{"id":"https://openalex.org/W2162997281","doi":"https://doi.org/10.1109/dicta.2007.4426830","title":"Convex Optimisation for Multiclass Image Labeling","display_name":"Convex Optimisation for Multiclass Image Labeling","publication_year":2007,"publication_date":"2007-12-01","ids":{"openalex":"https://openalex.org/W2162997281","doi":"https://doi.org/10.1109/dicta.2007.4426830","mag":"2162997281"},"language":"en","primary_location":{"id":"doi:10.1109/dicta.2007.4426830","is_oa":false,"landing_page_url":"https://doi.org/10.1109/dicta.2007.4426830","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"9th Biennial Conference of the Australian Pattern Recognition Society on Digital Image Computing Techniques and Applications (DICTA 2007)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5112557825","display_name":"Zhouyu Fu","orcid":null},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]},{"id":"https://openalex.org/I42894916","display_name":"Data61","ror":"https://ror.org/03q397159","country_code":"AU","type":"other","lineage":["https://openalex.org/I1292875679","https://openalex.org/I2801453606","https://openalex.org/I42894916","https://openalex.org/I4387156119"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Zhouyu Fu","raw_affiliation_strings":["NICTA, Canberra, ACT, Australia","RSISE, Australian National University, Canberra, ACT, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NICTA, Canberra, ACT, Australia","institution_ids":["https://openalex.org/I42894916"]},{"raw_affiliation_string":"RSISE, Australian National University, Canberra, ACT, Australia","institution_ids":["https://openalex.org/I118347636"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010621788","display_name":"Antonio Robles\u2010Kelly","orcid":"https://orcid.org/0000-0002-2465-5971"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]},{"id":"https://openalex.org/I42894916","display_name":"Data61","ror":"https://ror.org/03q397159","country_code":"AU","type":"other","lineage":["https://openalex.org/I1292875679","https://openalex.org/I2801453606","https://openalex.org/I42894916","https://openalex.org/I4387156119"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Antonio Robles-Kelly","raw_affiliation_strings":["NICTA, Canberra, ACT, Australia","RSISE, Australian National University, Canberra, ACT, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NICTA, Canberra, ACT, Australia","institution_ids":["https://openalex.org/I42894916"]},{"raw_affiliation_string":"RSISE, Australian National University, Canberra, ACT, Australia","institution_ids":["https://openalex.org/I118347636"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.24081265,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"438","last_page":"445"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9979000091552734,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9979000091552734,"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/T12923","display_name":"Digital Image Processing Techniques","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"}},{"id":"https://openalex.org/T13282","display_name":"Automated Road and Building Extraction","score":0.9833999872207642,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.7178584337234497},{"id":"https://openalex.org/keywords/submodular-set-function","display_name":"Submodular set function","score":0.6112716197967529},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.6100202202796936},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5396082997322083},{"id":"https://openalex.org/keywords/cholesky-decomposition","display_name":"Cholesky decomposition","score":0.5331786274909973},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5047370195388794},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.4911637008190155},{"id":"https://openalex.org/keywords/markov-random-field","display_name":"Markov random field","score":0.4483010172843933},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.41793251037597656},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.41756671667099},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.4136753976345062},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.41030994057655334},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.39876100420951843},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3741486966609955},{"id":"https://openalex.org/keywords/image-segmentation","display_name":"Image segmentation","score":0.31609460711479187},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.30727195739746094},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.26029086112976074},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.20148709416389465},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.13687235116958618},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.0955784022808075}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.7178584337234497},{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.6112716197967529},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.6100202202796936},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5396082997322083},{"id":"https://openalex.org/C34727166","wikidata":"https://www.wikidata.org/wiki/Q515375","display_name":"Cholesky