Any open bounded subset of Rn has the same homotopy type than its medial axis

Abstract

Medial Axis Transform is sometimes used as an intermediate representation in algorithms for meshing or recognition of shapes from digitized data. This raises the question whether the Medial Axis captures fundamental topological invariants of the object. The (positive) answer has been known already in the case of smooth objects. The main result presented here is the homotopy equivalence of any bounded open subset of Rn with its Medial Axis.