{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T19:08:22Z","timestamp":1783105702764,"version":"3.54.6"},"reference-count":94,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2025,2,3]],"date-time":"2025-02-03T00:00:00Z","timestamp":1738540800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001711","name":"Swiss National Science Foundation","doi-asserted-by":"crossref","award":["200502"],"award-info":[{"award-number":["200502"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2025,2,28]]},"abstract":"<jats:p>Efficient scene representations are essential for many computer graphics applications. A general unified representation that can handle both surfaces and volumes simultaneously remains a research challenge. In this work we propose a compact and efficient alternative to existing volumetric representations for rendering such as voxel grids. Inspired by recent methods for scene reconstruction that leverage mixtures of three-dimensional Gaussians to model radiance fields, we formalize and generalize the modeling of scattering and emissive media using mixtures of simple kernel-based volumetric primitives. We introduce closed-form solutions for transmittance and free-flight distance sampling for different kernels and propose several optimizations to use our method efficiently within any off-the-shelf volumetric path tracer. We demonstrate our method in both forward and inverse rendering of complex scattering media. Furthermore, we adapt and showcase our method in radiance field optimization and rendering, providing additional flexibility compared to current state of the art given its ray-tracing formulation. We also introduce the Epanechnikov kernel and demonstrate its potential as an efficient alternative to the traditionally used Gaussian kernel in scene reconstruction tasks. The versatility and physically based nature of our approach allows us to go beyond radiance fields and bring to kernel-based modeling and rendering any path-tracing enabled functionality such as scattering, relighting, and complex camera models.<\/jats:p>","DOI":"10.1145\/3711853","type":"journal-article","created":{"date-parts":[[2025,1,21]],"date-time":"2025-01-21T11:23:39Z","timestamp":1737458619000},"page":"1-17","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":22,"title":["Don't Splat your Gaussians: Volumetric Ray-Traced Primitives for Modeling and Rendering Scattering and Emissive Media"],"prefix":"10.1145","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9958-0118","authenticated-orcid":false,"given":"Jorge","family":"Condor","sequence":"first","affiliation":[{"name":"Meta Reality Labs, Zurich, Switzerland and Universita della Svizzera Italiana, Lugano, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6919-7567","authenticated-orcid":false,"given":"Sebastien","family":"Speierer","sequence":"additional","affiliation":[{"name":"Meta Reality Labs, Lausanne, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8710-8561","authenticated-orcid":false,"given":"Lukas","family":"Bode","sequence":"additional","affiliation":[{"name":"Meta Reality Labs, Zurich, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-2985-6921","authenticated-orcid":false,"given":"Aljaz","family":"Bozic","sequence":"additional","affiliation":[{"name":"Meta Reality Labs, Zurich, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-5323-1170","authenticated-orcid":false,"given":"Simon","family":"Green","sequence":"additional","affiliation":[{"name":"Meta Reality Labs, London, United Kingdom of Great Britain and Northern Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0768-8939","authenticated-orcid":false,"given":"Piotr","family":"Didyk","sequence":"additional","affiliation":[{"name":"Universita