Sets Reconstructable with Medial Axis

Abstract

The medial axis of a closed set is well established tool in pattern recognition, cherished for its power of reconstruction of domains. In this article we fill this gap answering the question which sets precisely are reconstructible from the medial axis information. We do not assume any additional structure of considered sets besides them being closed in n-dimensional Euclidean space.

arXiv commentv2 adds a proper introduction, visuals and a brief discussion of the stability