{"id":"https://openalex.org/W2054328864","doi":"https://doi.org/10.1137/050622213","title":"Segmentation with Depth: A Level Set Approach","display_name":"Segmentation with Depth: A Level Set Approach","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2054328864","doi":"https://doi.org/10.1137/050622213","mag":"2054328864"},"language":"en","primary_location":{"id":"doi:10.1137/050622213","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050622213","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101589678","display_name":"Wei Zhu","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wei Zhu","raw_affiliation_strings":["New York University","University of California at Los Angeles"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"New York University","institution_ids":["https://openalex.org/I57206974"]},{"raw_affiliation_string":"University of California at Los Angeles","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003735769","display_name":"Tony F. Chan","orcid":"https://orcid.org/0000-0001-6196-2068"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tony Chan","raw_affiliation_strings":["University of California at Los Angeles**"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California at Los Angeles**","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5097061952","display_name":"Selim Esedolu","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Selim Esedolu","raw_affiliation_strings":["University of California at Los Angeles**"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California at Los Angeles**","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9949,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.87620398,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"28","issue":"5","first_page":"1957","last_page":"1973"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9984999895095825,"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":0.9984999895095825,"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/T10831","display_name":"Cell Adhesion Molecules Research","score":0.9722999930381775,"subfield":{"id":"https://openalex.org/subfields/2723","display_name":"Immunology and Allergy"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9627000093460083,"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/segmentation","display_name":"Segmentation","score":0.7130096554756165},{"id":"https://openalex.org/keywords/sketch","display_name":"Sketch","score":0.6985471844673157},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5833456516265869},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5572004318237305},{"id":"https://openalex.org/keywords/image-segmentation","display_name":"Image segmentation","score":0.5466232895851135},{"id":"https://openalex.org/keywords/energy-functional","display_name":"Energy functional","score":0.5382314920425415},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5167907476425171},{"id":"https://openalex.org/keywords/level-set","display_name":"Level set (data structures)","score":0.5097994208335876},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4742628335952759},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.45006832480430603},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.44605520367622375},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4241962730884552},{"id":"https://openalex.org/keywords/segmentation-based-object-categorization","display_name":"Segmentation-based object categorization","score":0.4138690233230591},{"id":"https://openalex.org/keywords/scale-space-segmentation","display_name":"Scale-space segmentation","score":0.400208055973053},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36101096868515015},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33652031421661377},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21172353625297546},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.20136716961860657},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11829683184623718}],"concepts":[{"id":"https://openalex.org/C89600930","wikidata":"https://www.wikidata.org/wiki/Q1423946","display_name":"Segmentation","level":2,"score":0.7130096554756165},{"id":"https://openalex.org/C2779231336","wikidata":"https://www.wikidata.org/wiki/Q7534724","display_name":"Sketch","level":2,"score":0.6985471844673157},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5833456516265869},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5572004318237305},{"id":"https://openalex.org/C124504099","wikidata":"https://www.wikidata.org/wiki/Q56933","display_name":"Image segmentation","level":3,"score":0.5466232895851135},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.5382314920425415},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5167907476425171},{"id":"https://openalex.org/C153008295","wikidata":"https://www.wikidata.org/wiki/Q6535093","display_name":"Level set (data