{"id":"https://openalex.org/W2031555840","doi":"https://doi.org/10.1142/s0218001405003910","title":"A FIRST ORDER PREDICATE LOGIC FORMULATION OF THE 3D RECONSTRUCTION PROBLEM AND ITS SOLUTION SPACE","display_name":"A FIRST ORDER PREDICATE LOGIC FORMULATION OF THE 3D RECONSTRUCTION PROBLEM AND ITS SOLUTION SPACE","publication_year":2005,"publication_date":"2005-02-01","ids":{"openalex":"https://openalex.org/W2031555840","doi":"https://doi.org/10.1142/s0218001405003910","mag":"2031555840"},"language":"en","primary_location":{"id":"doi:10.1142/s0218001405003910","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218001405003910","pdf_url":null,"source":{"id":"https://openalex.org/S41486457","display_name":"International Journal of Pattern Recognition and Artificial Intelligence","issn_l":"0218-0014","issn":["0218-0014","1793-6381"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Pattern Recognition and Artificial Intelligence","raw_type":"journal-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/A5060072866","display_name":"Martin Robinson","orcid":"https://orcid.org/0000-0002-1572-6782"},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"The University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"MARTIN ROBINSON","raw_affiliation_strings":["Intelligent Real-Time Imaging and Sensing Group, School of ITEE, University of Queensland, QLD 4072, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Intelligent Real-Time Imaging and Sensing Group, School of ITEE, University of Queensland, QLD 4072, Australia","institution_ids":["https://openalex.org/I165143802"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039022842","display_name":"Kurt Kubik","orcid":null},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"The University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"KURT KUBIK","raw_affiliation_strings":["Intelligent Real-Time Imaging and Sensing Group, School of ITEE, University of Queensland, QLD 4072, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Intelligent Real-Time Imaging and Sensing Group, School of ITEE, University of Queensland, QLD 4072, Australia","institution_ids":["https://openalex.org/I165143802"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058539660","display_name":"Brian C. Lovell","orcid":"https://orcid.org/0000-0001-6722-1754"},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"The University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"BRIAN LOVELL","raw_affiliation_strings":["Intelligent Real-Time Imaging and Sensing Group, School of ITEE, University of Queensland, QLD 4072, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Intelligent Real-Time Imaging and Sensing Group, School of ITEE, University of Queensland, QLD 4072, Australia","institution_ids":["https://openalex.org/I165143802"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I165143802"],"apc_list":null,"apc_paid":null,"fwci":0.3438,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.69331873,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"01","first_page":"45","last_page":"62"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10531","display_name":"Advanced Vision and Imaging","score":0.9998999834060669,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9998999834060669,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.9980000257492065,"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/voxel","display_name":"Voxel","score":0.6243237257003784},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5853673815727234},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5605857968330383},{"id":"https://openalex.org/keywords/3d-reconstruction","display_name":"3D reconstruction","score":0.557877779006958},{"id":"https://openalex.org/keywords/pixel","display_name":"Pixel","score":0.5105265378952026},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.48771247267723083},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.484699010848999},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.48164501786231995},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4690796732902527},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.44405925273895264},{"id":"https://openalex.org/keywords/object","display_name":"Object (grammar)","score":0.42607882618904114},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40824705362319946},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3848484754562378}],"concepts":[{"id":"https://openalex.org/C54170458","wikidata":"https://www.wikidata.org/wiki/Q663554","display_name":"Voxel","level":2,"score":0.6243237257003784},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5853673815727234},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5605857968330383},{"id":"https://openalex.org/C109950114","wikidata":"https://www.wikidata.org/wiki/Q4464732","display_name":"3D