della Svizzera Italiana, Lugano, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9000-0466","authenticated-orcid":false,"given":"Adrian","family":"Jarabo","sequence":"additional","affiliation":[{"name":"Meta Reality Labs, Zaragoza, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2025,2,3]]},"reference":[{"issue":"4","key":"e_1_3_3_2_1","article-title":"An appearance model for textile fibers","volume":"36","author":"Aliaga Carlos","year":"2017","unstructured":"Carlos Aliaga, Carlos Castillo, Diego Guti\u00e9rrez, Miguel A. Otaduy, Jorge Lopez-Moreno, and Adri\u00e1n Jarabo. 2017. An appearance model for textile fibers. Comput.Graph. Forum 36, 4 (2017), 35\u201345.","journal-title":"Comput.Graph. Forum"},{"issue":"2","key":"e_1_3_3_3_1","article-title":"Refractive radiative transfer equation","volume":"33","author":"Ament Marco","year":"2014","unstructured":"Marco Ament, Christoph Bergmann, and Daniel Weiskopf. 2014. Refractive radiative transfer equation. ACM Trans. Graph. 33, 2, Article No.: 17 (2014), 1\u201322.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_3_4_1","volume-title":"Proceedings of ICCV","author":"Barron Jonathan T.","year":"2021","unstructured":"Jonathan T. Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P. Srinivasan. 2021. Mip-NeRF: A multiscale representation for anti-aliasing neural radiance fields. In Proceedings of ICCV."},{"key":"e_1_3_3_5_1","volume-title":"Proceedings of CVPR","author":"Barron Jonathan T.","year":"2022","unstructured":"Jonathan T. Barron, Ben Mildenhall, Dor Verbin, Pratul P. Srinivasan, and Peter Hedman. 2022. Mip-NeRF 360: Unbounded anti-aliased neural radiance fields. In Proceedings of CVPR."},{"issue":"6","key":"e_1_3_3_6_1","article-title":"A radiative transfer framework for non-exponential media","volume":"37","author":"Bitterli Benedikt","year":"2018","unstructured":"Benedikt Bitterli, Srinath Ravichandran, Thomas M\u00fcller, Magnus Wrenninge, Jan Nov\u00e1k, Steve Marschner, and Wojciech Jarosz. 2018. A radiative transfer framework for non-exponential media. ACM Trans. Graph. 37, 6, Article No.: 225 (2018), 1\u201317.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_3_7_1","article-title":"Neural assets: Volumetric object capture and rendering for interactive environments","author":"Bo\u017ei\u010d Alja\u017e","year":"2022","unstructured":"Alja\u017e Bo\u017ei\u010d, Denis Gladkov, Luke Doukakis, and Christoph Lassner. 2022. Neural assets: Volumetric object capture and rendering for interactive environments. arXiv:2212.06125. Retrieved from https:\/\/arxiv.org\/abs\/2212.06125","journal-title":"arXiv:2212.06125"},{"key":"e_1_3_3_8_1","volume-title":"Proceedings of the ANS Mathematics & Computation Topical Meeting","volume":"2","author":"Brown Forrest B.","year":"2003","unstructured":"Forrest B. Brown and William R. Martin. 2003. Direct sampling of Monte Carlo flight paths in media with continuously varying cross-sections. In Proceedings of the ANS Mathematics & Computation Topical Meeting, Vol. 2."},{"issue":"3","key":"e_1_3_3_9_1","article-title":"The design and evolution of Disney\u2019s Hyperion renderer","volume":"37","author":"Burley Brent","year":"2018","unstructured":"Brent Burley, David Adler, Matt Jen-Yuan Chiang, Hank Driskill, Ralf Habel, Patrick Kelly, Peter Kutz, Yining Karl Li, and Daniel Teece. 2018. The design and evolution of Disney\u2019s Hyperion renderer. ACM Trans. Graph. 37, 3, Article No.: 33 (2018), 1\u201322.","journal-title":"ACM Trans. Graph."