A Characterization of Discretized Polygonal Convex Regions by Discrete Moments

Abstract

AbstractFor a given planar region P its discretization on a discrete planar point set \(\mathcal{S}\) consists of the points from \(\mathcal{S}\) which fall into P. If P is bounded with a convex polygon having n vertices and the number of points from \(P \cap \mathcal{S}\) is finite, the obtained discretization of P will be called discrete convexn-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 \(\mathcal{S}\) is fixed. In this way, as an example, the matching of discrete convex n-gons can be done by comparing \(\frac{1}{2} \cdot (n + 1) \cdot (n + 2)\) 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.KeywordsDiscrete shapecodingmomentspattern matching