{"id":"https://openalex.org/W2014148112","doi":"https://doi.org/10.1109/cvpr.2010.5540088","title":"Geometric properties of multiple reflections in catadioptric camera with two planar mirrors","display_name":"Geometric properties of multiple reflections in catadioptric camera with two planar mirrors","publication_year":2010,"publication_date":"2010-06-01","ids":{"openalex":"https://openalex.org/W2014148112","doi":"https://doi.org/10.1109/cvpr.2010.5540088","mag":"2014148112"},"language":"en","primary_location":{"id":"doi:10.1109/cvpr.2010.5540088","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2010.5540088","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"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/A5015981200","display_name":"Xianghua Ying","orcid":"https://orcid.org/0000-0002-9785-0727"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xianghua Ying","raw_affiliation_strings":["Key Laboratory of Machine Perception, Ministry of Education, Peking University, Beijing, China","The Key Laboratory of Machine Perception (Ministry of Education), Peking University, Beijing, 100871, P.R. China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Machine Perception, Ministry of Education, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"The Key Laboratory of Machine Perception (Ministry of Education), Peking University, Beijing, 100871, P.R. China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011830457","display_name":"Kun Peng","orcid":"https://orcid.org/0000-0001-6885-9899"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kun Peng","raw_affiliation_strings":["Key Laboratory of Machine Perception, Ministry of Education, Peking University, Beijing, China","The Key Laboratory of Machine Perception (Ministry of Education), Peking University, Beijing, 100871, P.R. China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Machine Perception, Ministry of Education, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"The Key Laboratory of Machine Perception (Ministry of Education), Peking University, Beijing, 100871, P.R. China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Ren Ren","orcid":null},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ren Ren","raw_affiliation_strings":["Key Laboratory of Machine Perception, Ministry of Education, Peking University, Beijing, China","The Key Laboratory of Machine Perception (Ministry of Education), Peking University, Beijing, 100871, P.R. China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Machine Perception, Ministry of Education, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"The Key Laboratory of Machine Perception (Ministry of Education), Peking University, Beijing, 100871, P.R. China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017031914","display_name":"Hongbin Zha","orcid":"https://orcid.org/0000-0001-5860-4673"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongbin Zha","raw_affiliation_strings":["Key Laboratory of Machine Perception, Ministry of Education, Peking University, Beijing, China","The Key Laboratory of Machine Perception (Ministry of Education), Peking University, Beijing, 100871, P.R. China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Machine Perception, Ministry of Education, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"The Key Laboratory of Machine Perception (Ministry of Education), Peking University, Beijing, 100871, P.R. China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5015981200"],"corresponding_institution_ids":["https://openalex.org/I20231570"],"apc_list":null,"apc_paid":null,"fwci":2.2629,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.8874775,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1126","last_page":"1132"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10638","display_name":"Optical measurement and interference 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"}},"topics":[{"id":"https://openalex.org/T10638","display_name":"Optical measurement and interference 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/T10531","display_name":"Advanced Vision and Imaging","score":0.9997000098228455,"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/T12549","display_name":"Image and Object Detection Techniques","score":0.9988999962806702,"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/catadioptric-system","display_name":"Catadioptric system","score":0.9458188414573669},{"id":"https://openalex.org/keywords/pinhole-camera","display_name":"Pinhole camera","score":0.6360584497451782},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6168055534362793},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.6092819571495056},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.6059618592262268},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5734558701515198},{"id":"https://openalex.org/keywords/cross-ratio","display_name":"Cross-ratio","score":0.46683135628700256},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45753008127212524},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4441651999950409},{"id":"https://openalex.org/keywords/vanishing-point","display_name":"Vanishing point","score":0.4416215121746063},{"id":"https://openalex.org/keywords/pinhole-camera-model","display_name":"Pinhole camera model","score":0.4343460202217102},{"id":"https://openalex.org/keywords/reflection","display_name":"Reflection (computer programming)","score":0.42356932163238525},{"id":"https://openalex.org/keywords/camera-resectioning","display_name":"Camera resectioning","score":0.35428494215011597},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34812405705451965},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.3394956588745117},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.323172926902771},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.26095351576805115},{"id":"https://openalex.org/keywords/camera-auto-calibration","display_name":"Camera auto-calibration","score":0.2447769045829773},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23566386103630066},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.23074299097061157}],"concepts":[{"id":"https://openalex.org/C153396827","wikidata":"https://www.wikidata.org/wiki/Q1142960","display_name":"Catadioptric