{"id":"https://openalex.org/W1599944587","doi":"https://doi.org/10.2312/egpgv/egpgv09/025-032","title":"Parallelized Matrix Factorization for fast BTF Compression","display_name":"Parallelized Matrix Factorization for fast BTF Compression","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1599944587","doi":"https://doi.org/10.2312/egpgv/egpgv09/025-032","mag":"1599944587"},"language":"en","primary_location":{"id":"doi:10.2312/egpgv/egpgv09/025-032","is_oa":true,"landing_page_url":"https://doi.org/10.2312/egpgv/egpgv09/025-032","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":[],"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":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.2312/egpgv/egpgv09/025-032","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063677702","display_name":"Roland Ruiters","orcid":null},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Ruiters, Roland","raw_affiliation_strings":["Institute for Computer Science II, University of Bonn \u2020"],"affiliations":[{"raw_affiliation_string":"Institute for Computer Science II, University of Bonn \u2020","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065648001","display_name":"M. Rump","orcid":"https://orcid.org/0000-0003-4815-0959"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Rump, Martin","raw_affiliation_strings":["Institute for Computer Science II, University of Bonn \u2020"],"affiliations":[{"raw_affiliation_string":"Institute for Computer Science II, University of Bonn \u2020","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037976392","display_name":"Reinhard Klein","orcid":"https://orcid.org/0000-0002-5505-9347"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Klein, Reinhard","raw_affiliation_strings":["Institute for Computer Science II, University of Bonn \u2020"],"affiliations":[{"raw_affiliation_string":"Institute for Computer Science II, University of Bonn \u2020","institution_ids":["https://openalex.org/I135140700"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5063677702"],"corresponding_institution_ids":["https://openalex.org/I135140700"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9957000017166138,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9800000190734863,"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/computer-science","display_name":"Computer science","score":0.7651171684265137},{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"Principal component analysis","score":0.6507341265678406},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.6191701889038086},{"id":"https://openalex.org/keywords/data-compression","display_name":"Data compression","score":0.6104403138160706},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5909795165061951},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5703554153442383},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.5350345969200134},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5271334648132324},{"id":"https://openalex.org/keywords/graphics","display_name":"Graphics","score":0.5252758264541626},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.5247899889945984},{"id":"https://openalex.org/keywords/compression","display_name":"Compression (physics)","score":0.5182435512542725},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.47847577929496765},{"id":"https://openalex.org/keywords/graphics-processing-unit","display_name":"Graphics processing unit","score":0.4740167260169983},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.438226580619812},{"id":"https://openalex.org/keywords/non-negative-matrix-factorization","display_name":"Non-negative matrix factorization","score":0.41613033413887024},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.41024070978164673},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23593413829803467},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.13006073236465454},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.0998334288597107}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7651171684265137},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.6507341265678406},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.6191701889038086},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.6104403138160706},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5909795165061951},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5703554153442383},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.5350345969200134},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5271334648132324},{"id":"https://openalex.org/C21442007","wikidata":"https://www.wikidata.org/wiki/Q1027879","display_name":"Graphics","level":2,"score":0.5252758264541626},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.5247899889945984},{"id":"https://openalex.org/C180016635","wikidata":"https://www.wikidata.org/wiki/Q2712821","display_name":"Compression (physics)","level":2,"score":0.5182435512542725},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.47847577929496765},{"id":"https://openalex.org/C2779851693","wikidata":"https://www.wikidata.org/wiki/Q183484","display_name":"Graphics processing unit","level":2,"score":0.4740167260169983},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.438226580619812},{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.41613033413887024},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.41024070978164673},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23593413829803467},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.13006073236465454},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0998334288597107},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2312/egpgv/egpgv09/025-032","is_oa":true,"landing_page_url":"https://doi.org/10.2312/egpgv/egpgv09/025-032","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":[],"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":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.2312/egpgv/egpgv09/025-032","is_oa":true,"landing_page_url":"https://doi.org/10.2312/egpgv/egpgv09/025-032","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":[],"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":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W173038495","https://openalex.org/W1604568716","https://openalex.org/W1964477602","https://openalex.org/W2000123870","https://openalex.org/W2110121428","https://openalex.org/W2118010945","https://openalex.org/W2128944356","https://openalex.org/W2129138081","https://openalex.org/W2131858147","https://openalex.org/W2132896093","https://openalex.org/W2144018844","https://openalex.org/W2153763188","https://openalex.org/W2166956700","https://openalex.org/W2399847310"],"related_works":["https://openalex.org/W2108891011","https://openalex.org/W2612165548","https://openalex.org/W2171918950","https://openalex.org/W1972487413","https://openalex.org/W136655107","https://openalex.org/W2270860968","https://openalex.org/W2911431723","https://openalex.org/W2075315695","https://openalex.org/W1510309083","https://openalex.org/W1547791086","https://openalex.org/W1587394477","https://openalex.org/W2231281788","https://openalex.org/W1535940053","https://openalex.org/W2021958155","https://openalex.org/W2016716109","https://openalex.org/W2567078966","https://openalex.org/W1969819350","https://openalex.org/W2095759113","https://openalex.org/W2563054270","https://openalex.org/W2117993346"],"abstract_inverted_index":{"Dimensionality":[0],"reduction":[1],"methods":[2],"like":[3],"Principal":[4],"Component":[5],"Analysis":[6],"(PCA)":[7],"have":[8],"become":[9],"commonplace":[10],"for":[11,71,91,141],"the":[12,24,32,44,48,76,93,105,119,127,142,150,153],"compression":[13,25,56],"of":[14,26,34,47,75,78,152],"large":[15,45,80],"datasets":[16],"in":[17,53,101,108,183],"computer":[18],"graphics.":[19],"One":[20],"important":[21],"application":[22],"is":[23,85],"Bidirectional":[27],"Texture":[28],"Functions":[29],"(BTF).":[30],"However,":[31],"use":[33],"such":[35,109],"techniques":[36],"has":[37],"still":[38],"many":[39],"limitations":[40],"that":[41,112],"arise":[42],"from":[43],"size":[46],"input":[49],"data":[50],"which":[51,69,92],"results":[52],"impractically":[54],"high":[55],"times.":[57],"In":[58],"this":[59],"paper,":[60],"we":[61],"address":[62],"these":[63],"shortcomings":[64],"and":[65,99,177],"present":[66],"a":[67,79,110],"method":[68],"allows":[70,123],"efficient":[72],"parallelized":[73],"computation":[74],"PCA":[77,94,151],"BTF":[81],"matrix.":[82],"The":[83,138],"matrix":[84],"first":[86],"split":[87],"into":[88],"several":[89],"blocks":[90,144],"can":[95,114,162,180],"be":[96,115,163,181],"performed":[97],"independently":[98],"thus":[100],"parallel.":[102],"We":[103],"scale":[104],"single":[106],"subproblems":[107],"way,":[111],"they":[113],"solved":[116],"in-core":[117],"using":[118],"EM-PCA":[120],"algorithm.":[121],"This":[122,156],"us":[124],"to":[125,148],"perform":[126],"calculation":[128],"on":[129],"current":[130],"GPUs":[131],"exploiting":[132],"their":[133],"massive":[134],"parallel":[135],"computing":[136],"power.":[137],"eigenspaces":[139],"determined":[140],"individual":[143],"are":[145],"then":[146],"merged":[147],"obtain":[149],"whole":[154],"dataset.":[155],"way":[157],"nearly":[158],"arbitrarily":[159],"sized":[160],"matrices":[161],"processed":[164],"considerably":[165],"faster":[166],"than":[167],"by":[168],"serial":[169],"algorithms.":[170],"Thus,":[171],"BTFs":[172],"with":[173],"much":[174],"higher":[175],"spatial":[176],"angular":[178],"resolution":[179],"compressed":[182],"reasonable":[184],"time.":[185]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
