Hypersphere Fitting From Noisy Data Using an EM Algorithm

This letter studies a new expectation maximization (EM) algorithm to solve the problem of circle, sphere and more generally hypersphere fitting. This algorithm relies on the introduction of random latent vectors having a priori independent von Mises-Fisher distributions defined on the hypersphere. T...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	IEEE signal processing letters Ročník 28; s. 314 - 318
Hlavní autori:	Lesouple, Julien, Pilastre, Barbara, Altmann, Yoann, Tourneret, Jean-Yves
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York IEEE 01.01.2021 The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Institute of Electrical and Electronics Engineers
Predmet:	Algorithms Computer Science Distributed databases Engineering Sciences Expectation-Maximization Algorithm Fitting Hypersphere Fitting Hyperspheres Iterative algorithms Maximum likelihood estimation Noise measurement Signal and Image Processing Signal processing algorithms Statistical models Three-dimensional displays von Mises-Fisher distribution Maximum likelihood estimation von Mises-Fisher distribution Expectation-maximization algorithm Hypersphere fitting
ISSN:	1070-9908, 1558-2361
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Abstract	This letter studies a new expectation maximization (EM) algorithm to solve the problem of circle, sphere and more generally hypersphere fitting. This algorithm relies on the introduction of random latent vectors having a priori independent von Mises-Fisher distributions defined on the hypersphere. This statistical model leads to a complete data likelihood whose expected value, conditioned on the observed data, has a Von Mises-Fisher distribution. As a result, the inference problem can be solved with a simple EM algorithm. The performance of the resulting hypersphere fitting algorithm is evaluated for circle and sphere fitting.
AbstractList	This letter studies a new expectation maximization (EM) algorithm to solve the problem of circle, sphere and more generally hypersphere fitting. This algorithm relies on the introduction of random latent vectors having a priori independent von Mises-Fisher distributions defined on the hypersphere. This statistical model leads to a complete data likelihood whose expected value, conditioned on the observed data, has a Von Mises-Fisher distribution. As a result, the inference problem can be solved with a simple EM algorithm. The performance of the resulting hypersphere fitting algorithm is evaluated for circle and sphere fitting.
Author	Altmann, Yoann Lesouple, Julien Tourneret, Jean-Yves Pilastre, Barbara
Author_xml	– sequence: 1 givenname: Julien orcidid: 0000-0001-9944-8830 surname: Lesouple fullname: Lesouple, Julien email: julien.lesouple@tesa.prd.fr organization: TéSA, Toulouse, France – sequence: 2 givenname: Barbara surname: Pilastre fullname: Pilastre, Barbara email: barbara.pilastre@tesa.prd.fr organization: TéSA, Toulouse, France – sequence: 3 givenname: Yoann orcidid: 0000-0002-3177-9884 surname: Altmann fullname: Altmann, Yoann email: Y.Altmann@hw.ac.uk organization: School of Engineering, Heriot-Watt University, Edinburgh, U.K – sequence: 4 givenname: Jean-Yves orcidid: 0000-0001-5219-3455 surname: Tourneret fullname: Tourneret, Jean-Yves email: jean-yves.tourneret@enseeiht.fr organization: University of Toulouse, Toulouse, France
BackLink	https://hal.science/hal-03329377$$DView record in HAL
