{"id":"https://openalex.org/W2142035140","doi":"https://doi.org/10.1109/tip.2011.2182522","title":"A Direct Approach Toward Global Minimization for Multiphase Labeling and Segmentation Problems","display_name":"A Direct Approach Toward Global Minimization for Multiphase Labeling and Segmentation Problems","publication_year":2012,"publication_date":"2012-01-04","ids":{"openalex":"https://openalex.org/W2142035140","doi":"https://doi.org/10.1109/tip.2011.2182522","mag":"2142035140","pmid":"https://pubmed.ncbi.nlm.nih.gov/22231178"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2011.2182522","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2011.2182522","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Image Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5101875880","display_name":"Ying Gu","orcid":"https://orcid.org/0000-0001-6501-302X"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Ying Gu","raw_affiliation_strings":["Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112395743","display_name":"Li-Lian Wang","orcid":"https://orcid.org/0000-0002-2735-9019"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Li-Lian Wang","raw_affiliation_strings":["Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101951979","display_name":"Xue\u2010Cheng Tai","orcid":"https://orcid.org/0000-0003-3359-9104"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]},{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO","SG"],"is_corresponding":false,"raw_author_name":"Xue-Cheng Tai","raw_affiliation_strings":["Department of Mathematics, University of Bergen, Bergen, Norway","Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2212,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.89666594,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"21","issue":"5","first_page":"2399","last_page":"2411"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9966999888420105,"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":0.9966999888420105,"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/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.995199978351593,"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"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9891999959945679,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.8242673873901367},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.7594878673553467},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6632647514343262},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5715311765670776},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.532633364200592},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5269896388053894},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4910013973712921},{"id":"https://openalex.org/keywords/segmentation","display_name":"Segmentation","score":0.4825005531311035},{"id":"https://openalex.org/keywords/image-segmentation","display_name":"Image segmentation","score":0.4717990458011627},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4625709652900696},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.4574107825756073},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39911043643951416},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36170774698257446},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3188249468803406}],"concepts":[{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.8242673873901367},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.7594878673553467},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6632647514343262},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5715311765670776},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.532633364200592},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5269896388053894},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4910013973712921},{"id":"https://openalex.org/C89600930","wikidata":"https://www.wikidata.org/wiki/Q1423946","display_name":"Segmentation","level":2,"score":0.4825005531311035},{"id":"https://openalex.org/C124504099","wikidata":"https://www.wikidata.org/wiki/Q56933","display_name":"Image segmentation","level":3,"score":0.4717990458011627},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4625709652900696},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.4574107825756073},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39911043643951416},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36170774698257446},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3188249468803406},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":3,"locations":[{"id":"doi:10.1109/tip.2011.2182522","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2011.2182522","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Image Processing","raw_type":"journal-article"},{"id":"pmid:22231178","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/22231178","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on image processing : a publication of the IEEE Signal Processing Society","raw_type":null},{"id":"pmh:oai:dr.ntu.edu.sg:10356/98959","is_oa":false,"landing_page_url":"http://hdl.handle.net/10220/13483","pdf_url":null,"source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"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":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W43025103","https://openalex.org/W53515490","https://openalex.org/W74071737","https://openalex.org/W1579559187","https://openalex.org/W1593038947","https://openalex.org/W1593352143","https://openalex.org/W1978333359","https://openalex.org/W1998999283","https://openalex.org/W2003063671","https://openalex.org/W2005089986","https://openalex.org/W2020461703","https://openalex.org/W2022983148","https://openalex.org/W2026806415","https://openalex.org/W2038495454","https://openalex.org/W2041001120","https://openalex.org/W2042226984","https://openalex.org/W2056370273","https://openalex.org/W2080622120","https://openalex.org/W2092663520","https://openalex.org/W2093834886","https://openalex.org/W2097973572","https://openalex.org/W2103559027","https://openalex.org/W2104958086","https://openalex.org/W2111957738","https://openalex.org/W2113137767","https://openalex.org/W2114487471","https://openalex.org/W2116040950","https://openalex.org/W2122184585","https://openalex.org/W2138144773","https://openalex.org/W2140843581","https://openalex.org/W2142641029","https://openalex.org/W2143516773","https://openalex.org/W2155697938","https://openalex.org/W2159152281","https://openalex.org/W2159793005","https://openalex.org/W2160722640","https://openalex.org/W2165734775","https://openalex.org/W2317079468","https://openalex.org/W2326057307","https://openalex.org/W2798817241","https://openalex.org/W4253214256","https://openalex.org/W6602130781","https://openalex.org/W6677607857"],"related_works":["https://openalex.org/W2360271985","https://openalex.org/W2131718214","https://openalex.org/W2002987466","https://openalex.org/W2070276483","https://openalex.org/W2167308866","https://openalex.org/W1972437117","https://openalex.org/W1635517180","https://openalex.org/W1973889396","https://openalex.org/W2467306310","https://openalex.org/W1522162180"],"abstract_inverted_index":{"This":[0],"paper":[1],"intends":[2],"to":[3,36,78,127],"extend":[4],"the":[5,30,37,48,55,73,93,97,104,114],"minimization":[6,28],"algorithm":[7],"developed":[8],"by":[9],"Bae,":[10],"Yuan":[11],"and":[12,75,111,125],"Tai":[13],"[IJCV,":[14],"2011]":[15],"in":[16,92],"several":[17],"directions.":[18],"First,":[19],"we":[20,51,71,84],"propose":[21],"a":[22,67,80,90,102],"new":[23],"primal-dual":[24],"approach":[25],"for":[26,42],"global":[27,81,133],"of":[29,117],"continuous":[31],"Potts":[32],"model":[33,41],"with":[34,54],"applications":[35],"piecewise":[38],"constant":[39],"Mumford-Shah":[40],"multiphase":[43],"image":[44],"segmentation.":[45],"Different":[46],"from":[47,96],"existing":[49],"methods,":[50],"work":[52],"directly":[53],"binary":[56],"setting":[57],"without":[58],"using":[59],"convex":[60],"relaxation,":[61],"which":[62],"is":[63],"thereby":[64],"termed":[65],"as":[66],"direct":[68],"approach.":[69],"Second,":[70],"provide":[72,85],"sufficient":[74],"necessary":[76],"conditions":[77],"guarantee":[79],"optimum.":[82],"Moreover,":[83],"efficient":[86],"algorithms":[87,106],"based":[88],"on":[89],"reduction":[91],"intermediate":[94],"unknowns":[95,112],"augmented":[98,118],"Lagrangian":[99],"formulation.":[100],"As":[101],"result,":[103],"underlying":[105],"involve":[107],"significantly":[108],"fewer":[109],"parameters":[110],"than":[113],"naive":[115],"use":[116],"Lagrangian-based":[119],"methods;":[120],"hence,":[121],"they":[122,130],"are":[123],"fast":[124],"easy":[126],"implement.":[128],"Furthermore,":[129],"can":[131],"produce":[132],"optimums":[134],"under":[135],"mild":[136],"conditions.":[137]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2016-06-24T00:00:00"}