{"id":"https://openalex.org/W1978331308","doi":"https://doi.org/10.1007/s10851-011-0259-1","title":"On the Equivalence Between Hierarchical Segmentations and\u00a0Ultrametric Watersheds","display_name":"On the Equivalence Between Hierarchical Segmentations and\u00a0Ultrametric Watersheds","publication_year":2011,"publication_date":"2011-01-20","ids":{"openalex":"https://openalex.org/W1978331308","doi":"https://doi.org/10.1007/s10851-011-0259-1","mag":"1978331308"},"language":"en","primary_location":{"id":"doi:10.1007/s10851-011-0259-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10851-011-0259-1","pdf_url":null,"source":{"id":"https://openalex.org/S66221708","display_name":"Journal of Mathematical Imaging and Vision","issn_l":"0924-9907","issn":["0924-9907","1573-7683"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Imaging and Vision","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1002.1887","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052368829","display_name":"Laurent Najman","orcid":"https://orcid.org/0000-0002-6190-0235"},"institutions":[{"id":"https://openalex.org/I4210114274","display_name":"Laboratoire d\u2019Informatique et Syst\u00e8mes","ror":"https://ror.org/0257sgk90","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I143002897","https://openalex.org/I21491767","https://openalex.org/I4210114274"]},{"id":"https://openalex.org/I4210154111","display_name":"Universit\u00e9 Gustave Eiffel","ror":"https://ror.org/03x42jk29","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210154111"]},{"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/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210145102","https://openalex.org/I4210152518","https://openalex.org/I4210154111","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Laurent Najman","raw_affiliation_strings":["Laboratoire d\u2019Informatique Gaspard-Monge, Equipe A3SI, ESIEE, Universit\u00e9 Paris-Est, Paris, France","LIGM - Laboratoire d'Informatique Gaspard-Monge (Universit\u00e9 de Paris-Est Marne-la-Vall\u00e9e, Cit\u00e9 Descartes, B\u00e2timent Copernic, 5 bd Descartes, 77454 Marne-la-Vall\u00e9e Cedex 2 - France)","A2SI - Laboratoire Algorithmique et Architecture des Syst\u00e8mes Informatiques (France)"],"affiliations":[{"raw_affiliation_string":"Laboratoire d\u2019Informatique Gaspard-Monge, Equipe A3SI, ESIEE, Universit\u00e9 Paris-Est, Paris, France","institution_ids":["https://openalex.org/I4210152518","https://openalex.org/I4210154111"]},{"raw_affiliation_string":"LIGM - Laboratoire d'Informatique Gaspard-Monge (Universit\u00e9 de Paris-Est Marne-la-Vall\u00e9e, Cit\u00e9 Descartes, B\u00e2timent Copernic, 5 bd Descartes, 77454 Marne-la-Vall\u00e9e Cedex 2 - France)","institution_ids":["https://openalex.org/I4210152518","https://openalex.org/I4210154111"]},{"raw_affiliation_string":"A2SI - Laboratoire Algorithmique et Architecture des Syst\u00e8mes Informatiques (France)","institution_ids":["https://openalex.org/I4210114274"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052368829"],"corresponding_institution_ids":["https://openalex.org/I4210114274","https://openalex.org/I4210152518","https://openalex.org/I4210154111"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":null,"fwci":7.8412,"has_fulltext":true,"cited_by_count":63,"citation_normalized_percentile":{"value":0.97940716,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"40","issue":"3","first_page":"231","last_page":"247"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing 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/T12923","display_name":"Digital Image Processing 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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9983000159263611,"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/T11106","display_name":"Data Management and Algorithms","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ultrametric-space","display_name":"Ultrametric space","score":0.9857025146484375},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.8555269241333008},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6088356971740723},{"id":"https://openalex.org/keywords/bijection-injection-and-surjection","display_name":"Bijection, injection and surjection","score":0.5325825214385986},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.5173096656799316},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.49213117361068726},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.48086005449295044},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.47142237424850464},{"id":"https://openalex.org/keywords/watershed","display_name":"Watershed","score":0.4158889055252075},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.34996891021728516},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34953340888023376},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.29489946365356445},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2872403860092163}],"concepts":[{"id":"https://openalex.org/C61067352","wikidata":"https://www.wikidata.org/wiki/Q1897429","display_name":"Ultrametric