{"id":"https://openalex.org/W3136556271","doi":"https://doi.org/10.1109/tip.2021.3065799","title":"Robust Ellipse Fitting Using Hierarchical Gaussian Mixture Models","display_name":"Robust Ellipse Fitting Using Hierarchical Gaussian Mixture Models","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3136556271","doi":"https://doi.org/10.1109/tip.2021.3065799","mag":"3136556271","pmid":"https://pubmed.ncbi.nlm.nih.gov/33735080"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2021.3065799","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2021.3065799","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5114949187","display_name":"Mingyang Zhao","orcid":"https://orcid.org/0000-0001-6953-9731"},"institutions":[{"id":"https://openalex.org/I4210095018","display_name":"National Center for Mathematics and Interdisciplinary Sciences","ror":"https://ror.org/00s97k668","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210095018"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Mingyang Zhao","raw_affiliation_strings":["KLMM, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences (CAS), Beijing, China","School of Mathematical Sciences, University of Chinese Academy of Sciences (UCAS), Beijing, China"],"affiliations":[{"raw_affiliation_string":"KLMM, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences (CAS), Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I4210095018","https://openalex.org/I19820366"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences (UCAS), Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075570681","display_name":"Xiaohong Jia","orcid":"https://orcid.org/0000-0001-6206-3216"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210095018","display_name":"National Center for Mathematics and Interdisciplinary Sciences","ror":"https://ror.org/00s97k668","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210095018"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaohong Jia","raw_affiliation_strings":["KLMM, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences (CAS), Beijing, China","School of Mathematical Sciences, University of Chinese Academy of Sciences (UCAS), Beijing, China"],"affiliations":[{"raw_affiliation_string":"KLMM, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences (CAS), Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I4210095018","https://openalex.org/I19820366"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences (UCAS), Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101852941","display_name":"Lubin Fan","orcid":null},"institutions":[{"id":"https://openalex.org/I45928872","display_name":"Alibaba Group (China)","ror":"https://ror.org/00k642b80","country_code":"CN","type":"company","lineage":["https://openalex.org/I45928872"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lubin Fan","raw_affiliation_strings":["Alibaba Group, Hangzhou, China"],"affiliations":[{"raw_affiliation_string":"Alibaba Group, Hangzhou, China","institution_ids":["https://openalex.org/I45928872"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065014903","display_name":"Yuan Liang","orcid":"https://orcid.org/0000-0001-9816-2910"},"institutions":[{"id":"https://openalex.org/I45928872","display_name":"Alibaba Group (China)","ror":"https://ror.org/00k642b80","country_code":"CN","type":"company","lineage":["https://openalex.org/I45928872"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuan Liang","raw_affiliation_strings":["Alibaba Group, Hangzhou, China"],"affiliations":[{"raw_affiliation_string":"Alibaba Group, Hangzhou, China","institution_ids":["https://openalex.org/I45928872"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003969300","display_name":"Dong\u2010Ming Yan","orcid":"https://orcid.org/0000-0003-2209-2404"},"institutions":[{"id":"https://openalex.org/I4210112150","display_name":"Institute of Automation","ror":"https://ror.org/022c3hy66","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210112150"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210100255","display_name":"Beijing Academy of Artificial Intelligence","ror":"https://ror.org/016a74861","country_code":"CN","type":"other","lineage":["https://openalex.org/I4210100255"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dong-Ming Yan","raw_affiliation_strings":["National Laboratory of Pattern Recognition (NLPR), Institute of Automation, Chinese Academy of Sciences, Beijing, China","School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"National Laboratory of Pattern Recognition (NLPR), Institute of Automation, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210112150","https://openalex.org/I19820366"]},{"raw_affiliation_string":"School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210100255","https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5114949187"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210095018","https://openalex.org/I4210120485","https://openalex.org/I4210165038"],"apc_list":null,"apc_paid":null,"fwci":1.841,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.87211111,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"30","issue":null,"first_page":"3828","last_page":"3843"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12549","display_name":"Image and Object Detection Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T13114","display_name":"Image Processing Techniques and Applications","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9815000295639038,"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/ellipse","display_name":"Ellipse","score":0.7765072584152222},{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.754419207572937},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.7297881841659546},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.6547108292579651},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.646556556224823},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.5387969613075256},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5006117820739746},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.42311346530914307},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40434595942497253},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.34409230947494507},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3175056576728821}],"concepts":[{"id":"https://openalex.org/C74261601","wikidata":"https://www.wikidata.org/wiki/Q40112","display_name":"Ellipse","level":2,"score":0.7765072584152222},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.754419207572937},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7297881841659546},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6547108292579651},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.646556556224823},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5387969613075256},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5006117820739746},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.42311346530914307},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40434595942497253},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.34409230947494507},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3175056576728821},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tip.2021.3065799","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2021.3065799","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},{"id":"pmid:33735080","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33735080","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on