The Mid-sphere Cousin of the Medial Axis Transform
Computational Geometry
2025-04-22 v1 Algebraic Topology
Abstract
The medial axis of a smoothly embedded surface in consists of all points for which the Euclidean distance function on the surface has at least two minima. We generalize this notion to the mid-sphere axis, which consists of all points for which the Euclidean distance function has two interchanging saddles that swap their partners in the pairing by persistent homology. It offers a discrete-algebraic multi-scale approach to computing ridge-like structures on the surface. As a proof of concept, an algorithm that computes stair-case approximations of the mid-sphere axis is provided.
Keywords
Cite
@article{arxiv.2504.14743,
title = {The Mid-sphere Cousin of the Medial Axis Transform},
author = {Herbert Edelsbrunner and Elizabeth Stephenson and Martin Hafskjold Thoresen},
journal= {arXiv preprint arXiv:2504.14743},
year = {2025}
}