{"id":"https://openalex.org/W2019040237","doi":"https://doi.org/10.1109/tip.2011.2168409","title":"Variational Viewpoint of the Quadratic Markov Measure Field Models: Theory and Algorithms","display_name":"Variational Viewpoint of the Quadratic Markov Measure Field Models: Theory and Algorithms","publication_year":2011,"publication_date":"2011-09-22","ids":{"openalex":"https://openalex.org/W2019040237","doi":"https://doi.org/10.1109/tip.2011.2168409","mag":"2019040237","pmid":"https://pubmed.ncbi.nlm.nih.gov/21926023"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2011.2168409","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2011.2168409","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Image Processing","raw_type":"journal-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/A5060459506","display_name":"Mariano Rivera","orcid":"https://orcid.org/0000-0002-3211-2467"},"institutions":[{"id":"https://openalex.org/I124618812","display_name":"Mathematics Research Center","ror":"https://ror.org/02nhmp827","country_code":"MX","type":"facility","lineage":["https://openalex.org/I124618812"]},{"id":"https://openalex.org/I4210118279","display_name":"Mathematics Research Center","ror":null,"country_code":"MX","type":null,"lineage":["https://openalex.org/I4210118279"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"M. Rivera","raw_affiliation_strings":["Department of Computer Science, Center for Research in Mathematics, Guanajuato, Mexico. mrivera@cimat.mx","Dept. of Comput. Sci., Center for Res. in Math., Guanajuato, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Center for Research in Mathematics, Guanajuato, Mexico. mrivera@cimat.mx","institution_ids":["https://openalex.org/I4210118279"]},{"raw_affiliation_string":"Dept. of Comput. Sci., Center for Res. in Math., Guanajuato, Mexico","institution_ids":["https://openalex.org/I124618812"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011342780","display_name":"Oscar Dalmau","orcid":"https://orcid.org/0000-0002-1828-8458"},"institutions":[{"id":"https://openalex.org/I124618812","display_name":"Mathematics Research Center","ror":"https://ror.org/02nhmp827","country_code":"MX","type":"facility","lineage":["https://openalex.org/I124618812"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"O. Dalmau","raw_affiliation_strings":["Department of Computer Science, Center for Research in Mathematics, Guanajuato, Mexico","Dept. of Comput. Sci., Center for Res. in Math., Guanajuato, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Center for Research in Mathematics, Guanajuato, Mexico","institution_ids":["https://openalex.org/I124618812"]},{"raw_affiliation_string":"Dept. of Comput. Sci., Center for Res. in Math., Guanajuato, Mexico","institution_ids":["https://openalex.org/I124618812"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0468,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.79511712,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"21","issue":"3","first_page":"1246","last_page":"1257"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9993000030517578,"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":0.9993000030517578,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9861999750137329,"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/mathematics","display_name":"Mathematics","score":0.603308916091919},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5484932661056519},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5368760824203491},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.5238960981369019},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.45489850640296936},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.44424477219581604},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42464008927345276},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4124141335487366},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.309814989566803},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.22254431247711182}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.603308916091919},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5484932661056519},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5368760824203491},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.5238960981369019},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.45489850640296936},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.44424477219581604},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42464008927345276},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4124141335487366},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.309814989566803},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.22254431247711182},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tip.2011.2168409","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2011.2168409","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Image