{"id":"https://openalex.org/W2736701250","doi":"https://doi.org/10.1145/3072959.3073656","title":"Convergence analysis for anisotropic monte carlo sampling spectra","display_name":"Convergence analysis for anisotropic monte carlo sampling spectra","publication_year":2017,"publication_date":"2017-07-20","ids":{"openalex":"https://openalex.org/W2736701250","doi":"https://doi.org/10.1145/3072959.3073656","mag":"2736701250"},"language":"en","primary_location":{"id":"doi:10.1145/3072959.3073656","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3072959.3073656","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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","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"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dartmouth College","institution_ids":["https://openalex.org/I107672454","https://openalex.org/I4210166639"]}]},{"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"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dartmouth College","institution_ids":["https://openalex.org/I107672454","https://openalex.org/I4210166639"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.3589,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.96646562,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"36","issue":"4","first_page":"1","last_page":"14"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9987000226974487,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9986000061035156,"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/monte-carlo-method","display_name":"Monte Carlo method","score":0.8237283825874329},{"id":"https://openalex.org/keywords/monte-carlo-integration","display_name":"Monte Carlo integration","score":0.6486086845397949},{"id":"https://openalex.org/keywords/latin-hypercube-sampling","display_name":"Latin hypercube sampling","score":0.6096373796463013},{"id":"https://openalex.org/keywords/control-variates","display_name":"Control variates","score":0.5461302399635315},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5176708698272705},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.505540132522583},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.47933587431907654},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.455083429813385},{"id":"https://openalex.org/keywords/anisotropy","display_name":"Anisotropy","score":0.44473764300346375},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.44400322437286377},{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.4412553906440735},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.43878495693206787},{"id":"https://openalex.org/keywords/rendering","display_name":"Rendering (computer graphics)","score":0.4229191243648529},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4202956557273865},{"id":"https://openalex.org/keywords/variance-reduction","display_name":"Variance reduction","score":0.4200568199157715},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.4173000156879425},{"id":"https://openalex.org/keywords/quasi-monte-carlo-method","display_name":"Quasi-Monte Carlo method","score":0.41041794419288635},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38740286231040955},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38359305262565613},{"id":"https://openalex.org/keywords/hybrid-monte-carlo","display_name":"Hybrid Monte Carlo","score":0.35624366998672485},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3329720199108124},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23110103607177734},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16768255829811096},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.0906100869178772},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09020811319351196}],"concepts":[{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.8237283825874329},{"id":"https://openalex.org/C132725507","wikidata":"https://www.wikidata.org/wiki/Q39879","display_name":"Monte Carlo integration","level":5,"score":0.6486086845397949},{"id":"https://openalex.org/C20820323","wikidata":"https://www.wikidata.org/wiki/Q6496514","display_name":"Latin hypercube sampling","level":3,"score":0.6096373796463013},{"id":"https://openalex.org/C121683094","wikidata":"https://www.wikidata.org/wiki/Q3554721","display_name":"Control variates","level":5,"score":0.5461302399635315},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5176708698272705},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.505540132522583},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.47933587431907654},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.455083429813385},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.44473764300346375},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.44400322437286377},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.4412553906440735},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.43878495693206787},{"id":"https://openalex.org/C205711294","wikidata":"https://www.wikidata.org/wiki/Q176953","display_name":"Rendering (computer graphics)","level":2,"score":0.4229191243648529},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4202956557273865},{"id":"https://openalex.org/C62644790","wikidata":"https://www.wikidata.org/wiki/Q3454689","display_name":"Variance