{"id":"https://openalex.org/W2976714002","doi":"https://doi.org/10.1137/19m123779x","title":"The Multiphase Mumford--Shah Problem","display_name":"The Multiphase Mumford--Shah Problem","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2976714002","doi":"https://doi.org/10.1137/19m123779x","mag":"2976714002"},"language":"en","primary_location":{"id":"doi:10.1137/19m123779x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m123779x","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038744457","display_name":"Dorin Bucur","orcid":"https://orcid.org/0000-0002-8331-8481"},"institutions":[{"id":"https://openalex.org/I4210144844","display_name":"Laboratoire d\u2019Analyse et de Math\u00e9matiques Appliqu\u00e9es","ror":"https://ror.org/0581g8849","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I197681013","https://openalex.org/I4210141950","https://openalex.org/I4210144844","https://openalex.org/I4210154111"]},{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques Blaise Pascal","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]},{"id":"https://openalex.org/I70900168","display_name":"Universit\u00e9 Savoie Mont Blanc","ror":"https://ror.org/04gqg1a07","country_code":"FR","type":"education","lineage":["https://openalex.org/I70900168"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Dorin Bucur","raw_affiliation_strings":["LAMA - Laboratoire de Math\u00e9matiques (Universit\u00e9 Savoie Mont Blanc, Campus Scientifique, B\u00e2timent Le Chablais  73376 Le Bourget du Lac, France - France)"],"raw_orcid":"https://orcid.org/0000-0002-8331-8481","affiliations":[{"raw_affiliation_string":"LAMA - Laboratoire de Math\u00e9matiques (Universit\u00e9 Savoie Mont Blanc, Campus Scientifique, B\u00e2timent Le Chablais  73376 Le Bourget du Lac, France - France)","institution_ids":["https://openalex.org/I4210144844","https://openalex.org/I4210155549","https://openalex.org/I70900168"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054582414","display_name":"Ilaria Fragal\u00e0","orcid":"https://orcid.org/0000-0002-4716-2416"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ilaria Fragal\u00e0","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5021263907","display_name":"Alessandro Giacomini","orcid":"https://orcid.org/0000-0001-5193-3933"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alessandro Giacomini","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1502,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.41571552,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"12","issue":"3","first_page":"1561","last_page":"1583"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10399","display_name":"Hydrocarbon exploration and reservoir analysis","score":0.9854000210762024,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10399","display_name":"Hydrocarbon exploration and reservoir analysis","score":0.9854000210762024,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9726999998092651,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9599999785423279,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.7685031890869141},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6222800016403198},{"id":"https://openalex.org/keywords/energy-functional","display_name":"Energy functional","score":0.5077043771743774},{"id":"https://openalex.org/keywords/partition-of-unity","display_name":"Partition of unity","score":0.48549845814704895},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4329376518726349},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4017049968242645},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.35802751779556274},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27010026574134827},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17489707469940186},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12470999360084534},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.0637793242931366}],"concepts":[{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.7685031890869141},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6222800016403198},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.5077043771743774},{"id":"https://openalex.org/C102205669","wikidata":"https://www.wikidata.org/wiki/Q191690","display_name":"Partition of unity","level":3,"score":0.48549845814704895},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4329376518726349},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4017049968242645},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.35802751779556274},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27010026574134827},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17489707469940186},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12470999360084534},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0637793242931366},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/19m123779x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m123779x","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04723969v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04723969","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Imaging Sciences, 2019, 12 (3), pp.1561-1583. ⟨10.1137/19M123779X⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.unibs.it:11379/527627","is_oa":false,"landing_page_url":"http://hdl.handle.net/11379/527627","pdf_url":null,"source":{"id":"https://openalex.org/S4306400804","display_name":"Institutional Research Information System (Universit\u00e0 degli Studi di Brescia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1102894781","display_name":"Convergent Metrics for Digital Calculus","funder_award_id":"ANR-15-CE40-0006","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6175499886","display_name":"Systemes et Algorithmes Pervasifs au confluent des mondes physique et num\u00e9rique","funder_award_id":"ANR-11-LABX-0025","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320322893","display_name":"Institut Universitaire de France","ror":"https://ror.org/055khg266"},{"id":"https://openalex.org/F4320333369","display_name":"Gruppo Nazionale per l'Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1984250320","https://openalex.org/W2019393228","https://openalex.org/W2024720646","https://openalex.org/W2044243502","https://openalex.org/W2074453467","https://openalex.org/W2114487471","https://openalex.org/W2115836603","https://openalex.org/W2117785543","https://openalex.org/W2143015120","https://openalex.org/W2165734775","https://openalex.org/W2560585766","https://openalex.org/W2565695289"],"related_works":["https://openalex.org/W2963813038","https://openalex.org/W4307127933","https://openalex.org/W2785634710","https://openalex.org/W4301020713","https://openalex.org/W2131005613","https://openalex.org/W1984215587","https://openalex.org/W2381320429","https://openalex.org/W4299299922","https://openalex.org/W2593957634","https://openalex.org/W2352690124"],"abstract_inverted_index":{"We":[0],"perform":[1],"a":[2,23,51,72],"rigorous":[3],"analysis":[4],"of":[5,9,16,22,26,33,38,53,60,64,75],"the":[6,10,17,20,27,39,54,57,76],"multiphase":[7,73],"version":[8,74],"Mumford--Shah":[11],"functional.":[12],"A":[13],"characteristic":[14],"property":[15],"formulation":[18],"is":[19],"presence":[21,55],"true":[24],"partition":[25,40],"image":[28],"(so":[29],"in":[30,56],"two":[31],"dimensions":[32],"closed":[34],"contours),":[35],"each":[36],"cell":[37],"possibly":[41],"containing":[42],"inner":[43],"jumps.":[44],"The":[45],"nontrivial":[46],"partitioning":[47],"naturally":[48],"occurs":[49],"as":[50],"consequence":[52],"energy":[58],"functional":[59],"statistical":[61],"terms":[62],"or":[63],"phase":[65],"dependent":[66],"weights.":[67],"In":[68],"particular,":[69],"we":[70],"prove":[71],"De":[77],"Giorgi--Carriero--Leaci":[78],"result.":[79]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}