{"id":"https://openalex.org/W3121467366","doi":"https://doi.org/10.1109/lsp.2021.3051851","title":"Hypersphere Fitting From Noisy Data Using an EM Algorithm","display_name":"Hypersphere Fitting From Noisy Data Using an EM Algorithm","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3121467366","doi":"https://doi.org/10.1109/lsp.2021.3051851","mag":"3121467366"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2021.3051851","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2021.3051851","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://oatao.univ-toulouse.fr/27670/1/Lesouple_27670.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069539941","display_name":"Julien Lesouple","orcid":"https://orcid.org/0000-0001-9944-8830"},"institutions":[{"id":"https://openalex.org/I4210126970","display_name":"DGA Techniques a\u00e9rospatiales","ror":"https://ror.org/02q398w70","country_code":"FR","type":"government","lineage":["https://openalex.org/I2799681489","https://openalex.org/I2802818602","https://openalex.org/I4210126970","https://openalex.org/I95583923"]},{"id":"https://openalex.org/I4396570610","display_name":"T\u00e9SA","ror":"https://ror.org/01zgcd031","country_code":"FR","type":"nonprofit","lineage":["https://openalex.org/I4396570610"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Julien Lesouple","raw_affiliation_strings":["T\u00e9SA, Toulouse, France","T\u00e9SA - T\u00e9l\u00e9communications Spatiales et A\u00e9ronautiques - Telecommunications for Space ant Aeronautics (14-16, Port Saint-Etienne 31000 Toulouse - France)"],"raw_orcid":"https://orcid.org/0000-0001-9944-8830","affiliations":[{"raw_affiliation_string":"T\u00e9SA, Toulouse, France","institution_ids":["https://openalex.org/I4210126970"]},{"raw_affiliation_string":"T\u00e9SA - T\u00e9l\u00e9communications Spatiales et A\u00e9ronautiques - Telecommunications for Space ant Aeronautics (14-16, Port Saint-Etienne 31000 Toulouse - France)","institution_ids":["https://openalex.org/I4396570610"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048307427","display_name":"Barbara Pilastre","orcid":null},"institutions":[{"id":"https://openalex.org/I4210126970","display_name":"DGA Techniques a\u00e9rospatiales","ror":"https://ror.org/02q398w70","country_code":"FR","type":"government","lineage":["https://openalex.org/I2799681489","https://openalex.org/I2802818602","https://openalex.org/I4210126970","https://openalex.org/I95583923"]},{"id":"https://openalex.org/I4396570610","display_name":"T\u00e9SA","ror":"https://ror.org/01zgcd031","country_code":"FR","type":"nonprofit","lineage":["https://openalex.org/I4396570610"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Barbara Pilastre","raw_affiliation_strings":["T\u00e9SA, Toulouse, France","T\u00e9SA - T\u00e9l\u00e9communications Spatiales et A\u00e9ronautiques - Telecommunications for Space ant Aeronautics (14-16, Port Saint-Etienne 31000 Toulouse - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"T\u00e9SA, Toulouse, France","institution_ids":["https://openalex.org/I4210126970"]},{"raw_affiliation_string":"T\u00e9SA - T\u00e9l\u00e9communications Spatiales et A\u00e9ronautiques - Telecommunications for Space ant Aeronautics (14-16, Port Saint-Etienne 31000 Toulouse - France)","institution_ids":["https://openalex.org/I4396570610"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067973917","display_name":"Yoann Altmann","orcid":"https://orcid.org/0000-0002-3177-9884"},"institutions":[{"id":"https://openalex.org/I32062511","display_name":"Heriot-Watt University","ror":"https://ror.org/04mghma93","country_code":"GB","type":"education","lineage":["https://openalex.org/I32062511"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Yoann Altmann","raw_affiliation_strings":["School of Engineering, Heriot-Watt University, Edinburgh, U.K","HWU - Heriot-Watt University [Edinburgh] (Edinburgh, Scotland, UK EH14 4AS - United Kingdom)"],"raw_orcid":"https://orcid.org/0000-0002-3177-9884","affiliations":[{"raw_affiliation_string":"School of Engineering, Heriot-Watt University, Edinburgh, U.K","institution_ids":["https://openalex.org/I32062511"]},{"raw_affiliation_string":"HWU - Heriot-Watt University [Edinburgh] (Edinburgh, Scotland, UK EH14 4AS - United Kingdom)","institution_ids":["https://openalex.org/I32062511"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018816346","display_name":"Jean\u2010Yves