{"id":"https://openalex.org/W2993140656","doi":"https://doi.org/10.1137/18m1202980","title":"Linkage Between Piecewise Constant Mumford--Shah Model and Rudin--Osher--Fatemi Model and Its Virtue in Image Segmentation","display_name":"Linkage Between Piecewise Constant Mumford--Shah Model and Rudin--Osher--Fatemi Model and Its Virtue in Image Segmentation","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2993140656","doi":"https://doi.org/10.1137/18m1202980","mag":"2993140656"},"language":"en","primary_location":{"id":"doi:10.1137/18m1202980","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1202980","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://scholars.cityu.edu.hk/en/publications/linkage-between-piecewise-constant-mumford-shah-model-and-rudin-o","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078326698","display_name":"Xiaohao Cai","orcid":"https://orcid.org/0000-0003-0924-2834"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xiaohao Cai","raw_affiliation_strings":["University College London.; University of Cambridge"],"affiliations":[{"raw_affiliation_string":"University College London.; University of Cambridge","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004126693","display_name":"Raymond H. Chan","orcid":"https://orcid.org/0000-0003-0910-4685"},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Raymond Chan","raw_affiliation_strings":["Department of Mathematics"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics","institution_ids":["https://openalex.org/I530967"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033880300","display_name":"Carola\u2010Bibiane Sch\u00f6nlieb","orcid":"https://orcid.org/0000-0003-0099-6306"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Carola-Bibiane Sch\u00f6nlieb","raw_affiliation_strings":["Univ. of Cambridge"],"affiliations":[{"raw_affiliation_string":"Univ. of Cambridge","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108670527","display_name":"Gabriele Steidl","orcid":null},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]},{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gabriele Steidl","raw_affiliation_strings":["Technische Universitat Berlin; University of Kaiserslautern"],"affiliations":[{"raw_affiliation_string":"Technische Universitat Berlin; University of Kaiserslautern","institution_ids":["https://openalex.org/I153267046","https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059443966","display_name":"Tieyong Zeng","orcid":"https://orcid.org/0000-0002-0688-202X"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Tieyong Zeng","raw_affiliation_strings":["Chinese University of Hong Kong"],"affiliations":[{"raw_affiliation_string":"Chinese University of Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5078326698"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.839,"has_fulltext":true,"cited_by_count":31,"citation_normalized_percentile":{"value":0.88951591,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"41","issue":"6","first_page":"B1310","last_page":"B1340"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11885","display_name":"MRI in cancer diagnosis","score":0.9840999841690063,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.759711742401123},{"id":"https://openalex.org/keywords/segmentation","display_name":"Segmentation","score":0.70392906665802},{"id":"https://openalex.org/keywords/thresholding","display_name":"Thresholding","score":0.6808754801750183},{"id":"https://openalex.org/keywords/image-segmentation","display_name":"Image segmentation","score":0.6192293167114258},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5874284505844116},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.5039638876914978},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5037993788719177},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.48936527967453003},{"id":"https://openalex.org/keywords/scale-space-segmentation","display_name":"Scale-space segmentation","score":0.47927019000053406},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4589383006095886},{"id":"https://openalex.org/keywords/segmentation-based-object-categorization","display_name":"Segmentation-based object categorization","score":0.4533107876777649},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.3767731785774231},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07116425037384033}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.759711742401123},{"id":"https://openalex.org/C89600930","wikidata":"https://www.wikidata.org/wiki/Q1423946","display_name":"Segmentation","level":2,"score":0.70392906665802},{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.6808754801750183},{"id":"https://openalex.org/C124504099","wikidata":"https://www.wikidata.org/wiki/Q56933","display_name":"Image