{"id":"https://openalex.org/W2114898048","doi":"https://doi.org/10.1109/cvpr.2009.5206565","title":"Continuous maximal flows and Wulff shapes: Application to MRFs","display_name":"Continuous maximal flows and Wulff shapes: Application to MRFs","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2114898048","doi":"https://doi.org/10.1109/cvpr.2009.5206565","mag":"2114898048","pmid":"https://pubmed.ncbi.nlm.nih.gov/25729263"},"language":"en","primary_location":{"id":"doi:10.1109/cvpr.2009.5206565","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2009.5206565","pdf_url":null,"source":{"id":"https://openalex.org/S4363607795","display_name":"2009 IEEE Conference on Computer Vision and Pattern Recognition","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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE Conference on Computer Vision and Pattern Recognition","raw_type":"proceedings-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/A5020965719","display_name":"Christopher Zach","orcid":"https://orcid.org/0000-0003-2840-6187"},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Christopher Zach","raw_affiliation_strings":["University of North Carolina, Chapel Hill, NC","University of North Carolina\u2013Chapel Hill, NC, USA"],"affiliations":[{"raw_affiliation_string":"University of North Carolina, Chapel Hill, NC","institution_ids":["https://openalex.org/I114027177"]},{"raw_affiliation_string":"University of North Carolina\u2013Chapel Hill, NC, USA","institution_ids":["https://openalex.org/I114027177"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108610850","display_name":"Marc Niethammer","orcid":null},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Marc Niethammer","raw_affiliation_strings":["University of North Carolina, Chapel Hill, NC","University of North Carolina\u2013Chapel Hill, NC, USA"],"affiliations":[{"raw_affiliation_string":"University of North Carolina, Chapel Hill, NC","institution_ids":["https://openalex.org/I114027177"]},{"raw_affiliation_string":"University of North Carolina\u2013Chapel Hill, NC, USA","institution_ids":["https://openalex.org/I114027177"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018151384","display_name":"Jan\u2010Michael Frahm","orcid":null},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jan-Michael Frahm","raw_affiliation_strings":["University of North Carolina, Chapel Hill, NC","University of North Carolina\u2013Chapel Hill, NC, USA"],"affiliations":[{"raw_affiliation_string":"University of North Carolina, Chapel Hill, NC","institution_ids":["https://openalex.org/I114027177"]},{"raw_affiliation_string":"University of North Carolina\u2013Chapel Hill, NC, USA","institution_ids":["https://openalex.org/I114027177"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5020965719"],"corresponding_institution_ids":["https://openalex.org/I114027177"],"apc_list":null,"apc_paid":null,"fwci":2.347,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.9057623,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"57","issue":null,"first_page":"1911","last_page":"1918"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10627","display_name":"Advanced Image and Video Retrieval 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/T10627","display_name":"Advanced Image and Video Retrieval 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/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T11605","display_name":"Visual Attention and Saliency Detection","score":0.98089998960495,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.6734845042228699},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6173127889633179},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.564886212348938},{"id":"https://openalex.org/keywords/thresholding","display_name":"Thresholding","score":0.5128160119056702},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4685536324977875},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.45326539874076843},{"id":"https://openalex.org/keywords/markov-random-field","display_name":"Markov random field","score":0.44438982009887695},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.4353547692298889},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4351412057876587},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43458831310272217},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43314090371131897},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.43238240480422974},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4287894666194916},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.427593469619751},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39358827471733093},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20590761303901672},{"id":"https://openalex.org/keywords/image-segmentation","display_name":"Image segmentation","score":0.17426681518554688},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1602063775062561},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15475508570671082},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.12267255783081055}],"concepts":[{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6734845042228699},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6173127889633179},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.564886212348938},{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.5128160119056702},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4685536324977875},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.45326539874076843},{"id":"https://openalex.org/C2778045648","wikidata":"https://www.wikidata.org/wiki/Q176827","display_name":"Markov