reduction","level":3,"score":0.4200568199157715},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.4173000156879425},{"id":"https://openalex.org/C63320529","wikidata":"https://www.wikidata.org/wiki/Q7269435","display_name":"Quasi-Monte Carlo method","level":5,"score":0.41041794419288635},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38740286231040955},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38359305262565613},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.35624366998672485},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3329720199108124},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23110103607177734},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16768255829811096},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0906100869178772},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09020811319351196},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3072959.3073656","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3072959.3073656","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5299999713897705,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W115130976","https://openalex.org/W1510924284","https://openalex.org/W1513100075","https://openalex.org/W1564611446","https://openalex.org/W1600837800","https://openalex.org/W1969253908","https://openalex.org/W1972815766","https://openalex.org/W1980376149","https://openalex.org/W1982661771","https://openalex.org/W1984609374","https://openalex.org/W1989365484","https://openalex.org/W1996598508","https://openalex.org/W2000700694","https://openalex.org/W2002337266","https://openalex.org/W2004105474","https://openalex.org/W2005197983","https://openalex.org/W2017001763","https://openalex.org/W2020995339","https://openalex.org/W2026043300","https://openalex.org/W2041621129","https://openalex.org/W2045210063","https://openalex.org/W2046250075","https://openalex.org/W2049153601","https://openalex.org/W2051505609","https://openalex.org/W2051847608","https://openalex.org/W2064843545","https://openalex.org/W2066476997","https://openalex.org/W2068359544","https://openalex.org/W2079723463","https://openalex.org/W2086127053","https://openalex.org/W2088700913","https://openalex.org/W2093625674","https://openalex.org/W2097124770","https://openalex.org/W2102727143","https://openalex.org/W2107911446","https://openalex.org/W2109673564","https://openalex.org/W2113288858","https://openalex.org/W2116984406","https://openalex.org/W2125250006","https://openalex.org/W2128540422","https://openalex.org/W2132282325","https://openalex.org/W2144337074","https://openalex.org/W2149847160","https://openalex.org/W2150868589","https://openalex.org/W2153935912","https://openalex.org/W2157298636","https://openalex.org/W2173672816","https://openalex.org/W2464924971","https://openalex.org/W2484039423","https://openalex.org/W2489976270","https://openalex.org/W2515400514","https://openalex.org/W2528567655","https://openalex.org/W2616163540","https://openalex.org/W2798735774","https://openalex.org/W4213439949","https://openalex.org/W4230344947","https://openalex.org/W4232242135","https://openalex.org/W4232317953","https://openalex.org/W4236789552","https://openalex.org/W4252981580","https://openalex.org/W4300453772"],"related_works":["https://openalex.org/W2313927419","https://openalex.org/W1577753449","https://openalex.org/W2155294049","https://openalex.org/W2076304939","https://openalex.org/W2081241186","https://openalex.org/W1994596455","https://openalex.org/W1592208634","https://openalex.org/W1979154598","https://openalex.org/W1592894431","https://openalex.org/W2065756054"],"abstract_inverted_index":{"Traditional":[0],"Monte":[1,77,99],"Carlo":[2,78,100],"(MC)":[3],"integration":[4,44,101],"methods":[5],"use":[6],"point":[7],"samples":[8],"to":[9,63,89,142],"numerically":[10],"approximate":[11],"the":[12,20,30,38,65,72,91,95],"underlying":[13],"integral.":[14],"This":[15],"approximation":[16],"introduces":[17],"variance":[18,73,129],"in":[19,45,54,133],"integrated":[21],"result,":[22],"and":[23,93,112,124,130,136],"this":[24,81],"error":[25],"can":[26,127,140],"depend":[27],"critically":[28],"on":[29,71],"sampling":[31,106,123],"patterns":[32],"used":[33,41],"during":[34],"integration.":[35,79],"Most":[36],"of":[37,67,76,98,121],"well-known":[39],"samplers":[40,70],"for":[42],"MC":[43,134],"graphics---e.g.":[46],"jittered,":[47],"Latin-hypercube":[48],"(":[49],"N":[50],"-rooks),":[51],"multijittered---are":[52],"anisotropic":[53,69,122],"nature.":[55],"However,":[56],"there":[57],"are":[58],"currently":[59],"no":[60],"tools":[61],"available":[62],"analyze":[64,90],"impact":[66],"such":[68],"convergence":[74,96,131],"behavior":[75],"In":[80],"work,":[82],"we":[83],"develop":[84],"a":[85],"Fourier-domain":[86],"mathematical":[87],"tool":[88],"variance,":[92],"subsequently":[94],"rate,":[97],"using":[102],"any":[103],"arbitrary":[104],"(anisotropic)":[105,143],"power":[107],"spectrum.":[108],"We":[109],"also":[110],"validate":[111],"leverage":[113],"our":[114],"theoretical":[115],"analysis,":[116],"demonstrating":[117],"that":[118,137],"judicious":[119],"alignment":[120],"integrand":[125],"spectra":[126],"improve":[128],"rates":[132],"rendering,":[135],"similar":[138],"improvements":[139],"apply":[141],"deterministic":[144],"samplers.":[145]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}