Processing","raw_type":"journal-article"},{"id":"pmid:21926023","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21926023","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":"IEEE transactions on image processing : a publication of the IEEE Signal Processing Society","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.297.9377","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.297.9377","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cimat.mx/~mrivera/journals/rivera_qpseg_tip_2col.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.5099999904632568}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1480376833","https://openalex.org/W1587273192","https://openalex.org/W1651266332","https://openalex.org/W1785730614","https://openalex.org/W1969846144","https://openalex.org/W2012433182","https://openalex.org/W2019635781","https://openalex.org/W2020999234","https://openalex.org/W2079036931","https://openalex.org/W2088616581","https://openalex.org/W2097798120","https://openalex.org/W2101309634","https://openalex.org/W2107890570","https://openalex.org/W2113137767","https://openalex.org/W2114289522","https://openalex.org/W2119300483","https://openalex.org/W2121994130","https://openalex.org/W2124351162","https://openalex.org/W2125637308","https://openalex.org/W2125709799","https://openalex.org/W2135365788","https://openalex.org/W2143516773","https://openalex.org/W2165450509","https://openalex.org/W2169551590","https://openalex.org/W2171074980","https://openalex.org/W2293194425","https://openalex.org/W2395023550","https://openalex.org/W2568830674","https://openalex.org/W2904545066","https://openalex.org/W3035235874","https://openalex.org/W4251321576","https://openalex.org/W4293775970","https://openalex.org/W6638212498","https://openalex.org/W6674950339","https://openalex.org/W6731519819"],"related_works":["https://openalex.org/W1980381208","https://openalex.org/W2364594919","https://openalex.org/W1861706286","https://openalex.org/W3036464408","https://openalex.org/W2020990755","https://openalex.org/W2377851227","https://openalex.org/W4293088966","https://openalex.org/W2366868484","https://openalex.org/W2917463375","https://openalex.org/W2155219672"],"abstract_inverted_index":{"We":[0,51,129,157],"present":[1,24,53,116,158],"a":[2,15,25,42,95],"framework":[3],"for":[4,44,101,124,164],"image":[5],"segmentation":[6,150],"based":[7],"on":[8],"quadratic":[9,16,31,83],"programming,":[10],"i.e.,":[11],"by":[12,71,134],"minimization":[13,123],"of":[14,29,81,94,149],"regularized":[17,65],"energy":[18],"linearly":[19],"constrained.":[20],"In":[21,57],"particular,":[22],"we":[23,115],"new":[26],"variational":[27],"derivation":[28],"the":[30,58,60,63,79,82,92,112,126,131,146,161],"Markov":[32],"measure":[33,67],"field":[34,68],"(QMMF)":[35],"models,":[36],"which":[37],"can":[38],"be":[39],"understood":[40],"as":[41,143,145,170,172],"procedure":[43],"regularizing":[45],"model":[46],"preferences":[47],"(memberships":[48],"or":[49],"likelihoods).":[50],"also":[52],"efficient":[54,105,118],"optimization":[55],"algorithms.":[56],"QMMFs,":[59],"uncertainty":[61],"in":[62,176],"computed":[64],"probability":[66],"is":[69,89,109],"controlled":[70],"penalizing":[72],"Gini's":[73],"coefficient,":[74],"and":[75,100,136,151,153,167],"hence,":[76],"it":[77],"affects":[78],"convexity":[80],"programming":[84],"problem.":[85],"The":[86],"convex":[87],"case":[88],"reduced":[90],"to":[91,160],"solution":[93],"positive":[96],"definite":[97],"linear":[98],"system,":[99],"that":[102],"case,":[103],"an":[104,117,177],"Gauss-Seidel":[106],"(GS)":[107],"scheme":[108],"presented.":[110],"On":[111],"other":[113],"hand,":[114],"projected":[119],"GS":[120],"with":[121,139],"subspace":[122],"optimizing":[125],"nonconvex":[127],"case.":[128],"demonstrate":[130],"proposal":[132],"capabilities":[133],"experiments":[135],"numerical":[137],"comparisons":[138],"interactive":[140,178],"two-class":[141],"segmentation,":[142],"well":[144,171],"simultaneous":[147],"estimation":[148],"(parametric":[152],"nonparametric)":[154],"generative":[155],"models.":[156],"extensions":[159],"original":[162],"formulation":[163],"including":[165],"color":[166],"texture":[168],"clues,":[169],"imprecise":[173],"user":[174],"scribbles":[175],"framework.":[179]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
