{"id":"https://openalex.org/W4304480792","doi":"https://doi.org/10.1109/tpami.2022.3212595","title":"Revisiting Viewing Graph Solvability: An Effective Approach Based on Cycle Consistency","display_name":"Revisiting Viewing Graph Solvability: An Effective Approach Based on Cycle Consistency","publication_year":2022,"publication_date":"2022-10-10","ids":{"openalex":"https://openalex.org/W4304480792","doi":"https://doi.org/10.1109/tpami.2022.3212595","pmid":"https://pubmed.ncbi.nlm.nih.gov/36215371"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2022.3212595","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tpami.2022.3212595","pdf_url":"https://ieeexplore.ieee.org/ielx7/34/4359286/09913729.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://ieeexplore.ieee.org/ielx7/34/4359286/09913729.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049940550","display_name":"Federica Arrigoni","orcid":"https://orcid.org/0000-0003-0331-4032"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Federica Arrigoni","raw_affiliation_strings":["Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano, Milano, Italy","Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano, Italy"],"raw_orcid":"https://orcid.org/0000-0003-0331-4032","affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066624955","display_name":"Andrea Fusiello","orcid":"https://orcid.org/0000-0003-2963-0316"},"institutions":[{"id":"https://openalex.org/I129043915","display_name":"University of Udine","ror":"https://ror.org/05ht0mh31","country_code":"IT","type":"education","lineage":["https://openalex.org/I129043915"]},{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andrea Fusiello","raw_affiliation_strings":["Polytechnic Department of Engineering and Architecture (DPIA), University of Udine, Udine, Italy","Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano, Italy"],"raw_orcid":"https://orcid.org/0000-0003-2963-0316","affiliations":[{"raw_affiliation_string":"Polytechnic Department of Engineering and Architecture (DPIA), University of Udine, Udine, Italy","institution_ids":["https://openalex.org/I129043915"]},{"raw_affiliation_string":"Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061874157","display_name":"Rom\u00e9o Rizzi","orcid":"https://orcid.org/0000-0002-2387-0952"},"institutions":[{"id":"https://openalex.org/I119439378","display_name":"University of Verona","ror":"https://ror.org/039bp8j42","country_code":"IT","type":"education","lineage":["https://openalex.org/I119439378"]},{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Romeo Rizzi","raw_affiliation_strings":["Department of Computer Science, University of Verona, Verona, Italy","Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano, Italy"],"raw_orcid":"https://orcid.org/0000-0002-2387-0952","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Verona, Verona, Italy","institution_ids":["https://openalex.org/I119439378"]},{"raw_affiliation_string":"Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065059558","display_name":"Elisa Ricci","orcid":"https://orcid.org/0000-0002-0228-1147"},"institutions":[{"id":"https://openalex.org/I193223587","display_name":"University of Trento","ror":"https://ror.org/05trd4x28","country_code":"IT","type":"education","lineage":["https://openalex.org/I193223587"]},{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Elisa Ricci","raw_affiliation_strings":["Department of Information Engineering and Computer Science (DISI), University of Trento, Trento, Italy","Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano, Italy"],"raw_orcid":"https://orcid.org/0000-0002-0228-1147","affiliations":[{"raw_affiliation_string":"Department of Information Engineering and Computer Science (DISI), University of Trento, Trento, Italy","institution_ids":["https://openalex.org/I193223587"]},{"raw_affiliation_string":"Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043222506","display_name":"Tom\u00e1\u0161 Pajdla","orcid":"https://orcid.org/0000-0001-6325-0072"},"institutions":[{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]},{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["CZ","IT"],"is_corresponding":false,"raw_author_name":"Tomas Pajdla","raw_affiliation_strings":["Czech Institute of Informatics, Robotics and Cybernetics (CIIRC), Czech Technical University in Prague, Prague, Czech Republic","Czech Institute of Informatics, Robotics and Cybernetics (CIIRC), Czech Technical University in Prague, Czech Republic","Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano, Italy"],"raw_orcid":"https://orcid.org/0000-0001-6325-0072","affiliations":[{"raw_affiliation_string":"Czech Institute of Informatics, Robotics and Cybernetics (CIIRC), Czech Technical University in Prague, Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]},{"raw_affiliation_string":"Czech Institute of Informatics, Robotics and Cybernetics (CIIRC), Czech Technical University in Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]},{"raw_affiliation_string":"Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5692,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.63339993,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"47","issue":"5","first_page":"3271","last_page":"3284"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10531","display_name":"Advanced Vision and Imaging","score":0.9955000281333923,"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":0.9955000281333923,"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/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.9927999973297119,"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/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/mathematics","display_name":"Mathematics","score":0.5801861882209778},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5182790160179138},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.44247016310691833},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.42355233430862427},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.41759803891181946},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37505555152893066},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36715197563171387},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36334484815597534}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5801861882209778},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5182790160179138},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.44247016310691833},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.42355233430862427},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.41759803891181946},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37505555152893066},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36715197563171387},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36334484815597534},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tpami.2022.3212595","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tpami.2022.3212595","pdf_url":"https://ieeexplore.ieee.org/ielx7/34/4359286/09913729.