Delaunay Triangulations Approximate Anchor Hulls

Recent results establish that a subset of the Voronoi diagram of a point set that is sampled from the smooth boundary of a shape approximates the medial axis. The corresponding question for the dual Delaunay triangulation is not addressed in the literature. We show that, for two dimensional shapes, the Delaunay triangulation approximates a specific structure which we call anchor hulls. Since similar shapes have similar anchor hulls, they provide an useful tool in matching shapes. We demonstrate that our approximation result is useful in this application. 1