{"id":"https://openalex.org/W2139225412","doi":"https://doi.org/10.1109/tpami.2004.1262338","title":"Strong markov random field model","display_name":"Strong markov random field model","publication_year":2004,"publication_date":"2004-02-24","ids":{"openalex":"https://openalex.org/W2139225412","doi":"https://doi.org/10.1109/tpami.2004.1262338","mag":"2139225412","pmid":"https://pubmed.ncbi.nlm.nih.gov/15376887"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2004.1262338","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2004.1262338","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","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/A5085220973","display_name":"R. Paget","orcid":null},"institutions":[{"id":"https://openalex.org/I237525767","display_name":"Zurich Insurance Group (Switzerland)","ror":"https://ror.org/03cw8qd03","country_code":"CH","type":"company","lineage":["https://openalex.org/I237525767"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"R. Paget","raw_affiliation_strings":["Computer Vision Group, Gloriastrasse 35, ETH-Zentrum, CH-8092 Zurich, Switzerland. rpaget@vision.ee.ethz.ch","Comput. Vision Group, Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Computer Vision Group, Gloriastrasse 35, ETH-Zentrum, CH-8092 Zurich, Switzerland. rpaget@vision.ee.ethz.ch","institution_ids":[]},{"raw_affiliation_string":"Comput. Vision Group, Zurich, Switzerland","institution_ids":["https://openalex.org/I237525767"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5085220973"],"corresponding_institution_ids":["https://openalex.org/I237525767"],"apc_list":null,"apc_paid":null,"fwci":2.2432,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.89544824,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"26","issue":"3","first_page":"408","last_page":"413"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9832000136375427,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.7402973771095276},{"id":"https://openalex.org/keywords/markov-random-field","display_name":"Markov random field","score":0.6897549629211426},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6324659585952759},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5814753174781799},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5793757438659668},{"id":"https://openalex.org/keywords/random-field","display_name":"Random field","score":0.5711873769760132},{"id":"https://openalex.org/keywords/variable-order-markov-model","display_name":"Variable-order Markov model","score":0.4883801341056824},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.48264604806900024},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4226980209350586},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.4176764488220215},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3988170623779297},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3305862247943878},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3081079125404358},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.27308493852615356},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2601349949836731},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21262437105178833},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09230712056159973}],"concepts":[{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.7402973771095276},{"id":"https://openalex.org/C2778045648","wikidata":"https://www.wikidata.org/wiki/Q176827","display_name":"Markov random field","level":4,"score":0.6897549629211426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6324659585952759},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5814753174781799},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5793757438659668},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.5711873769760132},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.4883801341056824},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.48264604806900024},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4226980209350586},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4176764488220215},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3988170623779297},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3305862247943878},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3081079125404358},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27308493852615356},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2601349949836731},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21262437105178833},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09230712056159973},{"id":"https://openalex.org/C124504099","wikidata":"https://www.wikidata.org/wiki/Q56933","display_name":"Image segmentation","level":3,"score":0.0},{"id":"https://openalex.org/C89600930","wikidata":"https://www.wikidata.org/wiki/Q1423946","display_name":"Segmentation","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003196","descriptor_name":"Computer Graphics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003196","descriptor_name":"Computer Graphics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003196","descriptor_name":"Computer Graphics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D008390","descriptor_name":"Markov Chains","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008390","descriptor_name":"Markov Chains","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008390","descriptor_name":"Markov Chains","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009716","descriptor_name":"Numerical