{"id":"https://openalex.org/W2110306576","doi":"https://doi.org/10.1109/cvpr.2008.4587401","title":"Exact inference in multi-label CRFs with higher order cliques","display_name":"Exact inference in multi-label CRFs with higher order cliques","publication_year":2008,"publication_date":"2008-06-01","ids":{"openalex":"https://openalex.org/W2110306576","doi":"https://doi.org/10.1109/cvpr.2008.4587401","mag":"2110306576"},"language":"en","primary_location":{"id":"doi:10.1109/cvpr.2008.4587401","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2008.4587401","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 IEEE Conference on Computer Vision and Pattern Recognition","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/hal-01217304","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060350100","display_name":"Srikumar Ramalingam","orcid":"https://orcid.org/0000-0002-2598-0151"},"institutions":[{"id":"https://openalex.org/I124261462","display_name":"Oxford Brookes University","ror":"https://ror.org/04v2twj65","country_code":"GB","type":"education","lineage":["https://openalex.org/I124261462"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Srikumar Ramalingam","raw_affiliation_strings":["Oxford Brookes University, UK","Oxford Brookes University , Oxford"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Oxford Brookes University, UK","institution_ids":["https://openalex.org/I124261462"]},{"raw_affiliation_string":"Oxford Brookes University , Oxford","institution_ids":["https://openalex.org/I124261462"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013834379","display_name":"Pushmeet Kohli","orcid":"https://orcid.org/0000-0002-7466-7997"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I4210164937","display_name":"Microsoft Research (United Kingdom)","ror":"https://ror.org/05k87vq12","country_code":"GB","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210164937"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Pushmeet Kohli","raw_affiliation_strings":["Microsoft Research Limited, Cambridge, UK","Microsoft Research, Cambridge, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research Limited, Cambridge, UK","institution_ids":["https://openalex.org/I4210164937"]},{"raw_affiliation_string":"Microsoft Research, Cambridge, USA","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049440980","display_name":"Karteek Alahari","orcid":"https://orcid.org/0000-0002-1838-5936"},"institutions":[{"id":"https://openalex.org/I124261462","display_name":"Oxford Brookes University","ror":"https://ror.org/04v2twj65","country_code":"GB","type":"education","lineage":["https://openalex.org/I124261462"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Karteek Alahari","raw_affiliation_strings":["Oxford Brookes University, UK","Oxford Brookes University, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Oxford Brookes University, UK","institution_ids":["https://openalex.org/I124261462"]},{"raw_affiliation_string":"Oxford Brookes University, USA","institution_ids":["https://openalex.org/I124261462"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001534492","display_name":"Philip H. S. Torr","orcid":null},"institutions":[{"id":"https://openalex.org/I124261462","display_name":"Oxford Brookes University","ror":"https://ror.org/04v2twj65","country_code":"GB","type":"education","lineage":["https://openalex.org/I124261462"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Philip H. S. Torr","raw_affiliation_strings":["Oxford Brookes University, UK","Oxford Brookes University, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Oxford Brookes University, UK","institution_ids":["https://openalex.org/I124261462"]},{"raw_affiliation_string":"Oxford Brookes University, USA","institution_ids":["https://openalex.org/I124261462"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":14.9101,"has_fulltext":false,"cited_by_count":90,"citation_normalized_percentile":{"value":0.99217427,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9973000288009644,"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":0.9973000288009644,"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/T10036","display_name":"Advanced Neural Network Applications","score":0.9930999875068665,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.991599977016449,"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":[{"id":"https://openalex.org/keywords/submodular-set-function","display_name":"Submodular set function","score":0.701170027256012},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.6031050682067871},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5103263258934021},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.48248982429504395},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4424113631248474},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.41804760694503784},{"id":"https://openalex.org/keywords/encode","display_name":"ENCODE","score":0.4179132580757141},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4162346124649048},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.41007253527641296},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3741837441921234},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34191185235977173},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.34030425548553467},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3396269679069519}],"concepts":[{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.701170027256012},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.6031050682067871},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5103263258934021},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.48248982429504395},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4424113631248474},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.41804760694503784},{"id":"https://openalex.org/C66746571","wikidata":"https://www.wikidata.org/wiki/Q1134833","display_name":"ENCODE","level":3,"score":0.4179132580757141},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4162346124649048},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.41007253527641296},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3741837441921234},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34191185235977173},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34030425548553467},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3396269679069519},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/cvpr.2008.4587401","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2008.4587401","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 IEEE Conference on Computer Vision and Pattern Recognition","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.188.579","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.188.579","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://research.microsoft.com/en-us/um/people/pkohli/papers/rkat_CVPR08.