segmentation","level":3,"score":0.6192293167114258},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5874284505844116},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.5039638876914978},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5037993788719177},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.48936527967453003},{"id":"https://openalex.org/C65885262","wikidata":"https://www.wikidata.org/wiki/Q7429708","display_name":"Scale-space segmentation","level":4,"score":0.47927019000053406},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4589383006095886},{"id":"https://openalex.org/C25694479","wikidata":"https://www.wikidata.org/wiki/Q7446278","display_name":"Segmentation-based object categorization","level":5,"score":0.4533107876777649},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.3767731785774231},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07116425037384033}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/18m1202980","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1202980","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/linkage-between-piecewise-constant-mumford-shah-model-and-rudin-o","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:eprints.soton.ac.uk:438778","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:pure.atira.dk:publications/f3b0ac8b-13f0-4a83-bf25-4f71d327b941","is_oa":true,"landing_page_url":"https://hdl.handle.net/2031/f3b0ac8b-13f0-4a83-bf25-4f71d327b941","pdf_url":"https://scholars.cityu.edu.hk/files/188667140/42334681.pdf","source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"CAI, X, CHAN, R, SCHONLIEB, C-B, STEIDL, G & ZENG, T 2019, 'Linkage Between Piecewise Constant Mumford-Shah Model and Rudin-Osher-Fatemi Model and Its Virtue in Image Segmentation', SIAM Journal on Scientific Computing, vol. 41, no. 6, pp. B1310-B1340. https://doi.org/10.1137/18M1202980","raw_type":"article"}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/linkage-between-piecewise-constant-mumford-shah-model-and-rudin-o","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8199999928474426,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G1018969006","display_name":null,"funder_award_id":"EP/M00483X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1063058754","display_name":null,"funder_award_id":"983","funder_id":"https://openalex.org/F4320309893","funder_display_name":"City University of Hong Kong"},{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1289935930","display_name":null,"funder_award_id":"9380101","funder_id":"https://openalex.org/F4320309893","funder_display_name":"City University of Hong Kong"},{"id":"https://openalex.org/G1755984640","display_name":null,"funder_award_id":"EP/N014588/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1781405621","display_name":null,"funder_award_id":"EP/J009539/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1971714735","display_name":null,"funder_award_id":"4053296","funder_id":"https://openalex.org/F4320322942","funder_display_name":"Chinese University of Hong Kong"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2603039567","display_name":null,"funder_award_id":"RGC 14300219","funder_id":"https://openalex.org/F4320322942","funder_display_name":"Chinese University of Hong Kong"},{"id":"https://openalex.org/G2651498393","display_name":null,"funder_award_id":"HKRGC","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2978676218","display_name":null,"funder_award_id":"EP/S026045/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3195485356","display_name":null,"funder_award_id":"RGC 14300219","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3728093668","display_name":"Isaac Newton Institute for Mathematical Sciences","funder_award_id":"EP/K032208/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4421442999","display_name":null,"funder_award_id":"EP/K032208","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4514354982","display_name":null,"funder_award_id":"4053342","funder_id":"https://openalex.org/F4320322942","funder_display_name":"Chinese University of Hong Kong"},{"id":"https://openalex.org/G4984718776","display_name":null,"funder_award_id":"P/K032208/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5004321990","display_name":null,"funder_award_id":"CUHK14306316","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G5128091834","display_name":null,"funder_award_id":"EP/K032208/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5855033780","display_name":"Efficient computational tools for inverse imaging problems","funder_award_id":"EP/M00483X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6224090631","display_name":null,"funder_award_id":"14300219","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G6579398875","display_name":"EPSRC Centre for Mathematical and Statistical Analysis of Multimodal Clinical Imaging","funder_award_id":"EP/N014588/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6757166815","display_name":null,"funder_award_id":"start-up","funder_id":"https://openalex.org/F4320322942","funder_display_name":"Chinese