Divergence analysis of discrete 2-d shapes

Abstract

In this paper we introduce a second order differential operator in order to partition discrete objects into meaningful parts. One of these parts contains all points of the object’s medial axis which is a widely used shape descriptor. Since aliasing is a fundamental problem for methods based on the boundary of discrete objects we use a bilateral filter to reduce the artefacts significantly. As a result of the partitioning and filtering we obtain a lattice point set (a superset of the medial axis) which is robust against noise and aliasing and which is rotationally invariant. The lattice point set can be used for instance to compute the medial axis or similar shape descriptors.