{"id":"https://openalex.org/W2135973942","doi":"https://doi.org/10.1109/cvpr.2008.4587793","title":"A general solution to the P4P problem for camera with unknown focal length","display_name":"A general solution to the P4P problem for camera with unknown focal length","publication_year":2008,"publication_date":"2008-06-01","ids":{"openalex":"https://openalex.org/W2135973942","doi":"https://doi.org/10.1109/cvpr.2008.4587793","mag":"2135973942"},"language":"en","primary_location":{"id":"doi:10.1109/cvpr.2008.4587793","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2008.4587793","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 IEEE Conference on Computer Vision and Pattern Recognition","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/A5041467320","display_name":"Martin Bujnak","orcid":null},"institutions":[{"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"],"is_corresponding":false,"raw_author_name":"Martin Bujnak","raw_affiliation_strings":["Center for Machine Perception, Czech Technical University, Prague, Czech Republic","Center for Machine Perception, Czech Tech. Univ., Prague"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Machine Perception, Czech Technical University, Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]},{"raw_affiliation_string":"Center for Machine Perception, Czech Tech. Univ., Prague","institution_ids":["https://openalex.org/I44504214"]}]},{"author_position":"middle","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/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"],"is_corresponding":false,"raw_author_name":"Zuzana Kukelova","raw_affiliation_strings":["Center for Machine Perception, Czech Technical University, Prague, Czech Republic","Center for Machine Perception, Czech Tech. Univ., Prague"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Machine Perception, Czech Technical University, Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]},{"raw_affiliation_string":"Center for Machine Perception, Czech Tech. Univ., Prague","institution_ids":["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/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"],"is_corresponding":false,"raw_author_name":"Tomas Pajdla","raw_affiliation_strings":["Center for Machine Perception, Czech Technical University, Prague, Czech Republic","Center for Machine Perception, Czech Tech. Univ., Prague"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Machine Perception, Czech Technical University, Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]},{"raw_affiliation_string":"Center for Machine Perception, Czech Tech. Univ., Prague","institution_ids":["https://openalex.org/I44504214"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I44504214"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":168,"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":0.9998000264167786,"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/T10531","display_name":"Advanced Vision and Imaging","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/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/T10638","display_name":"Optical measurement and interference techniques","score":0.9983000159263611,"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/focal-length","display_name":"Focal length","score":0.7373561859130859},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7314957976341248},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.6594597697257996},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.6413609385490417},{"id":"https://openalex.org/keywords/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.6188490390777588},{"id":"https://openalex.org/keywords/orientation","display_name":"Orientation (vector space)","score":0.5541125535964966},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.5338837504386902},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5186606645584106},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5002436637878418},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49565184116363525},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.4872547686100006},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4737173914909363},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4240213632583618},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3385722041130066},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13728433847427368},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12095388770103455},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.05915066599845886}],"concepts":[{"id":"https://openalex.org/C82552819","wikidata":"https://www.wikidata.org/wiki/Q193540","display_name":"Focal length","level":3,"score":0.7373561859130859},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7314957976341248},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.6594597697257996},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.6413609385490417},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.6188490390777588},{"id":"https://openalex.org/C16345878","wikidata":"https://www.wikidata.org/wiki/Q107472979","display_name":"Orientation (vector space)","level":2,"score":0.5541125535964966},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.5338837504386902},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5186606645584106},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5002436637878418},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49565184116363525},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.4872547686100006},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4737173914909363},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4240213632583618},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3385722041130066},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13728433847427368},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12095388770103455},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.05915066599845886},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"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/C15336307","wikidata":"https://www.wikidata.org/wiki/Q1766051","display_name":"Lens (geology)","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cvpr.2008.4587793","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2008.4587793","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 IEEE Conference on Computer Vision and Pattern Recognition","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.152.892","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.152.892","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/Bujnak-Kukelova-Pajdla-CVPR-2008.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.329.3520","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.329.3520","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mplab.ucsd.edu/wp-content/uploads/CVPR2008/Conference/data/papers/453.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":24,"referenced_works":["https://openalex.org/W1483218536","https://openalex.org/W1535871240","https://openalex.org/W1882087933","https://openalex.org/W1985565156","https://openalex.org/W1988874269","https://openalex.org/W2036273537","https://openalex.org/W2037115209","https://openalex.org/W2085261163","https://openalex.org/W2092472536","https://openalex.org/W2109191068","https://openalex.org/W2109635530","https://openalex.org/W2124404372","https://openalex.org/W2125774547","https://openalex.org/W2129613645","https://openalex.org/W2130017587","https://openalex.org/W2134237713","https://openalex.org/W2144409879","https://openalex.org/W2148442626","https://openalex.org/W2150495450","https://openalex.org/W2154422144","https://openalex.org/W2171244244","https://openalex.org/W2319466955","https://openalex.org/W6632142354","https://openalex.org/W6679467917"],"related_works":["https://openalex.org/W2929921717","https://openalex.org/W627423529","https://openalex.org/W2949221213","https://openalex.org/W605041788","https://openalex.org/W3149342578","https://openalex.org/W2950958018","https://openalex.org/W2117849070","https://openalex.org/W1984961932","https://openalex.org/W2056822213","https://openalex.org/W2116004197"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,13,30,65,73],"general":[4],"solution":[5,67],"to":[6],"the":[7,10,33,55,61,80,90,107],"determination":[8],"of":[9,12,22,32,75,93],"pose":[11],"perspective":[14],"camera":[15,50,56],"with":[16],"unknown":[17],"focal":[18,57],"length":[19],"from":[20,68],"images":[21],"four":[23,45,69],"3D":[24],"reference":[25],"points.":[26],"Our":[27],"problem":[28,62],"is":[29],"generalization":[31],"P3P":[34],"and":[35,53,63,84,101],"P4P":[36],"problems":[37],"previously":[38],"developed":[39],"for":[40,88],"fully":[41],"calibrated":[42],"cameras.":[43],"Given":[44],"2D-to-3D":[46],"correspondences,":[47],"we":[48,104],"estimate":[49],"position,":[51],"orientation":[52],"recover":[54],"length.":[58],"We":[59,78],"formulate":[60],"provide":[64],"minimal":[66],"points":[70],"by":[71],"solving":[72,89],"system":[74],"algebraic":[76,91],"equations.":[77],"compare":[79],"Hidden":[81],"variable":[82],"resultant":[83],"Grobner":[85,108],"basis":[86,109],"techniques":[87],"equations":[92],"our":[94],"problem.":[95],"By":[96],"evaluating":[97],"them":[98],"on":[99,102],"synthetic":[100],"real-data,":[103],"show":[105],"that":[106],"technique":[110],"provides":[111],"stable":[112],"results.":[113]},"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":8}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
