{"id":"https://openalex.org/W4417000794","doi":"https://doi.org/10.1145/3763321","title":"Gaussian Integral Linear Operators for Precomputed Graphics","display_name":"Gaussian Integral Linear Operators for Precomputed Graphics","publication_year":2025,"publication_date":"2025-12-01","ids":{"openalex":"https://openalex.org/W4417000794","doi":"https://doi.org/10.1145/3763321"},"language":"en","primary_location":{"id":"doi:10.1145/3763321","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3763321","pdf_url":null,"source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1145/3763321","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054391338","display_name":"H Lu","orcid":"https://orcid.org/0009-0008-2595-2493"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Haolin Lu","raw_affiliation_strings":["MPI for Informatics, Saarbrucken, Germany"],"raw_orcid":"https://orcid.org/0009-0008-2595-2493","affiliations":[{"raw_affiliation_string":"MPI for Informatics, Saarbrucken, Germany","institution_ids":["https://openalex.org/I4210109712"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017453933","display_name":"Yash Belhe","orcid":"https://orcid.org/0009-0009-7070-2845"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yash Belhe","raw_affiliation_strings":["UC San Diego, La Jolla, USA"],"raw_orcid":"https://orcid.org/0009-0009-7070-2845","affiliations":[{"raw_affiliation_string":"UC San Diego, La Jolla, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022506083","display_name":"Gurprit Singh","orcid":"https://orcid.org/0000-0003-0970-5835"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gurprit Singh","raw_affiliation_strings":["MPI for Informatics, Saarbrucken, Germany"],"raw_orcid":"https://orcid.org/0000-0003-0970-5835","affiliations":[{"raw_affiliation_string":"MPI for Informatics, Saarbrucken, Germany","institution_ids":["https://openalex.org/I4210109712"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030293104","display_name":"Tzu\u2010Mao Li","orcid":"https://orcid.org/0000-0001-5443-470X"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tzu-Mao Li","raw_affiliation_strings":["UC San Diego, La Jolla, USA"],"raw_orcid":"https://orcid.org/0000-0001-5443-470X","affiliations":[{"raw_affiliation_string":"UC San Diego, La Jolla, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040844821","display_name":"Toshiya Hachisuka","orcid":"https://orcid.org/0000-0003-0284-3776"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Toshiya Hachisuka","raw_affiliation_strings":["University of Waterloo, Waterloo, Canada"],"raw_orcid":"https://orcid.org/0000-0003-0284-3776","affiliations":[{"raw_affiliation_string":"University of Waterloo, Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.54772311,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"44","issue":"6","first_page":"1","last_page":"15"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.6660000085830688,"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":0.6660000085830688,"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":0.21490000188350677,"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":0.015599999576807022,"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/kernel","display_name":"Kernel (algebra)","score":0.7325999736785889},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5828999876976013},{"id":"https://openalex.org/keywords/graphics","display_name":"Graphics","score":0.5820000171661377},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics","score":0.4715000092983246},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4481000006198883},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.3937999904155731},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.38370001316070557},{"id":"https://openalex.org/keywords/gaussian-function","display_name":"Gaussian function","score":0.38179999589920044},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.37689998745918274}],"concepts":[{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.7325999736785889},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6010000109672546},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5828999876976013},{"id":"https://openalex.org/C21442007","wikidata":"https://www.wikidata.org/wiki/Q1027879","display_name":"Graphics","level":2,"score":0.5820000171661377},{"id":"https://openalex.org/C77660652","wikidata":"https://www.wikidata.org/wiki/Q150971","display_name":"Computer graphics","level":2,"score":0.4715000092983246},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4553000032901764},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4481000006198883},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3937999904155731},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.38370001316070557},{"id":"https://openalex.org/C7218915","wikidata":"https://www.wikidata.org/wiki/Q1054475","display_name":"Gaussian