{"id":"https://openalex.org/W7027369900","doi":null,"title":"Continuous Procrustes Distance Between Two Surfaces","display_name":"Continuous Procrustes Distance Between Two Surfaces","publication_year":2016,"publication_date":"2016-08-16","ids":{"openalex":"https://openalex.org/W7027369900"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.755.1250","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.755.1250","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1106.4588.pdf","raw_type":"text"},"volume":null,"type":"preprint","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/A5039995559","display_name":"Yaron Lipman","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yaron Lipman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089474809","display_name":"Reema Al\u2010Aifari","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Reema Al-aifari","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5152637440","display_name":"Ingrid Daubechies","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ingrid Daubechies","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.32589998841285706,"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"}},"topics":[{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.32589998841285706,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.23880000412464142,"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"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.1477999985218048,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/shape-similarity","display_name":"shape similarity","score":0.7289999723434448},{"id":"https://openalex.org/keywords/two-dimensional-surfaces","display_name":"two-dimensional surfaces","score":0.6740000247955322},{"id":"https://openalex.org/keywords/area-preserving-diffeomorphisms","display_name":"area-preserving diffeomorphisms","score":0.9290000200271606},{"id":"https://openalex.org/keywords/conformal-mapping","display_name":"conformal mapping","score":0.9679999947547913},{"id":"https://openalex.org/keywords/landmark-based-shape-analysis","display_name":"landmark-based shape analysis","score":0.6460000276565552}],"concepts":[{"id":"https://openalex.org/C2778585274","wikidata":"https://www.wikidata.org/wiki/Q2845240","display_name":"Procrustes analysis","level":2,"score":0.9079999923706055},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7832000255584717},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6040999889373779},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.5580999851226807},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.49570000171661377},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.474700003862381},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.44909998774528503},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4058000147342682},{"id":"https://openalex.org/C5349765","wikidata":"https://www.wikidata.org/wiki/Q5282866","display_name":"Distance matrices in phylogeny","level":2,"score":0.3709999918937683},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3375999927520752},{"id":"https://openalex.org/C73621898","wikidata":"https://www.wikidata.org/wiki/Q2940504","display_name":"Distance transform","level":3,"score":0.3246000111103058},{"id":"https://openalex.org/C2639959","wikidata":"https://www.wikidata.org/wiki/Q1344778","display_name":"Distance measures","level":2,"score":0.31450000405311584},{"id":"https://openalex.org/C112604564","wikidata":"https://www.wikidata.org/wiki/Q7489226","display_name":"Shape analysis (program analysis)","level":3,"score":0.3021000027656555},{"id":"https://openalex.org/C29513896","wikidata":"https://www.wikidata.org/wiki/Q7489239","display_name":"Shape optimization","level":3,"score":0.30070000886917114},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2962000072002411},{"id":"https://openalex.org/C143271835","wikidata":"https://www.wikidata.org/wiki/Q254515","display_name":"Similitude","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26159998774528503}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.755.1250","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.755.1250","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1106.4588.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W16862691","https://openalex.org/W123452051","https://openalex.org/W1482513167","https://openalex.org/W1503893179","https://openalex.org/W1555017801","https://openalex.org/W1561974326","https://openalex.org/W1785505593","https://openalex.org/W1985222241","https://openalex.org/W1993747418","https://openalex.org/W1995980194","https://openalex.org/W1998438584","https://openalex.org/W1998563636","https://openalex.org/W2049981393","https://openalex.org/W2082582926","https://openalex.org/W2098578926","https://openalex.org/W2100607348","https://openalex.org/W2104845659","https://openalex.org/W2105106232","https://openalex.org/W2106025841","https://openalex.org/W2115245436","https://openalex.org/W2119851068","https://openalex.org/W2137674306","https://openalex.org/W2162155934","https://openalex.org/W2165053603","https://openalex.org/W2168022088","https://openalex.org/W2171944046","https://openalex.org/W2563408008","https://openalex.org/W2963350927","https://openalex.org/W4295632409"],"related_works":["https://openalex.org/W2950308434","https://openalex.org/W4229993135","https://openalex.org/W2285077570","https://openalex.org/W2070303252","https://openalex.org/W2905131155","https://openalex.org/W1589349242","https://openalex.org/W181609022","https://openalex.org/W2049610675","https://openalex.org/W4407393859","https://openalex.org/W6929617560"],"abstract_inverted_index":{"Abstract.":[0],"The":[1,149],"Procrustes":[2,46,80,132,151,178,185],"distance":[3,47,81,152,186],"is":[4,25,48,61,82,173],"used":[5,17],"to":[6,32,37,84,103,154,198,202,205],"quantify":[7],"the":[8,45,59,67,106,128,160,167,180,184],"similarity":[9],"or":[10],"dissimilarity":[11],"of":[12,98,109,130,162,166,170,183],"(3-dimensional)":[13],"shapes,":[14],"and":[15,44,66,134],"extensively":[16],"in":[18,74,125,146],"biological":[19],"morphometrics.":[20],"Typically":[21],"each":[22,38],"(normalized)":[23],"shape":[24,92],"represented":[26],"by":[27,93,191],"N":[28],"landmark":[29],"points,":[30,99],"chosen":[31],"be":[33,188],"homologous":[34],"(i.e.":[35],"corresponding":[36],"other),":[39],"as":[40,42,51],"much":[41],"possible,":[43],"then":[49],"computed":[50],"infR":[52],"\u2211N":[53],"j=1":[54],"\u2016Rxj":[55],"\u2212":[56],"x\u2032j\u20162,":[57],"where":[58],"minimization":[60],"over":[62,159],"all":[63,105],"Euclidean":[64],"transformations,":[65],"correspondences":[68],"xj":[69],"\u2194":[70],"x\u2032j":[71],"are":[72,119],"picked":[73],"an":[75,199],"optimal":[76],"way.":[77],"This":[78,195],"(discrete)":[79],"easy":[83],"compute":[85],"but":[86],"has":[87,113],"drawbacks":[88],"\u2013":[89],"representeding":[90],"a":[91,95,111,139,155,192],"only":[94],"finite":[96],"number":[97],"which":[100],"may":[101],"fail":[102],"capture":[104],"geometric":[107],"aspects":[108],"interest;":[110],"need":[112],"been":[114],"expressed":[115],"for":[116,142,175],"alternatives":[117],"that":[118,136,174],"still":[120],"computationally":[121],"tractable.":[122],"We":[123],"propose":[124],"this":[126,206],"paper":[127,172],"concept":[129],"continuous":[131,150,177],"distance,":[133],"prove":[135],"it":[137],"provides":[138],"true":[140],"metric":[141],"two-dimensional":[143],"surfaces":[144],"embedded":[145],"three":[147],"dimensions.":[148],"leads":[153,197],"hard":[156],"optimization":[157],"problem":[158],"group":[161],"area-preserving":[163],"diffeomorphisms.":[164],"One":[165],"core":[168],"observations":[169],"our":[171],"small":[176],"distances,":[179],"global":[181],"optimum":[182],"can":[187],"uniformly":[189],"approximated":[190],"conformal":[193],"map.":[194],"observation":[196],"efficient":[200],"algorithm":[201],"calculate":[203],"approximations":[204],"new":[207],"distance.":[208],"1.":[209]},"counts_by_year":[{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2025-10-27T00:00:00"}