BookMark	eNp9kM1rAjEQxUOxULW9F3pZ6KmHtZNks0mOYrUW7Ae0nkOMWY3oxiax4H_fFcVDDz3N8Pi9N8ProFbta4vQLYYexiAfJ58fPQIE9ygwLBi-QG3MmMgJLXGr2YFDLiWIK9SJcQUAoqHaSI73WxvidmmDzUYuJVcvslHwm-zNu7jPnnTS2TQeVF1nw9esv1744NJyc40uK72O9uY0u2g6Gn4Nxvnk_fll0J_khpY85aQqZrK02pSCU8xIxYkV1GjO5oaQOVhJWSkKbg0rJeg5L2BWaTG3wmpJjaFd9HDMXeq12ga30WGvvHZq3J-ogwaUEkk5_8ENe39kt8F_72xMauV3oW7eU6QQghccStlQcKRM8DEGW51jMahDmaopUx3KVKcyG0v5x2Jc0sn5OgXt1v8Z745GZ60935GUMABOfwGIx4C5
CODEN	ISPLEM
CitedBy_id	crossref_primary_10_1016_j_measurement_2022_111430 crossref_primary_10_1016_j_matdes_2023_112315 crossref_primary_10_1177_09544070231212531 crossref_primary_10_1109_TGRS_2022_3226581 crossref_primary_10_1186_s13634_024_01129_z crossref_primary_10_1016_j_aej_2025_04_099 crossref_primary_10_3389_fphys_2021_755468 crossref_primary_10_1371_journal_pone_0292480 crossref_primary_10_3390_s21227546
Cites_doi	10.1109/TIP.2005.863965 10.1109/TIM.2003.820472 10.1109/icc.2011.5963101 10.1016/S0024-3795(01)00263-4 10.3390/a13080177 10.1109/TSP.2015.2424194 10.1016/0734-189X(87)90116-2 10.1109/LRA.2017.2773668 10.1111/j.2517-6161.1977.tb01600.x 10.1002/9780470316979 10.1109/TIM.1976.6312298 10.1117/1.JRS.8.083588 10.1007/s10846-008-9235-4 10.1109/TAES.2013.120107 10.1016/0734-189X(89)90088-1 10.1109/LSP.2007.912964 10.1109/LSP.2011.2166956
ContentType	Journal Article
Copyright	Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2021 Distributed under a Creative Commons Attribution 4.0 International License
Copyright_xml	– notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2021 – notice: Distributed under a Creative Commons Attribution 4.0 International License
DBID	97E RIA RIE AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D 1XC VOOES
DOI	10.1109/LSP.2021.3051851
DatabaseName	IEEE Xplore (IEEE) IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Hyper Article en Ligne (HAL) Hyper Article en Ligne (HAL) (Open Access)
DatabaseTitle	CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional
DatabaseTitleList	Technology Research Database
Database_xml	– sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering Computer Science
EISSN	1558-2361
EndPage	318
ExternalDocumentID	oai:HAL:hal-03329377v1 10_1109_LSP_2021_3051851 9325007
Genre	orig-research
GrantInformation_xml	– fundername: Royal Academy of Engineering grantid: RF201617/16/31 funderid: 10.13039/501100000287
GroupedDBID	-~X .DC 0R~ 29I 3EH 4.4 5GY 5VS 6IK 85S 97E AAJGR AARMG AASAJ AAWTH AAYJJ ABAZT ABFSI ABQJQ ABVLG ACGFO ACGFS ACIWK AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 E.L EBS EJD F5P HZ~ H~9 ICLAB IFIPE IFJZH IPLJI JAVBF LAI M43 O9- OCL P2P RIA RIE RNS TAE TN5 VH1 AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D 1XC VOOES
ID	FETCH-LOGICAL-c367t-2f4b96eac6873152f72e83ca75dc22d0e9356847ec5690ad740bfa8de8ea93cc3
IEDL.DBID	RIE
ISICitedReferencesCount	13
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000617365200012&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	1070-9908
IngestDate	Sat Oct 25 11:21:50 EDT 2025 Sun Nov 30 05:25:54 EST 2025 Tue Nov 18 22:11:58 EST 2025 Sat Nov 29 03:38:51 EST 2025 Wed Aug 27 05:44:58 EDT 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Keywords	Maximum likelihood estimation von Mises-Fisher distribution Expectation-maximization algorithm Hypersphere fitting
Language	English
License	Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c367t-2f4b96eac6873152f72e83ca75dc22d0e9356847ec5690ad740bfa8de8ea93cc3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0001-5219-3455 0000-0002-3177-9884 0000-0001-9944-8830
OpenAccessLink	https://hal.science/hal-03329377
PQID	2488747069
PQPubID	75747
PageCount	5
ParticipantIDs	crossref_primary_10_1109_LSP_2021_3051851 crossref_citationtrail_10_1109_LSP_2021_3051851 ieee_primary_9325007 hal_primary_oai_HAL_hal_03329377v1 proquest_journals_2488747069
