{"id":"https://openalex.org/W4387870045","doi":"https://doi.org/10.1109/mlsp55844.2023.10285888","title":"Dual Quaternion Rotational and Translational Equivariance in 3D Rigid Motion Modelling","display_name":"Dual Quaternion Rotational and Translational Equivariance in 3D Rigid Motion Modelling","publication_year":2023,"publication_date":"2023-09-17","ids":{"openalex":"https://openalex.org/W4387870045","doi":"https://doi.org/10.1109/mlsp55844.2023.10285888"},"language":"en","primary_location":{"id":"doi:10.1109/mlsp55844.2023.10285888","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mlsp55844.2023.10285888","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE 33rd International Workshop on Machine Learning for Signal Processing (MLSP)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://iris.uniroma1.it/bitstream/11573/1693475/1/Vieira_Dual%20Quaternion%20Rotational_2023.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017180156","display_name":"Guilherme Vieira","orcid":"https://orcid.org/0000-0003-3361-6154"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Guilherme Vieira","raw_affiliation_strings":["Universidade Estadual de Campinas (Unicamp),Dept. of Applied Mathematics,Brazil","Dept. of Applied Mathematics, Universidade Estadual de Campinas (Unicamp), Brazil"],"affiliations":[{"raw_affiliation_string":"Universidade Estadual de Campinas (Unicamp),Dept. of Applied Mathematics,Brazil","institution_ids":["https://openalex.org/I181391015"]},{"raw_affiliation_string":"Dept. of Applied Mathematics, Universidade Estadual de Campinas (Unicamp), Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003606065","display_name":"Eleonora Grassucci","orcid":"https://orcid.org/0000-0003-4626-4506"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Eleonora Grassucci","raw_affiliation_strings":["Sapienza University of Rome,Dept. of Information Engineering, Electronics, and Telecomm.,Italy","Dept. of Information Engineering, Electronics, and Telecomm., Sapienza University of Rome, Italy"],"affiliations":[{"raw_affiliation_string":"Sapienza University of Rome,Dept. of Information Engineering, Electronics, and Telecomm.,Italy","institution_ids":["https://openalex.org/I861853513"]},{"raw_affiliation_string":"Dept. of Information Engineering, Electronics, and Telecomm., Sapienza University of Rome, Italy","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012009095","display_name":"Marcos Eduardo Valle","orcid":"https://orcid.org/0000-0003-4026-5110"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Marcos Eduardo Valle","raw_affiliation_strings":["Universidade Estadual de Campinas (Unicamp),Dept. of Applied Mathematics,Brazil","Dept. of Applied Mathematics, Universidade Estadual de Campinas (Unicamp), Brazil"],"affiliations":[{"raw_affiliation_string":"Universidade Estadual de Campinas (Unicamp),Dept. of Applied Mathematics,Brazil","institution_ids":["https://openalex.org/I181391015"]},{"raw_affiliation_string":"Dept. of Applied Mathematics, Universidade Estadual de Campinas (Unicamp), Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019647783","display_name":"Danilo Comminiello","orcid":"https://orcid.org/0000-0003-4067-4504"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Danilo Comminiello","raw_affiliation_strings":["Sapienza University of Rome,Dept. of Information Engineering, Electronics, and Telecomm.,Italy","Dept. of Information Engineering, Electronics, and Telecomm., Sapienza University of Rome, Italy"],"affiliations":[{"raw_affiliation_string":"Sapienza University of Rome,Dept. of Information Engineering, Electronics, and Telecomm.,Italy","institution_ids":["https://openalex.org/I861853513"]},{"raw_affiliation_string":"Dept. of Information Engineering, Electronics, and Telecomm., Sapienza University of Rome, Italy","institution_ids":["https://openalex.org/I861853513"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5017180156"],"corresponding_institution_ids":["https://openalex.org/I181391015"],"apc_list":null,"apc_paid":null,"fwci":0.6137,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.70217408,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10531","display_name":"Advanced Vision and Imaging","score":0.9979000091552734,"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":0.9979000091552734,"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":0.9950000047683716,"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/T10812","display_name":"Human Pose and Action Recognition","score":0.9925000071525574,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.9605053663253784},{"id":"https://openalex.org/keywords/dual-quaternion","display_name":"Dual quaternion","score":0.9055556058883667},{"id":"https://openalex.org/keywords/equivariant-map","display_name":"Equivariant map","score":0.6862825751304626},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.6687254309654236},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.6528868079185486},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5488196611404419},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5309616327285767},{"id":"https://openalex.org/keywords/quaternion-algebra","display_name":"Quaternion algebra","score":0.5217474699020386},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.515765905380249},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.49878978729248047},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4923044443130493},{"id":"https://openalex.org/keywords/object","display_name":"Object (grammar)","score":0.46753260493278503},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4620465636253357},{"id":"https://openalex.org/keywords/encode","display_name":"ENCODE","score":0.45009124279022217},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.44919371604919434},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4401158094406128},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43025654554367065},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.3857472538948059},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3388417959213257},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3328193128108978},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2114654779434204},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20873501896858215}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.9605053663253784},{"id":"https://openalex.org/C145941777","wikidata":"https://www.wikidata.org/wiki/Q5310237","display_name":"Dual