{"id":"https://openalex.org/W2464924971","doi":"https://doi.org/10.1145/2897826.2927356","title":"Fourier analysis of numerical integration in Monte Carlo rendering","display_name":"Fourier analysis of numerical integration in Monte Carlo rendering","publication_year":2016,"publication_date":"2016-07-12","ids":{"openalex":"https://openalex.org/W2464924971","doi":"https://doi.org/10.1145/2897826.2927356","mag":"2464924971"},"language":"en","primary_location":{"id":"doi:10.1145/2897826.2927356","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2897826.2927356","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM SIGGRAPH 2016 Courses","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/A5086009008","display_name":"Kartic Subr","orcid":"https://orcid.org/0000-0002-7302-4383"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kartic Subr","raw_affiliation_strings":["Heriot Watt University"],"affiliations":[{"raw_affiliation_string":"Heriot Watt University","institution_ids":[]}]},{"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/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]},{"id":"https://openalex.org/I4210166639","display_name":"Dartmouth Hospital","ror":"https://ror.org/02j3qj605","country_code":"GB","type":"healthcare","lineage":["https://openalex.org/I4210166639"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Gurprit Singh","raw_affiliation_strings":["Dartmouth College"],"affiliations":[{"raw_affiliation_string":"Dartmouth College","institution_ids":["https://openalex.org/I4210166639","https://openalex.org/I107672454"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009820805","display_name":"Wojciech Jarosz","orcid":"https://orcid.org/0000-0002-1652-0954"},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]},{"id":"https://openalex.org/I4210166639","display_name":"Dartmouth Hospital","ror":"https://ror.org/02j3qj605","country_code":"GB","type":"healthcare","lineage":["https://openalex.org/I4210166639"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Wojciech Jarosz","raw_affiliation_strings":["Dartmouth College"],"affiliations":[{"raw_affiliation_string":"Dartmouth College","institution_ids":["https://openalex.org/I4210166639","https://openalex.org/I107672454"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5086009008"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.5972,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.95040073,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"40"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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/T11666","display_name":"Color Science and Applications","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9921000003814697,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rendering","display_name":"Rendering (computer graphics)","score":0.758348286151886},{"id":"https://openalex.org/keywords/monte-carlo-integration","display_name":"Monte Carlo integration","score":0.7359269857406616},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.718845784664154},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.656335711479187},{"id":"https://openalex.org/keywords/global-illumination","display_name":"Global illumination","score":0.6563066244125366},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.5352829694747925},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5181059241294861},{"id":"https://openalex.org/keywords/radiance","display_name":"Radiance","score":0.492074191570282},{"id":"https://openalex.org/keywords/hybrid-monte-carlo","display_name":"Hybrid Monte Carlo","score":0.4766158163547516},{"id":"https://openalex.org/keywords/quasi-monte-carlo-method","display_name":"Quasi-Monte Carlo method","score":0.42258980870246887},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3431951403617859},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.3109897971153259},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2725553512573242},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.21246826648712158},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1078767478466034},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10290762782096863},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.09072238206863403},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07655897736549377}],"concepts":[{"id":"https://openalex.org/C205711294","wikidata":"https://www.wikidata.org/wiki/Q176953","display_name":"Rendering (computer graphics)","level":2,"score":0.758348286151886},{"id":"https://openalex.org/C132725507","wikidata":"https://www.wikidata.org/wiki/Q39879","display_name":"Monte Carlo integration","level":5,"score":0.7359269857406616},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.718845784664154},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.656335711479187},{"id":"https://openalex.org/C89720835","wikidata":"https://www.wikidata.org/wiki/Q1531701","display_name":"Global