{"id":"https://openalex.org/W4205152234","doi":"https://doi.org/10.1109/tro.2021.3128328","title":"Approximating Displacements in ${\\mathbb {R}}^3$ by Rotations in ${\\mathbb {R}}^4$ and Its Application to Pointcloud Registration","display_name":"Approximating Displacements in ${\\mathbb {R}}^3$ by Rotations in ${\\mathbb {R}}^4$ and Its Application to Pointcloud Registration","publication_year":2021,"publication_date":"2021-12-07","ids":{"openalex":"https://openalex.org/W4205152234","doi":"https://doi.org/10.1109/tro.2021.3128328"},"language":"en","primary_location":{"id":"doi:10.1109/tro.2021.3128328","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tro.2021.3128328","pdf_url":null,"source":{"id":"https://openalex.org/S144620930","display_name":"IEEE Transactions on Robotics","issn_l":"1552-3098","issn":["1552-3098","1941-0468"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Robotics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2117/378956","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013335218","display_name":"Soheil Sarabandi","orcid":"https://orcid.org/0000-0002-2103-1610"},"institutions":[{"id":"https://openalex.org/I4210093282","display_name":"Institut de Rob\u00f2tica i Inform\u00e0tica Industrial","ror":"https://ror.org/00mcdyn90","country_code":"ES","type":"facility","lineage":["https://openalex.org/I134820265","https://openalex.org/I4210093282","https://openalex.org/I9617848"]},{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Soheil Sarabandi","raw_affiliation_strings":["Institut de Rob&#x00F2;tica i Inform&#x00E0;tica Industrial (CSIC-UPC), Barcelona, Spain"],"raw_orcid":"https://orcid.org/0000-0002-2103-1610","affiliations":[{"raw_affiliation_string":"Institut de Rob&#x00F2;tica i Inform&#x00E0;tica Industrial (CSIC-UPC), Barcelona, Spain","institution_ids":["https://openalex.org/I9617848","https://openalex.org/I4210093282"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048388116","display_name":"Federico Thomas","orcid":"https://orcid.org/0000-0001-9341-5528"},"institutions":[{"id":"https://openalex.org/I4210093282","display_name":"Institut de Rob\u00f2tica i Inform\u00e0tica Industrial","ror":"https://ror.org/00mcdyn90","country_code":"ES","type":"facility","lineage":["https://openalex.org/I134820265","https://openalex.org/I4210093282","https://openalex.org/I9617848"]},{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Federico Thomas","raw_affiliation_strings":["Institut de Rob&#x00F2;tica i Inform&#x00E0;tica Industrial (CSIC-UPC), Barcelona, Spain"],"raw_orcid":"https://orcid.org/0000-0001-9341-5528","affiliations":[{"raw_affiliation_string":"Institut de Rob&#x00F2;tica i Inform&#x00E0;tica Industrial (CSIC-UPC), Barcelona, Spain","institution_ids":["https://openalex.org/I9617848","https://openalex.org/I4210093282"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013335218"],"corresponding_institution_ids":["https://openalex.org/I4210093282","https://openalex.org/I9617848"],"apc_list":null,"apc_paid":null,"fwci":3.2844,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.94693204,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"38","issue":"4","first_page":"2652","last_page":"2664"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T12549","display_name":"Image and Object Detection Techniques","score":0.9998000264167786,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9977999925613403,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.5888450145721436},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.5832065939903259},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5304146409034729},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.5294175744056702},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.46380141377449036},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42943334579467773},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3857883810997009},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3820246160030365},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19279852509498596},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.09845408797264099}],"concepts":[{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.5888450145721436},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5832065939903259},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5304146409034729},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.5294175744056702},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.46380141377449036},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42943334579467773},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3857883810997009},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3820246160030365},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19279852509498596},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.09845408797264099},{"id":"https://openalex.org/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tro.2021.3128328","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tro.2021.3128328","pdf_url":null,"source":{"id":"https://openalex.org/S144620930","display_name":"IEEE Transactions on