{"id":"https://openalex.org/W2133813984","doi":"https://doi.org/10.1109/iccv.2007.4409190","title":"Two Minimal Problems for Cameras with Radial Distortion","display_name":"Two Minimal Problems for Cameras with Radial Distortion","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2133813984","doi":"https://doi.org/10.1109/iccv.2007.4409190","mag":"2133813984"},"language":"en","primary_location":{"id":"doi:10.1109/iccv.2007.4409190","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iccv.2007.4409190","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE 11th International Conference on Computer Vision","raw_type":"proceedings-article"},"type":"conference-paper","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/A5071099164","display_name":"Zuzana K\u00fakelov\u00e1","orcid":"https://orcid.org/0000-0002-1916-8829"},"institutions":[{"id":"https://openalex.org/I4210161785","display_name":"Abiola Ajimobi Technical University Ibadan","ror":"https://ror.org/05tb13r23","country_code":"NG","type":"education","lineage":["https://openalex.org/I4210161785"]},{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ","NG"],"is_corresponding":false,"raw_author_name":"Zuzana Kukelova","raw_affiliation_strings":["Center for Machine Perception, Department of Cybernetics,  Faculty of Elec. Engineering, Czech Technical University, Prague, Czech Republic","Czech Tech. Univ., Prague"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Machine Perception, Department of Cybernetics,  Faculty of Elec. Engineering, Czech Technical University, Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]},{"raw_affiliation_string":"Czech Tech. Univ., Prague","institution_ids":["https://openalex.org/I4210161785","https://openalex.org/I44504214"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043222506","display_name":"Tom\u00e1\u0161 Pajdla","orcid":"https://orcid.org/0000-0001-6325-0072"},"institutions":[{"id":"https://openalex.org/I4210161785","display_name":"Abiola Ajimobi Technical University Ibadan","ror":"https://ror.org/05tb13r23","country_code":"NG","type":"education","lineage":["https://openalex.org/I4210161785"]},{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ","NG"],"is_corresponding":false,"raw_author_name":"Tomas Pajdla","raw_affiliation_strings":["Center for Machine Perception, Department of Cybernetics,  Faculty of Elec. Engineering, Czech Technical University, Prague, Czech Republic","Czech Tech. Univ., Prague"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Machine Perception, Department of Cybernetics,  Faculty of Elec. Engineering, Czech Technical University, Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]},{"raw_affiliation_string":"Czech Tech. Univ., Prague","institution_ids":["https://openalex.org/I4210161785","https://openalex.org/I44504214"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T10638","display_name":"Optical measurement and interference techniques","score":0.9995999932289124,"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":0.9954000115394592,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/epipolar-geometry","display_name":"Epipolar geometry","score":0.9799070358276367},{"id":"https://openalex.org/keywords/fundamental-matrix","display_name":"Fundamental matrix (linear differential equation)","score":0.6846433877944946},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.6014277935028076},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5651060938835144},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4985220432281494},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.476578950881958},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.46178796887397766},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.46020764112472534},{"id":"https://openalex.org/keywords/image-rectification","display_name":"Image rectification","score":0.4232233464717865},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41968023777008057},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32627540826797485},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.3099071681499481},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24093449115753174},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12507906556129456}],"concepts":[{"id":"https://openalex.org/C23379248","wikidata":"https://www.wikidata.org/wiki/Q200904","display_name":"Epipolar geometry","level":3,"score":0.9799070358276367},{"id":"https://openalex.org/C2780427248","wikidata":"https://www.wikidata.org/wiki/Q17014996","display_name":"Fundamental matrix (linear differential