{"id":"https://openalex.org/W2128000934","doi":"https://doi.org/10.1109/tpami.2008.173","title":"Watershed Cuts: Minimum Spanning Forests and the Drop of Water Principle","display_name":"Watershed Cuts: Minimum Spanning Forests and the Drop of Water Principle","publication_year":2009,"publication_date":"2009-03-09","ids":{"openalex":"https://openalex.org/W2128000934","doi":"https://doi.org/10.1109/tpami.2008.173","mag":"2128000934","pmid":"https://pubmed.ncbi.nlm.nih.gov/19542572"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2008.173","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00622410/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060281976","display_name":"Jean Cousty","orcid":"https://orcid.org/0000-0002-2163-9714"},"institutions":[{"id":"https://openalex.org/I4210152518","display_name":"Laboratoire d'Informatique Gaspard-Monge","ror":"https://ror.org/04t50yk91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210145102","https://openalex.org/I4210152518","https://openalex.org/I4210154111","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I4210154111","display_name":"Universit\u00e9 Gustave Eiffel","ror":"https://ror.org/03x42jk29","country_code":"FR","type":"funder","lineage":["https://openalex.org/I4210154111"]},{"id":"https://openalex.org/I4210150884","display_name":"Fondation Sophia Antipolis","ror":"https://ror.org/05nkcfv27","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210150884"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"J. Cousty","raw_affiliation_strings":["I.N.R.I.A. Sophia Antipolis, France","Laboratoire d'Informatique Gaspard-Monge, Equipe A3SI, ESIEE, Universit\u00e9 Paris-Est, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique Gaspard-Monge, Equipe A3SI, ESIEE, Universit\u00e9 Paris-Est, France","institution_ids":["https://openalex.org/I4210152518","https://openalex.org/I4210154111"]},{"raw_affiliation_string":"I.N.R.I.A. Sophia Antipolis, France","institution_ids":["https://openalex.org/I4210150884","https://openalex.org/I1326498283"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084597676","display_name":"Gilles Bertrand","orcid":"https://orcid.org/0009-0004-7294-7081"},"institutions":[{"id":"https://openalex.org/I4210152518","display_name":"Laboratoire d'Informatique Gaspard-Monge","ror":"https://ror.org/04t50yk91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210145102","https://openalex.org/I4210152518","https://openalex.org/I4210154111","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I4210154111","display_name":"Universit\u00e9 Gustave Eiffel","ror":"https://ror.org/03x42jk29","country_code":"FR","type":"funder","lineage":["https://openalex.org/I4210154111"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"G. Bertrand","raw_affiliation_strings":["Laboratoire d'Informatique Gaspard-Monge, Equipe A3SI, ESIEE, Universit\u00e9 Paris-Est, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique Gaspard-Monge, Equipe A3SI, ESIEE, Universit\u00e9 Paris-Est, France","institution_ids":["https://openalex.org/I4210152518","https://openalex.org/I4210154111"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052368829","display_name":"Laurent Najman","orcid":"https://orcid.org/0000-0002-6190-0235"},"institutions":[{"id":"https://openalex.org/I4210152518","display_name":"Laboratoire d'Informatique Gaspard-Monge","ror":"https://ror.org/04t50yk91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210145102","https://openalex.org/I4210152518","https://openalex.org/I4210154111","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I4210154111","display_name":"Universit\u00e9 Gustave Eiffel","ror":"https://ror.org/03x42jk29","country_code":"FR","type":"funder","lineage":["https://openalex.org/I4210154111"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"L. Najman","raw_affiliation_strings":["Laboratoire d'Informatique Gaspard-Monge, Equipe A3SI, ESIEE, Universit\u00e9 Paris-Est, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique Gaspard-Monge, Equipe A3SI, ESIEE, Universit\u00e9 Paris-Est, France","institution_ids":["https://openalex.org/I4210152518","https://openalex.org/I4210154111"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056488908","display_name":"Michel Couprie","orcid":"https://orcid.org/0000-0003-1728-636X"},"institutions":[{"id":"https://openalex.org/I4210152518","display_name":"Laboratoire d'Informatique Gaspard-Monge","ror":"https://ror.org/04t50yk91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210145102","https://openalex.org/I4210152518","https://openalex.org/I4210154111","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I4210154111","display_name":"Universit\u00e9 Gustave Eiffel","ror":"https://ror.org/03x42jk29","country_code":"FR","type":"funder","lineage":["https://openalex.org/I4210154111"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"M. Couprie","raw_affiliation_strings":["Laboratoire d'Informatique Gaspard-Monge, Equipe A3SI, ESIEE, Universit\u00e9 Paris-Est, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique Gaspard-Monge, Equipe A3SI, ESIEE, Universit\u00e9 Paris-Est, France","institution_ids":["https://openalex.org/I4210152518","https://openalex.org/I4210154111"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":20.771,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":331,"citation_normalized_percentile":{"value":0.999922,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"31","issue":"8","first_page":"1362","last_page":"1374"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9968,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9968,"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/T13282","display_name":"Automated Road and Building