},{"issue":"4","key":"e_1_3_3_10_1","doi-asserted-by":"crossref","DOI":"10.13182\/NSE72-1","article-title":"Monte Carlo sampling with continuously varying cross sections along flight paths","volume":"48","author":"Carter L. L.","year":"1972","unstructured":"L. L. Carter, E. D. Cashwell, and W. M. Taylor. 1972. Monte Carlo sampling with continuously varying cross sections along flight paths. Nucl. Sci. Eng. 48, 4 (1972), 403\u2013411.","journal-title":"Nucl. Sci. Eng."},{"key":"e_1_3_3_11_1","volume-title":"Radiative Transfer","author":"Chandrasekhar Subrahmanyan","year":"1960","unstructured":"Subrahmanyan Chandrasekhar. 1960. Radiative Transfer. Courier Corporation."},{"key":"e_1_3_3_12_1","volume-title":"Proceedings of CVPR","author":"Chen Zhiqin","year":"2023","unstructured":"Zhiqin Chen, Thomas Funkhouser, Peter Hedman, and Andrea Tagliasacchi. 2023. Mobilenerf: Exploiting the polygon rasterization pipeline for efficient neural field rendering on mobile architectures. In Proceedings of CVPR."},{"issue":"3","key":"e_1_3_3_13_1","article-title":"RenderMan: An advanced path-tracing architecture for movie rendering","volume":"37","author":"Christensen Per","year":"2018","unstructured":"Per Christensen, Julian Fong, Jonathan Shade, Wayne Wooten, Brenden Schubert, Andrew Kensler, Stephen Friedman, Charlie Kilpatrick, Cliff Ramshaw, Marc Bannister, et al.. 2018. RenderMan: An advanced path-tracing architecture for movie rendering. ACM Trans. Graph. 37, 3, Article No.: 30 (2018), 1\u201321.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_3_14_1","volume-title":"Proceedings of EGSR","author":"Condor Jorge","year":"2022","unstructured":"Jorge Condor and Adri\u00e1n Jarabo. 2022. A learned radiance-field representation for complex luminaires. In Proceedings of EGSR."},{"key":"e_1_3_3_15_1","volume-title":"ACM SIGGRAPH Conference Papers","author":"Condor Jorge","year":"2023","unstructured":"Jorge Condor, Michal Piovar\u010di, Bernd Bickel, and Piotr Didyk. 2023. Gloss-aware color correction for 3D printing. In ACM SIGGRAPH Conference Papers."},{"issue":"2","key":"e_1_3_3_16_1","doi-asserted-by":"crossref","DOI":"10.13182\/NSE78-A27154","article-title":"Application of the fictitious scattering radiation transport model for deep-penetration Monte Carlo calculations","volume":"65","author":"Cramer S. N.","year":"1978","unstructured":"S. N. Cramer. 1978. Application of the fictitious scattering radiation transport model for deep-penetration Monte Carlo calculations. Nucl. Sci. Eng. 65, 2 (1978), 237\u2013253.","journal-title":"Nucl. Sci. Eng."},{"issue":"3","key":"e_1_3_3_17_1","article-title":"Primary-space adaptive control variates using piecewise-polynomial approximations","volume":"40","author":"Crespo Miguel","year":"2021","unstructured":"Miguel Crespo, Adrian Jarabo, and Adolfo Mu\u00f1oz. 2021. Primary-space adaptive control variates using piecewise-polynomial approximations. ACM Trans. Graph. 40, 3, Article No.: 25 (2021), 1\u201315.","journal-title":"ACM Trans. Graph."},{"issue":"6","key":"e_1_3_3_18_1","article-title":"Scattering-aware texture reproduction for 3D printing","volume":"36","author":"Elek Oskar","year":"2017","unstructured":"Oskar Elek, Denis Sumin, Ran Zhang, Tim Weyrich, Karol Myszkowski, Bernd Bickel, Alexander Wilkie, and Jaroslav K\u0159iv\u00e1nek. 2017. Scattering-aware texture reproduction for 3D printing. ACM Trans. Graph. 36, 6, Article No.: 241 (2017), 1\u201315.","journal-title":"ACM Trans. Graph."},{"issue":"3","key":"e_1_3_3_19_1","article-title":"Manuka: A batch-shading architecture for spectral path tracing in movie production","volume":"37","author":"Fascione Luca","year":"2018","unstructured":"Luca Fascione, Johannes Hanika, Mark Leone, Marc Droske, Jorge Schwarzhaupt, Tom\u00e1\u0161 Davidovi\u010d, Andrea Weidlich, and Johannes Meng. 2018. Manuka: A batch-shading architecture for spectral path tracing in movie production. ACM Trans. Graph. 