{"id":"https://openalex.org/W4280621934","doi":"https://doi.org/10.1145/3528233.3530725","title":"A Theoretical Analysis of Compactness of the Light Transport Operator","display_name":"A Theoretical Analysis of Compactness of the Light Transport Operator","publication_year":2022,"publication_date":"2022-07-20","ids":{"openalex":"https://openalex.org/W4280621934","doi":"https://doi.org/10.1145/3528233.3530725"},"language":"en","primary_location":{"id":"doi:10.1145/3528233.3530725","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3528233.3530725","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Special Interest Group on Computer Graphics and Interactive Techniques Conference Proceedings","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.research.ed.ac.uk/files/292275176/A_Theoretical_Analysis_SOLER_DOA28032022_AFV.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024277541","display_name":"Cyril Soler","orcid":"https://orcid.org/0000-0003-3214-4183"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]},{"id":"https://openalex.org/I4210099593","display_name":"Computer Algorithms for Medicine","ror":"https://ror.org/00zky6d38","country_code":"AT","type":"facility","lineage":["https://openalex.org/I4210099593"]}],"countries":["AT","FR"],"is_corresponding":true,"raw_author_name":"Cyril Soler","raw_affiliation_strings":["INRIA, France and Grenoble University, France","Models and Algorithms for Visualization and Rendering"],"affiliations":[{"raw_affiliation_string":"INRIA, France and Grenoble University, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I899635006"]},{"raw_affiliation_string":"Models and Algorithms for Visualization and Rendering","institution_ids":["https://openalex.org/I4210099593"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027069080","display_name":"Ronak Molazem","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]},{"id":"https://openalex.org/I4210099593","display_name":"Computer Algorithms for Medicine","ror":"https://ror.org/00zky6d38","country_code":"AT","type":"facility","lineage":["https://openalex.org/I4210099593"]}],"countries":["AT","FR"],"is_corresponding":false,"raw_author_name":"Ronak Molazem","raw_affiliation_strings":["INRIA, France and Grenoble University, France","Models and Algorithms for Visualization and Rendering"],"affiliations":[{"raw_affiliation_string":"INRIA, France and Grenoble University, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I899635006"]},{"raw_affiliation_string":"Models and Algorithms for Visualization and Rendering","institution_ids":["https://openalex.org/I4210099593"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086009008","display_name":"Kartic Subr","orcid":"https://orcid.org/0000-0002-7302-4383"},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]},{"id":"https://openalex.org/I4210099593","display_name":"Computer Algorithms for Medicine","ror":"https://ror.org/00zky6d38","country_code":"AT","type":"facility","lineage":["https://openalex.org/I4210099593"]}],"countries":["AT","GB"],"is_corresponding":false,"raw_author_name":"Kartic Subr","raw_affiliation_strings":["University of Edinburgh, United Kingdom","Models and Algorithms for Visualization and Rendering"],"affiliations":[{"raw_affiliation_string":"University of Edinburgh, United Kingdom","institution_ids":["https://openalex.org/I98677209"]},{"raw_affiliation_string":"Models and Algorithms for Visualization and Rendering","institution_ids":["https://openalex.org/I4210099593"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5024277541"],"corresponding_institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I4210099593","https://openalex.org/I899635006"],"apc_list":null,"apc_paid":null,"fwci":1.1012,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.83051153,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"9"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9979000091552734,"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/T11019","display_name":"Image Enhancement Techniques","score":0.9957000017166138,"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/rendering","display_name":"Rendering (computer graphics)","score":0.8223786354064941},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7739959955215454},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6254830360412598},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.5944730639457703},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5545293688774109},{"id":"https://openalex.org/keywords/compact-operator","display_name":"Compact