University of Hong Kong"},{"id":"https://openalex.org/G7145166970","display_name":null,"funder_award_id":"11671002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7306601982","display_name":null,"funder_award_id":"14300219","funder_id":"https://openalex.org/F4320322942","funder_display_name":"Chinese University of Hong Kong"},{"id":"https://openalex.org/G7393500401","display_name":null,"funder_award_id":"EP/M00483X/1","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"},{"id":"https://openalex.org/G822482273","display_name":null,"funder_award_id":"M0048","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8452545418","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320309893","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23"},{"id":"https://openalex.org/F4320313467","display_name":"Alan Turing Institute","ror":"https://ror.org/035dkdb55"},{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"},{"id":"https://openalex.org/F4320322909","display_name":"Isaac Newton Trust","ror":"https://ror.org/02gn6ta77"},{"id":"https://openalex.org/F4320322942","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48"},{"id":"https://openalex.org/F4320330232","display_name":"Sorbonne Universit\u00e9","ror":null},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1640336024","https://openalex.org/W1964590153","https://openalex.org/W1984509217","https://openalex.org/W1995450389","https://openalex.org/W2003063671","https://openalex.org/W2020999234","https://openalex.org/W2038283125","https://openalex.org/W2038495454","https://openalex.org/W2042597321","https://openalex.org/W2053884636","https://openalex.org/W2062271656","https://openalex.org/W2092663520","https://openalex.org/W2101745321","https://openalex.org/W2103559027","https://openalex.org/W2114487471","https://openalex.org/W2116040950","https://openalex.org/W2140843581","https://openalex.org/W2141250374","https://openalex.org/W2142058898","https://openalex.org/W2155280009","https://openalex.org/W2159152281","https://openalex.org/W2165351422","https://openalex.org/W2165734775","https://openalex.org/W2528476743","https://openalex.org/W4249142012","https://openalex.org/W4292363360"],"related_works":["https://openalex.org/W3144569342","https://openalex.org/W2945274617","https://openalex.org/W2185902295","https://openalex.org/W2103507220","https://openalex.org/W2055202857","https://openalex.org/W4205800335","https://openalex.org/W2371519352","https://openalex.org/W2386644571","https://openalex.org/W2372421320","https://openalex.org/W2901890255"],"abstract_inverted_index":{"The":[0,186],"piecewise":[1],"constant":[2],"Mumford--Shah":[3],"(PCMS)":[4],"model":[5,10,47,141],"and":[6,19,126,194,198],"the":[7,37,45,53,56,93,98,103,116,121,136,139,161,176,189],"Rudin--Osher--Fatemi":[8],"(ROF)":[9],"are":[11,200],"two":[12],"important":[13],"variational":[14],"models":[15],"in":[16,106,142],"image":[17,20,78,84,180,183],"segmentation":[18,39,67,76,79,104,129,168,181],"restoration,":[21],"respectively.":[22],"In":[23],"this":[24],"paper,":[25],"we":[26,164],"explore":[27],"a":[28,41,74,158,166],"linkage":[29,61],"between":[30],"these":[31],"models.":[32],"We":[33],"prove":[34],"that":[35],"for":[36,65],"two-phase":[38],"problem":[40],"partial":[42],"minimizer":[43,54],"of":[44,55,97,138,160,178,188],"PCMS":[46,99,117],"can":[48,80],"be":[49,81],"obtained":[50],"by":[51],"thresholding":[52],"ROF":[57,140],"model.":[58],"A":[59],"similar":[60],"is":[62,124,192],"still":[63],"valid":[64],"multiphase":[66],"under":[68],"specific":[69],"assumptions.":[70],"Thus":[71],"it":[72],"opens":[73],"new":[75,89,162],"paradigm:":[77],"done":[82],"via":[83],"restoration":[85,184],"plus":[86],"thresholding.":[87],"This":[88],"paradigm,":[90,163],"which":[91],"circumvents":[92],"innate":[94],"nonconvex":[95],"property":[96],"model,":[100,118],"therefore,":[101],"improves":[102],"performance":[105],"both":[107],"efficiency":[108],"(much":[109],"faster":[110],"than":[111],"state-of-the-art":[112],"methods":[113],"based":[114],"on":[115],"particularly":[119],"when":[120],"phase":[122],"number":[123],"high)the":[125],"effectiveness":[127],"(producing":[128],"results":[130,197],"with":[131,154],"better":[132],"quality)":[133],"due":[134],"to":[135,174],"flexibility":[137],"tackling":[143],"degraded":[144],"images,":[145,149,151],"such":[146],"as":[147],"noisy":[148],"blurry":[150],"or":[152],"images":[153],"information":[155],"loss.":[156],"As":[157],"by-product":[159],"derive":[165],"novel":[167],"method,":[169,173],"called":[170],"thresholded-ROF":[171],"(T-ROF)":[172],"illustrate":[175],"virtue":[177],"managing":[179],"through":[182],"techniques.":[185],"convergence":[187],"T-ROF":[190],"method":[191],"proved,":[193],"elaborate":[195],"experimental":[196],"comparisons":[199],"presented.":[201]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2}],"updated_date":"2026-04-14T08:04:32.555800","created_date":"2025-10-10T00:00:00"}