37, 3, Article No.: 31 (2018), 1\u201318.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_3_20_1","volume-title":"ACM SIGGRAPH 2017 Courses","author":"Fong Julian","year":"2017","unstructured":"Julian Fong, Magnus Wrenninge, Christopher Kulla, and Ralf Habel. 2017. Production volume rendering. In ACM SIGGRAPH 2017 Courses."},{"key":"e_1_3_3_21_1","volume-title":"Proceedings of CVPR","author":"Fridovich-Keil Sara","year":"2022","unstructured":"Sara Fridovich-Keil, Alex Yu, Matthew Tancik, Qinhong Chen, Benjamin Recht, and Angjoo Kanazawa. 2022. Plenoxels: Radiance fields without neural networks. In Proceedings of CVPR."},{"key":"e_1_3_3_22_1","article-title":"Integral formulation of null-collision Monte Carlo algorithms","volume":"125","author":"Galtier Mathieu","year":"2013","unstructured":"Mathieu Galtier, Stephane Blanco, Cyril Caliot, Christophe Coustet, J\u00e9r\u00e9mi Dauchet, Mouna El Hafi, Vincent Eymet, Richard Fournier, Jacques Gautrais, Anais Khuong, et\u00a0al. 2013. Integral formulation of null-collision Monte Carlo algorithms. J. Quant. Spectrosc. Radiat. Transf. 125 (2013), 57\u201368.","journal-title":"J. Quant. Spectrosc. Radiat. Transf."},{"issue":"3","key":"e_1_3_3_23_1","article-title":"Arnold: A brute-force production path tracer","volume":"37","author":"Georgiev Iliyan","year":"2018","unstructured":"Iliyan Georgiev, Thiago Ize, Mike Farnsworth, Ram\u00f3n Montoya-Vozmediano, Alan King, Brecht Van Lommel, Angel Jimenez, Oscar Anson, Shinji Ogaki, Eric Johnston, et al.2018. Arnold: A brute-force production path tracer. ACM Trans. Graph. 37, 3, Article No.: 32 (2018), 1\u201312.","journal-title":"ACM Trans. Graph."},{"issue":"6","key":"e_1_3_3_24_1","article-title":"Integral formulations of volumetric transmittance","volume":"38","author":"Georgiev Iliyan","year":"2019","unstructured":"Iliyan Georgiev, Zackary Misso, Toshiya Hachisuka, Derek Nowrouzezahrai, Jaroslav K\u0159iv\u00e1nek, and Wojciech Jarosz. 2019. Integral formulations of volumetric transmittance. ACM Trans. Graph. 38, 6, Article No.: 154 (2019), 1\u201317.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_3_25_1","volume-title":"Proceedings of ECCV","author":"Gkioulekas Ioannis","year":"2016","unstructured":"Ioannis Gkioulekas, Anat Levin, and Todd Zickler. 2016. An evaluation of computational imaging techniques for heterogeneous inverse scattering. In Proceedings of ECCV."},{"key":"e_1_3_3_26_1","volume-title":"Proceedings of I3D","author":"Green Paul","year":"2006","unstructured":"Paul Green, Jan Kautz, Wojciech Matusik, and Fr\u00e9do Durand. 2006. View-dependent precomputed light transport using nonlinear Gaussian function approximations. In Proceedings of I3D."},{"key":"e_1_3_3_27_1","volume-title":"Proceedings of ICCV","author":"Hedman Peter","year":"2021","unstructured":"Peter Hedman, Pratul P. Srinivasan, Ben Mildenhall, Jonathan T. Barron, and Paul Debevec. 2021. Baking neural radiance fields for real-time view synthesis. In Proceedings of ICCV."},{"issue":"4","key":"e_1_3_3_28_1","article-title":"The SGGX microflake distribution","volume":"34","author":"Heitz Eric","year":"2015","unstructured":"Eric Heitz, Jonathan Dupuy, Cyril Crassin, and Carsten Dachsbacher. 2015. The SGGX microflake distribution. ACM Trans. Graph. 34, 4, Article No.: 48 (2015), 1\u201311.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_3_29_1","unstructured":"Wenzel Jakob. 2010. Mitsuba Renderer."},{"issue":"4","key":"e_1_3_3_30_1","article-title":"A radiative transfer framework for rendering materials with anisotropic structure","volume":"29","author":"Jakob Wenzel","year":"2010","unstructured":"Wenzel Jakob, Adam Arbree, Jonathan T Moon, Kavita Bala, and Steve Marschner. 