{"publication":"Foundations of Data Science","related_material":{"record":[{"id":"15091","status":"public","relation":"earlier_version"}]},"day":"01","publication_status":"epub_ahead","volume":8,"publication_identifier":{"eissn":["2639-8001"]},"acknowledgement":"This project has received funding from the European Research\r\nCouncil (ERC) under the European Union’s Horizon 2020 research and innovation\r\nprogramme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund\r\n(FWF), grant no. Z 342-N31, and from the DFG Collaborative Research Center TRR\r\n109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF),\r\ngrant no. I 02979-N35.","citation":{"ieee":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “Chromatic alpha complexes,” <i>Foundations of Data Science</i>, vol. 8. American Institute of Mathematical Sciences, pp. 30–62, 2025.","mla":"Cultrera di Montesano, Sebastiano, et al. “Chromatic Alpha Complexes.” <i>Foundations of Data Science</i>, vol. 8, American Institute of Mathematical Sciences, 2025, pp. 30–62, doi:<a href=\"https://doi.org/10.3934/fods.2025003\">10.3934/fods.2025003</a>.","chicago":"Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “Chromatic Alpha Complexes.” <i>Foundations of Data Science</i>. American Institute of Mathematical Sciences, 2025. <a href=\"https://doi.org/10.3934/fods.2025003\">https://doi.org/10.3934/fods.2025003</a>.","apa":"Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., &#38; Saghafian, M. (2025). Chromatic alpha complexes. <i>Foundations of Data Science</i>. American Institute of Mathematical Sciences. <a href=\"https://doi.org/10.3934/fods.2025003\">https://doi.org/10.3934/fods.2025003</a>","short":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, Foundations of Data Science 8 (2025) 30–62.","ista":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. 2025. Chromatic alpha complexes. Foundations of Data Science. 8, 30–62.","ama":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic alpha complexes. <i>Foundations of Data Science</i>. 2025;8:30-62. doi:<a href=\"https://doi.org/10.3934/fods.2025003\">10.3934/fods.2025003</a>"},"intvolume":"         8","year":"2025","page":"30-62","status":"public","department":[{"_id":"HeEd"}],"arxiv":1,"date_published":"2025-03-01T00:00:00Z","project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","call_identifier":"FWF"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"_id":"20585","article_type":"original","abstract":[{"lang":"eng","text":"Motivated by applications in medical sciences, we study finite chromatic sets in Euclidean space from a topological perspective. Based on the persistent homology for images, kernels and cokernels, we design provably stable homological quantifiers that describe the geometric micro- and macro-structure of how the color classes mingle. These can be efficiently computed using chromatic variants of Delaunay and alpha complexes, and code that does these computations is provided."}],"OA_type":"green","ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastiano","last_name":"Cultrera di Montesano","orcid":"0000-0001-6249-0832","full_name":"Cultrera di Montesano, Sebastiano"},{"first_name":"Ondrej","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","full_name":"Draganov, Ondrej","orcid":"0000-0003-0464-3823","last_name":"Draganov"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza","last_name":"Saghafian"}],"date_created":"2025-11-02T23:01:33Z","publisher":"American Institute of Mathematical Sciences","external_id":{"arxiv":["2212.03128"]},"corr_author":"1","language":[{"iso":"eng"}],"type":"journal_article","oa_version":"Preprint","article_processing_charge":"No","date_updated":"2025-11-04T12:25:47Z","OA_place":"repository","title":"Chromatic alpha complexes","scopus_import":"1","quality_controlled":"1","month":"03","doi":"10.3934/fods.2025003"}