Tourneret","orcid":"https://orcid.org/0000-0001-5219-3455"},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]},{"id":"https://openalex.org/I205747304","display_name":"Institut National Polytechnique de Toulouse","ror":"https://ror.org/033p9g875","country_code":"FR","type":"education","lineage":["https://openalex.org/I205747304"]},{"id":"https://openalex.org/I3131550300","display_name":"Universit\u00e9 Toulouse-I-Capitole","ror":"https://ror.org/0443n9e75","country_code":"FR","type":"education","lineage":["https://openalex.org/I3131550300"]},{"id":"https://openalex.org/I4210119061","display_name":"Institut de Recherche en Informatique de Toulouse","ror":"https://ror.org/01rx4qw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I205747304","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]},{"id":"https://openalex.org/I4210152422","display_name":"Universit\u00e9 Toulouse - Jean Jaur\u00e8s","ror":"https://ror.org/04ezk3x31","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210152422"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Yves Tourneret","raw_affiliation_strings":["University of Toulouse, Toulouse, France","IRIT-MINDS - CoMputational imagINg anD viSion (IRIT\r\n118 Route de Narbonne\r\n31062 Toulouse Cedex 9  - France)","Toulouse INP - Institut National Polytechnique (Toulouse) (France)"],"raw_orcid":"https://orcid.org/0000-0001-5219-3455","affiliations":[{"raw_affiliation_string":"University of Toulouse, Toulouse, France","institution_ids":["https://openalex.org/I17866349"]},{"raw_affiliation_string":"IRIT-MINDS - CoMputational imagINg anD viSion (IRIT\r\n118 Route de Narbonne\r\n31062 Toulouse Cedex 9  - France)","institution_ids":["https://openalex.org/I134560555","https://openalex.org/I3131550300","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4210160189"]},{"raw_affiliation_string":"Toulouse INP - Institut National Polytechnique (Toulouse) (France)","institution_ids":["https://openalex.org/I205747304"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":10,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3621,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.80318741,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"28","issue":null,"first_page":"314","last_page":"318"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12549","display_name":"Image and Object Detection Techniques","score":0.9973999857902527,"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/T12549","display_name":"Image and Object Detection Techniques","score":0.9973999857902527,"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/T14339","display_name":"Image Processing and 3D Reconstruction","score":0.9962999820709229,"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":0.9890999794006348,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hypersphere","display_name":"Hypersphere","score":0.9825698137283325},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6159430146217346},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5793562531471252},{"id":"https://openalex.org/keywords/expectation\u2013maximization-algorithm","display_name":"Expectation\u2013maximization algorithm","score":0.5638322830200195},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36506378650665283},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32280921936035156},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.1864958107471466},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15695178508758545}],"concepts":[{"id":"https://openalex.org/C2776562905","wikidata":"https://www.wikidata.org/wiki/Q306610","display_name":"Hypersphere","level":2,"score":0.9825698137283325},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6159430146217346},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5793562531471252},{"id":"https://openalex.org/C182081679","wikidata":"https://www.wikidata.org/wiki/Q1275153","display_name":"Expectation\u2013maximization algorithm","level":3,"score":0.5638322830200195},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36506378650665283},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32280921936035156},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.1864958107471466},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15695178508758545},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/lsp.2021.3051851","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2021.3051851","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai:oatao.univ-toulouse.fr:27670","is_oa":true,"landing_page_url":null,"pdf_url":"https://oatao.univ-toulouse.fr/27670/1/Lesouple_27670.pdf","source":{"id":"https://openalex.org/S4306401987","display_name":"Open