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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:36215371","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36215371","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:air.uniud.it:11390/1236145","is_oa":true,"landing_page_url":"https://hdl.handle.net/11390/1236145","pdf_url":null,"source":{"id":"https://openalex.org/S4306401163","display_name":"Institutional Research Information System (University of Udine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I129043915","host_organization_name":"University of Udine","host_organization_lineage":["https://openalex.org/I129043915"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:re.public.polimi.it:11311/1223975","is_oa":true,"landing_page_url":"https://hdl.handle.net/11311/1223975","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1109/tpami.2022.3212595","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tpami.2022.3212595","pdf_url":"https://ieeexplore.ieee.org/ielx7/34/4359286/09913729.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G291036901","display_name":null,"funder_award_id":"CZ.02","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G3490171961","display_name":null,"funder_award_id":"CZ.02.1.01","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G3622461675","display_name":null,"funder_award_id":"CZ.02.1.01","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G434337789","display_name":null,"funder_award_id":"HORIZON2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8258793481","display_name":"Socially Pertinent Robots in Gerontological Healthcare","funder_award_id":"871245","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4304480792.pdf","grobid_xml":"https://content.openalex.org/works/W4304480792.grobid-xml"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W607586325","https://openalex.org/W1511510478","https://openalex.org/W1524190946","https://openalex.org/W1551235990","https://openalex.org/W1602894818","https://openalex.org/W1823013803","https://openalex.org/W1900151113","https://openalex.org/W1901341728","https://openalex.org/W1958116060","https://openalex.org/W1976011992","https://openalex.org/W2013472030","https://openalex.org/W2017483928","https://openalex.org/W2025304499","https://openalex.org/W2033819227","https://openalex.org/W2061715373","https://openalex.org/W2081681998","https://openalex.org/W2112634643","https://openalex.org/W2119467698","https://openalex.org/W2123691039","https://openalex.org/W2129201358","https://openalex.org/W2136777038","https://openalex.org/W2143703915","https://openalex.org/W2155094592","https://openalex.org/W2156598602","https://openalex.org/W2197209490","https://openalex.org/W2471962767","https://openalex.org/W2522940611","https://openalex.org/W2592782547","https://openalex.org/W2808879566","https://openalex.org/W2963210849","https://openalex.org/W2963221299","https://openalex.org/W2963247163","https://openalex.org/W2964001621","https://openalex.org/W2978166726","https://openalex.org/W2991052179","https://openalex.org/W3035536052","https://openalex.org/W4214528542","https://openalex.org/W4243047861","https://openalex.org/W4243425824","https://openalex.org/W4289549000","https://openalex.org/W4299482635","https://openalex.org/W4300076833","https://openalex.org/W4385482704","https://openalex.org/W4387928059","https://openalex.org/W6632992769","https://openalex.org/W6754984195","https://openalex.org/W6771004125"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1603736412","https://openalex.org/W4304185162","https://openalex.org/W2061685118","https://openalex.org/W3006282800","https://openalex.org/W2462100143","https://openalex.org/W1770503332","https://openalex.org/W3125207769","https://openalex.org/W2577825108","https://openalex.org/W2142539551"],"abstract_inverted_index":{"In":[0],"the":[1,5,12,20,23,59,97,107,114,126,160,163],"structure":[2],"from":[3],"motion,":[4],"viewing":[6,38,63],"graph":[7,10,39],"is":[8,40,92,151],"a":[9,28,37,45,75,81,93],"where":[11],"vertices":[13],"correspond":[14],"to":[15,69,95,121,131,136,154],"cameras":[16],"(or":[17],"images)":[18],"and":[19,31,156],"edges":[21],"represent":[22],"fundamental":[24],"matrices.":[25],"We":[26,105],"provide":[27],"new":[29],"formulation":[30],"an":[32,142,172],"algorithm":[33],"for":[34],"determining":[35],"whether":[36],"solvable,":[41],"i.e.,":[42],"uniquely":[43],"determines":[44],"set":[46],"of":[47,61,77,84,89,99,109,116,129],"projective":[48],"cameras.":[49],"The":[50,86],"known":[51],"theoretical":[52],"conditions":[53],"either":[54],"do":[55],"not":[56,152],"fully":[57],"characterize":[58],"solvability":[60,110,130,150],"all":[62,117],"graphs,":[64],"or":[65],"are":[66],"extremely":[67],"difficult":[68],"compute":[70],"because":[71],"they":[72],"involve":[73],"solving":[74],"system":[76],"polynomial":[78],"equations":[79],"with":[80,134,162],"large":[82],"number":[83,98],"unknowns.":[85],"main":[87],"result":[88],"this":[90],"paper":[91],"method":[94],"reduce":[96],"unknowns":[100],"by":[101,111,146],"exploiting":[102],"cycle":[103],"consistency.":[104],"advance":[106],"understanding":[108],"(i)":[112],"finishing":[113],"classification":[115],"minimal":[118,132],"graphs":[119,133,181],"up":[120,135],"9":[122],"nodes,":[123,138],"(ii)":[124],"extending":[125],"practical":[127],"verification":[128],"90":[137],"(iii)":[139],"finally":[140],"answering":[141],"open":[143],"research":[144],"question":[145],"showing":[147],"that":[148,177,179],"finite":[149],"equivalent":[153],"solvability,":[155],"(iv)":[157],"formally":[158],"drawing":[159],"connection":[161],"calibrated":[164],"case":[165],"(i.e.,":[166],"parallel":[167],"rigidity).":[168],"Finally,":[169],"we":[170],"present":[171],"experiment":[173],"on":[174],"real":[175],"data":[176],"shows":[178],"unsolvable":[180],"may":[182],"appear":[183],"in":[184],"practice.":[185]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5}],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2025-10-10T00:00:00"}