decomposition","level":3,"score":0.5331786274909973},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5047370195388794},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.4911637008190155},{"id":"https://openalex.org/C2778045648","wikidata":"https://www.wikidata.org/wiki/Q176827","display_name":"Markov random field","level":4,"score":0.4483010172843933},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.41793251037597656},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.41756671667099},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.4136753976345062},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.41030994057655334},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.39876100420951843},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3741486966609955},{"id":"https://openalex.org/C124504099","wikidata":"https://www.wikidata.org/wiki/Q56933","display_name":"Image segmentation","level":3,"score":0.31609460711479187},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.30727195739746094},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.26029086112976074},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.20148709416389465},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.13687235116958618},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0955784022808075},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/dicta.2007.4426830","is_oa":false,"landing_page_url":"https://doi.org/10.1109/dicta.2007.4426830","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"9th Biennial Conference of the Australian Pattern Recognition Society on Digital Image Computing Techniques and Applications (DICTA 2007)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.6299999952316284}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1520511539","https://openalex.org/W1578099820","https://openalex.org/W1603839367","https://openalex.org/W1651266332","https://openalex.org/W1914102109","https://openalex.org/W2020999234","https://openalex.org/W2101309634","https://openalex.org/W2106315703","https://openalex.org/W2113997865","https://openalex.org/W2121927366","https://openalex.org/W2125637308","https://openalex.org/W2139823104","https://openalex.org/W2140666719","https://openalex.org/W2143516773","https://openalex.org/W2149760002","https://openalex.org/W2154455818","https://openalex.org/W2169551590","https://openalex.org/W2401213470","https://openalex.org/W2914338616","https://openalex.org/W6634702315","https://openalex.org/W6636296250","https://openalex.org/W6680434193","https://openalex.org/W6682494755","https://openalex.org/W6712925784"],"related_works":["https://openalex.org/W2403987929","https://openalex.org/W2374847384","https://openalex.org/W2107649022","https://openalex.org/W2356488190","https://openalex.org/W2079508979","https://openalex.org/W2966537581","https://openalex.org/W2104481679","https://openalex.org/W604331851","https://openalex.org/W2784059180","https://openalex.org/W1554970110"],"abstract_inverted_index":{"In":[0,141],"this":[1],"paper,":[2],"we":[3,31,53,121,158],"address":[4],"multiclass":[5,42,56],"pairwise":[6,106,165],"labeling":[7,35,44,57],"problems":[8],"by":[9,37,87,104,133],"proposing":[10],"an":[11],"alternative":[12],"approach":[13],"to":[14,45,67,143,184],"continuous":[15,129],"relaxation":[16,130],"techniques":[17],"which":[18,62],"makes":[19],"use":[20],"of":[21,41,81,91,98,127,154,162,180],"a":[22,46,59,135],"quadratic":[23],"cost":[24,60,83,100,156],"function":[25,61,70,84,101,157],"over":[26],"the":[27,33,39,68,79,88,92,96,99,105,111,115,124,128,149,151,155,178],"class":[28],"labels.":[29],"Here,":[30],"relax":[32],"discrete":[34,73],"problem":[36,40,131],"abstracting":[38],"semi-supervised":[43],"graph":[47,89],"regularisation":[48],"one.":[49],"By":[50],"doing":[51],"this,":[52],"can":[54,122],"perform":[55],"using":[58,138],"is":[63,85,102,117,160],"convex":[64],"and":[65,172,176],"related":[66],"target":[69],"used":[71],"in":[72,110,119,148],"Markov":[74],"Random":[75],"Field":[76],"approaches.":[77,186],"Moreover,":[78],"Hessian":[80,116],"our":[82,181],"given":[86],"Laplacian":[90],"adjacency":[93],"matrix.":[94],"Therefore,":[95],"optimisation":[97],"governed":[103],"interactions":[107],"between":[108],"pixels":[109],"local":[112],"neighbourhood.":[113],"Since":[114],"sparse":[118],"nature,":[120],"find":[123],"global":[125],"minimum":[126],"efficiently":[132],"solving":[134],"linear":[136],"equation":[137],"Cholesky":[139],"factorization.":[140],"constrast":[142],"other":[144],"segmentation":[145],"algorithms":[146],"elsewhere":[147],"literature,":[150],"general":[152],"nature":[153],"employ":[159],"capable":[161],"capturing":[163],"arbitrary":[164],"relations.":[166],"We":[167],"provide":[168],"results":[169],"on":[170],"synthetic":[171],"real-":[173],"world":[174],"imagery":[175],"demonstrate":[177],"efficacy":[179],"method":[182],"compared":[183],"competing":[185]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