2010. A radiative transfer framework for rendering materials with anisotropic structure. ACM Trans. Graph. 29, 4, Article No.: 53 (2010), 1\u201313.","journal-title":"ACM Trans. Graph."},{"issue":"4","key":"e_1_3_3_31_1","article-title":"Progressive expectation\u2013maximization for hierarchical volumetric photon mapping","volume":"30","author":"Jakob Wenzel","year":"2011","unstructured":"Wenzel Jakob, Christian Regg, and Wojciech Jarosz. 2011. Progressive expectation\u2013maximization for hierarchical volumetric photon mapping. Computer Graphics Forum 30, 4 (2011), 1287\u20131297.","journal-title":"Computer Graphics Forum"},{"key":"e_1_3_3_32_1","volume-title":"Mitsuba 3 Renderer","author":"Jakob Wenzel","year":"2022","unstructured":"Wenzel Jakob, S\u00e9bastien Speierer, Nicolas Roussel, Merlin Nimier-David, Delio Vicini, Tizian Zeltner, Baptiste Nicolet, Miguel Crespo, Vincent Leroy, and Ziyi Zhang. 2022b. Mitsuba 3 Renderer. Retrieved from https:\/\/mitsuba-renderer.org"},{"issue":"4","key":"e_1_3_3_33_1","article-title":"Dr.Jit: A just-in-time compiler for differentiable rendering","volume":"41","author":"Jakob Wenzel","year":"2022","unstructured":"Wenzel Jakob, S\u00e9bastien Speierer, Nicolas Roussel, and Delio Vicini. 2022a. Dr.Jit: A just-in-time compiler for differentiable rendering. ACM Trans. Graph. 41, 4, Article No.: 124 (2022), 1\u201319.","journal-title":"ACM Trans. Graph."},{"issue":"4","key":"e_1_3_3_34_1","article-title":"A radiative transfer framework for spatially-correlated materials","volume":"37","author":"Jarabo Adrian","year":"2018","unstructured":"Adrian Jarabo, Carlos Aliaga, and Diego Gutierrez. 2018. A radiative transfer framework for spatially-correlated materials. ACM Trans. Graph. 37, 4, Article No.: 83 (2018), 1\u201313.","journal-title":"ACM Trans. Graph."},{"issue":"4","key":"e_1_3_3_35_1","doi-asserted-by":"crossref","DOI":"10.1145\/15922.15902","article-title":"The rendering equation","volume":"20","author":"Kajiya James T.","year":"1986","unstructured":"James T. Kajiya. 1986. The rendering equation. SIGGRAPH Comput. Graph. 20, 4 (1986).","journal-title":"SIGGRAPH Comput. Graph."},{"issue":"6","key":"e_1_3_3_36_1","article-title":"Deep scattering: Rendering atmospheric clouds with radiance-predicting neural networks","volume":"36","author":"Kallweit Simon","year":"2017","unstructured":"Simon Kallweit, Thomas M\u00fcller, Brian Mcwilliams, Markus Gross, and Jan Nov\u00e1k. 2017. Deep scattering: Rendering atmospheric clouds with radiance-predicting neural networks. ACM Trans. Graph. 36, 6, Article No.: 231 (2017), 1\u201311.","journal-title":"ACM Trans. Graph."},{"issue":"4","key":"e_1_3_3_37_1","article-title":"3D Gaussian splatting for real-time radiance field rendering","volume":"42","author":"Kerbl Bernhard","year":"2023","unstructured":"Bernhard Kerbl, Georgios Kopanas, Thomas Leimk\u00fchler, and George Drettakis. 2023. 3D Gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42, 4, Article No.: 139 (2023), 1\u201314.","journal-title":"ACM Trans. Graph."},{"issue":"4","key":"e_1_3_3_38_1","article-title":"An unbiased ray-marching transmittance estimator","volume":"40","author":"Kettunen Markus","year":"2021","unstructured":"Markus Kettunen, Eugene D\u2019Eon, Jacopo Pantaleoni, and Jan Nov\u00e1k. 2021. An unbiased ray-marching transmittance estimator. ACM Trans. Graph. 40, 4, Article No.: 137 (2021), 1\u201320.","journal-title":"ACM Trans. Graph."