operator","score":0.42521196603775024},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3849153220653534},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3768027126789093},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.342897891998291},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.2571832835674286},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2524414658546448}],"concepts":[{"id":"https://openalex.org/C205711294","wikidata":"https://www.wikidata.org/wiki/Q176953","display_name":"Rendering (computer graphics)","level":2,"score":0.8223786354064941},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7739959955215454},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6254830360412598},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.5944730639457703},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5545293688774109},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.42521196603775024},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3849153220653534},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3768027126789093},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.342897891998291},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.2571832835674286},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2524414658546448},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"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/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3528233.3530725","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3528233.3530725","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Special Interest Group on Computer Graphics and Interactive Techniques Conference Proceedings","raw_type":"proceedings-article"},{"id":"pmh:oai:pure.ed.ac.uk:openaire/112f547f-a571-43e6-95ce-3efc99d8b1f8","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/112f547f-a571-43e6-95ce-3efc99d8b1f8","pdf_url":"https://www.research.ed.ac.uk/files/292275176/A_Theoretical_Analysis_SOLER_DOA28032022_AFV.pdf","source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Soler, C, Molazem, R & Subr, K 2022, A Theoretical Analysis of Compactness of the Light Transport Operator. in M Nandigjav, N J Mitra & A Hertzmann (eds), ACM SIGGRAPH 2022 Conference Proceedings., 17, SIGGRAPH 2022, Vancouver, Canada, 8/08/22. https://doi.org/10.1145/3528233.3530725, https://doi.org/10.1145/3528233.3530725","raw_type":"contributionToPeriodical"},{"id":"pmh:oai:HAL:hal-03673578v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-03673578","pdf_url":null,"source":{"id":"https://openalex.org/S4406922461","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIGGRAPH 2022 - ACM Conference and Exhibition on Computer Graphics and Interactive Techniques, Aug 2022, Vancouver, Canada. pp.1-9, &#x27E8;10.1145/3528233.3530725&#x27E9;","raw_type":"Conference papers"},{"id":"pmh:oai:pure.ed.ac.uk:publications/112f547f-a571-43e6-95ce-3efc99d8b1f8","is_oa":true,"landing_page_url":"https://hdl.handle.net/20.500.11820/112f547f-a571-43e6-95ce-3efc99d8b1f8","pdf_url":null,"source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Soler, C, Molazem, R & Subr, K 2022, A Theoretical Analysis of Compactness of the Light Transport Operator. in M Nandigjav, N J Mitra & A Hertzmann (eds), ACM SIGGRAPH 2022 Conference Proceedings., 17, SIGGRAPH 2022, Vancouver, Canada, 8/08/22. https://doi.org/10.1145/3528233.3530725, https://doi.org/10.1145/3528233.3530725","raw_type":"contributionToPeriodical"}],"best_oa_location":{"id":"pmh:oai:pure.ed.ac.uk:openaire/112f547f-a571-43e6-95ce-3efc99d8b1f8","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/112f547f-a571-43e6-95ce-3efc99d8b1f8","pdf_url":"https://www.research.ed.ac.uk/files/292275176/A_Theoretical_Analysis_SOLER_DOA28032022_AFV.pdf","source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Soler, C, Molazem, R & Subr, K 2022, A Theoretical Analysis of Compactness of the Light Transport Operator. in M Nandigjav, N J Mitra & A Hertzmann (eds), ACM SIGGRAPH 2022 Conference Proceedings., 17, SIGGRAPH 2022, Vancouver, Canada, 8/08/22. https://doi.org/10.1145/3528233.3530725, https://doi.org/10.1145/3528233.3530725","raw_type":"contributionToPeriodical"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3470135451","display_name":null,"funder_award_id":"ANR-16-CE33-0026","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5996122743","display_name":null,"funder_award_id":"16-CE33-0026 (CaLiTrOp)","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4280621934.pdf","grobid_xml":"https://content.openalex.org/works/W4280621934.grobid-xml"},"referenced_works_count":53,"referenced_works":["https://openalex.org/W1557781800","https://openalex.org/W1589251945","https://openalex.org/W1597741994","https://openalex.org/W1600837800","https://openalex.org/W1963723779","https://openalex.org/W1972272788","https://openalex.org/W1993594485","https://openalex.org/W1996598508","https://openalex.org/W2000861327","https://openalex.org/W2004117080","https://openalex.org/W2023237845","https://openalex.org/W2035653341","https://openalex.org/W2040284954","https://openalex.org/W2048110094","https://openalex.org/W2058810187","https://openalex.org/W2066476997","https://openalex.org/W2067316110","https://openalex.org/W2093029576","https://openalex.org/W2093206971","https://openalex.org/W2093685536","https://openalex.org/W2096348897","https://openalex.org/W2099478163","https://openalex.org/W2104814486","https://openalex.org/W2111886617","https://openalex.org/W2117756735","https://openalex.org/W2124777959","https://openalex.org/W2138624212","https://openalex.org/W2153935912","https://openalex.org/W2158149834","https://openalex.org/W2158294804","https://openalex.org/W2166693708","https://openalex.org/W2173197174","https://openalex.org/W2769971250","https://openalex.org/W2799267564","https://openalex.org/W2911463214","https://openalex.org/W2912424718","https://openalex.org/W2912892010","https://openalex.org/W2951412969","https://openalex.org/W2983159878","https://openalex.org/W2986860185","https://openalex.org/W3004728147","https://openalex.org/W3048751201","https://openalex.org/W3080202818","https://openalex.org/W3109585842","https://openalex.org/W3167294693","https://openalex.org/W3177919874","https://openalex.org/W3179416528","https://openalex.org/W3216034703","https://openalex.org/W4210697527","https://openalex.org/W4213439949","https://openalex.org/W4235867684","https://openalex.org/W4237796884","https://openalex.org/W4245551996"],"related_works":["https://openalex.org/W4253623673","https://openalex.org/W2119181102","https://openalex.org/W2489729785","https://openalex.org/W2060341540","https://openalex.org/W2031935416","https://openalex.org/W4391034219","https://openalex.org/W4300823139","https://openalex.org/W2313724791","https://openalex.org/W2362578218","https://openalex.org/W2952168670"],"abstract_inverted_index":{"Rendering":[0],"photorealistic":[1],"visuals":[2],"of":[3,12,27,36,44,81,97,148,189,195],"virtual":[4],"scenes":[5,149],"requires":[6],"tractable":[7],"models":[8],"for":[9,139],"the":[10,25,42,87,91,137,187,193],"simulation":[11],"light.":[13],"The":[14],"rendering":[15,37,140,207],"equation":[16],"describes":[17],"one":[18],"such":[19],"model":[20],"using":[21,145],"an":[22],"integral":[23,32],"equation,":[24],"crux":[26],"which":[28,85],"is":[29,79,109,125,165],"a":[30,75,95,120,146,182],"continuous":[31],"operator.":[33,68],"A":[34],"majority":[35],"algorithms":[38,141,208],"aim":[39],"to":[40,89,127,142],"approximate":[41,90],"effect":[43],"this":[45,67,70,107],"light":[46,132],"transport":[47],"operator":[48,92,108],"via":[49],"discretization":[50,83,116],"(using":[51],"rays,":[52],"particles,":[53],"patches,":[54],"etc.).":[55],"Research":[56],"spanning":[57],"four":[58],"decades":[59],"has":[60],"uncovered":[61],"interesting":[62],"properties":[63],"and":[64,84,112,150,172,179],"intuition":[65],"surrounding":[66],"In":[69],"paper":[71],"we":[72],"analyze":[73],"compactness,":[74],"key":[76],"property":[77],"that":[78,106,114,117,156,200],"independent":[80],"its":[82,157],"characterizes":[86],"ability":[88],"uniformly":[93],"by":[94],"sequence":[96],"finite":[98],"rank":[99],"operators.":[100],"We":[101,153,185,198],"conclusively":[102],"prove":[103],"lingering":[104],"suspicions":[105],"not":[110,166],"compact":[111,167],"therefore":[113],"any":[115],"relies":[118],"on":[119],"finite-rank":[121],"or":[122],"nonadaptive":[123],"finite-bases":[124],"susceptible":[126],"unbounded":[128],"error":[129],"over":[130],"arbitrary":[131],"distributions.":[133],"Our":[134],"result":[135],"justifies":[136],"expectation":[138],"be":[143],"evaluated":[144],"variety":[147],"illumination":[151],"conditions.":[152],"also":[154],"discover":[155],"lower":[158],"dimensional":[159],"counterpart":[160],"(over":[161],"purely":[162],"diffuse":[163],"scenes)":[164],"except":[168],"in":[169,192],"special":[170],"cases,":[171],"uncover":[173],"connections":[174],"with":[175],"it":[176],"being":[177],"noninvertible":[178],"acting":[180],"as":[181],"low-pass":[183],"filter.":[184],"explain":[186],"relevance":[188],"our":[190,201],"results":[191,203],"context":[194],"previous":[196],"work.":[197],"believe":[199],"theoretical":[202],"will":[204],"inform":[205],"future":[206],"regarding":[209],"practical":[210],"choices.":[211]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}
