{"id":"https://openalex.org/W2006483807","doi":"https://doi.org/10.1109/cvpr.2012.6247850","title":"General and nested Wiberg minimization","display_name":"General and nested Wiberg minimization","publication_year":2012,"publication_date":"2012-06-01","ids":{"openalex":"https://openalex.org/W2006483807","doi":"https://doi.org/10.1109/cvpr.2012.6247850","mag":"2006483807"},"language":"en","primary_location":{"id":"doi:10.1109/cvpr.2012.6247850","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2012.6247850","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 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/A5073777450","display_name":"Dennis Strelow","orcid":null},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"D. Strelow","raw_affiliation_strings":["Google, Inc., Mountain View, CA, USA","Google, Mountain View, CA;"],"affiliations":[{"raw_affiliation_string":"Google, Inc., Mountain View, CA, USA","institution_ids":["https://openalex.org/I1291425158"]},{"raw_affiliation_string":"Google, Mountain View, CA;","institution_ids":["https://openalex.org/I1291425158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073777450"],"corresponding_institution_ids":["https://openalex.org/I1291425158"],"apc_list":null,"apc_paid":null,"fwci":4.1971,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.93770742,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"23","issue":null,"first_page":"1584","last_page":"1591"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9980999827384949,"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":0.994700014591217,"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/minification","display_name":"Minification","score":0.5183383226394653},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.4794415533542633},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.475710928440094},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.43189185857772827},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42218029499053955},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42202210426330566},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3189021944999695},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.07493442296981812}],"concepts":[{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5183383226394653},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.4794415533542633},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.475710928440094},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.43189185857772827},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42218029499053955},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42202210426330566},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3189021944999695},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.07493442296981812}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cvpr.2012.6247850","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2012.6247850","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE Conference on Computer Vision and Pattern Recognition","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.231.3199","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.231.3199","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dennis-strelow.com/papers/documents/strelow_cvpr12.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":19,"referenced_works":["https://openalex.org/W1508960934","https://openalex.org/W1606018923","https://openalex.org/W1902027874","https://openalex.org/W1943001502","https://openalex.org/W1977280501","https://openalex.org/W1992989752","https://openalex.org/W2033819227","https://openalex.org/W2040763577","https://openalex.org/W2101117936","https://openalex.org/W2103305137","https://openalex.org/W2121578809","https://openalex.org/W2124584309","https://openalex.org/W2150064935","https://openalex.org/W2282344314","https://openalex.org/W2787523326","https://openalex.org/W2904871600","https://openalex.org/W4234534407","https://openalex.org/W6675479683","https://openalex.org/W7073876970"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2794559785","https://openalex.org/W1754499339","https://openalex.org/W2013873776","https://openalex.org/W2053286651","https://openalex.org/W2950281908","https://openalex.org/W2963117165","https://openalex.org/W2980963558"],"abstract_inverted_index":{"Wiberg":[0,98,112,137,169,191],"matrix":[1,5,40],"factorization":[2,75,181],"breaks":[3],"a":[4,96,128,135,164,177,197],"Y":[6],"into":[7],"low-rank":[8],"factors":[9,38],"U":[10,34],"and":[11,27,50,152,175],"V":[12,16,23,44],"by":[13],"solving":[14,147],"for":[15,100,139,148,192,200,201],"in":[17,84],"closed":[18],"form":[19],"given":[20],"U,":[21,26],"linearizing":[22],"(U)":[24],"about":[25],"iteratively":[28],"minimizing":[29,63],"\u2225Y-UV":[30,64],"(U)\u2225with":[31],"respect":[32],"to":[33,57,76],"only.":[35],"This":[36],"approach":[37,56,73],"the":[39,46,93],"while":[41],"effectively":[42,119],"removing":[43,120],"from":[45,127],"minimization.":[47,129],"Recently":[48],"Eriksson":[49],"van":[51],"den":[52],"Hengel":[53],"extended":[54],"this":[55,132],"L":[58,101,140,158,170,187],"<sub":[59,66,102,141,159,171,188],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[60,67,103,142,160,172,189],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[61,68,104,143,161,173,190],",":[62],"(U)\u2225":[65],".":[69],"We":[70,91,107,130,155],"generalize":[71],"their":[72],"beyond":[74],"minimize":[77],"an":[78],"arbitrary":[79],"function":[80],"that":[81,110],"is":[82],"nonlinear":[83],"each":[85],"of":[86,89,122,125,168],"two":[87,121],"sets":[88,124],"variables.":[90],"demonstrate":[92,131],"idea":[94,133],"with":[95,134],"practical":[97],"algorithm":[99,138],"bundle":[105,145],"adjustment.":[106],"also":[108,156],"show":[109],"one":[111],"minimization":[113],"can":[114],"be":[115],"nested":[116,136],"inside":[117],"another,":[118],"three":[123],"variables":[126],"projective":[144,153],"adjustment,":[146],"camera":[149],"matrices,":[150],"points,":[151],"depths.":[154],"revisit":[157],"factorization,":[162,174],"giving":[163],"greatly":[165],"simplified":[166],"presentation":[167],"presenting":[176],"successive":[178],"linear":[179,184],"programming":[180,185],"algorithm.":[182],"Successive":[183],"outperforms":[186],"most":[193],"large":[194],"inputs,":[195],"establishing":[196],"new":[198],"state-of-the-art":[199],"those":[202],"cases.":[203]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}