},{"issue":"1","key":"e_1_3_3_39_1","article-title":"Matching real fabrics with micro-appearance models.","volume":"35","author":"Khungurn Pramook","year":"2015","unstructured":"Pramook Khungurn, Daniel Schroeder, Shuang Zhao, Kavita Bala, and Steve Marschner. 2015. Matching real fabrics with micro-appearance models. ACM Trans. Graph. 35, 1, Article No.: 1 (2015), 1\u201326.","journal-title":"ACM Trans. Graph."},{"issue":"2","key":"e_1_3_3_40_1","article-title":"NeuralVDB: High-resolution sparse volume representation using hierarchical neural networks","volume":"43","author":"Kim Doyub","year":"2024","unstructured":"Doyub Kim, Minjae Lee, and Ken Museth. 2024. NeuralVDB: High-resolution sparse volume representation using hierarchical neural networks. ACM Trans. Graph. 43, 2, Article No.: 20 (2024), 1\u201321.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_3_41_1","unstructured":"Diederik P. Kingma and Jimmy Ba. 2017. Adam: A method for stochastic optimization. arxiv:1412.6980. Retrieved from https:\/\/arxiv.org\/abs\/1412.6980"},{"key":"e_1_3_3_42_1","volume-title":"Proceedings of ISMM","author":"Kirk David","year":"2007","unstructured":"David Kirk. 2007. NVIDIA CUDA software and GPU parallel computing architecture. In Proceedings of ISMM."},{"issue":"4","key":"e_1_3_3_43_1","article-title":"Tanks and temples: Benchmarking large-scale scene reconstruction","volume":"36","author":"Knapitsch Arno","year":"2017","unstructured":"Arno Knapitsch, Jaesik Park, Qian-Yi Zhou, and Vladlen Koltun. 2017. Tanks and temples: Benchmarking large-scale scene reconstruction. ACM Trans. Graph. 36, 4, Article No.: 78 (2017), 1\u201313.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_3_44_1","volume-title":"Ray Tracing Gems II","author":"Knoll Aaron","year":"2021","unstructured":"Aaron Knoll, Gregory P. Johnson, and Johannes Meng. 2021. Path tracing RBF particle volumes. In Ray Tracing Gems II, Adam Marrs, Peter Shirley, and Ingo Wald (Eds.). Apress."},{"issue":"4","key":"e_1_3_3_45_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3072959.3073665","article-title":"Spectral and decomposition tracking for rendering heterogeneous volumes","volume":"36","author":"Kutz Peter","year":"2017","unstructured":"Peter Kutz, Ralf Habel, Yining Karl Li, and Jan Nov\u00e1k. 2017. Spectral and decomposition tracking for rendering heterogeneous volumes. ACM Trans. Graph. 36, 4, Article No.: 111 (2017), 1\u201316.","journal-title":"ACM Trans. Graph."},{"issue":"4","key":"e_1_3_3_46_1","article-title":"Laplacian kernel splatting for efficient depth-of-field and motion blur synthesis or reconstruction","volume":"37","author":"Leimk\u00fchler Thomas","year":"2018","unstructured":"Thomas Leimk\u00fchler, Hans-Peter Seidel, and Tobias Ritschel. 2018. Laplacian kernel splatting for efficient depth-of-field and motion blur synthesis or reconstruction. ACM Trans. Graph. 37, 4, Article No.: 55 (2018), 1\u201311.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_3_47_1","article-title":"Three-dimensional Epanechnikov mixture regression in image coding","volume":"185","author":"Liu Boning","year":"2021","unstructured":"Boning Liu, Yan Zhao, Xiaomeng Jiang, and Shigang Wang. 2021. Three-dimensional Epanechnikov mixture regression in image coding. Sign. Process. 185 (2021), 108090.","journal-title":"Sign. Process."},{"issue":"4","key":"e_1_3_3_48_1","article-title":"Mixture of volumetric primitives for efficient neural rendering","volume":"40","author":"Lombardi Stephen","year":"2021","unstructured":"Stephen Lombardi, Tomas Simon, Gabriel Schwartz, Michael Zollhoefer, Yaser Sheikh, and Jason Saragih. 2021. Mixture of volumetric primitives for efficient neural rendering. ACM Trans. Graph. 40, 4, Article No.: 59 (2021), 1\u201313.","journal-title":"ACM Trans. Graph."