{"id":"https://openalex.org/W2887891181","doi":"https://doi.org/10.2312/sre.20181169","title":"Matrix Bidirectional Path Tracing","display_name":"Matrix Bidirectional Path Tracing","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2887891181","doi":"https://doi.org/10.2312/sre.20181169","mag":"2887891181"},"language":"en","primary_location":{"id":"doi:10.2312/sre.20181169","is_oa":true,"landing_page_url":"https://doi.org/10.2312/sre.20181169","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-journal"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.2312/sre.20181169","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080422360","display_name":"Chakravarty R. Alla Chaitanya","orcid":null},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]},{"id":"https://openalex.org/I70931966","display_name":"Universit\u00e9 de Montr\u00e9al","ror":"https://ror.org/0161xgx34","country_code":"CA","type":"education","lineage":["https://openalex.org/I70931966"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Chaitanya, Chakravarty Reddy Alla","raw_affiliation_strings":["McGill University and University of Montreal#TAB#"],"affiliations":[{"raw_affiliation_string":"McGill University and University of Montreal#TAB#","institution_ids":["https://openalex.org/I5023651","https://openalex.org/I70931966"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037928047","display_name":"Laurent Belcour","orcid":"https://orcid.org/0000-0002-1982-0717"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Belcour, Laurent","raw_affiliation_strings":["Unity Technologies#TAB#"],"affiliations":[{"raw_affiliation_string":"Unity Technologies#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040844821","display_name":"Toshiya Hachisuka","orcid":"https://orcid.org/0000-0003-0284-3776"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hachisuka, Toshiya","raw_affiliation_strings":["The University of Tokyo,"],"affiliations":[{"raw_affiliation_string":"The University of Tokyo,","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028841214","display_name":"Simon Premo\u017ee","orcid":null},"institutions":[{"id":"https://openalex.org/I70931966","display_name":"Universit\u00e9 de Montr\u00e9al","ror":"https://ror.org/0161xgx34","country_code":"CA","type":"education","lineage":["https://openalex.org/I70931966"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Premoze, Simon","raw_affiliation_strings":["University of Montreal"],"affiliations":[{"raw_affiliation_string":"University of Montreal","institution_ids":["https://openalex.org/I70931966"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027345065","display_name":"Jacopo Pantaleoni","orcid":"https://orcid.org/0000-0001-6260-6815"},"institutions":[{"id":"https://openalex.org/I1304085615","display_name":"Nvidia (United Kingdom)","ror":"https://ror.org/02kr42612","country_code":"GB","type":"company","lineage":["https://openalex.org/I1304085615","https://openalex.org/I4210127875"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Pantaleoni, Jacopo","raw_affiliation_strings":["NVIDIA Research"],"affiliations":[{"raw_affiliation_string":"NVIDIA Research","institution_ids":["https://openalex.org/I1304085615"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053824527","display_name":"Derek Nowrouzezahrai","orcid":"https://orcid.org/0000-0002-4279-1774"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Nowrouzezahrai, Derek","raw_affiliation_strings":["McGill University"],"affiliations":[{"raw_affiliation_string":"McGill University","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5080422360"],"corresponding_institution_ids":["https://openalex.org/I5023651","https://openalex.org/I70931966"],"apc_list":null,"apc_paid":null,"fwci":4.4773,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.94752187,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"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":0.9997000098228455,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.996399998664856,"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/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/path-tracing","display_name":"Path tracing","score":0.7942609190940857},{"id":"https://openalex.org/keywords/global-illumination","display_name":"Global illumination","score":0.7025790810585022},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7023983001708984},{"id":"https://openalex.org/keywords/ray-tracing","display_name":"Ray tracing (physics)","score":0.5836654901504517},{"id":"https://openalex.org/keywords/rendering","display_name":"Rendering (computer graphics)","score":0.5784804821014404},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.56370609998703},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5585551261901855},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.5530216097831726},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.498185396194458},{"id":"https://openalex.org/keywords/pixel","display_name":"Pixel","score":0.4715854227542877},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.4175611734390259},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3782368004322052},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.23278942704200745},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.13991087675094604},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12476593255996704},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.10071402788162231}],"concepts":[{"id":"https://openalex.org/C110541219","wikidata":"https://www.wikidata.org/wiki/Q72948","display_name":"Path