Extraction","score":0.9951,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9949,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C150547873","wikidata":"https://www.wikidata.org/wiki/Q947851","display_name":"Watershed","level":2,"score":0.82955015},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.54027206},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.49616942},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4841557},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.4147449},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35351712},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32420343},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29963386},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2837471},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.15171984},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.12769064},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.08834499}],"mesh":[],"locations_count":5,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2008.173","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://hal.science/hal-00622410","pdf_url":"https://hal.science/hal-00622410/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://hal-upec-upem.archives-ouvertes.fr/hal-00622410/file/flow_watershedPAMI.pdf","pdf_url":"https://hal-upec-upem.archives-ouvertes.fr/hal-00622410/file/flow_watershedPAMI.pdf","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://hal-upec-upem.archives-ouvertes.fr/hal-00622410/document","pdf_url":"https://hal-upec-upem.archives-ouvertes.fr/hal-00622410/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/19542572","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_indexed_in_scopus":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":["National Institutes of Health"],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://hal.science/hal-00622410","pdf_url":"https://hal.science/hal-00622410/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life on land","score":0.64}],"grants":[],"datasets":[],"versions":[],"referenced_works_count":65,"referenced_works":["https://openalex.org/W116833144","https://openalex.org/W1482143660","https://openalex.org/W1528708751","https://openalex.org/W153102467","https://openalex.org/W1550355854","https://openalex.org/W1556421066","https://openalex.org/W1574184510","https://openalex.org/W1596012320","https://openalex.org/W1607787580","https://openalex.org/W1608608406","https://openalex.org/W1619429901","https://openalex.org/W1652775531","https://openalex.org/W195453467","https://openalex.org/W1965680834","https://openalex.org/W1972969203","https://openalex.org/W1973884997","https://openalex.org/W1975610128","https://openalex.org/W1986022261","https://openalex.org/W1989217148","https://openalex.org/W1995215698","https://openalex.org/W1997709480","https://openalex.org/W2015291970","https://openalex.org/W2017927472","https://openalex.org/W2025818287","https://openalex.org/W2032841680","https://openalex.org/W203596501","https://openalex.org/W2058388410","https://openalex.org/W2062448549","https://openalex.org/W2066167065","https://openalex.org/W2066406368","https://openalex.org/W2068934234","https://openalex.org/W2069562432","https://openalex.org/W2069702698","https://openalex.org/W2071346873","https://openalex.org/W2071937242","https://openalex.org/W2074113357","https://openalex.org/W2078065491","https://openalex.org/W2084134149","https://openalex.org/W2086262162","https://openalex.org/W2087216833","https://openalex.org/W2089026470","https://openalex.org/W2091578155","https://openalex.org/W2099096599","https://openalex.org/W2109040335","https://openalex.org/W2113622874","https://openalex.org/W2115284428","https://openalex.org/W2123340627","https://openalex.org/W2124260943","https://openalex.org/W2128356031","https://openalex.org/W2143516773","https://openalex.org/W2145871057","https://openalex.org/W2157147477","https://openalex.org/W2159329531","https://openalex.org/W2164741953","https://openalex.org/W2282030987","https://openalex.org/W2505399031","https://openalex.org/W2596316842","https://openalex.org/W2597248654","https://openalex.org/W2769043187","https://openalex.org/W2798588639","https://openalex.org/W3004540582","https://openalex.org/W3013741643","https://openalex.org/W3017143921","https://openalex.org/W4255306344","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4387955966","https://openalex.org/W2493062119","https://openalex.org/W2364060089","https://openalex.org/W2343332128","https://openalex.org/W2144571534","https://openalex.org/W214080024","https://openalex.org/W2045564889","https://openalex.org/W1992288292","https://openalex.org/W1980614686","https://openalex.org/W1134571055"],"abstract_inverted_index":{"We":[0,7,25],"study":[1],"the":[2,9,13,28,49,57,87,101,105,117,127,130,135,138],"watersheds":[3],"in":[4,71,97,111,114,122],"edge-weighted":[5],"graphs.":[6],"define":[8],"watershed":[10],"cuts":[11],"following":[12],"intuitive":[14],"idea":[15],"of":[16,18,30,59,73,89,140],"drops":[17],"water":[19,60],"flowing":[20],"on":[21,134],"a":[22,43,80],"topographic":[23],"surface.":[24],"first":[26],"establish":[27],"consistency":[29],"these":[31,53],"watersheds:":[32],"they":[33],"can":[34],"be":[35],"equivalently":[36],"defined":[37,118],"by":[38,48],"their":[39,69],"\"catchment":[40],"basinsrdquo":[41],"(through":[42,56],"steepest":[44],"descent":[45],"property)":[46],"or":[47],"\"dividing":[50],"linesrdquo":[51],"separating":[52],"catchment":[54],"basins":[55],"drop":[58],"principle).":[61],"Then,":[62],"we":[63,78],"prove,":[64],"through":[65],"an":[66],"equivalence":[67],"theorem,":[68],"optimality":[70],"terms":[72],"minimum":[74],"spanning":[75],"forests.":[76],"Afterward,":[77],"introduce":[79],"linear-time":[81],"algorithm":[82,103],"to":[83,126],"compute":[84],"them.":[85],"To":[86],"best":[88],"our":[90],"knowledge,":[91],"similar":[92],"properties":[93],"are":[94,120],"not":[95],"verified":[96],"other":[98],"frameworks":[99],"and":[100,113],"proposed":[102,131],"is":[104],"most":[106],"efficient":[107],"existing":[108],"algorithm,":[109],"both":[110],"theory":[112],"practice.":[115],"Finally,":[116],"concepts":[119],"illustrated":[121],"image":[123],"segmentation,":[124],"leading":[125],"conclusion":[128],"that":[129],"approach":[132],"improves,":[133],"tested":[136],"images,":[137],"quality":[139],"watershed-based":[141],"segmentations.":[142]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2128000934","counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":18},{"year":2022,"cited_by_count":23},{"year":2021,"cited_by_count":31},{"year":2020,"cited_by_count":18},{"year":2019,"cited_by_count":25},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":25},{"year":2016,"cited_by_count":16},{"year":2015,"cited_by_count":28},{"year":2014,"cited_by_count":27},{"year":2013,"cited_by_count":16},{"year":2012,"cited_by_count":26}],"updated_date":"2025-03-26T10:22:30.838790","created_date":"2016-06-24"}