this paper we show that discrete moments having the order up to n characterize uniquely the corresponding discrete convex n-gon if the discretizing set S is fixed. In this way, as an example, the matching of discrete convex n-gons can be done by comparing 1/2 · (n + 1) · (n + 2) discrete moments what can be much efficient than the comparison "point-by-point" since a digital convex n-gon can consist of an arbitrary large number of points.