{"id":"https://openalex.org/W1602986186","doi":null,"title":"A useful bound for region merging algorithms in a Bayesian model","display_name":"A useful bound for region merging algorithms in a Bayesian model","publication_year":2003,"publication_date":"2003-02-01","ids":{"openalex":"https://openalex.org/W1602986186","mag":"1602986186"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.13.6936","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.13.6936","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://crpit.com/confpapers/CRPITV16Tao.pdf","raw_type":"text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5051447429","display_name":"Trevor Chi-Yuen Tao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I5681781","display_name":"The University of Adelaide","ror":"https://ror.org/00892tw58","country_code":"AU","type":"education","lineage":["https://openalex.org/I4405259444","https://openalex.org/I5681781"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Trevor Chi-Yuen Tao","raw_affiliation_strings":["Department of Applied Mathematics, University of Adelaide and Intelligence, Surveillance & Reconnaissance Division, Defence Science & Technology Organisation, Edinburg and Centre for Sensor Signal ...#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Adelaide and Intelligence, Surveillance & Reconnaissance Division, Defence Science & Technology Organisation, Edinburg and Centre for Sensor Signal ...#TAB#","institution_ids":["https://openalex.org/I5681781"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057210274","display_name":"David James Crisp","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I5681781","display_name":"The University of Adelaide","ror":"https://ror.org/00892tw58","country_code":"AU","type":"education","lineage":["https://openalex.org/I4405259444","https://openalex.org/I5681781"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"David J. Crisp","raw_affiliation_strings":["Department of Applied Mathematics, University of Adelaide and Intelligence, Surveillance & Reconnaissance Division, Defence Science & Technology Organisation, Edinburg and Centre for Sensor Signal ...#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Adelaide and Intelligence, Surveillance & Reconnaissance Division, Defence Science & Technology Organisation, Edinburg and Centre for Sensor Signal ...#TAB#","institution_ids":["https://openalex.org/I5681781"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I5681781"],"apc_list":null,"apc_paid":null,"fwci":0.6306,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.74778483,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"95","last_page":"100"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9965999722480774,"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":0.9965999722480774,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.0017999999690800905,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/region-merging","display_name":"region merging","score":0.8339999914169312},{"id":"https://openalex.org/keywords/mumford-shah-model","display_name":"Mumford-Shah model","score":0.9190000295639038},{"id":"https://openalex.org/keywords/bayesian-image-segmentation","display_name":"Bayesian image segmentation","score":0.9020000100135803},{"id":"https://openalex.org/keywords/energy-functional-minimization","display_name":"energy functional minimization","score":0.7110000252723694},{"id":"https://openalex.org/keywords/image-segmentation","display_name":"image segmentation","score":0.7429999709129333}],"concepts":[{"id":"https://openalex.org/C140142295","wikidata":"https://www.wikidata.org/wiki/Q617417","display_name":"Isoperimetric inequality","level":2,"score":0.7951072454452515},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6191039085388184},{"id":"https://openalex.org/C89600930","wikidata":"https://www.wikidata.org/wiki/Q1423946","display_name":"Segmentation","level":2,"score":0.5867931842803955},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.573728084564209},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5653231143951416},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5582319498062134},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.5321487784385681},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.512010395526886},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4952303469181061},{"id":"https://openalex.org/C124504099","wikidata":"https://www.wikidata.org/wiki/Q56933","display_name":"Image segmentation","level":3,"score":0.4835779070854187},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.44498398900032043},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3542090058326721},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2988375425338745},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29476481676101685},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13618072867393494},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07460907101631165},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.13.6936","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.13.6936","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://crpit.com/confpapers/CRPITV16Tao.pdf","raw_type":"text"},{"id":"pmh:oai:digital.library.adelaide.edu.au:2440/28981","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/2440/28981","pdf_url":null,"source":{"id":"https://openalex.org/S4306401835","display_name":"Adelaide Research & Scholarship (AR&S) (University of Adelaide)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I5681781","host_organization_name":"The University of Adelaide","host_organization_lineage":["https://openalex.org/I5681781"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference paper"},{"id":"mag:1602986186","doi":null,"is_oa":false,"landing_page_url":"https://crpit.com/confpapers/CRPITV16Tao.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1560055494","https://openalex.org/W1979432452","https://openalex.org/W1998683784","https://openalex.org/W2114487471","https://openalex.org/W2121927366","https://openalex.org/W2156808562","https://openalex.org/W2171909264"],"related_works":["https://openalex.org/W2049692135","https://openalex.org/W6991006195","https://openalex.org/W4391353519","https://openalex.org/W1605834937","https://openalex.org/W2777576817","https://openalex.org/W107244636","https://openalex.org/W1583585034","https://openalex.org/W1511563899","https://openalex.org/W1783292685","https://openalex.org/W2147146843"],"abstract_inverted_index":{"A":[0],"well":[1],"known":[2],"and":[3,40,105],"effective":[4],"approach":[5],"to":[6,79,124,153],"image":[7,22,109],"segmentation":[8,19,122],"is":[9,23,37,77],"based":[10],"on":[11],"the":[12,26,44,55,81,90,93,108,116,120,158],"Mumford-Shah":[13,121],"model,":[14],"where":[15,75],"finding":[16],"an":[17,21,29,59,134],"optimal":[18],"of":[20,28,34,43,64,88,92,107,113,115,138,157],"posed":[24],"as":[25],"minimization":[27],"energy":[30,83],"functional.":[31],"The":[32,146],"simplest":[33],"these":[35],"models":[36],"mathematically":[38],"tractable":[39],"desirable":[41,155],"properties":[42,156],"resulting":[45],"segmentations":[46,74],"have":[47],"been":[48],"rigorously":[49],"established.":[50],"An":[51],"important":[52],"step":[53],"in":[54,142],"proofs":[56],"involves":[57],"establishing":[58],"\"inverse":[60,135],"isoperimetric":[61],"\"":[62],"type":[63,137],"bound.":[65],"In":[66,128],"particular,":[67],"it":[68,76],"can":[69,149],"be":[70,99,151],"shown":[71],"that":[72,133],"for":[73],"impossible":[78],"decrease":[80],"functional":[82],"by":[84,102],"merging":[85],"any":[86],"pair":[87],"regions,":[89],"length":[91],"boundary":[94],"between":[95],"two":[96],"regions":[97],"must":[98],"bounded":[100],"above":[101],"their":[103],"areas":[104],"variation":[106],"itself.":[110],"Recent":[111],"work":[112],"one":[114],"authors":[117],"has":[118],"extended":[119],"model":[123],"a":[125],"Bayeasian":[126],"setting.":[127,145],"this":[129,143],"report":[130],"we":[131],"show":[132],"isoperimetric\"":[136],"bound":[139,148],"also":[140],"exists":[141],"new":[144,147],"likewise":[150],"used":[152],"prove":[154],"corresponding":[159],"segmentations.":[160]},"counts_by_year":[],"updated_date":"2026-09-22T06:50:58.402377","created_date":"2016-06-24T00:00:00"}