PublicationCentury	2000
PublicationDate	2021-01-01
PublicationDateYYYYMMDD	2021-01-01
PublicationDate_xml	– month: 01 year: 2021 text: 2021-01-01 day: 01
PublicationDecade	2020
PublicationPlace	New York
PublicationPlace_xml	– name: New York
PublicationTitle	IEEE signal processing letters
PublicationTitleAbbrev	LSP
PublicationYear	2021
Publisher	IEEE The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Institute of Electrical and Electronics Engineers
Publisher_xml	– name: IEEE – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) – name: Institute of Electrical and Electronics Engineers
References	eberly (ref14) 1999 ref24 ref12 geiger (ref8) 0 ref15 epstein (ref1) 2020; 13 ref10 ref21 tóth (ref23) 0 olver (ref17) 2010 ref2 ref16 sumith (ref22) 2015 ref19 ref18 pan (ref9) 2011; 18 lesouple (ref20) 2020 ref3 ref6 ref5 sandoval (ref4) 2008; 15 golub (ref13) 2001; 331 lin (ref7) 0 thomas (ref11) 1989; 45
References_xml	– ident: ref16 doi: 10.1109/TIP.2005.863965 – ident: ref10 doi: 10.1109/TIM.2003.820472 – ident: ref15 doi: 10.1109/icc.2011.5963101 – volume: 331 start-page: 43 year: 2001 ident: ref13 article-title: Hyperspheres and hyperplanes fitted seamlessly by algebraic constrained total least-squares publication-title: Linear Algebra Appl doi: 10.1016/S0024-3795(01)00263-4 – volume: 13 year: 2020 ident: ref1 article-title: Sphere fitting with applications to machine tracking publication-title: Algorithms doi: 10.3390/a13080177 – year: 2015 ident: ref22 article-title: Fast geometric fit algorithm for sphere using exact solution – start-page: 8580 year: 0 ident: ref23 article-title: Automatic LiDAR-camera calibration of extrinsic parameters using a spherical target publication-title: Proc IEEE Int Conf Robot Automat – year: 2010 ident: ref17 publication-title: NIST Handbook of Mathematical Functions – ident: ref3 doi: 10.1109/TSP.2015.2424194 – start-page: 1167 year: 0 ident: ref7 article-title: Real-time eye detection using face-circle fitting and dark-pixel filtering publication-title: Proc IEEE Int Conf Multimedia Expo – ident: ref12 doi: 10.1016/0734-189X(87)90116-2 – ident: ref5 doi: 10.1109/LRA.2017.2773668 – ident: ref18 doi: 10.1111/j.2517-6161.1977.tb01600.x – start-page: 3354 year: 0 ident: ref8 publication-title: Proc IEEE Int Conf Conf Comput Vis Pattern Recognit – ident: ref19 doi: 10.1002/9780470316979 – ident: ref21 doi: 10.1109/TIM.1976.6312298 – ident: ref24 doi: 10.1117/1.JRS.8.083588 – year: 1999 ident: ref14 article-title: Least squares fitting of data – ident: ref6 doi: 10.1007/s10846-008-9235-4 – year: 2020 ident: ref20 article-title: Hypersphere fitting from noisy data using an EM algorithm - supplementary material publication-title: TeSA Lab – ident: ref2 doi: 10.1109/TAES.2013.120107 – volume: 45 start-page: 362 year: 1989 ident: ref11 article-title: Simple approach for the estimation of circular arc center and its radius publication-title: Comput Vis Graph Image Process doi: 10.1016/0734-189X(89)90088-1 – volume: 15 start-page: 127 year: 2008 ident: ref4 article-title: An algorithm for fitting 2-D data on the circle: Applications to mobile robotics publication-title: IEEE Signal Process Lett doi: 10.1109/LSP.2007.912964 – volume: 18 start-page: 639 year: 2011 ident: ref9 article-title: Fast and robust circular object detection with probabilistic pairwise voting publication-title: IEEE Signal Process Lett doi: 10.1109/LSP.2011.2166956
SSID	ssj0008185
Score	2.4156356
Snippet	This letter studies a new expectation maximization (EM) algorithm to solve the problem of circle, sphere and more generally hypersphere fitting. This algorithm...
