{"id":"https://openalex.org/W2028268998","doi":"https://doi.org/10.1109/cvpr.2011.5995596","title":"Beyond Alhazen's problem: Analytical projection model for non-central catadioptric cameras with quadric mirrors","display_name":"Beyond Alhazen's problem: Analytical projection model for non-central catadioptric cameras with quadric mirrors","publication_year":2011,"publication_date":"2011-06-01","ids":{"openalex":"https://openalex.org/W2028268998","doi":"https://doi.org/10.1109/cvpr.2011.5995596","mag":"2028268998"},"language":"en","primary_location":{"id":"doi:10.1109/cvpr.2011.5995596","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2011.5995596","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"CVPR 2011","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/A5087306796","display_name":"Amit Agrawal","orcid":"https://orcid.org/0000-0002-9619-7623"},"institutions":[{"id":"https://openalex.org/I4210159266","display_name":"Mitsubishi Electric (United States)","ror":"https://ror.org/053jnhe44","country_code":"US","type":"company","lineage":["https://openalex.org/I1306287861","https://openalex.org/I4210133125","https://openalex.org/I4210159266"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Amit Agrawal","raw_affiliation_strings":["Mitsubishi Electric Research Laboratories, Inc., Cambridge, MA, USA","Mitsubishi Electric Research Labs (MERL), Cambridge MA, USA"],"affiliations":[{"raw_affiliation_string":"Mitsubishi Electric Research Laboratories, Inc., Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210159266"]},{"raw_affiliation_string":"Mitsubishi Electric Research Labs (MERL), Cambridge MA, USA","institution_ids":["https://openalex.org/I4210159266"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008067705","display_name":"Yuichi Taguchi","orcid":null},"institutions":[{"id":"https://openalex.org/I4210159266","display_name":"Mitsubishi Electric (United States)","ror":"https://ror.org/053jnhe44","country_code":"US","type":"company","lineage":["https://openalex.org/I1306287861","https://openalex.org/I4210133125","https://openalex.org/I4210159266"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuichi Taguchi","raw_affiliation_strings":["Mitsubishi Electric Research Laboratories, Inc., Cambridge, MA, USA","Mitsubishi Electric Research Labs (MERL), Cambridge MA, USA"],"affiliations":[{"raw_affiliation_string":"Mitsubishi Electric Research Laboratories, Inc., Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210159266"]},{"raw_affiliation_string":"Mitsubishi Electric Research Labs (MERL), Cambridge MA, USA","institution_ids":["https://openalex.org/I4210159266"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060350100","display_name":"Srikumar Ramalingam","orcid":"https://orcid.org/0000-0002-2598-0151"},"institutions":[{"id":"https://openalex.org/I4210159266","display_name":"Mitsubishi Electric (United States)","ror":"https://ror.org/053jnhe44","country_code":"US","type":"company","lineage":["https://openalex.org/I1306287861","https://openalex.org/I4210133125","https://openalex.org/I4210159266"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Srikumar Ramalingam","raw_affiliation_strings":["Mitsubishi Electric Research Laboratories, Inc., Cambridge, MA, USA","Mitsubishi Electric Research Labs (MERL), Cambridge MA, USA"],"affiliations":[{"raw_affiliation_string":"Mitsubishi Electric Research Laboratories, Inc., Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210159266"]},{"raw_affiliation_string":"Mitsubishi Electric Research Labs (MERL), Cambridge MA, USA","institution_ids":["https://openalex.org/I4210159266"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087306796"],"corresponding_institution_ids":["https://openalex.org/I4210159266"],"apc_list":null,"apc_paid":null,"fwci":3.4007,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.93680673,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"25","issue":null,"first_page":"2993","last_page":"3000"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10531","display_name":"Advanced Vision and Imaging","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/T10531","display_name":"Advanced Vision and Imaging","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/T10638","display_name":"Optical measurement and interference 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"}},{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.988261342048645},{"id":"https://openalex.org/keywords/quadric","display_name":"Quadric","score":0.723225474357605},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.6362749338150024},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.630270779132843},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.576024055480957},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.559816300868988},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4463377594947815},{"id":"https://openalex.org/keywords/bundle-adjustment","display_name":"Bundle adjustment","score":0.43452924489974976},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.38805192708969116},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32506006956100464},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.24680256843566895},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24652326107025146},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24399885535240173},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.14452821016311646},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08683794736862183},{"id":"https://openalex.org/keywords/lens","display_name":"Lens (geology)","score":0.08162105083465576}],"concepts":[{"id":"https://openalex.org/C153396827","wikidata":"https://www.wikidata.org/wiki/Q1142960","display_name":"Catadioptric