Robotics","issn_l":"1552-3098","issn":["1552-3098","1941-0468"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Robotics","raw_type":"journal-article"},{"id":"pmh:oai:digital.csic.es:10261/295772","is_oa":false,"landing_page_url":"http://hdl.handle.net/10261/295772","pdf_url":null,"source":{"id":"https://openalex.org/S4306400616","display_name":"DIGITAL.CSIC (Spanish National Research Council (CSIC))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I134820265","host_organization_name":"Consejo Superior de Investigaciones Cient\u00edficas","host_organization_lineage":["https://openalex.org/I134820265"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"art\u00edculo"},{"id":"pmh:oai:upcommons.upc.edu:2117/378956","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/378956","pdf_url":null,"source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:upcommons.upc.edu:2117/378956","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/378956","pdf_url":null,"source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W203335271","https://openalex.org/W1496770315","https://openalex.org/W1817644897","https://openalex.org/W1883517952","https://openalex.org/W1988874269","https://openalex.org/W1993267444","https://openalex.org/W2001515960","https://openalex.org/W2001828104","https://openalex.org/W2016606481","https://openalex.org/W2016959837","https://openalex.org/W2022193415","https://openalex.org/W2037610551","https://openalex.org/W2043887556","https://openalex.org/W2049981393","https://openalex.org/W2050204708","https://openalex.org/W2053269485","https://openalex.org/W2058244961","https://openalex.org/W2079361630","https://openalex.org/W2094694151","https://openalex.org/W2107646992","https://openalex.org/W2113362463","https://openalex.org/W2118104180","https://openalex.org/W2121349631","https://openalex.org/W2128019145","https://openalex.org/W2136567909","https://openalex.org/W2158306674","https://openalex.org/W2159593339","https://openalex.org/W2165053603","https://openalex.org/W2271206385","https://openalex.org/W2289110059","https://openalex.org/W2322579771","https://openalex.org/W2372932456","https://openalex.org/W2585959050","https://openalex.org/W2803474737","https://openalex.org/W2953219581","https://openalex.org/W3008534187","https://openalex.org/W3039659384","https://openalex.org/W3098637820","https://openalex.org/W3152344982","https://openalex.org/W3216912029","https://openalex.org/W4317651351","https://openalex.org/W6629635258","https://openalex.org/W6692368849","https://openalex.org/W6745206811"],"related_works":["https://openalex.org/W1655720158","https://openalex.org/W2369361542","https://openalex.org/W647759170","https://openalex.org/W2366854666","https://openalex.org/W2492925340","https://openalex.org/W2595523213","https://openalex.org/W2006176066","https://openalex.org/W1499828956","https://openalex.org/W103088352","https://openalex.org/W2900275675"],"abstract_inverted_index":{"No":[0],"proper":[1],"norm":[2,97],"exists":[3],"to":[4,36,64,156,175,180],"measure":[5],"the":[6,41,53,71,75,131,137,181],"distance":[7],"between":[8,142],"two":[9,143],"object":[10,76],"poses":[11],"essentially":[12],"because":[13],"a":[14,20,23,34,85,96,160,162],"general":[15],"pose":[16,77],"is":[17,130,170,173],"defined":[18],"by":[19,84],"rotation":[21,86,139],"and":[22,25,68,119,140],"translation,":[24],"thus,":[26],"it":[27],"involves":[28],"magnitudes":[29],"with":[30],"different":[31],"units.":[32],"As":[33,159],"means":[35],"solve":[37],"this":[38,65,105,126,168],"dimensional-inhomogeneity":[39],"problem,":[40],"concept":[42],"of":[43,55,60,107,125,128,145],"<italic":[44],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[45,80,89],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">characteristic":[46],"length</i>":[47],"has":[48],"been":[49],"put":[50],"forward":[51],"in":[52,78,87,135],"area":[54],"kinematics.":[56],"The":[57],"idea":[58],"consists":[59],"scaling":[61],"translations":[62,118],"according":[63],"characteristic":[66],"length":[67],"then":[69],"approximating":[70],"corresponding":[72,146],"displacement":[73],"defining":[74],"<inline-formula":[79,88],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[81,90],"notation=\"LaTeX\">${\\mathbb":[82,91],"{R}}^3$</tex-math></inline-formula>":[83],"{R}}^4$</tex-math></inline-formula>":[92],",":[93],"for":[94,166],"which":[95,109,136,172],"exists.":[98],"This":[99],"article":[100],"sheds":[101],"new":[102],"light":[103],"on":[104],"kind":[106,127],"approximations":[108],"permits":[110],"simplifying":[111],"optimization":[112],"problem":[113,134,169],"whose":[114],"cost":[115],"functions":[116],"involve":[117],"rotations":[120],"simultaneously.":[121],"A":[122],"good":[123],"example":[124],"problems":[129],"pointcloud":[132],"registration":[133],"optimal":[138],"translation":[141],"sets":[144],"3-D":[147],"point":[148],"data,":[149],"so":[150],"that":[151],"they":[152],"are":[153],"aligned/registered,":[154],"have":[155],"be":[157,176],"found.":[158],"result,":[161],"simple":[163],"closed-form":[164],"formula":[165],"solving":[167],"presented":[171],"shown":[174],"an":[177],"attractive":[178],"alternative":[179],"previous":[182],"approaches.":[183]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2022-01-26T00:00:00"}