Archive Toulouse Archive Ouverte (University of Toulouse)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I17866349","host_organization_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","host_organization_lineage":["https://openalex.org/I17866349"],"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":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-03329377v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03329377","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"https://ieeexplore.ieee.org/document/9325007","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:oatao.univ-toulouse.fr:27670","is_oa":true,"landing_page_url":null,"pdf_url":"https://oatao.univ-toulouse.fr/27670/1/Lesouple_27670.pdf","source":{"id":"https://openalex.org/S4306401987","display_name":"Open Archive Toulouse Archive Ouverte (University of Toulouse)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I17866349","host_organization_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","host_organization_lineage":["https://openalex.org/I17866349"],"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":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8145101974","display_name":null,"funder_award_id":"RF201617/16/31","funder_id":"https://openalex.org/F4320320005","funder_display_name":"Royal Academy of Engineering"}],"funders":[{"id":"https://openalex.org/F4320320005","display_name":"Royal Academy of Engineering","ror":"https://ror.org/0526snb40"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3121467366.pdf","grobid_xml":"https://content.openalex.org/works/W3121467366.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W44078798","https://openalex.org/W1971867870","https://openalex.org/W1998680315","https://openalex.org/W2007097714","https://openalex.org/W2028974272","https://openalex.org/W2029143333","https://openalex.org/W2046641306","https://openalex.org/W2049633694","https://openalex.org/W2053175924","https://openalex.org/W2058568645","https://openalex.org/W2102591969","https://openalex.org/W2104399424","https://openalex.org/W2120062331","https://openalex.org/W2126896405","https://openalex.org/W2150066425","https://openalex.org/W2152803642","https://openalex.org/W2167790077","https://openalex.org/W2168338244","https://openalex.org/W2170886978","https://openalex.org/W2224693261","https://openalex.org/W2768158397","https://openalex.org/W3044275847","https://openalex.org/W3090824333","https://openalex.org/W4246202668","https://openalex.org/W6601788909","https://openalex.org/W6675799351"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2099702253","https://openalex.org/W2059484267","https://openalex.org/W1970780628","https://openalex.org/W2069017679","https://openalex.org/W2133653616","https://openalex.org/W2921850681","https://openalex.org/W2079494444","https://openalex.org/W4389755575","https://openalex.org/W4283069864"],"abstract_inverted_index":{"This":[0,21,42],"letter":[1],"studies":[2],"a":[3,32,47,60,65,74],"new":[4],"expectation":[5],"maximization":[6],"(EM)":[7],"algorithm":[8,22,85],"to":[9,46],"solve":[10],"the":[11,25,40,56,67,81],"problem":[12,69],"of":[13,27,80],"circle,":[14],"sphere":[15,91],"and":[16,90],"more":[17],"generally":[18],"hypersphere":[19,83],"fitting.":[20,92],"relies":[23],"on":[24,39,55],"introduction":[26],"random":[28],"latent":[29],"vectors":[30],"having":[31],"priori":[33],"independent":[34],"von":[35],"Mises-Fisher":[36,62],"distributions":[37],"defined":[38],"hypersphere.":[41],"statistical":[43],"model":[44],"leads":[45],"complete":[48],"data":[49],"likelihood":[50],"whose":[51],"expected":[52],"value,":[53],"conditioned":[54],"observed":[57],"data,":[58],"has":[59],"Von":[61],"distribution.":[63],"As":[64],"result,":[66],"inference":[68],"can":[70],"be":[71],"solved":[72],"with":[73],"simple":[75],"EM":[76],"algorithm.":[77],"The":[78],"performance":[79],"resulting":[82],"fitting":[84],"is":[86],"evaluated":[87],"for":[88],"circle":[89]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}