@inproceedings{20658,
  abstract     = {The medial axis of a smoothly embedded surface in R^3 consists of all points for which the Euclidean distance function on the surface has at least two global 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.},
  author       = {Edelsbrunner, Herbert and Stephenson, Elizabeth R and Thoresen, Martin H},
  booktitle    = {4th International Joint Conference on Discrete Geometry and Mathematical Morphology},
  isbn         = {9783032095435},
  issn         = {1611-3349},
  location     = {Groningen, The Netherlands},
  pages        = {133--147},
  publisher    = {Springer Nature},
  title        = {{The mid-sphere cousin of the medial axis transform}},
  doi          = {10.1007/978-3-032-09544-2_10},
  volume       = {16296},
  year         = {2025},
}