{"id":"https://openalex.org/W2146527621","doi":"https://doi.org/10.1111/j.1467-8659.2010.01778.x","title":"M\u00f6bius Transformations For Global Intrinsic Symmetry Analysis","display_name":"M\u00f6bius Transformations For Global Intrinsic Symmetry Analysis","publication_year":2010,"publication_date":"2010-07-01","ids":{"openalex":"https://openalex.org/W2146527621","doi":"https://doi.org/10.1111/j.1467-8659.2010.01778.x","mag":"2146527621"},"language":"en","primary_location":{"id":"doi:10.1111/j.1467-8659.2010.01778.x","is_oa":false,"landing_page_url":"https://doi.org/10.1111/j.1467-8659.2010.01778.x","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","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/A5041004771","display_name":"Vladimir G. Kim","orcid":"https://orcid.org/0000-0002-3996-6588"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vladimir G. Kim","raw_affiliation_strings":["Princeton University","Princeton University#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Princeton University#TAB#","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039995559","display_name":"Yaron Lipman","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yaron Lipman","raw_affiliation_strings":["Princeton University","Princeton University#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Princeton University#TAB#","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048584559","display_name":"Xiaobai Chen","orcid":"https://orcid.org/0000-0003-1166-6927"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaobai Chen","raw_affiliation_strings":["Princeton University","Princeton University#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Princeton University#TAB#","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016776229","display_name":"Thomas Funkhouser","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thomas Funkhouser","raw_affiliation_strings":["Princeton University","Princeton University#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Princeton University#TAB#","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":6.8853,"has_fulltext":false,"cited_by_count":86,"citation_normalized_percentile":{"value":0.97499378,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"29","issue":"5","first_page":"1689","last_page":"1700"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9959999918937683,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9934999942779541,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.774858832359314},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.6535005569458008},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.562872588634491},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5014212131500244},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.49587544798851013},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.47344207763671875},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.46770402789115906},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.4446674585342407},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4102919399738312},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.367536723613739},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3330141305923462},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.24620738625526428},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23997357487678528},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17496836185455322}],"concepts":[{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.774858832359314},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.6535005569458008},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.562872588634491},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5014212131500244},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.49587544798851013},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.47344207763671875},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.46770402789115906},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4446674585342407},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4102919399738312},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.367536723613739},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3330141305923462},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.24620738625526428},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23997357487678528},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17496836185455322},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1111/j.1467-8659.2010.01778.x","is_oa":false,"landing_page_url":"https://doi.org/10.1111/j.1467-8659.2010.01778.x","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1490337999","https://openalex.org/W1534713745","https://openalex.org/W1566328901","https://openalex.org/W1583417382","https://openalex.org/W1590776313","https://openalex.org/W1969076082","https://openalex.org/W1970279742","https://openalex.org/W1974956622","https://openalex.org/W1989191365","https://openalex.org/W1994232247","https://openalex.org/W2010209818","https://openalex.org/W2023507039","https://openalex.org/W2023933031","https://openalex.org/W2024975831","https://openalex.org/W2060206980","https://openalex.org/W2077031952","https://openalex.org/W2100549190","https://openalex.org/W2105106232","https://openalex.org/W2130595631","https://openalex.org/W2148892491","https://openalex.org/W2155957710","https://openalex.org/W2161420750","https://openalex.org/W2168022088","https://openalex.org/W4232014598","https://openalex.org/W4241829961","https://openalex.org/W4301049628","https://openalex.org/W6648999939","https://openalex.org/W6670021685"],"related_works":["https://openalex.org/W1557607869","https://openalex.org/W2366350639","https://openalex.org/W2028455732","https://openalex.org/W4313703117","https://openalex.org/W2087496541","https://openalex.org/W1577721981","https://openalex.org/W1566328901","https://openalex.org/W2392521623","https://openalex.org/W2263923500","https://openalex.org/W2770089535"],"abstract_inverted_index":{"Abstract":[0],"The":[1,125],"goal":[2],"of":[3,16,44,56,68,84,91,99,128,135,148,162,184],"our":[4],"work":[5],"is":[6,26,174],"to":[7,103,176],"develop":[8],"an":[9,77],"algorithm":[10,78,130,173],"for":[11,152,180],"automatic":[12],"and":[13,58,108,144],"robust":[14],"detection":[15],"global":[17],"intrinsic":[18,52,178],"symmetries":[19,53,179],"in":[20,63,138],"3D":[21],"surface":[22,122],"meshes.":[23],"Our":[24],"approach":[25],"based":[27],"on":[28,72],"two":[29],"core":[30],"observations.":[31],"First,":[32],"symmetry":[33],"invariant":[34],"point":[35,142],"sets":[36],"can":[37],"be":[38],"detected":[39],"robustly":[40],"using":[41],"critical":[42,89],"points":[43,86,90,102],"the":[45,64,92,116,121,133,136,145,149,172],"Average":[46],"Geodesic":[47],"Distance":[48],"(AGD)":[49],"function.":[50],"Second,":[51],"are":[54,61],"self\u2010isometries":[55],"surfaces":[57],"as":[59],"such":[60],"contained":[62],"low":[65,146],"dimensional":[66],"group":[67,151],"M\u00f6bius":[69,106,114,150],"transformations.":[70],"Based":[71],"these":[73],"observations,":[74],"we":[75,169],"propose":[76],"that:":[79],"1)":[80],"generates":[81],"a":[82,159,181],"set":[83,161],"symmetric":[85,141,167],"by":[87],"detecting":[88],"AGD":[93,137],"function,":[94],"2)":[95],"enumerates":[96],"small":[97],"subsets":[98],"those":[100,112],"feature":[101],"generate":[104],"candidate":[105,113],"transformations,":[107],"3)":[109],"selects":[110],"among":[111],"transformations":[115],"one(s)":[117],"that":[118,171],"best":[119],"map":[120],"onto":[123],"itself.":[124],"main":[126],"advantages":[127],"this":[129],"stem":[131],"from":[132,190],"stability":[134],"predicting":[139],"potential":[140,154],"features":[143],"dimensionality":[147],"enumerating":[153],"self\u2010mappings.":[155],"During":[156],"experiments":[157],"with":[158,165,187],"benchmark":[160],"meshes":[163],"augmented":[164],"human\u2010specified":[166],"correspondences,":[168],"find":[170,177],"able":[175],"wide":[182],"variety":[183],"object":[185],"types":[186],"moderate":[188],"deviations":[189],"perfect":[191],"symmetry.":[192]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":12}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}