{"id":"https://openalex.org/W2964222388","doi":"https://doi.org/10.1109/tpami.2019.2930051","title":"Rotation Averaging with the Chordal Distance: Global Minimizers and Strong Duality","display_name":"Rotation Averaging with the Chordal Distance: Global Minimizers and Strong Duality","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2964222388","doi":"https://doi.org/10.1109/tpami.2019.2930051","mag":"2964222388","pmid":"https://pubmed.ncbi.nlm.nih.gov/31352332"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2019.2930051","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2019.2930051","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/A5069883194","display_name":"Anders Eriksson","orcid":"https://orcid.org/0000-0003-2652-7110"},"institutions":[{"id":"https://openalex.org/I160993911","display_name":"Queensland University of Technology","ror":"https://ror.org/03pnv4752","country_code":"AU","type":"education","lineage":["https://openalex.org/I160993911"]},{"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":"Anders Eriksson","raw_affiliation_strings":["School of Information Technology and Electrical Engineering, University of Queensland, Brisbane, QLD, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Technology and Electrical Engineering, University of Queensland, Brisbane, QLD, Australia","institution_ids":["https://openalex.org/I160993911","https://openalex.org/I165143802"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101505222","display_name":"Carl Olsson","orcid":"https://orcid.org/0000-0003-3545-7695"},"institutions":[{"id":"https://openalex.org/I187531555","display_name":"Lund University","ror":"https://ror.org/012a77v79","country_code":"SE","type":"education","lineage":["https://openalex.org/I187531555"]},{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Carl Olsson","raw_affiliation_strings":["Chalmers University of Technology, Gothenburg, Sweden","Lund University, Lund, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chalmers University of Technology, Gothenburg, Sweden","institution_ids":["https://openalex.org/I66862912"]},{"raw_affiliation_string":"Lund University, Lund, Sweden","institution_ids":["https://openalex.org/I187531555"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112556001","display_name":"Fredrik Kahl","orcid":null},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Fredrik Kahl","raw_affiliation_strings":["Chalmers University of Technology, Gothenburg, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chalmers University of Technology, Gothenburg, Sweden","institution_ids":["https://openalex.org/I66862912"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027317977","display_name":"Tat-Jun Chin","orcid":"https://orcid.org/0000-0003-2423-9342"},"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/I5681781"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Tat-Jun Chin","raw_affiliation_strings":["School of Computer Science, The University of Adelaide, Adelaide, SA, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, The University of Adelaide, Adelaide, SA, Australia","institution_ids":["https://openalex.org/I5681781"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0843,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.90062425,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"43","issue":"1","first_page":"1","last_page":"1"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10531","display_name":"Advanced Vision and Imaging","score":0.992900013923645,"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":0.992900013923645,"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/T10534","display_name":"Structural Health Monitoring Techniques","score":0.9835000038146973,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9803000092506409,"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/parallelizable-manifold","display_name":"Parallelizable manifold","score":0.6230644583702087},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.571407675743103},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.551693320274353},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.54514479637146},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.5338180065155029},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4935418367385864},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46435263752937317},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.44796162843704224},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4386461675167084},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38234955072402954},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.29920896887779236},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.1509838104248047},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11691007018089294}],"concepts":[{"id":"https://openalex.org/C148047603","wikidata":"https://www.wikidata.org/wiki/Q1014612","display_name":"Parallelizable manifold","level":2,"score":0.6230644583702087},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.571407675743103},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.551693320274353},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.54514479637146},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.5338180065155029},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4935418367385864},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46435263752937317},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.44796162843704224},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4386461675167084},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38234955072402954},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.29920896887779236},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.1509838104248047},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11691007018089294}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tpami.2019.2930051","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2019.2930051","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:31352332","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/31352332","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:digital.library.adelaide.edu.au:2440/133077","is_oa":false,"landing_page_url":"https://hdl.handle.net/2440/133077","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,"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":"http://dx.doi.org/10.1109/tpami.2019.2930051","raw_type":"Journal