},{"issue":"2","key":"e_1_3_3_49_1","article-title":"Hybrid mesh-volume LoDs for all-scale pre-filtering of complex 3D assets","volume":"36","author":"Loubet Guillaume","year":"2017","unstructured":"Guillaume Loubet and Fabrice Neyret. 2017. Hybrid mesh-volume LoDs for all-scale pre-filtering of complex 3D assets. Computer Graphics Forum 36, 2 (2017), 431\u2013442.","journal-title":"Computer Graphics Forum"},{"issue":"2","key":"e_1_3_3_50_1","article-title":"ATOMLLL: ATOMS with shading and highlights","volume":"13","author":"Max Nelson L.","year":"1979","unstructured":"Nelson L. Max. 1979. ATOMLLL: ATOMS with shading and highlights. ACM SIGGRAPH Comput. Graph. 13, 2 (1979), 165\u2013173.","journal-title":"ACM SIGGRAPH Comput. Graph."},{"issue":"4","key":"e_1_3_3_51_1","article-title":"Multi-scale modeling and rendering of granular materials","volume":"34","author":"Meng Johannes","year":"2015","unstructured":"Johannes Meng, Marios Papas, Ralf Habel, Carsten Dachsbacher, Steve Marschner, Markus Gross, and Wojciech Jarosz. 2015. Multi-scale modeling and rendering of granular materials. ACM Trans. Graph. 34, 4, Article No.: 49 (2015), 1\u201313.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_3_52_1","volume-title":"Proceedings of ECCV","author":"Mildenhall Ben","year":"2020","unstructured":"Ben Mildenhall, Pratul P. Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, and Ren Ng. 2020. NeRF: Representing scenes as neural radiance fields for view synthesis. In Proceedings of ECCV."},{"key":"e_1_3_3_53_1","volume-title":"ACM SIGGRAPH Conference Papers","author":"Misso Zackary","year":"2023","unstructured":"Zackary Misso, Yining Karl Li, Brent Burley, Daniel Teece, and Wojciech Jarosz. 2023. Progressive null-tracking for volumetric rendering. In ACM SIGGRAPH Conference Papers."},{"key":"e_1_3_3_54_1","volume-title":"Proceedings of EGSR","author":"Moon Jonathan T.","year":"2007","unstructured":"Jonathan T. Moon, Bruce Walter, and Stephen R. Marschner. 2007. Rendering discrete random media using precomputed scattering solutions. In Proceedings of EGSR."},{"issue":"6","key":"e_1_3_3_55_1","article-title":"The expectation-maximization algorithm","volume":"13","author":"Moon T. K.","year":"1996","unstructured":"T. K. Moon. 1996. The expectation-maximization algorithm. IEEE Sign. Process. Mag. 13, 6 (1996), 47\u201360.","journal-title":"IEEE Sign. Process. Mag."},{"issue":"4","key":"e_1_3_3_56_1","article-title":"Instant neural graphics primitives with a multiresolution hash encoding","volume":"41","author":"M\u00fcller Thomas","year":"2022","unstructured":"Thomas M\u00fcller, Alex Evans, Christoph Schied, and Alexander Keller. 2022. Instant neural graphics primitives with a multiresolution hash encoding. ACM Trans. Graph. 41, 4, Article No.: 102 (2022), 1\u201315.","journal-title":"ACM Trans. Graph."},{"issue":"6","key":"e_1_3_3_57_1","article-title":"Efficient rendering of heterogeneous polydisperse granular media","volume":"35","author":"M\u00fcller Thomas","year":"2016","unstructured":"Thomas M\u00fcller, Marios Papas, Markus Gross, Wojciech Jarosz, and Jan Nov\u00e1k. 2016. Efficient rendering of heterogeneous polydisperse granular media. ACM Trans. Graph. 35, 6, Article No.: 168 (2016), 1\u201314.","journal-title":"ACM Trans. Graph."},{"issue":"8","key":"e_1_3_3_58_1","article-title":"Higher order ray marching","volume":"33","author":"Mu\u00f1oz Adolfo","year":"2014","unstructured":"Adolfo Mu\u00f1oz. 2014. Higher order ray marching. Comput. Graph. Forum 33, 8 (2014), 167\u2013176.","journal-title":"Comput. Graph. Forum"},{"issue":"3","key":"e_1_3_3_59_1","article-title":"VDB: High-resolution sparse volumes with dynamic topology","volume":"32","author":"Museth Ken","year":"2013","unstructured":"Ken Museth. 