SourceID	hal proquest crossref ieee
SourceType	Open Access Repository Aggregation Database Enrichment Source Index Database Publisher
StartPage	314
SubjectTerms	Algorithms Computer Science Distributed databases Engineering Sciences Expectation-Maximization Algorithm Fitting Hypersphere Fitting Hyperspheres Iterative algorithms Maximum likelihood estimation Noise measurement Signal and Image Processing Signal processing algorithms Statistical models Three-dimensional displays von Mises-Fisher distribution
Title	Hypersphere Fitting From Noisy Data Using an EM Algorithm
URI	https://ieeexplore.ieee.org/document/9325007 https://www.proquest.com/docview/2488747069 https://hal.science/hal-03329377
Volume	28
WOSCitedRecordID	wos000617365200012&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVIEE databaseName: IEEE Electronic Library (IEL) customDbUrl: eissn: 1558-2361 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0008185 issn: 1070-9908 databaseCode: RIE dateStart: 19940101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3da9swEBdJ6UP3sHVtx7KlQ4y-FOpEtmxLegxbQx7SUFg7-mbks9QEkngkTmH__U6yYzpaBnsT4gTiTrq7n3QfhFzYPBdpnMggLnITxDq0gYKcB5prDQkzkPss_p9TMZvJhwd12yFXbS6MMcYHn5mBG_q__KKEnXsqG6KvkfjU8a4Qos7VarWuMzx1fCELUMPK_ZckU8Ppj1sEglE4wLONVOFfJqg7dwGQvrPKC3Xsbcz43f_t7pi8bXxJOqqF_550zPqEvHlWYfCUqAniTISuKBlDxwsf5EzHm3JFZ-Vi-5t-15WmPmyA6jW9vqGj5WO5WVTz1Rm5H1_ffZsETbeEAHgqqiCyca5S1KOpFBytshWRkRy0SAqIooIZxZMUbZGBBBGxLkTMcqtlYaTRigPwD-RgXa7NR0KVBR5ZSKMiDtHBYgogTBEbWgWSy8L2yHDPwAyaUuKuo8Uy85CCqQxZnjmWZw3Le-SyXfGrLqPxD9qvKJOWzNW_noymmZtjnKN7IsQTEp06CbRUDfN7pL8XYdZcxm0WoZJC1MRS9en1VZ_JkdtA_bLSJwfVZmfOySE8VYvt5os_Z38AMczNsQ
linkProvider	IEEE
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3daxQxEB9qFdQHv6r0atUgvghuL5vsbpLHo_Y4cXsUrNK3kM0m9qC9LXfbgv99J9m9xaIIvoUwgTCTzMwvmQ-AD76qRJHlMsnqyiWZSX2ibMUTw42xOXW2iln8P0oxn8uzM3WyBZ-GXBjnXAw-cwdhGP_y68Zeh6eyMfoaeUwdv59nGUu7bK1B7wbT00UY0gR1rNx8SlI1Lr-dIBRk6QGebqRK7xihe-chBDL2VvlDIUcrM336f_t7Bk96b5JMOvE_hy23fAGPf6sxuANqhkgTwSvKxpHpIoY5k-mquSTzZrH-RT6b1pAYOEDMkhwdk8nFz2a1aM8vX8L36dHp4Szp-yUklheiTZjPKlWgJi2k4GiXvWBOcmtEXlvGauoUzwu0Rs7miIlNLTJaeSNrJ51R3Fr-CraXzdLtAlHecuZtweosRReLKmvTAtGhV1ZyWfsRjDcM1LYvJh56WlzoCCqo0shyHViue5aP4OOw4qorpPEP2vcok4EsVMCeTUod5ijn6KAIcYNEO0ECA1XP_BHsb0So--u41gzVFOImWqi9v696Bw9np8elLr_Mv76GR2Ez3TvLPmy3q2v3Bh7Ym3axXr2NZ-4WEs3Q-A
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Hypersphere+Fitting+From+Noisy+Data+Using+an+EM+Algorithm&rft.jtitle=IEEE+signal+processing+letters&rft.au=Lesouple%2C+Julien&rft.au=Pilastre%2C+Barbara&rft.au=Altmann%2C+Yoann&rft.au=Tourneret%2C+Jean-Yves&rft.date=2021-01-01&rft.pub=The+Institute+of+Electrical+and+Electronics+Engineers%2C+Inc.+%28IEEE%29&rft.issn=1070-9908&rft.eissn=1558-2361&rft.volume=28&rft.spage=314&rft_id=info:doi/10.1109%2FLSP.2021.3051851&rft.externalDBID=NO_FULL_TEXT
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1070-9908&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1070-9908&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1070-9908&client=summon