reconstruction","level":2,"score":0.557877779006958},{"id":"https://openalex.org/C160633673","wikidata":"https://www.wikidata.org/wiki/Q355198","display_name":"Pixel","level":2,"score":0.5105265378952026},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.48771247267723083},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.484699010848999},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48164501786231995},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4690796732902527},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.44405925273895264},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.42607882618904114},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40824705362319946},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3848484754562378},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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":2,"locations":[{"id":"doi:10.1142/s0218001405003910","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218001405003910","pdf_url":null,"source":{"id":"https://openalex.org/S41486457","display_name":"International Journal of Pattern Recognition and Artificial Intelligence","issn_l":"0218-0014","issn":["0218-0014","1793-6381"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Pattern Recognition and Artificial Intelligence","raw_type":"journal-article"},{"id":"pmh:oai:espace.library.uq.edu.au:UQ:77939","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402388","display_name":"Queensland's institutional digital repository (The University of Queensland)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I165143802","host_organization_name":"The University of Queensland","host_organization_lineage":["https://openalex.org/I165143802"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.6800000071525574,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1480061940","https://openalex.org/W1518320452","https://openalex.org/W1604112931","https://openalex.org/W1622297907","https://openalex.org/W1908470451","https://openalex.org/W1987156984","https://openalex.org/W2030496844","https://openalex.org/W2096388650","https://openalex.org/W2097667312","https://openalex.org/W2115820560","https://openalex.org/W2129389525","https://openalex.org/W2142540472","https://openalex.org/W2159242687","https://openalex.org/W2168545424","https://openalex.org/W2169877261","https://openalex.org/W2570617923","https://openalex.org/W4302423224"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W2340777379","https://openalex.org/W4206138983"],"abstract_inverted_index":{"This":[0,88,246],"paper":[1,89,148],"defines":[2],"the":[3,8,47,67,78,81,85,95,128,150,159,190,202,208,223,248,254,268,272,274,283,291],"3D":[4,13,40,96,155],"reconstruction":[5,41,97,156],"problem":[6,29,151],"as":[7],"process":[9],"of":[10,20,59,94,123,152,166,189,206,225,267,271,293],"reconstructing":[11],"a":[12,56,91,100,121,137,179,212,258,285],"scene":[14,203],"from":[15],"numerous":[16,33],"2D":[17],"visual":[18],"images":[19,125,186],"that":[21,27,76,132,139,172,222,265,296],"scene.":[22],"It":[23,169],"is":[24,30,140,170,174,200,227,263],"well":[25],"known":[26],"this":[28,118,145,147],"ill-posed,":[31],"and":[32,35,61,103,157],"constraints":[34,52,63,114,251,295],"assumptions":[36],"are":[37,64,187,217,297],"used":[38],"in":[39,43,55,80,154,201],"algorithms":[42],"order":[44,105],"to":[45,84,177,210,243,252,257,288],"reduce":[46,253],"solution":[48,138,160,255,275],"space.":[49],"Unfortunately,":[50],"most":[51,68,142],"only":[53],"work":[54],"certain":[57],"range":[58],"situations":[60],"often":[62],"built":[65],"into":[66],"fundamental":[69],"methods":[70],"(e.g.":[71],"Area":[72],"Based":[73],"Matching":[74],"assumes":[75],"all":[77,127],"pixels":[79],"window":[82],"belong":[83],"same":[86],"object).":[87],"presents":[90],"novel":[92],"formulation":[93,119,209,284],"problem,":[98],"using":[99,207],"voxel":[101,215,234,239],"framework":[102],"first":[104],"logic":[106],"equations,":[107],"which":[108],"does":[109],"not":[110,175],"contain":[111],"any":[112,294],"additional":[113],"or":[115,194],"assumptions.":[116],"Solving":[117],"for":[120,131,163,230,250],"set":[122],"input":[124,167],"gives":[126,241],"possible":[129,176],"solutions":[130,226],"set,":[133],"rather":[134],"than":[135],"picking":[136],"deemed":[141],"likely.":[143],"Using":[144],"formulation,":[146,273],"studies":[149],"uniqueness":[153],"how":[158,184,196],"space":[161,240,256,276],"changes":[162],"different":[164],"configurations":[165],"images.":[168],"found":[171],"it":[173,262],"guarantee":[178],"unique":[180],"solution,":[181],"no":[182],"matter":[183],"many":[185],"taken":[188],"scene,":[191],"their":[192],"orientation":[193],"even":[195,231],"much":[197],"color":[198],"variation":[199],"itself.":[204],"Results":[205],"reconstruct":[211],"few":[213],"small":[214,233],"spaces":[216,235],"also":[218],"presented.":[219],"They":[220],"show":[221],"number":[224],"extremely":[228],"large":[229],"very":[232],"(5":[236],"\u00d7":[237],"5":[238],"10":[242],"107":[244],"solutions).":[245],"shows":[247],"need":[249],"reasonable":[259],"size.":[260],"Finally,":[261],"noted":[264],"because":[266],"discrete":[269],"nature":[270],"size":[277],"can":[278],"be":[279],"easily":[280],"calculated,":[281],"making":[282],"useful":[286],"tool":[287],"numerically":[289],"evaluate":[290],"usefulness":[292],"added.":[298]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}