{"id":"https://openalex.org/W2169066680","doi":"https://doi.org/10.1109/cvpr.2009.5206739","title":"Minimizing sparse higher order energy functions of discrete variables","display_name":"Minimizing sparse higher order energy functions of discrete variables","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2169066680","doi":"https://doi.org/10.1109/cvpr.2009.5206739","mag":"2169066680"},"language":"en","primary_location":{"id":"doi:10.1109/cvpr.2009.5206739","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2009.5206739","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"],"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/A5102921586","display_name":"Carsten Rother","orcid":null},"institutions":[{"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"],"is_corresponding":true,"raw_author_name":"Carsten Rother","raw_affiliation_strings":["Microsoft Research Cambridge, UK"],"affiliations":[{"raw_affiliation_string":"Microsoft Research Cambridge, UK","institution_ids":["https://openalex.org/I4210164937"]}]},{"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/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"],"is_corresponding":false,"raw_author_name":"Pushmeet Kohli","raw_affiliation_strings":["Microsoft Research Cambridge, UK"],"affiliations":[{"raw_affiliation_string":"Microsoft Research Cambridge, UK","institution_ids":["https://openalex.org/I4210164937"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100721881","display_name":"Wei Feng","orcid":"https://orcid.org/0000-0003-3809-1086"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Feng","raw_affiliation_strings":["Chinese University of Hong Kong, Hong Kong, China"],"affiliations":[{"raw_affiliation_string":"Chinese University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052856441","display_name":"Jiaya Jia","orcid":"https://orcid.org/0000-0002-1246-553X"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiaya Jia","raw_affiliation_strings":["Chinese University of Hong Kong, Hong Kong, China"],"affiliations":[{"raw_affiliation_string":"Chinese University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5102921586"],"corresponding_institution_ids":["https://openalex.org/I4210164937"],"apc_list":null,"apc_paid":null,"fwci":9.3311,"has_fulltext":false,"cited_by_count":162,"citation_normalized_percentile":{"value":0.97845601,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"1382","last_page":"1389"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9977999925613403,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9977999925613403,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9962000250816345,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.9919999837875366,"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/computer-science","display_name":"Computer science","score":0.5684286952018738},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.537169873714447},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.47983452677726746},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3935427665710449},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.29256075620651245},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11849650740623474}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5684286952018738},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.537169873714447},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.47983452677726746},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3935427665710449},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29256075620651245},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11849650740623474},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cvpr.2009.5206739","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2009.5206739","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":"pmh:oai:CiteSeerX.psu:10.1.1.156.9085","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.156.9085","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cse.cuhk.edu.hk/~leojia/all_final_papers/sparse_highorder_cvpr09.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.187.7808","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.187.7808","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/rkfj_cvpr09.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7900000214576721,"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":33,"referenced_works":["https://openalex.org/W59895198","https://openalex.org/W1502653686","https://openalex.org/W1507297895","https://openalex.org/W1549521126","https://openalex.org/W1601035521","https://openalex.org/W1968678581","https://openalex.org/W2074078071","https://openalex.org/W2098387242","https://openalex.org/W2103498186","https://openalex.org/W2107723815","https://openalex.org/W2108619558","https://openalex.org/W2111559961","https://openalex.org/W2116877738","https://openalex.org/W2121845348","https://openalex.org/W2128059732","https://openalex.org/W2128680590","https://openalex.org/W2131686571","https://openalex.org/W2137117160","https://openalex.org/W2140200866","https://openalex.org/W2140789035","https://openalex.org/W2143075689","https://openalex.org/W2143516773","https://openalex.org/W2150920547","https://openalex.org/W2153396823","https://openalex.org/W2164918853","https://openalex.org/W2165949176","https://openalex.org/W4252621450","https://openalex.org/W6630102353","https://openalex.org/W6630295433","https://openalex.org/W6636093472","https://openalex.org/W6677988828","https://openalex.org/W6680857110","https://openalex.org/W6680866351"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052","https://openalex.org/W4402327032","https://openalex.org/W2382290278"],"abstract_inverted_index":{"Higher":[0],"order":[1,49,65,89,137],"energy":[2,90],"functions":[3,50,138],"have":[4,16,72],"the":[5,36,73,82,97,147],"ability":[6],"to":[7,19,142],"encode":[8],"high":[9,75],"level":[10],"structural":[11],"dependencies":[12],"between":[13],"pixels,":[14],"which":[15],"been":[17],"shown":[18],"be":[20,111,140],"extremely":[21],"powerful":[22],"for":[23,122,146],"image":[24],"labeling":[25],"problems.":[26],"Their":[27],"use,":[28],"however,":[29],"is":[30,127],"severely":[31],"hampered":[32],"in":[33,52],"practice":[34],"by":[35,95],"intractable":[37],"complexity":[38],"of":[39,62,84],"representing":[40],"and":[41,70],"minimizing":[42,85],"such":[43,86],"functions.":[44,91],"We":[45],"observed":[46],"that":[47],"higher":[48,64,88,136],"encountered":[51],"computer":[53],"vision":[54],"are":[55,67],"very":[56],"often":[57],"\u201csparse\u201d,":[58],"i.e.":[59],"many":[60],"labelings":[61],"a":[63,129],"clique":[66],"equally":[68],"unlikely":[69],"hence":[71],"same":[74],"cost.":[76],"In":[77],"this":[78,126],"paper,":[79,131],"we":[80],"address":[81],"problem":[83,98],"sparse":[87],"Our":[92],"method":[93],"works":[94],"transforming":[96],"into":[99],"an":[100],"equivalent":[101],"quadratic":[102,108],"function":[103,109],"minimization":[104],"problem.":[105,151],"The":[106],"resulting":[107],"can":[110,139],"minimized":[112],"using":[113],"popular":[114],"message":[115],"passing":[116],"or":[117],"graph":[118],"cut":[119],"based":[120],"algorithms":[121],"MAP":[123],"inference.":[124],"Although":[125],"primarily":[128],"theoretical":[130],"it":[132],"also":[133],"shows":[134],"how":[135],"used":[141],"obtain":[143],"impressive":[144],"results":[145],"binary":[148],"texture":[149],"restoration":[150]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":25},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":27}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}