equation)","level":2,"score":0.6846433877944946},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.6014277935028076},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5651060938835144},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4985220432281494},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.476578950881958},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.46178796887397766},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.46020764112472534},{"id":"https://openalex.org/C171614847","wikidata":"https://www.wikidata.org/wiki/Q1262415","display_name":"Image rectification","level":4,"score":0.4232233464717865},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41968023777008057},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32627540826797485},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.3099071681499481},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24093449115753174},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12507906556129456},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C50942859","wikidata":"https://www.wikidata.org/wiki/Q4967193","display_name":"Rectification","level":3,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/iccv.2007.4409190","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iccv.2007.4409190","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE 11th International Conference on Computer Vision","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.152.3110","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.152.3110","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://cmp.felk.cvut.cz/~kukelova/publications/Kukelova-Pajdla-OMNIVIS-2007.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1483218536","https://openalex.org/W1496447336","https://openalex.org/W1509632079","https://openalex.org/W1604184456","https://openalex.org/W1683871780","https://openalex.org/W1819864338","https://openalex.org/W2033819227","https://openalex.org/W2085261163","https://openalex.org/W2096837062","https://openalex.org/W2097382602","https://openalex.org/W2097649661","https://openalex.org/W2103569660","https://openalex.org/W2109635530","https://openalex.org/W2124404372","https://openalex.org/W2125774547","https://openalex.org/W2128687423","https://openalex.org/W2131412102","https://openalex.org/W2139016873","https://openalex.org/W2142105429","https://openalex.org/W2142262446","https://openalex.org/W2150207818","https://openalex.org/W2150495450","https://openalex.org/W2155799618","https://openalex.org/W2160888640","https://openalex.org/W2169664520","https://openalex.org/W2213827023","https://openalex.org/W2319466955","https://openalex.org/W4234426551","https://openalex.org/W6628696307","https://openalex.org/W6629766475","https://openalex.org/W6637311827","https://openalex.org/W6658838613","https://openalex.org/W6678393340","https://openalex.org/W6681356515","https://openalex.org/W6684359657"],"related_works":["https://openalex.org/W2755641224","https://openalex.org/W2394408411","https://openalex.org/W2113560889","https://openalex.org/W3168103620","https://openalex.org/W2370708703","https://openalex.org/W2002328018","https://openalex.org/W1570293554","https://openalex.org/W2393556269","https://openalex.org/W2134036553","https://openalex.org/W2119104081"],"abstract_inverted_index":{"Epipolar":[0],"geometry":[1,71,100],"and":[2,21,172],"relative":[3],"camera":[4],"pose":[5],"computation":[6],"for":[7,68,83,97,132],"uncalibrated":[8,133],"cameras":[9,51,73,86,103,134],"with":[10,74,87,135],"radial":[11,75,89,137],"distortion":[12],"has":[13,34],"recently":[14],"been":[15,35],"formulated":[16],"as":[17],"a":[18,80,129,157],"minimal":[19,40,66,81,130],"problem":[20,119,143],"successfully":[22],"solved":[23,146],"in":[24,122,150,162],"floating":[25],"point":[26],"arithmetics.":[27,125,165],"The":[28],"singularity":[29],"of":[30,42,72,101,108,159],"the":[31,39,50,92,98,106,118,142,168],"fundamental":[32],"matrix":[33],"used":[36],"to":[37,44,104,113],"reduce":[38,105],"number":[41,107],"points":[43,110,149],"eight.":[45],"It":[46],"was":[47],"assumed":[48],"that":[49,117,141],"were":[52],"not":[53],"calibrated":[54,85,102],"but":[55],"had":[56],"same":[57,88],"distortions.":[58,138],"In":[59],"this":[60],"paper":[61],"we":[62,78,127],"formulate":[63],"two":[64,151],"new":[65],"problems":[67],"estimating":[69],"epipolar":[70,99],"distortion.":[76,90],"First":[77],"present":[79,128],"algorithm":[82,131],"partially":[84],"Using":[91],"trace":[93],"constraint":[94],"which":[95],"holds":[96],"necessary":[109],"from":[111],"eight":[112],"six.":[114],"We":[115,139,166],"demonstrate":[116,167],"is":[120],"solvable":[121],"exact":[123,163],"rational":[124,164],"Secondly,":[126],"different":[136],"show":[140],"can":[144],"be":[145],"using":[147],"nine":[148],"views":[152],"by":[153,156],"manipulating":[154],"polynomials":[155],"sequence":[158],"Gauss-Jordan":[160],"eliminations":[161],"algorithms":[169],"on":[170],"synthetic":[171],"real":[173],"data.":[174]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