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.301.4843","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.301.4843","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://cms.brookes.ac.uk/staff/PhilipTorr/Papers/2008/CVPR08/ggcuts.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.409.132","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.409.132","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mplab.ucsd.edu/wp-content/uploads/cvpr2008/conference/data/papers/061.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01217304v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01217304","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":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":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"CVPR - IEEE Conference on Computer Vision & Pattern Recognition, Jun 2008, Anchorage, United States. &#x27E8;10.1109/CVPR.2008.4587401&#x27E9;","raw_type":"Conference papers"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:555af060-de83-4734-a589-ca03086e8745","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:555af060-de83-4734-a589-ca03086e8745","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"Conference item"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01217304v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01217304","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":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":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"CVPR - IEEE Conference on Computer Vision & Pattern Recognition, Jun 2008, Anchorage, United States. &#x27E8;10.1109/CVPR.2008.4587401&#x27E9;","raw_type":"Conference papers"},"sustainable_development_goals":[{"score":0.8999999761581421,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W10769007","https://openalex.org/W87158640","https://openalex.org/W1569330617","https://openalex.org/W1680923786","https://openalex.org/W1755572302","https://openalex.org/W1835647349","https://openalex.org/W1886770168","https://openalex.org/W1994007819","https://openalex.org/W2021902776","https://openalex.org/W2050511894","https://openalex.org/W2051852418","https://openalex.org/W2074078071","https://openalex.org/W2098678088","https://openalex.org/W2101309634","https://openalex.org/W2104974755","https://openalex.org/W2116877738","https://openalex.org/W2118825986","https://openalex.org/W2121845348","https://openalex.org/W2125310925","https://openalex.org/W2131686571","https://openalex.org/W2135165032","https://openalex.org/W2135968022","https://openalex.org/W2135997060","https://openalex.org/W2137117160","https://openalex.org/W2140502500","https://openalex.org/W2143516773","https://openalex.org/W2146036075","https://openalex.org/W2165949176","https://openalex.org/W2169415915","https://openalex.org/W2540072873","https://openalex.org/W4249262284","https://openalex.org/W4252621450","https://openalex.org/W6600410068","https://openalex.org/W6638847846","https://openalex.org/W6677988828","https://openalex.org/W6680187402","https://openalex.org/W6729147144"],"related_works":["https://openalex.org/W1595919516","https://openalex.org/W2945022594","https://openalex.org/W2194604332","https://openalex.org/W4379619607","https://openalex.org/W1989453388","https://openalex.org/W2922450688","https://openalex.org/W4313349366","https://openalex.org/W3141561286","https://openalex.org/W4288560659","https://openalex.org/W2142114659"],"abstract_inverted_index":{"This":[0],"paper":[1],"addresses":[2],"the":[3,8,79,114,121,126,149],"problem":[4],"of":[5,13,31,81,116,130,151,188,200],"exactly":[6,57,159],"inferring":[7],"maximum":[9],"a":[10,25,82],"posteriori":[11],"solutions":[12,199],"discrete":[14],"multi-label":[15,32,84],"MRFs":[16],"or":[17,73,107],"CRFs":[18],"with":[19],"higher":[20,33,167,189],"order":[21,34,39,168,190],"cliques.":[22],"We":[23,112,180],"present":[24],"framework":[26],"to":[27,36,43,70,77,132,173,195],"transform":[28,125],"special":[29],"classes":[30],"functions":[35,41,131,154,192],"submodular":[37,152],"second":[38],"Boolean":[40,75],"(referred":[42],"as":[44],"F":[45,133],"<sub":[46,134],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[47,50,135,138],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">s</sub>":[48,136],"<sup":[49,137],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[51,139],"),":[52],"which":[53,91,104],"can":[54,93,124,156,170],"be":[55,94,157,171],"minimized":[56,158],"using":[58,160],"graph":[59,161],"cuts":[60],"and":[61,96,119],"we":[62,147,164],"characterize":[63],"those":[64],"classes.":[65],"The":[66],"basic":[67],"idea":[68],"is":[69],"use":[71],"two":[72],"more":[74],"variables":[76],"encode":[78],"states":[80],"single":[83,175],"variable.":[85],"There":[86],"are":[87,105,144],"many":[88],"ways":[89,103],"in":[90,101,109,198],"this":[92],"done":[95],"much":[97],"interesting":[98],"research":[99],"lies":[100],"finding":[102],"optimal":[106],"minimal":[108],"some":[110],"sense.":[111],"study":[113],"space":[115],"possible":[117],"encodings":[118],"find":[120],"ones":[122],"that":[123,155,182],"most":[127],"general":[128],"class":[129],".":[140],"Our":[141],"main":[142],"contributions":[143],"two-fold.":[145],"First,":[146],"extend":[148],"subclass":[150],"energy":[153,191],"cuts.":[162],"Second,":[163],"show":[165],"how":[166],"potentials":[169],"used":[172],"improve":[174],"view":[176],"3D":[177],"reconstruction":[178],"results.":[179],"believe":[181],"our":[183],"work":[184],"on":[185],"exact":[186],"minimization":[187],"will":[193],"lead":[194],"similar":[196],"improvements":[197],"other":[201],"labelling":[202],"problems.":[203]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":8}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
