{"id":"https://openalex.org/W3111442496","doi":"https://doi.org/10.1109/ipta50016.2020.9286628","title":"Analysis of the weighted Van der Waals-Cahn-Hilliard model for image segmentation","display_name":"Analysis of the weighted Van der Waals-Cahn-Hilliard model for image segmentation","publication_year":2020,"publication_date":"2020-11-09","ids":{"openalex":"https://openalex.org/W3111442496","doi":"https://doi.org/10.1109/ipta50016.2020.9286628","mag":"3111442496"},"language":"en","primary_location":{"id":"doi:10.1109/ipta50016.2020.9286628","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ipta50016.2020.9286628","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 Tenth International Conference on Image Processing Theory, Tools and Applications (IPTA)","raw_type":"proceedings-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/A5083557091","display_name":"Zo\u00e9 Lambert","orcid":"https://orcid.org/0000-0003-1680-3716"},"institutions":[{"id":"https://openalex.org/I4392021175","display_name":"Laboratoire de Math\u00e9matiques de l'INSA de Rouen","ror":"https://ror.org/009rwsd77","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210105918","https://openalex.org/I4392021175","https://openalex.org/I88814501"]},{"id":"https://openalex.org/I62396329","display_name":"Universit\u00e9 de Rouen Normandie","ror":"https://ror.org/03nhjew95","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I62396329"]},{"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/I88814501","display_name":"Institut National des Sciences Appliqu\u00e9es Rouen Normandie","ror":"https://ror.org/020ws7586","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I88814501"]},{"id":"https://openalex.org/I4210105918","display_name":"Normandie Universit\u00e9","ror":"https://ror.org/01k40cz91","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Zoe Lambert","raw_affiliation_strings":["Normandie Univ, INSA Rouen, LMI, Rouen, France","LMI - Laboratoire de Math\u00e9matiques de l'INSA de Rouen Normandie (685 Avenue de l'Universit\u00e9\r\n76800 Saint-Etienne-du-Rouvray - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Normandie Univ, INSA Rouen, LMI, Rouen, France","institution_ids":["https://openalex.org/I88814501","https://openalex.org/I62396329","https://openalex.org/I4210105918"]},{"raw_affiliation_string":"LMI - Laboratoire de Math\u00e9matiques de l'INSA de Rouen Normandie (685 Avenue de l'Universit\u00e9\r\n76800 Saint-Etienne-du-Rouvray - France)","institution_ids":["https://openalex.org/I62396329","https://openalex.org/I4210155549","https://openalex.org/I88814501","https://openalex.org/I4392021175"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018848158","display_name":"Carole Le Guyader","orcid":"https://orcid.org/0000-0003-2192-6630"},"institutions":[{"id":"https://openalex.org/I88814501","display_name":"Institut National des Sciences Appliqu\u00e9es Rouen Normandie","ror":"https://ror.org/020ws7586","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I88814501"]},{"id":"https://openalex.org/I62396329","display_name":"Universit\u00e9 de Rouen Normandie","ror":"https://ror.org/03nhjew95","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I62396329"]},{"id":"https://openalex.org/I4210105918","display_name":"Normandie Universit\u00e9","ror":"https://ror.org/01k40cz91","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918"]},{"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/I4392021175","display_name":"Laboratoire de Math\u00e9matiques de l'INSA de Rouen","ror":"https://ror.org/009rwsd77","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210105918","https://openalex.org/I4392021175","https://openalex.org/I88814501"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Carole Le Guyader","raw_affiliation_strings":["Normandie Univ, INSA Rouen, LMI, Rouen, France","LMI - Laboratoire de Math\u00e9matiques de l'INSA de Rouen Normandie (685 Avenue de l'Universit\u00e9\r\n76800 Saint-Etienne-du-Rouvray - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Normandie Univ, INSA Rouen, LMI, Rouen, France","institution_ids":["https://openalex.org/I88814501","https://openalex.org/I62396329","https://openalex.org/I4210105918"]},{"raw_affiliation_string":"LMI - Laboratoire de Math\u00e9matiques de l'INSA de Rouen Normandie (685 Avenue de l'Universit\u00e9\r\n76800 Saint-Etienne-du-Rouvray - France)","institution_ids":["https://openalex.org/I62396329","https://openalex.org/I4210155549","https://openalex.org/I88814501","https://openalex.org/I4392021175"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010409710","display_name":"Caroline Petitjean","orcid":"https://orcid.org/0000-0003-0013-5370"},"institutions":[{"id":"https://openalex.org/I4210108118","display_name":"Laboratoire d'Informatique, du Traitement de l'Information et des Syst\u00e8mes","ror":"https://ror.org/01f1vfy95","country_code":"FR","type":"facility","lineage":["https://openalex.org/I141576021","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210108118","https://openalex.org/I62396329","https://openalex.org/I88814501"]},{"id":"https://openalex.org/I62396329","display_name":"Universit\u00e9 de Rouen Normandie","ror":"https://ror.org/03nhjew95","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I62396329"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Caroline Petitjean","raw_affiliation_strings":["Universit\u00e9 de Rouen Normandie, LITIS, Saint-Etienne-du-Rouvray Cedex, France","LITIS - Laboratoire d'Informatique, du Traitement de l'Information et des Syst\u00e8mes (Avenue de l'Universit\u00e9 76800 Saint-\u00c9tienne-du-Rouvray - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Rouen Normandie, LITIS, Saint-Etienne-du-Rouvray Cedex, France","institution_ids":["https://openalex.org/I62396329","https://openalex.org/I4210108118"]},{"raw_affiliation_string":"LITIS - Laboratoire d'Informatique, du Traitement de l'Information et des Syst\u00e8mes (Avenue de l'Universit\u00e9 76800 Saint-\u00c9tienne-du-Rouvray - France)","institution_ids":["https://openalex.org/I4210108118"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5083557091"],"corresponding_institution_ids":["https://openalex.org/I4210105918","https://openalex.org/I4210155549","https://openalex.org/I4392021175","https://openalex.org/I62396329","https://openalex.org/I88814501"],"apc_list":null,"apc_paid":null,"fwci":0.0814,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.36891566,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"27","issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9858999848365784,"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"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9817000031471252,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/van-der-waals-force","display_name":"van