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. As an application we demonstrate that our approximation result is useful for the problem of shape matching.