{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T15:03:44Z","timestamp":1775055824210,"version":"3.50.1"},"reference-count":49,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2017,7,20]],"date-time":"2017-07-20T00:00:00Z","timestamp":1500508800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CNS-1205521"],"award-info":[{"award-number":["CNS-1205521"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Activision"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2017,8,31]]},"abstract":"<jats:p>\n            We develop a theory of volumetric density estimation which generalizes prior photon point (0D) and beam (1D) approaches to a broader class of estimators using \"\n            <jats:italic>n<\/jats:italic>\n            D\" samples along photon and\/or camera subpaths. Volumetric photon mapping performs density estimation by point sampling propagation distances within the medium and performing density estimation over the generated points (0D). Beam-based (1D) approaches consider the expected value of this distance sampling process along the last camera and\/or light subpath segments. Our theory shows how to replace propagation distance sampling steps across\n            <jats:italic>multiple bounces<\/jats:italic>\n            to form higher-dimensional samples such as photon planes (2D), photon volumes (3D), their camera path equivalents, and beyond. We perform a theoretical error analysis which reveals that in scenarios where beams already outperform points, each additional dimension of\n            <jats:italic>n<\/jats:italic>\n            D samples compounds these benefits further. Moreover, each additional sample dimension reduces the required dimensionality of the blurring needed for density estimation, allowing us to formulate, for the first time,\n            <jats:italic>fully unbiased<\/jats:italic>\n            forms of volumetric photon mapping. We demonstrate practical implementations of several of the new estimators our theory predicts, including both biased and unbiased variants, and show that they outperform state-of-the-art beam-based volumetric photon mapping by a factor of 2.4--40\u00d7.\n          <\/jats:p>","DOI":"10.1145\/3072959.3073698","type":"journal-article","created":{"date-parts":[[2017,7,21]],"date-time":"2017-07-21T12:24:07Z","timestamp":1500639847000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":37,"title":["Beyond points and beams"],"prefix":"10.1145","volume":"36","author":[{"given":"Benedikt","family":"Bitterli","sequence":"first","affiliation":[{"name":"Dartmouth College"}]},{"given":"Wojciech","family":"Jarosz","sequence":"additional","affiliation":[{"name":"Dartmouth College"}]}],"member":"320","published-online":{"date-parts":[[2017,7,20]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"Transfer Functions in Global Illumination. In ACM SIGGRAPH '93 Course Notes - Global Illumination.","author":"Arvo James","year":"1993"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/97879.97886"},{"key":"e_1_2_2_3_1","unstructured":"James Richard Arvo. 1995a. Analytic methods for simulated light transport. Ph.D. Dissertation. Yale University.  James Richard Arvo. 1995a. Analytic methods for simulated light transport. Ph.D. Dissertation. Yale University."},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/218380.218467"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2366145.2366181"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12948"},{"key":"e_1_2_2_7_1","unstructured":"Subrahmanyan Chandrasekhar. 1960. Radiative Transfer. Dover Publications.  Subrahmanyan Chandrasekhar. 1960. Radiative Transfer. Dover Publications."},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-6242-2_3"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-6303-0_13"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12256"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/2010324.1964951"},{"key":"e_1_2_2_12_1","article-title":"Light transport simulation with vertex connection and merging","volume":"31","author":"Georgiev Iliyan","year":"2012","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/2508363.2508411"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-21617-1"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/1964921.1964949"},{"key":"e_1_2_2_16_1","volume-title":"Proceedings of HPG.","author":"Gribel Carl Johan","year":"2010"},{"key":"e_1_2_2_17_1","article-title":"Stochastic progressive photon mapping","volume":"28","author":"Hachisuka Toshiya","year":"2009","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_2_2_18_1","article-title":"Progressive Photon Mapping","volume":"27","author":"Hachisuka Toshiya","year":"2008","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_2_2_19_1","article-title":"A path space extension for robust light transport simulation","volume":"31","author":"Hachisuka Toshiya","year":"2012","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_2_2_20_1","doi-asserted-by":"crossref","unstructured":"Vlastimil Havran Jiri Bittner Robert Herzog and Hans-Peter Seidel. 2005. Ray Maps for Global Illumination. In Rendering Techniques (Proc. EGSR).  Vlastimil Havran Jiri Bittner Robert Herzog and Hans-Peter Seidel. 