tracing","level":3,"score":0.7942609190940857},{"id":"https://openalex.org/C89720835","wikidata":"https://www.wikidata.org/wiki/Q1531701","display_name":"Global illumination","level":3,"score":0.7025790810585022},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7023983001708984},{"id":"https://openalex.org/C121483023","wikidata":"https://www.wikidata.org/wiki/Q7298343","display_name":"Ray tracing (physics)","level":2,"score":0.5836654901504517},{"id":"https://openalex.org/C205711294","wikidata":"https://www.wikidata.org/wiki/Q176953","display_name":"Rendering (computer graphics)","level":2,"score":0.5784804821014404},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.56370609998703},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5585551261901855},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.5530216097831726},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.498185396194458},{"id":"https://openalex.org/C160633673","wikidata":"https://www.wikidata.org/wiki/Q355198","display_name":"Pixel","level":2,"score":0.4715854227542877},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4175611734390259},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3782368004322052},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.23278942704200745},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.13991087675094604},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12476593255996704},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.10071402788162231},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2312/sre.20181169","is_oa":true,"landing_page_url":"https://doi.org/10.2312/sre.20181169","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-journal"}],"best_oa_location":{"id":"doi:10.2312/sre.20181169","is_oa":true,"landing_page_url":"https://doi.org/10.2312/sre.20181169","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-journal"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W190660021","https://openalex.org/W1536739775","https://openalex.org/W1559769428","https://openalex.org/W1564611446","https://openalex.org/W1588580784","https://openalex.org/W1797096580","https://openalex.org/W1907223193","https://openalex.org/W2008693968","https://openalex.org/W2018754550","https://openalex.org/W2021131939","https://openalex.org/W2040284954","https://openalex.org/W2098077797","https://openalex.org/W2142380402","https://openalex.org/W2154891655","https://openalex.org/W2294159033","https://openalex.org/W2398697046","https://openalex.org/W2912424718","https://openalex.org/W3136243606"],"related_works":["https://openalex.org/W1967246499","https://openalex.org/W2352021735","https://openalex.org/W2120324771","https://openalex.org/W2197110775","https://openalex.org/W3026381212","https://openalex.org/W2156862682","https://openalex.org/W2110082271","https://openalex.org/W2088591013","https://openalex.org/W2405384444","https://openalex.org/W1424001099","https://openalex.org/W2057408700","https://openalex.org/W2035013967","https://openalex.org/W2899489828","https://openalex.org/W3106481070","https://openalex.org/W2962906584","https://openalex.org/W2383845299","https://openalex.org/W2927087829","https://openalex.org/W2738533173","https://openalex.org/W2785368021","https://openalex.org/W2592869444"],"abstract_inverted_index":{"Sampled":[0],"paths":[1,48,86,128],"in":[2,22,72,87,103,152],"Monte":[3],"Carlo":[4],"ray":[5],"tracing":[6],"can":[7,52],"be":[8,53],"arbitrarily":[9,54],"close":[10],"to":[11,15,27,80,142,157],"each":[12,35],"other":[13],"due":[14],"its":[16],"stochastic":[17],"nature.":[18],"Such":[19],"clumped":[20,55],"samples":[21],"the":[23,88,158],"path":[24,145],"space":[25,124],"tend":[26],"contribute":[28],"little":[29],"toward":[30],"an":[31,134],"accurate":[32],"estimate":[33],"of":[34,49,62,110],"pixel.":[36],"Bidirectional":[37],"light":[38,64],"transport":[39,65],"methods":[40],"make":[41],"this":[42,73,140],"issue":[43],"further":[44],"complicated":[45],"since":[46],"connecting":[47],"sampled":[50],"subpaths":[51],"again.":[56],"We":[57,132],"propose":[58],"a":[59,108,122,149],"matrix":[60,105],"formulation":[61,106],"bidirectional":[63,96],"that":[66,138],"enables":[67],"stratification":[68,77],"(and":[69],"low-discrepancy":[70],"sampling)":[71],"connection":[74],"space.":[75],"This":[76],"allows":[78],"us":[79],"distribute":[81],"computation":[82],"evenly":[83],"across":[84],"contributing":[85,127],"image,":[89],"which":[90],"is":[91],"not":[92],"possible":[93],"with":[94],"standard":[95],"or":[97],"Markov":[98],"chain":[99],"solutions.":[100],"Each":[101],"element":[102],"our":[104],"represents":[107],"pair":[109],"connected":[111],"eye-":[112],"and":[113],"light-subpaths.":[114],"By":[115],"carefully":[116],"reordering":[117],"these":[118],"elements,":[119],"we":[120],"build":[121],"2D":[123],"where":[125],"equally":[126],"are":[129],"distributed":[130],"coherently.":[131],"devise":[133],"unbiased":[135],"rendering":[136],"algorithm":[137],"leverages":[139],"coherence":[141],"effectively":[143],"sample":[144],"space,":[146],"consistently":[147],"achieving":[148],"2-3x":[150],"speedup":[151],"radiometrically":[153],"complex":[154],"scenes":[155],"compared":[156],"state-of-the-art.":[159]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}