der Waals force","score":0.5526512265205383},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.493489146232605},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.4881592392921448},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4481724798679352},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.44279274344444275},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4197996258735657},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4186428487300873},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3650987148284912},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3374229073524475},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33600714802742004},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3319757580757141},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2653045654296875},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2302614450454712},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11014038324356079},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09732377529144287}],"concepts":[{"id":"https://openalex.org/C126061179","wikidata":"https://www.wikidata.org/wiki/Q189627","display_name":"van der Waals force","level":3,"score":0.5526512265205383},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.493489146232605},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.4881592392921448},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4481724798679352},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.44279274344444275},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4197996258735657},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4186428487300873},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3650987148284912},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3374229073524475},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33600714802742004},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3319757580757141},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2653045654296875},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2302614450454712},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11014038324356079},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09732377529144287},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C32909587","wikidata":"https://www.wikidata.org/wiki/Q11369","display_name":"Molecule","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/ipta50016.2020.9286628","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ipta50016.2020.9286628","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 Tenth International Conference on Image Processing Theory, Tools and Applications (IPTA)","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-04456812v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04456812","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":"2020 Tenth International Conference on Image Processing Theory, Tools and Applications (IPTA), Nov 2020, Paris, France. pp.1-6, &#x27E8;10.1109/IPTA50016.2020.9286628&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7900000214576721,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W202688680","https://openalex.org/W1489458628","https://openalex.org/W1496099826","https://openalex.org/W1593038947","https://openalex.org/W1599695456","https://openalex.org/W1868831826","https://openalex.org/W1990541396","https://openalex.org/W2086926544","https://openalex.org/W2093626071","https://openalex.org/W2103559027","https://openalex.org/W2114487471","https://openalex.org/W2146832981","https://openalex.org/W2159152281","https://openalex.org/W2232280848","https://openalex.org/W2560946873","https://openalex.org/W2795823403","https://openalex.org/W2964094677","https://openalex.org/W3211330693","https://openalex.org/W4232499108","https://openalex.org/W6629620515","https://openalex.org/W6689357185","https://openalex.org/W6730484666"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W4390756076","https://openalex.org/W2969742028"],"abstract_inverted_index":{"In":[0,99],"the":[1,11,25,38,45,48,58,86,94,116,126,135,142,159,166,177,181,188,191,196],"seminal":[2],"paper":[3,157],"The":[4],"Gradient":[5],"Theory":[6],"of":[7,30,40,42,44,47,61,85,104,134,141,161,180,190,198],"Phase":[8],"Transitions":[9],"and":[10,73,111,125],"Minimal":[12],"Interface":[13],"Criterion,":[14],"1987,":[15],"L.":[16],"Modica":[17],"(":[18],"[13])":[19],"proves":[20],"some":[21],"conjectures":[22],"related":[23,143],"to":[24,36,56,65,165],"Van":[26],"der":[27],"Waals-Cahn-Hilliard":[28],"theory":[29,34],"phase":[31],"transitions.":[32],"This":[33],"intends":[35],"overcome":[37],"issue":[39],"lack":[41],"uniqueness":[43],"solution":[46],"initially":[49],"considered":[50],"minimization":[51,144,197],"problem":[52,145],"-":[53,90],"which":[54],"aims":[55],"minimize":[57],"total":[59],"energy":[60,77,122],"a":[62,66,81,102,113,149],"fluid":[63],"confined":[64],"bounded":[67],"container":[68],"\u03a9\u2282\u211d":[69],"<sup":[70,131],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[71,132,139],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[72],"with":[74,185],"Gibbs":[75],"free":[76],"per":[78],"unit":[79],"volume,":[80],"prescribed":[82],"function":[83],"W":[84],"density":[87,117],"distribution":[88],"u":[89,137],"by":[91,107,153],"enforcing":[92],"that":[93,100,172],"interface":[95],"has":[96],"minimal":[97],"surface.":[98],"purpose,":[101],"family":[103],"functionals":[105],"parameterized":[106],"\u03b5":[108],">":[109],"0":[110],"including":[112],"dependency":[114],"on":[115],"gradient":[118],"modelling":[119],"this":[120,154,156,163,173],"interfacial":[121],"is":[123,146,170],"introduced,":[124],"asymptotic":[127],"behavior":[128],"as":[129],"\u03b5\u21920":[130],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">+</sup>":[133],"solutions":[136],"<sub":[138],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03b5</sub>":[140],"analyzed":[147],"through":[148],"\u0393-convergence":[150,192],"result.":[151],"Motivated":[152],"work,":[155],"addresses":[158],"question":[160],"extending":[162],"result":[164],"weighted":[167,199],"case.":[168],"It":[169],"shown":[171],"new":[174],"model":[175],"inherits":[176],"fine":[178],"properties":[179],"original":[182],"unweighted":[183],"one":[184],"in":[186],"particular,":[187],"validity":[189],"result,":[193],"useful":[194],"for":[195,202],"perimeter,":[200],"relevant":[201],"image":[203],"segmentation.":[204]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}