illumination","level":3,"score":0.6563066244125366},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.5352829694747925},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5181059241294861},{"id":"https://openalex.org/C23690007","wikidata":"https://www.wikidata.org/wiki/Q1411145","display_name":"Radiance","level":2,"score":0.492074191570282},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.4766158163547516},{"id":"https://openalex.org/C63320529","wikidata":"https://www.wikidata.org/wiki/Q7269435","display_name":"Quasi-Monte Carlo method","level":5,"score":0.42258980870246887},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3431951403617859},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.3109897971153259},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2725553512573242},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.21246826648712158},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1078767478466034},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10290762782096863},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.09072238206863403},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07655897736549377}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2897826.2927356","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2897826.2927356","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM SIGGRAPH 2016 Courses","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W115130976","https://openalex.org/W174441044","https://openalex.org/W1523557403","https://openalex.org/W1536331463","https://openalex.org/W1944260052","https://openalex.org/W1965491113","https://openalex.org/W1965744692","https://openalex.org/W1969253908","https://openalex.org/W1974950197","https://openalex.org/W1976454752","https://openalex.org/W1980376149","https://openalex.org/W1984609374","https://openalex.org/W1985093013","https://openalex.org/W1989365484","https://openalex.org/W1996598508","https://openalex.org/W2001026944","https://openalex.org/W2002337266","https://openalex.org/W2004105474","https://openalex.org/W2005197983","https://openalex.org/W2010269264","https://openalex.org/W2011172006","https://openalex.org/W2011343791","https://openalex.org/W2015643205","https://openalex.org/W2022874045","https://openalex.org/W2025019477","https://openalex.org/W2041621129","https://openalex.org/W2043682027","https://openalex.org/W2046250075","https://openalex.org/W2066476997","https://openalex.org/W2086127053","https://openalex.org/W2088700913","https://openalex.org/W2099114783","https://openalex.org/W2109516608","https://openalex.org/W2109673564","https://openalex.org/W2113288858","https://openalex.org/W2131413095","https://openalex.org/W2132282325","https://openalex.org/W2142380402","https://openalex.org/W2144337074","https://openalex.org/W2150593711","https://openalex.org/W2150868589","https://openalex.org/W2153935912","https://openalex.org/W2167993412","https://openalex.org/W2173197174","https://openalex.org/W2173672816","https://openalex.org/W2488758846","https://openalex.org/W2616163540","https://openalex.org/W3137826879","https://openalex.org/W3139527867","https://openalex.org/W4229788702","https://openalex.org/W4230344947","https://openalex.org/W4230673942","https://openalex.org/W4236789552","https://openalex.org/W4256238177","https://openalex.org/W4301884499"],"related_works":["https://openalex.org/W4294677683","https://openalex.org/W2082240576","https://openalex.org/W590971457","https://openalex.org/W1548972748","https://openalex.org/W2488809685","https://openalex.org/W4367155567","https://openalex.org/W4327802989","https://openalex.org/W3565757","https://openalex.org/W2153934880","https://openalex.org/W3016438207"],"abstract_inverted_index":{"Since":[0],"being":[1,122],"introduced":[2,23],"to":[3,24,65],"graphics":[4],"in":[5,49],"the":[6,15,26,70,77,91,100,103,107,113],"1980s,":[7],"Monte":[8,34],"Carlo":[9,35],"sampling":[10,57],"and":[11,90,112],"integration":[12,47,55],"has":[13,36],"become":[14,38],"cornerstone":[16],"of":[17,28,80,94,102,106,115],"most":[18],"modern":[19],"rendering":[20],"algorithms.":[21],"Originally":[22],"combat":[25],"effect":[27],"aliasing":[29],"when":[30],"estimating":[31],"pixels":[32],"values,":[33],"since":[37],"a":[39,58,73],"more":[40],"general":[41],"tool":[42],"for":[43],"solving":[44],"complex,":[45],"multi-dimensional":[46,78],"problems":[48],"rendering.":[50],"In":[51],"this":[52,86,95],"context,":[53],"MC":[54],"involves":[56],"function":[59],"at":[60],"various":[61],"stochastically":[62],"placed":[63],"points":[64,110],"approximate":[66],"an":[67],"integral,":[68],"e.g.":[69],"radiance":[71],"through":[72],"pixel":[74],"integrated":[75],"across":[76],"space":[79],"possible":[81],"light":[82],"transport":[83],"paths.":[84],"Unfortunately,":[85],"estimation":[87],"is":[88,121],"error-prone,":[89],"visual":[92],"manifestation":[93],"error":[96],"depends":[97],"critically":[98],"on":[99],"properties":[101],"integrand,":[104],"placement":[105],"stochastic":[108],"sample":[109],"used,":[111],"type":[114],"problem":[116],"(integration":[117],"vs.":[118],"reconstruction)":[119],"that":[120],"solved":[123],"with":[124],"these":[125],"samples.":[126]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2025-10-10T00:00:00"}