---
OA_place: repository
OA_type: green
_id: '20658'
abstract:
- lang: eng
  text: 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.
alternative_title:
- LNCS
article_processing_charge: No
arxiv: 1
author:
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
- first_name: Elizabeth R
  full_name: Stephenson, Elizabeth R
  id: 2D04F932-F248-11E8-B48F-1D18A9856A87
  last_name: Stephenson
  orcid: 0000-0002-6862-208X
- first_name: Martin H
  full_name: Thoresen, Martin H
  id: 47CB1472-F248-11E8-B48F-1D18A9856A87
  last_name: Thoresen
citation:
  ama: 'Edelsbrunner H, Stephenson ER, Thoresen MH. The mid-sphere cousin of the medial
    axis transform. In: <i>4th International Joint Conference on Discrete Geometry
    and Mathematical Morphology</i>. Vol 16296. Springer Nature; 2025:133-147. doi:<a
    href="https://doi.org/10.1007/978-3-032-09544-2_10">10.1007/978-3-032-09544-2_10</a>'
  apa: 'Edelsbrunner, H., Stephenson, E. R., &#38; Thoresen, M. H. (2025). The mid-sphere
    cousin of the medial axis transform. In <i>4th International Joint Conference
    on Discrete Geometry and Mathematical Morphology</i> (Vol. 16296, pp. 133–147).
    Groningen, The Netherlands: Springer Nature. <a href="https://doi.org/10.1007/978-3-032-09544-2_10">https://doi.org/10.1007/978-3-032-09544-2_10</a>'
  chicago: Edelsbrunner, Herbert, Elizabeth R Stephenson, and Martin H Thoresen. “The
    Mid-Sphere Cousin of the Medial Axis Transform.” In <i>4th International Joint
    Conference on Discrete Geometry and Mathematical Morphology</i>, 16296:133–47.
    Springer Nature, 2025. <a href="https://doi.org/10.1007/978-3-032-09544-2_10">https://doi.org/10.1007/978-3-032-09544-2_10</a>.
  ieee: H. Edelsbrunner, E. R. Stephenson, and M. H. Thoresen, “The mid-sphere cousin
    of the medial axis transform,” in <i>4th International Joint Conference on Discrete
    Geometry and Mathematical Morphology</i>, Groningen, The Netherlands, 2025, vol.
    16296, pp. 133–147.
  ista: 'Edelsbrunner H, Stephenson ER, Thoresen MH. 2025. The mid-sphere cousin of the medial
    axis transform. 4th International Joint Conference on Discrete Geometry and Mathematical
    Morphology. DGMM: Discrete Geometry and Mathematical Morphology, LNCS, vol. 16296,
    133–147.'
  mla: Edelsbrunner, Herbert, et al. “The Mid-Sphere Cousin of the Medial Axis Transform.”
    <i>4th International Joint Conference on Discrete Geometry and Mathematical Morphology</i>,
    vol. 16296, Springer Nature, 2025, pp. 133–47, doi:<a href="https://doi.org/10.1007/978-3-032-09544-2_10">10.1007/978-3-032-09544-2_10</a>.
  short: H. Edelsbrunner, E.R. Stephenson, M.H. Thoresen, in:, 4th International Joint
    Conference on Discrete Geometry and Mathematical Morphology, Springer Nature,
    2025, pp. 133–147.
conference:
  end_date: 2025-11-06
  location: Groningen, The Netherlands
  name: 'DGMM: Discrete Geometry and Mathematical Morphology'
  start_date: 2025-11-03
date_created: 2025-11-23T23:01:37Z
date_published: 2025-11-01T00:00:00Z
date_updated: 2025-11-24T10:05:11Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-032-09544-2_10
external_id:
  arxiv:
  - '2504.14743'
intvolume: '     16296'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2504.14743
month: '11'
oa: 1
oa_version: Preprint
page: 133-147
publication: 4th International Joint Conference on Discrete Geometry and Mathematical
  Morphology
publication_identifier:
  eissn:
  - 1611-3349
  isbn:
  - '9783032095435'
  issn:
  - 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The mid-sphere cousin of the medial axis transform
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 16296
year: '2025'
...