{"id":"https://openalex.org/W2127365346","doi":"https://doi.org/10.1109/cvpr.2009.5206829","title":"A minimal parameterization of the trifocal tensor","display_name":"A minimal parameterization of the trifocal tensor","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2127365346","doi":"https://doi.org/10.1109/cvpr.2009.5206829","mag":"2127365346"},"language":"en","primary_location":{"id":"doi:10.1109/cvpr.2009.5206829","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2009.5206829","pdf_url":null,"source":{"id":"https://openalex.org/S4363607795","display_name":"2009 IEEE Conference on Computer Vision and Pattern Recognition","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE 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/A5075929754","display_name":"Klas Nordberg","orcid":null},"institutions":[{"id":"https://openalex.org/I102134673","display_name":"Link\u00f6ping University","ror":"https://ror.org/05ynxx418","country_code":"SE","type":"education","lineage":["https://openalex.org/I102134673"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Klas Nordberg","raw_affiliation_strings":["Computer Vision Laboratory, Link\u00f6ping University, Sweden","Comput. Vision Lab., Linkoping Univ., Linkoping, Sweden"],"affiliations":[{"raw_affiliation_string":"Computer Vision Laboratory, Link\u00f6ping University, Sweden","institution_ids":["https://openalex.org/I102134673"]},{"raw_affiliation_string":"Comput. Vision Lab., Linkoping Univ., Linkoping, Sweden","institution_ids":["https://openalex.org/I102134673"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5075929754"],"corresponding_institution_ids":["https://openalex.org/I102134673"],"apc_list":null,"apc_paid":null,"fwci":0.2471,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.61284514,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1224","last_page":"1230"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10531","display_name":"Advanced Vision and Imaging","score":0.9740999937057495,"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":0.9740999937057495,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9700000286102295,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9520999789237976,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6920398473739624},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6284621953964233},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.584604024887085},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4702916145324707},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39167994260787964},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.323208212852478},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2626945972442627},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.240997314453125},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18449127674102783}],"concepts":[{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6920398473739624},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6284621953964233},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.584604024887085},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4702916145324707},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39167994260787964},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.323208212852478},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2626945972442627},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.240997314453125},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18449127674102783}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cvpr.2009.5206829","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2009.5206829","pdf_url":null,"source":{"id":"https://openalex.org/S4363607795","display_name":"2009 IEEE Conference on Computer Vision and Pattern Recognition","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE Conference on Computer Vision and Pattern Recognition","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7300000190734863,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1531454918","https://openalex.org/W1586310141","https://openalex.org/W2033819227","https://openalex.org/W2102481828","https://openalex.org/W2137638987","https://openalex.org/W2138620157","https://openalex.org/W2147169432","https://openalex.org/W2170026011","https://openalex.org/W2170625182","https://openalex.org/W2209124607","https://openalex.org/W3022352042","https://openalex.org/W6632010472","https://openalex.org/W6635263668"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2047382916","https://openalex.org/W2142176343"],"abstract_inverted_index":{"The":[0,67],"paper":[1,68],"describes":[2,70],"a":[3,33,71,84,106,111,115,152,186],"minimal":[4],"set":[5],"of":[6,32,83,110,124,137,167,181,197],"18":[7],"parameters":[8,21,28],"that":[9,117,177,201],"can":[10,101,129],"represent":[11],"any":[12],"trifocal":[13,48,139,183],"tensor":[14,35,49,113,116,140,184],"consistent":[15],"with":[16,37,147],"the":[17,59,63,76,81,94,119,138,143,148,157,162,168,178,182,195,198,202],"internal":[18,95,120],"constraints.":[19,121],"9":[20,27],"describe":[22,29],"three":[23,77],"orthogonal":[24,60,78],"matrices":[25,61,79],"and":[26],"10":[30],"elements":[31,39],"sparse":[34],"T\u0303":[36,56],"17":[38],"in":[40,62,80,127,207],"well-defined":[41],"positions":[42,196],"equal":[43],"to":[44,104,114,132,161],"zero.":[45],"Any":[46],"valid":[47],"is":[50,205],"then":[51],"given":[52,200],"as":[53,151],"some":[54],"specific":[55],"transformed":[57],"by":[58,194],"respective":[64],"image":[65,209],"domain.":[66],"also":[69],"simple":[72],"approach":[73],"for":[74,165],"estimating":[75],"case":[82],"general":[85,112],"3":[86,88,90],"\u00d7":[87,89],"tensor,":[91],"i.e.,":[92],"when":[93],"constraints":[96],"are":[97],"not":[98],"satisfied.":[99],"This":[100,122,155],"be":[102,130],"used":[103,131],"accomplish":[105],"least":[107],"squares":[108],"approximation":[109],"satisfies":[118],"type":[123],"constraint":[125,149,179,203],"enforcement,":[126,192],"turn,":[128],"obtain":[133],"an":[134],"improved":[135],"estimate":[136],"based":[141],"on":[142,173],"normalized":[144,208],"linear":[145],"algorithm,":[146],"enforcement":[150,180,204],"final":[153],"step.":[154],"makes":[156],"algorithm":[158,164],"more":[159],"similar":[160],"corresponding":[163],"estimation":[166],"fundamental":[169],"matrix.":[170],"An":[171],"experiment":[172],"synthetic":[174],"data":[175],"shows":[176],"produces":[185],"significantly":[187],"better":[188],"result":[189],"than":[190],"without":[191],"expressed":[193],"epipoles,":[199],"made":[206],"coordinates.":[210]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}