---
_id: '11428'
abstract:
- lang: eng
  text: The medial axis of a set consists of the points in the ambient space without
    a unique closest point on the original set. Since its introduction, the medial
    axis has been used extensively in many applications as a method of computing a
    topologically equivalent skeleton. Unfortunately, one limiting factor in the use
    of the medial axis of a smooth manifold is that it is not necessarily topologically
    stable under small perturbations of the manifold. To counter these instabilities
    various prunings of the medial axis have been proposed. Here, we examine one type
    of pruning, called burning. Because of the good experimental results, it was hoped
    that the burning method of simplifying the medial axis would be stable. In this
    work we show a simple example that dashes such hopes based on Bing’s house with
    two rooms, demonstrating an isotopy of a shape where the medial axis goes from
    collapsible to non-collapsible.
acknowledgement: 'Partially supported by the DFG Collaborative Research Center TRR
  109, “Discretization in Geometry and Dynamics” and the European Research Council
  (ERC), grant no. 788183, “Alpha Shape Theory Extended”. Erin Chambers: Supported
  in part by the National Science Foundation through grants DBI-1759807, CCF-1907612,
  and CCF-2106672. Mathijs Wintraecken: Supported by the European Union’s Horizon
  2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement
  No. 754411. The Austrian science fund (FWF) M-3073 Acknowledgements We thank André
  Lieutier, David Letscher, Ellen Gasparovic, Kathryn Leonard, and Tao Ju for early
  discussions on this work. We also thank Lu Liu, Yajie Yan and Tao Ju for sharing
  code to generate the examples.'
article_processing_charge: No
author:
- first_name: Erin
  full_name: Chambers, Erin
  last_name: Chambers
- first_name: Christopher D
  full_name: Fillmore, Christopher D
  id: 35638A5C-AAC7-11E9-B0BF-5503E6697425
  last_name: Fillmore
- 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: Mathijs
  full_name: Wintraecken, Mathijs
  id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
  last_name: Wintraecken
  orcid: 0000-0002-7472-2220
citation:
  ama: 'Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. A cautionary tale:
    Burning the medial axis is unstable. In: Goaoc X, Kerber M, eds. <i>38th International
    Symposium on Computational Geometry</i>. Vol 224. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum
    für Informatik; 2022:66:1-66:9. doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2022.66">10.4230/LIPIcs.SoCG.2022.66</a>'
  apa: 'Chambers, E., Fillmore, C. D., Stephenson, E. R., &#38; Wintraecken, M. (2022).
    A cautionary tale: Burning the medial axis is unstable. In X. Goaoc &#38; M. Kerber
    (Eds.), <i>38th International Symposium on Computational Geometry</i> (Vol. 224,
    p. 66:1-66:9). Berlin, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
    <a href="https://doi.org/10.4230/LIPIcs.SoCG.2022.66">https://doi.org/10.4230/LIPIcs.SoCG.2022.66</a>'
  chicago: 'Chambers, Erin, Christopher D Fillmore, Elizabeth R Stephenson, and Mathijs
    Wintraecken. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” In <i>38th
    International Symposium on Computational Geometry</i>, edited by Xavier Goaoc
    and Michael Kerber, 224:66:1-66:9. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum
    für Informatik, 2022. <a href="https://doi.org/10.4230/LIPIcs.SoCG.2022.66">https://doi.org/10.4230/LIPIcs.SoCG.2022.66</a>.'
  ieee: 'E. Chambers, C. D. Fillmore, E. R. Stephenson, and M. Wintraecken, “A cautionary
    tale: Burning the medial axis is unstable,” in <i>38th International Symposium
    on Computational Geometry</i>, Berlin, Germany, 2022, vol. 224, p. 66:1-66:9.'
  ista: 'Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. 2022. A cautionary
    tale: Burning the medial axis is unstable. 38th International Symposium on Computational
    Geometry. SoCG: Symposium on Computational GeometryLIPIcs vol. 224, 66:1-66:9.'
  mla: 'Chambers, Erin, et al. “A Cautionary Tale: Burning the Medial Axis Is Unstable.”
    <i>38th International Symposium on Computational Geometry</i>, edited by Xavier
    Goaoc and Michael Kerber, vol. 224, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
    2022, p. 66:1-66:9, doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2022.66">10.4230/LIPIcs.SoCG.2022.66</a>.'
  short: E. Chambers, C.D. Fillmore, E.R. Stephenson, M. Wintraecken, in:, X. Goaoc,
    M. Kerber (Eds.), 38th International Symposium on Computational Geometry, Schloss
    Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9.
conference:
  end_date: 2022-06-10
  location: Berlin, Germany
  name: 'SoCG: Symposium on Computational Geometry'
  start_date: 2022-06-07
date_created: 2022-06-01T14:18:04Z
date_published: 2022-06-01T00:00:00Z
date_updated: 2023-02-21T09:50:52Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2022.66
ec_funded: 1
editor:
- first_name: Xavier
  full_name: Goaoc, Xavier
  last_name: Goaoc
- first_name: Michael
  full_name: Kerber, Michael
  last_name: Kerber
file:
- access_level: open_access
  checksum: b25ce40fade4ebc0bcaae176db4f5f1f
  content_type: application/pdf
  creator: dernst
  date_created: 2022-06-07T07:58:30Z
  date_updated: 2022-06-07T07:58:30Z
  file_id: '11437'
  file_name: 2022_LIPICs_Chambers.pdf
  file_size: 17580705
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file_date_updated: 2022-06-07T07:58:30Z
has_accepted_license: '1'
intvolume: '       224'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '06'
oa: 1
oa_version: Published Version
page: 66:1-66:9
project:
- _id: fc390959-9c52-11eb-aca3-afa58bd282b2
  grant_number: M03073
  name: Learning and triangulating manifolds via collapses
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '788183'
  name: Alpha Shape Theory Extended
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: 38th International Symposium on Computational Geometry
publication_identifier:
  isbn:
  - 978-3-95977-227-3
  issn:
  - 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
series_title: LIPIcs
status: public
title: 'A cautionary tale: Burning the medial axis is unstable'
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 224
year: '2022'
...