image processing : a publication of the IEEE Signal Processing Society","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G386194012","display_name":null,"funder_award_id":"61772523","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4371026006","display_name":null,"funder_award_id":"2020YFB1708900","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G4809064858","display_name":null,"funder_award_id":"2019YFB2204104","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G4905733801","display_name":null,"funder_award_id":"61872354","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5528792445","display_name":null,"funder_award_id":"Z190004","funder_id":"https://openalex.org/F4320322919","funder_display_name":"Natural Science Foundation of Beijing Municipality"},{"id":"https://openalex.org/G8592004755","display_name":null,"funder_award_id":"L182059","funder_id":"https://openalex.org/F4320322919","funder_display_name":"Natural Science Foundation of Beijing Municipality"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322919","display_name":"Natural Science Foundation of Beijing Municipality","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":64,"referenced_works":["https://openalex.org/W10195015","https://openalex.org/W602807700","https://openalex.org/W1514891652","https://openalex.org/W1562713904","https://openalex.org/W1578518384","https://openalex.org/W1585344678","https://openalex.org/W1601795611","https://openalex.org/W1621083205","https://openalex.org/W1663973292","https://openalex.org/W1832278448","https://openalex.org/W1904579930","https://openalex.org/W1973316212","https://openalex.org/W1986291329","https://openalex.org/W2004492169","https://openalex.org/W2009953720","https://openalex.org/W2013985817","https://openalex.org/W2019132656","https://openalex.org/W2026131180","https://openalex.org/W2030228182","https://openalex.org/W2032190425","https://openalex.org/W2046434485","https://openalex.org/W2054585288","https://openalex.org/W2065154920","https://openalex.org/W2068400867","https://openalex.org/W2073596188","https://openalex.org/W2097062302","https://openalex.org/W2098976465","https://openalex.org/W2100068633","https://openalex.org/W2104241941","https://openalex.org/W2105248082","https://openalex.org/W2106309274","https://openalex.org/W2120072289","https://openalex.org/W2124150263","https://openalex.org/W2140427427","https://openalex.org/W2145023731","https://openalex.org/W2146605017","https://openalex.org/W2149659501","https://openalex.org/W2150190641","https://openalex.org/W2151984205","https://openalex.org/W2152701363","https://openalex.org/W2159061344","https://openalex.org/W2163002569","https://openalex.org/W2166809538","https://openalex.org/W2277164366","https://openalex.org/W2316495833","https://openalex.org/W2343416886","https://openalex.org/W2346890885","https://openalex.org/W2463041620","https://openalex.org/W2509404275","https://openalex.org/W2515884307","https://openalex.org/W2613049942","https://openalex.org/W2756307947","https://openalex.org/W2769684747","https://openalex.org/W2798103654","https://openalex.org/W2912293426","https://openalex.org/W2969075423","https://openalex.org/W3003964240","https://openalex.org/W3023212445","https://openalex.org/W3101139917","https://openalex.org/W3121570115","https://openalex.org/W4242010931","https://openalex.org/W6600413851","https://openalex.org/W6633870064","https://openalex.org/W6639669981"],"related_works":["https://openalex.org/W2371136327","https://openalex.org/W4293234107","https://openalex.org/W2370549269","https://openalex.org/W2386824811","https://openalex.org/W2354618530","https://openalex.org/W2081226903","https://openalex.org/W2363452175","https://openalex.org/W2375225935","https://openalex.org/W1970319972","https://openalex.org/W2953254336"],"abstract_inverted_index":{"Fitting":[0],"ellipses":[1],"from":[2,133],"unrecognized":[3],"data":[4,76,105],"is":[5,62],"a":[6,32],"fundamental":[7],"problem":[8],"in":[9,27,46],"computer":[10],"vision":[11],"and":[12,34,49,73,79,112,131,146,163,168],"pattern":[13],"recognition.":[14],"Classic":[15],"least-squares":[16],"based":[17],"methods":[18,145],"are":[19,101],"sensitive":[20],"to":[21,67,83,110,116],"outliers.":[22],"To":[23],"address":[24],"this":[25,28],"problem,":[26],"paper,":[29],"we":[30],"present":[31],"novel":[33],"effective":[35],"method":[36,61,151],"called":[37],"hierarchical":[38],"Gaussian":[39,56],"mixture":[40,57],"models":[41,58],"(HGMM)":[42],"for":[43,75],"ellipse":[44,97],"fitting":[45,71,166],"noisy,":[47],"outliers-contained,":[48],"occluded":[50],"settings":[51],"on":[52,103,121],"the":[53,87,91],"basis":[54],"of":[55,90,142],"(GMM).":[59],"This":[60],"crafted":[63],"into":[64],"two":[65],"layers":[66],"significantly":[68],"improve":[69],"its":[70,158],"accuracy":[72],"robustness":[74,160],"containing":[77],"outliers/noise":[78],"has":[80,152],"been":[81],"proven":[82],"effectively":[84],"narrow":[85],"down":[86],"iterative":[88],"interval":[89],"kernel":[92],"bandwidth,":[93],"thereby":[94],"speeding":[95],"up":[96],"fitting.":[98],"Extensive":[99],"experiments":[100],"conducted":[102],"synthetic":[104],"including":[106,124],"substantial":[107],"outliers":[108,162],"(up":[109,115],"60%)":[111],"strong":[113],"noise":[114],"200%)":[117],"as":[118,120,157],"well":[119],"real":[122],"images":[123,127,132],"complex":[125],"benchmark":[126],"with":[128,140],"heavy":[129],"occlusion":[130],"versatile":[134],"applications.":[135],"We":[136],"compare":[137],"our":[138,149],"results":[139],"those":[141],"representative":[143],"state-of-the-art":[144],"demonstrate":[147],"that":[148],"proposed":[150],"several":[153],"salient":[154],"advantages,":[155],"such":[156],"high":[159,165],"against":[161],"noise,":[164],"accuracy,":[167],"improved":[169],"performance.":[170]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-03-26T15:22:09.906841","created_date":"2025-10-10T00:00:00"}