Geometric definition of a new skeletonization concept

TL;DR

This paper introduces the Divider set, a new skeletonization concept based on topology and differential geometry, offering an alternative to existing medial axis definitions with potential applications.

Contribution

It provides a formal mathematical definition of the Divider set and compares it with other medial axis concepts, expanding the theoretical framework.

Findings

Divider set as a new skeletonization concept

Comparison with existing medial axes

Potential applications discussed

Abstract

The Divider set, as an innovative alternative concept to maximal disks, Voronoi sets and cut loci, is presented with a formal definition based on topology and differential geometry. The relevant mathematical theory by previous authors and a comparison with other medial axis definitions is presented. Appropriate applications are proposed and examined.