---
_id: '11440'
abstract:
- lang: eng
  text: To compute the persistent homology of a grayscale digital image one needs
    to build a simplicial or cubical complex from it. For cubical complexes, the two
    commonly used constructions (corresponding to direct and indirect digital adjacencies)
    can give different results for the same image. The two constructions are almost
    dual to each other, and we use this relationship to extend and modify the cubical
    complexes to become dual filtered cell complexes. We derive a general relationship
    between the persistent homology of two dual filtered cell complexes, and also
    establish how various modifications to a filtered complex change the persistence
    diagram. Applying these results to images, we derive a method to transform the
    persistence diagram computed using one type of cubical complex into a persistence
    diagram for the other construction. This means software for computing persistent
    homology from images can now be easily adapted to produce results for either of
    the two cubical complex constructions without additional low-level code implementation.
acknowledgement: This project started during the Women in Computational Topology workshop
  held in Canberra in July of 2019. All authors are very grateful for its organisation
  and the financial support for the workshop from the Mathematical Sciences Institute
  at ANU, the US National Science Foundation through the award CCF-1841455, the Australian
  Mathematical Sciences Institute and the Association for Women in Mathematics. AG
  is supported by the Swiss National Science Foundation grant CRSII5_177237. TH is
  supported by the European Research Council (ERC) Horizon 2020 project “Alpha Shape
  Theory Extended” No. 788183. KM is supported by the ERC Horizon 2020 research and
  innovation programme under the Marie Sklodowska-Curie grant agreement No. 859860.
  VR was supported by Australian Research Council Future Fellowship FT140100604 during
  the early stages of this project.
alternative_title:
- Association for Women in Mathematics Series
article_processing_charge: No
arxiv: 1
author:
- first_name: Bea
  full_name: Bleile, Bea
  last_name: Bleile
- first_name: Adélie
  full_name: Garin, Adélie
  last_name: Garin
- first_name: Teresa
  full_name: Heiss, Teresa
  id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
  last_name: Heiss
  orcid: 0000-0002-1780-2689
- first_name: Kelly
  full_name: Maggs, Kelly
  last_name: Maggs
- first_name: Vanessa
  full_name: Robins, Vanessa
  last_name: Robins
citation:
  ama: 'Bleile B, Garin A, Heiss T, Maggs K, Robins V. The persistent homology of
    dual digital image constructions. In: Gasparovic E, Robins V, Turner K, eds. <i>Research
    in Computational Topology 2</i>. Vol 30. 1st ed. AWMS. Cham: Springer Nature;
    2022:1-26. doi:<a href="https://doi.org/10.1007/978-3-030-95519-9_1">10.1007/978-3-030-95519-9_1</a>'
  apa: 'Bleile, B., Garin, A., Heiss, T., Maggs, K., &#38; Robins, V. (2022). The
    persistent homology of dual digital image constructions. In E. Gasparovic, V.
    Robins, &#38; K. Turner (Eds.), <i>Research in Computational Topology 2</i> (1st
    ed., Vol. 30, pp. 1–26). Cham: Springer Nature. <a href="https://doi.org/10.1007/978-3-030-95519-9_1">https://doi.org/10.1007/978-3-030-95519-9_1</a>'
  chicago: 'Bleile, Bea, Adélie Garin, Teresa Heiss, Kelly Maggs, and Vanessa Robins.
    “The Persistent Homology of Dual Digital Image Constructions.” In <i>Research
    in Computational Topology 2</i>, edited by Ellen Gasparovic, Vanessa Robins, and
    Katharine Turner, 1st ed., 30:1–26. AWMS. Cham: Springer Nature, 2022. <a href="https://doi.org/10.1007/978-3-030-95519-9_1">https://doi.org/10.1007/978-3-030-95519-9_1</a>.'
  ieee: 'B. Bleile, A. Garin, T. Heiss, K. Maggs, and V. Robins, “The persistent homology
    of dual digital image constructions,” in <i>Research in Computational Topology
    2</i>, 1st ed., vol. 30, E. Gasparovic, V. Robins, and K. Turner, Eds. Cham: Springer
    Nature, 2022, pp. 1–26.'
  ista: 'Bleile B, Garin A, Heiss T, Maggs K, Robins V. 2022.The persistent homology
    of dual digital image constructions. In: Research in Computational Topology 2.
    Association for Women in Mathematics Series, vol. 30, 1–26.'
  mla: Bleile, Bea, et al. “The Persistent Homology of Dual Digital Image Constructions.”
    <i>Research in Computational Topology 2</i>, edited by Ellen Gasparovic et al.,
    1st ed., vol. 30, Springer Nature, 2022, pp. 1–26, doi:<a href="https://doi.org/10.1007/978-3-030-95519-9_1">10.1007/978-3-030-95519-9_1</a>.
  short: B. Bleile, A. Garin, T. Heiss, K. Maggs, V. Robins, in:, E. Gasparovic, V.
    Robins, K. Turner (Eds.), Research in Computational Topology 2, 1st ed., Springer
    Nature, Cham, 2022, pp. 1–26.
date_created: 2022-06-07T08:21:11Z
date_published: 2022-01-27T00:00:00Z
date_updated: 2022-06-07T08:32:42Z
day: '27'
department:
- _id: HeEd
doi: 10.1007/978-3-030-95519-9_1
ec_funded: 1
edition: '1'
editor:
- first_name: Ellen
  full_name: Gasparovic, Ellen
  last_name: Gasparovic
- first_name: Vanessa
  full_name: Robins, Vanessa
  last_name: Robins
- first_name: Katharine
  full_name: Turner, Katharine
  last_name: Turner
external_id:
  arxiv:
  - '2102.11397'
intvolume: '        30'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: ' https://doi.org/10.48550/arXiv.2102.11397'
month: '01'
oa: 1
oa_version: Preprint
page: 1-26
place: Cham
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '788183'
  name: Alpha Shape Theory Extended
publication: Research in Computational Topology 2
publication_identifier:
  eisbn:
  - '9783030955199'
  isbn:
  - '9783030955182'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: AWMS
status: public
title: The persistent homology of dual digital image constructions
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 30
year: '2022'
...