system","level":3,"score":0.988261342048645},{"id":"https://openalex.org/C2779219049","wikidata":"https://www.wikidata.org/wiki/Q852117","display_name":"Quadric","level":2,"score":0.723225474357605},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.6362749338150024},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.630270779132843},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.576024055480957},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.559816300868988},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4463377594947815},{"id":"https://openalex.org/C179458375","wikidata":"https://www.wikidata.org/wiki/Q1020763","display_name":"Bundle adjustment","level":3,"score":0.43452924489974976},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.38805192708969116},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32506006956100464},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.24680256843566895},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24652326107025146},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24399885535240173},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.14452821016311646},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08683794736862183},{"id":"https://openalex.org/C15336307","wikidata":"https://www.wikidata.org/wiki/Q1766051","display_name":"Lens (geology)","level":2,"score":0.08162105083465576}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cvpr.2011.5995596","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2011.5995596","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"CVPR 2011","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.224.9166","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.224.9166","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.umiacs.umd.edu/%7Eaagrawal/cvpr11/fp/AnalyticalForwardProjection.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W165571211","https://openalex.org/W175991304","https://openalex.org/W1485649967","https://openalex.org/W1595986982","https://openalex.org/W1851037202","https://openalex.org/W1968032174","https://openalex.org/W1988519517","https://openalex.org/W2018464134","https://openalex.org/W2022159412","https://openalex.org/W2031998857","https://openalex.org/W2043278864","https://openalex.org/W2051317734","https://openalex.org/W2096629663","https://openalex.org/W2103684937","https://openalex.org/W2111844217","https://openalex.org/W2117248954","https://openalex.org/W2121470318","https://openalex.org/W2125579377","https://openalex.org/W2132139399","https://openalex.org/W2132815208","https://openalex.org/W2138821028","https://openalex.org/W2140898451","https://openalex.org/W2141229670","https://openalex.org/W2146535213","https://openalex.org/W2153448067","https://openalex.org/W2168545424","https://openalex.org/W2321208537","https://openalex.org/W2342745611","https://openalex.org/W4234122739","https://openalex.org/W6628955725","https://openalex.org/W6635642175","https://openalex.org/W6677345097","https://openalex.org/W6679698672","https://openalex.org/W6682900524"],"related_works":["https://openalex.org/W2084759888","https://openalex.org/W2350925281","https://openalex.org/W2107738794","https://openalex.org/W1503278857","https://openalex.org/W2117804033","https://openalex.org/W165571211","https://openalex.org/W3138324983","https://openalex.org/W4300294291","https://openalex.org/W2037983021","https://openalex.org/W2735015004"],"abstract_inverted_index":{"Catadioptric":[0],"cameras":[1,136],"are":[2,21,52,224],"widely":[3],"used":[4,171],"to":[5,23,35,61,181,199],"increase":[6],"the":[7,30,36,39,62,90,102,113,143,148,197],"field":[8],"of":[9,64,92,105,150,206],"view":[10],"using":[11,55,184,216],"mirrors.":[12,211],"Central":[13],"catadioptric":[14,43,80,135,167],"systems":[15,44],"having":[16],"an":[17,65,74,84,121,139,220],"effective":[18],"single":[19,130],"viewpoint":[20],"easy":[22],"model":[24,77],"and":[25,72,116,191,213,219],"use,":[26],"but":[27,51],"severely":[28],"constraint":[29],"camera":[31,49,114,144,159,168,207,223],"positioning":[32],"with":[33,109,208],"respect":[34],"mirror.":[37],"On":[38],"other":[40],"hand,":[41],"non-central":[42,79,134,166],"allow":[45,156],"greater":[46],"flexibility":[47],"in":[48,128],"placement,":[50,115],"often":[53],"approximated":[54],"central":[56],"or":[57],"linear":[58],"models":[59],"due":[60],"lack":[63],"exact":[66,75],"model.":[67],"We":[68,82],"bridge":[69],"this":[70,162],"gap":[71],"describe":[73],"projection":[76,91],"for":[78,89,172,203],"systems.":[81],"derive":[83],"analytical":[85,163],"`forward":[86],"projection'":[87],"equation":[88,127],"a":[93,98,106,129,151,165],"3D":[94,178],"point":[95],"reflected":[96],"by":[97],"quadric":[99,210],"mirror":[100],"on":[101,112,147],"imaging":[103],"plane":[104,192],"perspective":[107,182,222],"camera,":[108],"no":[110],"restrictions":[111],"show":[117,200],"that":[118],"it":[119],"is":[120,145,196],"8":[122],"<sup":[123],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[124],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">th</sup>":[125],"degree":[126],"unknown.":[131],"While":[132],"previous":[133],"primarily":[137],"use":[138],"axial":[140],"configuration":[141],"where":[142],"placed":[146],"axis":[149],"rotationally":[152],"symmetric":[153],"mirror,":[154],"we":[155],"off-axis":[157,204,221],"(any)":[158],"placement.":[160],"Using":[161],"model,":[164],"can":[169],"be":[170],"sparse":[173],"as":[174,176,188],"well":[175],"dense":[177],"reconstruction":[179],"similar":[180],"cameras,":[183],"well-known":[185],"algorithms":[186],"such":[187,201],"bundle":[189],"adjustment":[190],"sweeping.":[193],"Our":[194],"paper":[195],"first":[198],"results":[202,215],"placement":[205],"multiple":[209],"Simulation":[212],"real":[214],"parabolic":[217],"mirrors":[218],"demonstrated.":[225]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