system","level":3,"score":0.9458188414573669},{"id":"https://openalex.org/C2776374813","wikidata":"https://www.wikidata.org/wiki/Q313742","display_name":"Pinhole camera","level":2,"score":0.6360584497451782},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6168055534362793},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6092819571495056},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.6059618592262268},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5734558701515198},{"id":"https://openalex.org/C101586328","wikidata":"https://www.wikidata.org/wiki/Q899539","display_name":"Cross-ratio","level":2,"score":0.46683135628700256},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45753008127212524},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4441651999950409},{"id":"https://openalex.org/C99404194","wikidata":"https://www.wikidata.org/wiki/Q163362","display_name":"Vanishing point","level":3,"score":0.4416215121746063},{"id":"https://openalex.org/C199996500","wikidata":"https://www.wikidata.org/wiki/Q14369636","display_name":"Pinhole camera model","level":4,"score":0.4343460202217102},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.42356932163238525},{"id":"https://openalex.org/C110898773","wikidata":"https://www.wikidata.org/wiki/Q2933935","display_name":"Camera resectioning","level":2,"score":0.35428494215011597},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34812405705451965},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.3394956588745117},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.323172926902771},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26095351576805115},{"id":"https://openalex.org/C94816000","wikidata":"https://www.wikidata.org/wiki/Q5026006","display_name":"Camera auto-calibration","level":3,"score":0.2447769045829773},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23566386103630066},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.23074299097061157},{"id":"https://openalex.org/C15336307","wikidata":"https://www.wikidata.org/wiki/Q1766051","display_name":"Lens (geology)","level":2,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cvpr.2010.5540088","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2010.5540088","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1504729745","https://openalex.org/W1507681844","https://openalex.org/W1514635661","https://openalex.org/W1555348440","https://openalex.org/W1605885907","https://openalex.org/W1885010708","https://openalex.org/W1982365346","https://openalex.org/W1989046233","https://openalex.org/W1991749495","https://openalex.org/W1992989752","https://openalex.org/W2006188145","https://openalex.org/W2019769120","https://openalex.org/W2031998857","https://openalex.org/W2033819227","https://openalex.org/W2035837348","https://openalex.org/W2043146861","https://openalex.org/W2099162634","https://openalex.org/W2101185402","https://openalex.org/W2104039528","https://openalex.org/W2104508476","https://openalex.org/W2107738794","https://openalex.org/W2113455062","https://openalex.org/W2119848854","https://openalex.org/W2120433755","https://openalex.org/W2126644701","https://openalex.org/W2132653682","https://openalex.org/W2140427427","https://openalex.org/W2141728365","https://openalex.org/W2150289470","https://openalex.org/W2156100165","https://openalex.org/W2162265152","https://openalex.org/W2162767881","https://openalex.org/W2169664520","https://openalex.org/W6630162374","https://openalex.org/W6630265477","https://openalex.org/W6631024501","https://openalex.org/W6661259537","https://openalex.org/W6675124635","https://openalex.org/W6677227242","https://openalex.org/W6678251113","https://openalex.org/W6684359657","https://openalex.org/W6858345623"],"related_works":["https://openalex.org/W2799243310","https://openalex.org/W2198274805","https://openalex.org/W2083937863","https://openalex.org/W2097181751","https://openalex.org/W2169009293","https://openalex.org/W2370621620","https://openalex.org/W1993371703","https://openalex.org/W1979815726","https://openalex.org/W2014148112","https://openalex.org/W2297046152"],"abstract_inverted_index":{"A":[0],"catadioptric":[1],"system":[2],"consisting":[3],"of":[4,67,93,149],"a":[5,24,71,85,94,100,110,114,141],"pinhole":[6],"camera":[7],"and":[8,26,59,80,97,105],"two":[9,19,132,157],"planar":[10],"mirrors":[11,20],"is":[12,34,112,143,164,171],"deeply":[13],"investigated":[14],"in":[15,41,140],"this":[16],"paper.":[17],"The":[18],"combine":[21],"to":[22,109,122,147],"form":[23],"corner":[25,44],"face-to-face":[27],"with":[28,145],"the":[29,42,49,57,89,106,150,169],"pinhole.":[30],"Their":[31],"relative":[32],"pose":[33],"unknown.":[35],"An":[36],"object":[37,58,69],"will":[38],"be":[39,129,161],"reflected":[40],"mirror":[43],"one-time":[45],"or":[46],"multiple-times.":[47],"Using":[48],"pinhole,":[50],"we":[51],"may":[52],"take":[53],"an":[54,68],"image":[55],"containing":[56],"its":[60,81,98],"reflections,":[61,99],"i.e.,":[62],"simultaneously":[63],"imaging":[64],"multiple":[65],"views":[66],"by":[70,137],"single":[72],"camera.":[73],"We":[74,87],"discovered":[75],"that":[76],"each":[77,126],"3D":[78,95,151],"point":[79,90,96],"reflections":[82],"lie":[83],"on":[84,166],"circle.":[86,116],"call":[88],"set":[91],"composed":[92],"Reflection":[101],"Point":[102],"Group":[103],"(RPG),":[104],"circle":[107],"related":[108],"RPG":[111,115,118,127],"called":[113],"All":[117],"circles":[119],"are":[120],"parallel":[121,167],"one":[123],"another.":[124],"Furthermore,":[125],"can":[128,160],"partitioned":[130],"into":[131],"separate":[133],"subgroups.":[134],"Shape":[135],"formed":[136],"all":[138],"points":[139],"subgroup":[142],"invariant":[144,176],"respect":[146],"location":[148],"point.":[152],"From":[153],"these":[154],"geometric":[155],"properties,":[156],"calibration":[158],"approaches":[159],"utilized:":[162],"One":[163],"based":[165],"circles;":[168],"other":[170],"using":[172],"2D":[173],"homographies":[174],"among":[175],"shapes.":[177],"Experiments":[178],"validate":[179],"our":[180],"approaches.":[181]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