space","level":3,"score":0.9857025146484375},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.8555269241333008},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6088356971740723},{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.5325825214385986},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.5173096656799316},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.49213117361068726},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.48086005449295044},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47142237424850464},{"id":"https://openalex.org/C150547873","wikidata":"https://www.wikidata.org/wiki/Q947851","display_name":"Watershed","level":2,"score":0.4158889055252075},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34996891021728516},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34953340888023376},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.29489946365356445},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2872403860092163},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"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/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10851-011-0259-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10851-011-0259-1","pdf_url":null,"source":{"id":"https://openalex.org/S66221708","display_name":"Journal of Mathematical Imaging and Vision","issn_l":"0924-9907","issn":["0924-9907","1573-7683"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Imaging and Vision","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1002.1887","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1002.1887","pdf_url":"https://arxiv.org/pdf/1002.1887","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:HAL:hal-00419373v2","is_oa":true,"landing_page_url":"https://hal.science/hal-00419373","pdf_url":"https://hal.science/hal-00419373v2/file/ultrametrics_long.pdf","source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Mathematical Imaging and Vision, 2011, 40 (3), pp.231-247. ⟨10.1007/s10851-011-0259-1⟩","raw_type":"Journal articles"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.395.8953","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.395.8953","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal-enpc.archives-ouvertes.fr/docs/00/54/79/05/PDF/ultrametrics_long.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1002.1887","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1002.1887","pdf_url":"https://arxiv.org/pdf/1002.1887","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[{"score":0.6200000047683716,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W33671499","https://openalex.org/W95634490","https://openalex.org/W108464071","https://openalex.org/W427156551","https://openalex.org/W642169424","https://openalex.org/W1481353708","https://openalex.org/W1502127700","https://openalex.org/W1515906871","https://openalex.org/W1530383550","https://openalex.org/W1575496704","https://openalex.org/W1652775531","https://openalex.org/W1667517793","https://openalex.org/W1965680834","https://openalex.org/W1973884997","https://openalex.org/W1977257110","https://openalex.org/W1991556951","https://openalex.org/W1991863948","https://openalex.org/W1995215698","https://openalex.org/W1998871699","https://openalex.org/W2052594950","https://openalex.org/W2062448549","https://openalex.org/W2074494048","https://openalex.org/W2084887209","https://openalex.org/W2085390747","https://openalex.org/W2086262162","https://openalex.org/W2091578155","https://openalex.org/W2099096599","https://openalex.org/W2109040335","https://openalex.org/W2123340627","https://openalex.org/W2124032926","https://openalex.org/W2128000934","https://openalex.org/W2128356031","https://openalex.org/W2134002877","https://openalex.org/W2137120608","https://openalex.org/W2146842130","https://openalex.org/W2158396120","https://openalex.org/W2167459948","https://openalex.org/W2171147867","https://openalex.org/W2798588639","https://openalex.org/W2911923452","https://openalex.org/W2913584032","https://openalex.org/W3039948875","https://openalex.org/W3123440550","https://openalex.org/W3157598734","https://openalex.org/W3162977411","https://openalex.org/W4236155230","https://openalex.org/W4251431888"],"related_works":["https://openalex.org/W2952259524","https://openalex.org/W2160566290","https://openalex.org/W2806276129","https://openalex.org/W2963449060","https://openalex.org/W4299611798","https://openalex.org/W1893226401","https://openalex.org/W2885368579","https://openalex.org/W2030568854","https://openalex.org/W2110957471","https://openalex.org/W2952466037"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":11}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}