random field","level":4,"score":0.44438982009887695},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.4353547692298889},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4351412057876587},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43458831310272217},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43314090371131897},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.43238240480422974},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4287894666194916},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.427593469619751},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39358827471733093},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20590761303901672},{"id":"https://openalex.org/C124504099","wikidata":"https://www.wikidata.org/wiki/Q56933","display_name":"Image segmentation","level":3,"score":0.17426681518554688},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1602063775062561},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15475508570671082},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.12267255783081055},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cvpr.2009.5206565","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2009.5206565","pdf_url":null,"source":{"id":"https://openalex.org/S4363607795","display_name":"2009 IEEE Conference on Computer Vision and Pattern Recognition","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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE Conference on Computer Vision and Pattern Recognition","raw_type":"proceedings-article"},{"id":"pmid:25729263","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/25729263","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":"Proceedings. IEEE Computer Society Conference on Computer Vision and Pattern Recognition","raw_type":null},{"id":"pmh:oai:europepmc.org:3304176","is_oa":false,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/4339955","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.8999999761581421}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1509803206","https://openalex.org/W1533665822","https://openalex.org/W1554489567","https://openalex.org/W1649464328","https://openalex.org/W1890886205","https://openalex.org/W2005089986","https://openalex.org/W2019599312","https://openalex.org/W2084115655","https://openalex.org/W2096139825","https://openalex.org/W2101309634","https://openalex.org/W2104404402","https://openalex.org/W2111957738","https://openalex.org/W2112058288","https://openalex.org/W2114487471","https://openalex.org/W2114741181","https://openalex.org/W2137017911","https://openalex.org/W2140502500","https://openalex.org/W2143516773","https://openalex.org/W2155280009","https://openalex.org/W2157394577","https://openalex.org/W2159152281","https://openalex.org/W2160014001","https://openalex.org/W2164918853","https://openalex.org/W2170984511","https://openalex.org/W3211330693","https://openalex.org/W4285719527","https://openalex.org/W4302155765","https://openalex.org/W6639338203","https://openalex.org/W6655383422","https://openalex.org/W6683115248"],"related_works":["https://openalex.org/W2953058328","https://openalex.org/W1542224353","https://openalex.org/W1661087619","https://openalex.org/W2750730210","https://openalex.org/W2116854923","https://openalex.org/W2236974868","https://openalex.org/W4312766348","https://openalex.org/W2730764323","https://openalex.org/W4233939244","https://openalex.org/W1976727107"],"abstract_inverted_index":{"Convex":[0],"and":[1,47,96],"continuous":[2,79,87,97],"energy":[3],"formulations":[4],"for":[5,14,99],"low":[6],"level":[7],"vision":[8],"problems":[9],"enable":[10],"efficient":[11,48],"search":[12],"procedures":[13],"the":[15,25,34,63,78,85,119,122],"corresponding":[16],"globally":[17,68],"optimal":[18,69],"solutions.":[19],"In":[20,81],"this":[21],"work":[22],"we":[23,54,83],"extend":[24],"well-established":[26],"continuous,":[27],"isotropic":[28],"capacity-based":[29],"maximal":[30,88],"flow":[31,89],"framework":[32],"to":[33,62,109,117],"anisotropic":[35,65,86],"setting.":[36],"By":[37],"using":[38],"powerful":[39],"results":[40,71,114],"from":[41],"convex":[42,95],"analysis,":[43],"a":[44,92],"very":[45],"simple":[46],"minimization":[49],"procedure":[50],"is":[51],"derived.":[52],"Further,":[53],"show":[55],"that":[56],"many":[57],"important":[58],"properties":[59],"carry":[60],"over":[61],"new":[64],"framework,":[66],"e.g.":[67],"binary":[70],"can":[72],"be":[73,110],"achieved":[74],"simply":[75],"by":[76],"thresholding":[77],"solution.":[80],"addition,":[82],"unify":[84],"approach":[90],"with":[91],"recently":[93],"proposed":[94,123],"formulation":[98],"Markov":[100],"random":[101],"fields,":[102],"thereby":[103],"allowing":[104],"more":[105],"general":[106],"smoothness":[107],"priors":[108],"incorporated.":[111],"Dense":[112],"stereo":[113],"are":[115],"included":[116],"illustrate":[118],"capabilities":[120],"of":[121],"approach.":[124]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}