Analysis, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D009716","descriptor_name":"Numerical Analysis, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D009716","descriptor_name":"Numerical Analysis, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D013382","descriptor_name":"Subtraction Technique","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013382","descriptor_name":"Subtraction Technique","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013382","descriptor_name":"Subtraction Technique","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016247","descriptor_name":"Information Storage and Retrieval","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D016247","descriptor_name":"Information Storage and Retrieval","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D016247","descriptor_name":"Information Storage and Retrieval","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false}],"locations_count":6,"locations":[{"id":"doi:10.1109/tpami.2004.1262338","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2004.1262338","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:15376887","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/15376887","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 pattern analysis and machine intelligence","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.19.2154","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.19.2154","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.vision.ee.ethz.ch/~rpaget/papers/strong_mrf.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.20.4211","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.20.4211","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.vision.ee.ethz.ch/~rpaget/papers/Paget_PAMI_2002.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.5.8080","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.5.8080","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.vision.ee.ethz.ch/~rpaget/papers/Paget_PAMI_2004.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.69.5524","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.69.5524","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.texturesynthesis.com/papers/Paget_PAMI_2004.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6600000262260437,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W23603788","https://openalex.org/W107938046","https://openalex.org/W1502772503","https://openalex.org/W1518016839","https://openalex.org/W1533179050","https://openalex.org/W1554544485","https://openalex.org/W1604521381","https://openalex.org/W1972212960","https://openalex.org/W1978238148","https://openalex.org/W1993472818","https://openalex.org/W1994464771","https://openalex.org/W2020999234","https://openalex.org/W2022118638","https://openalex.org/W2029668118","https://openalex.org/W2040661328","https://openalex.org/W2041808839","https://openalex.org/W2045370718","https://openalex.org/W2053914723","https://openalex.org/W2068623560","https://openalex.org/W2074673068","https://openalex.org/W2081985429","https://openalex.org/W2084134149","https://openalex.org/W2099835437","https://openalex.org/W2101614294","https://openalex.org/W2107495274","https://openalex.org/W2108637230","https://openalex.org/W2113751297","https://openalex.org/W2114220616","https://openalex.org/W2115361143","https://openalex.org/W2116013899","https://openalex.org/W2126002540","https://openalex.org/W2135157209","https://openalex.org/W2138243517","https://openalex.org/W2170120409","https://openalex.org/W2232702494","https://openalex.org/W2316114989","https://openalex.org/W2422766945","https://openalex.org/W2801464996","https://openalex.org/W2994982620","https://openalex.org/W3017143921","https://openalex.org/W4233254181","https://openalex.org/W4239783220","https://openalex.org/W4294910234","https://openalex.org/W6631087165","https://openalex.org/W6675482652"],"related_works":["https://openalex.org/W2130519334","https://openalex.org/W2030382593","https://openalex.org/W1983122994","https://openalex.org/W2078379274","https://openalex.org/W2033503400","https://openalex.org/W2118728396","https://openalex.org/W1985664346","https://openalex.org/W987019958","https://openalex.org/W4233015508","https://openalex.org/W2099971354"],"abstract_inverted_index":{"The":[0,16],"strong":[1,47,52],"Markov":[2],"random":[3],"field":[4,23],"(strong-MRF)":[5],"model":[6,18,81],"is":[7,24,41,74,113],"a":[8,20,29,42,46,56,92],"submodel":[9],"of":[10,45],"the":[11,51,61,75,79,89,96,107],"more":[12,57],"general":[13,108],"MRF-Gibbs":[14],"model.":[15],"strong-MRF":[17,80],"defines":[19],"system":[21,54],"whose":[22],"Markovian":[25,48,53],"with":[26,82],"respect":[27,83],"to":[28,77,84,95],"defined":[30],"neighborhood,":[31],"and":[32],"all":[33],"subneighborhoods":[34],"are":[35],"also":[36],"Markovian.":[37],"A":[38],"checkerboard":[39],"pattern":[40],"perfect":[43],"example":[44],"system.":[49],"Although":[50],"requires":[55],"stringent":[58],"assumption":[59],"about":[60],"field,":[62],"it":[63],"does":[64],"have":[65],"some":[66],"very":[67],"nice":[68],"mathematical":[69,72],"properties.":[70],"One":[71],"property":[73],"ability":[76],"define":[78],"its":[85],"marginal":[86],"distributions":[87],"over":[88],"cliques.":[90],"Also,":[91],"direct":[93],"equivalence":[94],"Analysis-of-Variance":[97],"(ANOVA)":[98],"log-linear":[99,110],"construction":[100,111],"can":[101],"be":[102],"proven.":[103],"From":[104],"this":[105],"proof,":[106],"ANOVA":[109],"formula":[112],"acquired.":[114]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