function","level":3,"score":0.38179999589920044},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.37689998745918274},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.36239999532699585},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.35589998960494995},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.3353999853134155},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3312999904155731},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3138999938964844},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3027999997138977},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2957000136375427},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.29010000824928284},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.28600001335144043},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.2766000032424927},{"id":"https://openalex.org/C134517425","wikidata":"https://www.wikidata.org/wiki/Q16000131","display_name":"Kernel embedding of distributions","level":4,"score":0.2759000062942505},{"id":"https://openalex.org/C18945957","wikidata":"https://www.wikidata.org/wiki/Q5597193","display_name":"Graphics hardware","level":3,"score":0.2667999863624573},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.26460000872612},{"id":"https://openalex.org/C182335926","wikidata":"https://www.wikidata.org/wiki/Q17093020","display_name":"Kernel principal component analysis","level":4,"score":0.25110000371932983}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3763321","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3763321","pdf_url":null,"source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1145/3763321","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3763321","pdf_url":null,"source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W2000468482","https://openalex.org/W2030884885","https://openalex.org/W2036750154","https://openalex.org/W2038305449","https://openalex.org/W2047161559","https://openalex.org/W2066334759","https://openalex.org/W2091019609","https://openalex.org/W2100184913","https://openalex.org/W2151047098","https://openalex.org/W2418844298","https://openalex.org/W2473361822","https://openalex.org/W2496551394","https://openalex.org/W2619671517","https://openalex.org/W2884234834","https://openalex.org/W2888943822","https://openalex.org/W2956299176","https://openalex.org/W2959164675","https://openalex.org/W2964213305","https://openalex.org/W2979786244","https://openalex.org/W2981485484","https://openalex.org/W2982565196","https://openalex.org/W2998555201","https://openalex.org/W3000472182","https://openalex.org/W3005817654","https://openalex.org/W3185033788","https://openalex.org/W4200458628","https://openalex.org/W4308883545","https://openalex.org/W4311034031","https://openalex.org/W4313135476","https://openalex.org/W4320491672","https://openalex.org/W4366608399","https://openalex.org/W4385318467","https://openalex.org/W4389539479","https://openalex.org/W4399253033","https://openalex.org/W4412588102"],"related_works":[],"abstract_inverted_index":{"Integral":[0],"linear":[1],"operators":[2,125],"play":[3],"a":[4,80,151],"key":[5],"role":[6],"in":[7,109,135],"many":[8],"graphics":[9,154],"problems,":[10,155,162],"but":[11],"solutions":[12],"obtained":[13],"via":[14],"Monte":[15],"Carlo":[16],"methods":[17,42],"often":[18],"suffer":[19],"from":[20],"high":[21],"variance.":[22],"A":[23],"common":[24],"strategy":[25],"to":[26,36,101,106],"improve":[27],"the":[28,38,50,62,69,72,86,89,98,120,143],"efficiency":[29],"of":[30,64,71,123,139,147,153],"integration":[31],"across":[32,150],"various":[33],"inputs":[34],"is":[35,132],"precompute":[37],"kernel":[39,73,87,110],"function.":[40],"Traditional":[41],"typically":[43],"rely":[44],"on":[45],"basis":[46],"expansions":[47],"for":[48],"both":[49,85],"input":[51,90],"and":[52,67,88,112,126,145,163],"output":[53,58,65,113],"functions.":[54],"However,":[55],"using":[56,92],"fixed":[57],"bases":[59],"can":[60],"restrict":[61],"precision":[63],"reconstruction":[66],"limit":[68],"compactness":[70],"representation.":[74,114],"In":[75],"this":[76],"work,":[77],"we":[78],"introduce":[79],"new":[81],"method":[82,117],"that":[83],"approximates":[84],"function":[91],"Gaussian":[93],"mixtures.":[94],"This":[95],"formulation":[96],"allows":[97],"integral":[99],"operator":[100,129],"be":[102],"evaluated":[103],"analytically,":[104],"leading":[105],"improved":[107],"flexibility":[108],"storage":[111],"Moreover,":[115],"our":[116,148],"naturally":[118],"supports":[119],"sequential":[121],"application":[122],"multiple":[124],"enables":[127],"closed-form":[128],"composition,":[130],"which":[131],"particularly":[133],"beneficial":[134],"tasks":[136],"involving":[137],"chains":[138],"operators.":[140],"We":[141],"demonstrate":[142],"versatility":[144],"effectiveness":[146],"approach":[149],"variety":[152],"including":[156],"environment":[157],"map":[158],"relighting,":[159],"boundary":[160],"value":[161],"fluorescence":[164],"rendering.":[165]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-12-04T00:00:00"}