2005. Ray Maps for Global Illumination. In Rendering Techniques (Proc. EGSR).","DOI":"10.1145\/1186223.1186319"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/15922.15901"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/2070781.2024215"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/2024156.2024215"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/1401132.1401137"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1201\/b10685"},{"key":"e_1_2_2_26_1","volume-title":"Proc. SIGGRAPH.","author":"Jensen Henrik Wann"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-6303-0_18"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/15922.15902"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/1966394.1966404"},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601219"},{"key":"e_1_2_2_31_1","volume-title":"Proc. Compugraphics.","author":"Lafortune Eric","year":"1993"},{"key":"e_1_2_2_32_1","doi-asserted-by":"crossref","unstructured":"Eric Lafortune and Yves Willems. 1996. Rendering participating media with bidirectional path tracing. Photorealistic Rendering Techniques (Proc. EGWR) (1996).  Eric Lafortune and Yves Willems. 1996. Rendering participating media with bidirectional path tracing. Photorealistic Rendering Techniques (Proc. EGWR) (1996).","DOI":"10.1007\/978-3-7091-7484-5_10"},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.13182\/NSE78-A27241"},{"key":"e_1_2_2_34_1","doi-asserted-by":"crossref","unstructured":"Jan Nov\u00e1k Derek Nowrouzezahrai Carsten Dachsbacher and Wojciech Jarosz. 2012a. Progressive Virtual Beam Lights. Computer Graphics Forum (Proc. EGSR) 31 4 (2012).  Jan Nov\u00e1k Derek Nowrouzezahrai Carsten Dachsbacher and Wojciech Jarosz. 2012a. Progressive Virtual Beam Lights. Computer Graphics Forum (Proc. EGSR) 31 4 (2012).","DOI":"10.1111\/j.1467-8659.2012.03136.x"},{"key":"e_1_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185556"},{"key":"e_1_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12257"},{"key":"e_1_2_2_37_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-6303-0_2"},{"key":"e_1_2_2_38_1","doi-asserted-by":"crossref","unstructured":"Vincent Pegoraro and Steven G. Parker. 2009. An Analytical Solution to Single Scattering in Homogeneous Participating Media. Computer Graphics Forum (Proc. Eurographics) 28 2 (2009).  Vincent Pegoraro and Steven G. Parker. 2009. An Analytical Solution to Single Scattering in Homogeneous Participating Media. Computer Graphics Forum (Proc. Eurographics) 28 2 (2009).","DOI":"10.1111\/j.1467-8659.2009.01372.x"},{"key":"e_1_2_2_39_1","unstructured":"Matt Pharr Wenzel Jakob and Greg Humphreys. 2016. Physically Based Rendering: From Theory To Implementation (3rd ed.).  Matt Pharr Wenzel Jakob and Greg Humphreys. 2016. Physically Based Rendering: From Theory To Implementation (3rd ed.)."},{"key":"e_1_2_2_40_1","doi-asserted-by":"publisher","DOI":"10.1145\/166117.166138"},{"key":"e_1_2_2_41_1","doi-asserted-by":"publisher","DOI":"10.1137\/0114059"},{"key":"e_1_2_2_42_1","doi-asserted-by":"crossref","unstructured":"Jerome Spanier and Ely Meyer Gelbard. 1969. Monte Carlo principles and neutron transport problems. Addison-Wesley.  Jerome Spanier and Ely Meyer Gelbard. 1969. Monte Carlo principles and neutron transport problems. Addison-Wesley.","DOI":"10.1063\/1.3022338"},{"key":"e_1_2_2_43_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073309"},{"key":"e_1_2_2_44_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778791"},{"key":"e_1_2_2_45_1","volume-title":"Proceedings of HPG.","author":"Tzeng Stanley"},{"key":"e_1_2_2_46_1","unstructured":"Eric Veach. 1997. Robust Monte Carlo methods for light transport simulation. Ph.D. Dissertation. Stanford CA USA.  Eric Veach. 1997. Robust Monte Carlo methods for light transport simulation. Ph.D. Dissertation. Stanford CA USA."},{"key":"e_1_2_2_47_1","doi-asserted-by":"crossref","unstructured":"Eric Veach and Leonidas Guibas. 1994. Bidirectional estimators for light transport. In Photorealistic Rendering Techniques (Proc. EGWR).  Eric Veach and Leonidas Guibas. 1994. Bidirectional estimators for light transport. In Photorealistic Rendering Techniques (Proc. EGWR).","DOI":"10.1007\/978-3-642-87825-1_11"},{"key":"e_1_2_2_48_1","doi-asserted-by":"publisher","DOI":"10.1145\/218380.218498"},{"key":"e_1_2_2_49_1","doi-asserted-by":"publisher","DOI":"10.1145\/258734.258775"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3072959.3073698","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3072959.3073698","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3072959.3073698","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T03:30:23Z","timestamp":1750217423000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3072959.3073698"}},"subtitle":["higher-dimensional photon samples for volumetric light transport"],"short-title":[],"issued":{"date-parts":[[2017,7,20]]},"references-count":49,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,8,31]]}},"alternative-id":["10.1145\/3072959.3073698"],"URL":"https:\/\/doi.org\/10.1145\/3072959.3073698","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,7,20]]},"assertion":[{"value":"2017-07-20","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}