structures)","level":2,"score":0.5097994208335876},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4742628335952759},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.45006832480430603},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.44605520367622375},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4241962730884552},{"id":"https://openalex.org/C25694479","wikidata":"https://www.wikidata.org/wiki/Q7446278","display_name":"Segmentation-based object categorization","level":5,"score":0.4138690233230591},{"id":"https://openalex.org/C65885262","wikidata":"https://www.wikidata.org/wiki/Q7429708","display_name":"Scale-space segmentation","level":4,"score":0.400208055973053},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36101096868515015},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33652031421661377},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21172353625297546},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.20136716961860657},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11829683184623718},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050622213","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050622213","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:repository.hkust.edu.hk:1783.1-48470","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-48470","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"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":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W121940661","https://openalex.org/W1520537649","https://openalex.org/W1538356049","https://openalex.org/W1560055494","https://openalex.org/W1989893875","https://openalex.org/W1991113069","https://openalex.org/W1994875376","https://openalex.org/W2022454744","https://openalex.org/W2024896351","https://openalex.org/W2034976587","https://openalex.org/W2047331886","https://openalex.org/W2081160575","https://openalex.org/W2093834886","https://openalex.org/W2096201928","https://openalex.org/W2104095591","https://openalex.org/W2114487471","https://openalex.org/W2116040950","https://openalex.org/W2131831293","https://openalex.org/W2132363464","https://openalex.org/W2144133758","https://openalex.org/W2149184914","https://openalex.org/W2153932305","https://openalex.org/W2155280009","https://openalex.org/W2160010354","https://openalex.org/W2297652851","https://openalex.org/W3211330693"],"related_works":["https://openalex.org/W3144569342","https://openalex.org/W2185902295","https://openalex.org/W2945274617","https://openalex.org/W2372421320","https://openalex.org/W2057775483","https://openalex.org/W2041871225","https://openalex.org/W2386644571","https://openalex.org/W2387793296","https://openalex.org/W1558398159","https://openalex.org/W2373659438"],"abstract_inverted_index":{"Segmentation":[0],"with":[1,27],"depth":[2,28,115],"is":[3,29,133],"the":[4,19,23,34,41,49,67,102,106,109,121,139,144,159,163],"challenging":[5],"problem":[6,137],"of":[7,25,36,54,66,94,143,166],"obtaining":[8],"three":[9],"dimensional":[10,16,123],"information":[11],"from":[12,120],"a":[13,91,127,134,152],"single":[14],"two":[15,122],"image.":[17],"Unlike":[18,162],"standard":[20],"segmentation":[21,26],"problem,":[22],"goal":[24],"to":[30,48,98,117,193],"determine":[31],"not":[32],"only":[33],"boundaries":[35],"objects":[37,110],"that":[38,108],"appear":[39],"in":[40,64,83,174],"image,":[42],"but":[43],"also":[44],"their":[45,99,113],"relative":[46,114],"distances":[47],"observer":[50],"by":[51,125],"making":[52],"use":[53],"occlusion":[55],"relations.":[56],"Nitzberg,":[57],"Mumford,":[58],"and":[59,79,112,170,186],"Shiota":[60],"[The":[61],"2.1D":[62,103],"sketch,":[63],"Proceedings":[65],"Third":[68],"International":[69],"Conference":[70],"on":[71],"Computer":[72],"Vision,":[73],"Osaka,":[74],"Japan,":[75],"1990;":[76],"Filtering,":[77],"Segmentation,":[78,169],"Depth,":[80,171],"Lecture":[81,172],"Notes":[82,173],"Comput.":[84,175],"Sci.":[85,176],"662,":[86,177],"Springer\u2010Verlag,":[87,178],"Berlin,":[88,179],"1993]":[89],"proposed":[90],"variational":[92],"formulation":[93],"this":[95,132,148],"problem;":[96],"according":[97],"model,":[100,105],"called":[101],"sketch":[104],"regions":[107],"occupy":[111],"are":[116],"be":[118],"extracted":[119],"image":[124],"minimizing":[126,158],"curvature":[128],"based":[129,155],"functional.":[130],"Numerically,":[131],"highly":[135],"nontrivial":[136],"as":[138],"functional":[140],"involves":[141],"curvatures":[142],"unknown":[145],"contours.":[146],"In":[147],"paper,":[149],"we":[150],"develop":[151],"level":[153],"set":[154],"procedure":[156],"for":[157,189],"Nitzberg\u2013Mumford\u2013Shiota":[160,167],"energy.":[161],"minimization":[164],"technique":[165,182],"[Filtering,":[168],"1993],":[180],"our":[181],"represents":[183],"contours":[184],"implicitly":[185],"thus":[187],"allows":[188],"connections":[190],"between":[191],"T\u2010junctions":[192],"take":[194],"place":[195],"automatically.":[196]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-25T15:57:00.446498","created_date":"2025-10-10T00:00:00"}