article"},{"id":"pmh:oai:research.chalmers.se:519774","is_oa":false,"landing_page_url":"https://research.chalmers.se/en/publication/519774","pdf_url":null,"source":{"id":"https://openalex.org/S4306402469","display_name":"Chalmers Research (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"pmh:oai:research.chalmers.se:521549","is_oa":false,"landing_page_url":"https://research.chalmers.se/en/publication/fbc042f6-900a-4c86-a785-72ddab6c2775","pdf_url":null,"source":{"id":"https://openalex.org/S4306402469","display_name":"Chalmers Research (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/17","display_name":"Partnerships for the goals","score":0.4300000071525574}],"awards":[{"id":"https://openalex.org/G1411116544","display_name":null,"funder_award_id":"no. 2017-01942","funder_id":"https://openalex.org/F4320321030","funder_display_name":"VINNOVA"},{"id":"https://openalex.org/G3192416481","display_name":null,"funder_award_id":"Perceptron, no. 2017-01942","funder_id":"https://openalex.org/F4320321030","funder_display_name":"VINNOVA"},{"id":"https://openalex.org/G7744349448","display_name":"The role of strong duality in computer vision","funder_award_id":"FT170100072","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320321030","display_name":"VINNOVA","ror":"https://ror.org/01kd5m353"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W608582638","https://openalex.org/W1501520364","https://openalex.org/W1536617987","https://openalex.org/W1554704324","https://openalex.org/W1587744656","https://openalex.org/W1812613173","https://openalex.org/W1967073510","https://openalex.org/W1981745143","https://openalex.org/W1993228150","https://openalex.org/W2007806707","https://openalex.org/W2011479004","https://openalex.org/W2042965115","https://openalex.org/W2043995994","https://openalex.org/W2044739225","https://openalex.org/W2071616405","https://openalex.org/W2072062192","https://openalex.org/W2084613528","https://openalex.org/W2105413810","https://openalex.org/W2107156416","https://openalex.org/W2151870994","https://openalex.org/W2153405862","https://openalex.org/W2171244244","https://openalex.org/W2200568569","https://openalex.org/W2296319761","https://openalex.org/W2408654640","https://openalex.org/W2520592772","https://openalex.org/W2547811925","https://openalex.org/W2567544418","https://openalex.org/W2598300585","https://openalex.org/W2798791152","https://openalex.org/W3029645440","https://openalex.org/W4248598408","https://openalex.org/W4250589301","https://openalex.org/W4285719527","https://openalex.org/W4293775970","https://openalex.org/W4297964008","https://openalex.org/W6618429421","https://openalex.org/W6638295633","https://openalex.org/W6676375303","https://openalex.org/W6687743519","https://openalex.org/W6729209368","https://openalex.org/W6734994037"],"related_works":["https://openalex.org/W4220928172","https://openalex.org/W2725387418","https://openalex.org/W2201555914","https://openalex.org/W2593555778","https://openalex.org/W2614523486","https://openalex.org/W2080941243","https://openalex.org/W2136200239","https://openalex.org/W2056178476","https://openalex.org/W3213165575","https://openalex.org/W1687657632"],"abstract_inverted_index":{"In":[0,25],"this":[1,45,59],"paper":[2],"we":[3,88],"explore":[4],"the":[5,11,62,101,154],"role":[6],"of":[7,13,23,64,117,176,179],"duality":[8,98],"principles":[9],"within":[10],"problem":[12,46,156],"rotation":[14,29,38],"averaging,":[15],"a":[16,20,34,80,115,138,174],"fundamental":[17],"task":[18],"in":[19,92,121,160],"wide":[21],"range":[22],"applications.":[24],"its":[26],"conventional":[27],"form,":[28],"averaging":[30],"is":[31,47,71,74,96,150,167],"stated":[32],"as":[33],"minimization":[35],"over":[36],"multiple":[37],"constraints.":[39],"As":[40],"these":[41],"constraints":[42],"are":[43,104,171],"non-convex,":[44],"generally":[48],"considered":[49],"challenging":[50],"to":[51,57,78,109,114,144,152],"solve":[52],"globally.":[53],"We":[54,124],"show":[55],"how":[56],"circumvent":[58],"difficulty":[60],"through":[61],"use":[63],"Lagrangian":[65],"duality.":[66],"While":[67],"such":[68],"an":[69,127],"approach":[70,149],"well-known":[72],"it":[73,166],"normally":[75],"not":[76],"guaranteed":[77],"provide":[79],"tight":[81],"relaxation.":[82],"Based":[83],"on":[84],"spectral":[85],"graph":[86],"theory,":[87],"analytically":[89],"prove":[90],"that":[91,131],"many":[93],"cases":[94],"there":[95],"no":[97],"gap":[99],"unless":[100],"noise":[102],"levels":[103],"severe.":[105],"This":[106],"allows":[107],"us":[108],"obtain":[110],"certifiably":[111],"global":[112],"solutions":[113],"class":[116],"important":[118],"non-convex":[119],"problems":[120],"polynomial":[122],"time.":[123],"also":[125],"propose":[126],"efficient,":[128],"scalable":[129],"algorithm":[130],"outperforms":[132],"general":[133],"purpose":[134],"numerical":[135],"solvers":[136],"by":[137],"large":[139,155],"margin":[140],"and":[141,165,182],"compares":[142],"favourably":[143],"current":[145],"state-of-the-art.":[146],"Further,":[147],"our":[148],"able":[151],"handle":[153],"instances":[157,178],"commonly":[158],"occurring":[159],"structure":[161],"from":[162],"motion":[163],"settings":[164],"trivially":[168],"parallelizable.":[169],"Experiments":[170],"presented":[172],"for":[173],"number":[175],"different":[177],"both":[180],"synthetic":[181],"real-world":[183],"data.":[184]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}