{"month":"01","article_processing_charge":"No","date_updated":"2022-06-07T08:32:42Z","type":"book_chapter","day":"27","department":[{"_id":"HeEd"}],"abstract":[{"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.","lang":"eng"}],"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2102.11397","open_access":"1"}],"date_published":"2022-01-27T00:00:00Z","publication_status":"published","publisher":"Springer Nature","scopus_import":"1","oa":1,"oa_version":"Preprint","series_title":"AWMS","date_created":"2022-06-07T08:21:11Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","alternative_title":["Association for Women in Mathematics Series"],"quality_controlled":"1","title":"The persistent homology of dual digital image constructions","status":"public","external_id":{"arxiv":["2102.11397"]},"publication_identifier":{"isbn":["9783030955182"],"eisbn":["9783030955199"]},"edition":"1","place":"Cham","doi":"10.1007/978-3-030-95519-9_1","page":"1-26","author":[{"full_name":"Bleile, Bea","first_name":"Bea","last_name":"Bleile"},{"full_name":"Garin, Adélie","first_name":"Adélie","last_name":"Garin"},{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","full_name":"Heiss, Teresa","first_name":"Teresa","last_name":"Heiss","orcid":"0000-0002-1780-2689"},{"full_name":"Maggs, Kelly","first_name":"Kelly","last_name":"Maggs"},{"first_name":"Vanessa","last_name":"Robins","full_name":"Robins, Vanessa"}],"publication":"Research in Computational Topology 2","editor":[{"first_name":"Ellen","last_name":"Gasparovic","full_name":"Gasparovic, Ellen"},{"full_name":"Robins, Vanessa","first_name":"Vanessa","last_name":"Robins"},{"full_name":"Turner, Katharine","first_name":"Katharine","last_name":"Turner"}],"language":[{"iso":"eng"}],"_id":"11440","ec_funded":1,"citation":{"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.","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>.","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.","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>","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.","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>."},"year":"2022","intvolume":"        30","volume":30,"project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","call_identifier":"H2020"}],"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."}