quaternion","level":3,"score":0.9055556058883667},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.6862825751304626},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.6687254309654236},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.6528868079185486},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5488196611404419},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5309616327285767},{"id":"https://openalex.org/C151640129","wikidata":"https://www.wikidata.org/wiki/Q2835967","display_name":"Quaternion algebra","level":5,"score":0.5217474699020386},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.515765905380249},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.49878978729248047},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4923044443130493},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.46753260493278503},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4620465636253357},{"id":"https://openalex.org/C66746571","wikidata":"https://www.wikidata.org/wiki/Q1134833","display_name":"ENCODE","level":3,"score":0.45009124279022217},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.44919371604919434},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4401158094406128},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43025654554367065},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.3857472538948059},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3388417959213257},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3328193128108978},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2114654779434204},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20873501896858215},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.0},{"id":"https://openalex.org/C100899422","wikidata":"https://www.wikidata.org/wiki/Q5058347","display_name":"Cellular algebra","level":4,"score":0.0},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","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},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/mlsp55844.2023.10285888","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mlsp55844.2023.10285888","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE 33rd International Workshop on Machine Learning for Signal Processing (MLSP)","raw_type":"proceedings-article"},{"id":"pmh:oai:iris.uniroma1.it:11573/1693475","is_oa":true,"landing_page_url":"https://hdl.handle.net/11573/1693475","pdf_url":"https://iris.uniroma1.it/bitstream/11573/1693475/1/Vieira_Dual%20Quaternion%20Rotational_2023.pdf","source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:iris.uniroma1.it:11573/1693475","is_oa":true,"landing_page_url":"https://hdl.handle.net/11573/1693475","pdf_url":"https://iris.uniroma1.it/bitstream/11573/1693475/1/Vieira_Dual%20Quaternion%20Rotational_2023.pdf","source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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/conferenceObject"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4387870045.pdf"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1517452805","https://openalex.org/W2062625299","https://openalex.org/W2523915674","https://openalex.org/W2803747201","https://openalex.org/W2923153064","https://openalex.org/W2964002966","https://openalex.org/W2964203186","https://openalex.org/W2966878259","https://openalex.org/W2979708657","https://openalex.org/W2991332406","https://openalex.org/W3025086266","https://openalex.org/W3034961902","https://openalex.org/W3045019771","https://openalex.org/W3048912365","https://openalex.org/W3101017148","https://openalex.org/W3163462841","https://openalex.org/W3176095614","https://openalex.org/W3182910206","https://openalex.org/W3205898917","https://openalex.org/W3215587491","https://openalex.org/W4210600196","https://openalex.org/W4213332096","https://openalex.org/W4226095941","https://openalex.org/W4285288115","https://openalex.org/W4289792697","https://openalex.org/W4312518484","https://openalex.org/W4312652333","https://openalex.org/W6727446090","https://openalex.org/W6752114883","https://openalex.org/W6784282185"],"related_works":["https://openalex.org/W2156842304","https://openalex.org/W2128405419","https://openalex.org/W4321633639","https://openalex.org/W2528648357","https://openalex.org/W4235237238","https://openalex.org/W1499641851","https://openalex.org/W2749494690","https://openalex.org/W4387870045","https://openalex.org/W2949293769","https://openalex.org/W2015733920"],"abstract_inverted_index":{"Objects'":[0],"rigid":[1,75,153],"motions":[2,76,154],"in":[3,45,60,77,113,124,136,155],"3D":[4,46,61,79,156],"space":[5,80],"are":[6],"described":[7],"by":[8],"rotations":[9,44,84],"and":[10,39,85,103,116],"translations":[11,86],"of":[12,16,74,87,92,146],"a":[13,70,96,137],"highly-correlated":[14],"set":[15],"points,":[17],"each":[18,91],"with":[19,130],"associated":[20],"x,":[21],"y,":[22],"z":[23],"coordinates":[24],"that":[25,81],"real-valued":[26],"networks":[27],"consider":[28],"as":[29,95,121],"separate":[30],"entities,":[31],"losing":[32],"information.":[33],"Previous":[34],"works":[35],"exploit":[36],"quaternion":[37,72,150],"algebra":[38],"their":[40],"ability":[41],"to":[42,57,143],"model":[43],"space.":[47,157],"However,":[48],"these":[49,66],"algebras":[50],"do":[51],"not":[52,109],"properly":[53],"encode":[54],"translations,":[55],"leading":[56],"sub-optimal":[58],"performance":[59],"learning":[62],"tasks.":[63],"To":[64],"overcome":[65],"limitations,":[67],"we":[68,122],"employ":[69],"dual":[71,149],"representation":[73],"the":[78,93,114,125,144,147],"jointly":[82],"describes":[83],"point":[88],"sets,":[89],"processing":[90],"points":[94],"single":[97],"entity.":[98],"Our":[99],"approach":[100],"is":[101],"translation":[102],"rotation":[104],"equivariant,":[105],"so":[106],"it":[107],"does":[108],"suffer":[110],"from":[111],"shifts":[112],"data":[115],"better":[117],"learns":[118],"object":[119],"trajectories,":[120],"validate":[123],"experimental":[126],"evaluations.":[127],"Models":[128],"endowed":[129],"this":[131],"formulation":[132,151],"outperform":[133],"previous":[134],"approaches":[135],"human":[138],"pose":[139],"forecasting":[140],"application,":[141],"attesting":[142],"effectiveness":[145],"proposed":[148],"for":[152]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3}],"updated_date":"2026-03-11T14:59:36.786465","created_date":"2025-10-10T00:00:00"}