2013. VDB: High-resolution sparse volumes with dynamic topology. ACM Trans. Graph. 32, 3, Article No.: 27 (2013), 1\u201322.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_3_60_1","volume-title":"ACM SIGGRAPH 2021 Talks","author":"Museth Ken","year":"2021","unstructured":"Ken Museth. 2021. NanoVDB: A GPU-friendly and portable VDB data structure for real-time rendering and simulation. In ACM SIGGRAPH 2021 Talks."},{"issue":"1","key":"e_1_3_3_61_1","article-title":"Modeling, animating, and rendering complex scenes using volumetric textures","volume":"4","author":"Neyret Fabrice","year":"1998","unstructured":"Fabrice Neyret. 1998. Modeling, animating, and rendering complex scenes using volumetric textures. IEEE Trans. Vis. Comput. Graph. 4, 1 (1998), 55\u201370.","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"issue":"4","key":"e_1_3_3_62_1","article-title":"Unbiased inverse volume rendering with differential trackers","volume":"41","author":"Nimier-David Merlin","year":"2022","unstructured":"Merlin Nimier-David, Thomas M\u00fcller, Alexander Keller, and Wenzel Jakob. 2022. Unbiased inverse volume rendering with differential trackers. ACM Trans. Graph. 41, 4, Article No.: 44 (2022), 1\u201320.","journal-title":"ACM Trans. Graph."},{"issue":"4","key":"e_1_3_3_63_1","article-title":"A gradient-based framework for 3D print appearance optimization","volume":"40","author":"Nindel Thomas Klaus","year":"2021","unstructured":"Thomas Klaus Nindel, Tom\u00e1\u0161 Iser, Tobias Rittig, Alexander Wilkie, and Jaroslav K\u0159iv\u00e1nek. 2021. A gradient-based framework for 3D print appearance optimization. ACM Trans. Graph. 40, 4, Article No.: 178 (2021), 1\u201315.","journal-title":"ACM Trans. Graph."},{"issue":"2","key":"e_1_3_3_64_1","article-title":"Monte Carlo methods for volumetric light transport simulation","volume":"37","author":"Nov\u00e1k Jan","year":"2018","unstructured":"Jan Nov\u00e1k, Iliyan Georgiev, Johannes Hanika, and Wojciech Jarosz. 2018. Monte Carlo methods for volumetric light transport simulation. Comput. Graph. Forum 37, 2 (2018), 551\u2013576.","journal-title":"Comput. Graph. Forum"},{"issue":"6","key":"e_1_3_3_65_1","article-title":"Residual ratio tracking for estimating attenuation in participating media","volume":"33","author":"Nov\u00e1k Jan","year":"2014","unstructured":"Jan Nov\u00e1k, Andrew Selle, and Wojciech Jarosz. 2014. Residual ratio tracking for estimating attenuation in participating media. ACM Trans. Graph. 33, 6, Article No.: 179 (2014), 1\u201311.","journal-title":"ACM Trans. Graph."},{"issue":"4","key":"e_1_3_3_66_1","article-title":"OptiX: A general purpose ray tracing engine","volume":"29","author":"Parker Steven G.","year":"2010","unstructured":"Steven G. Parker, James Bigler, Andreas Dietrich, Heiko Friedrich, Jared Hoberock, David Luebke, David McAllister, Morgan McGuire, Keith Morley, Austin Robison, et al.. 2010. OptiX: A general purpose ray tracing engine. ACM Trans. Graph. 29, 4, Article No.: 66 (2010), 1\u201313.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_3_67_1","first-page":"10","volume-title":"Proceedings of SIGGRAPH","author":"Perlin K.","year":"1989","unstructured":"K. Perlin and E. M. Hoffert. 1989. Hypertexture. In Proceedings of SIGGRAPH. 10 pages."},{"key":"e_1_3_3_68_1","volume-title":"Physically Based Rendering: From Theory to Implementation","author":"Pharr Matt","year":"2023","unstructured":"Matt Pharr, Wenzel Jakob, and Greg Humphreys. 2023. Physically Based Rendering: From Theory to Implementation. MIT Press."},{"key":"e_1_3_3_69_1","volume-title":"Monte Carlo and Quasi-Monte Carlo Methods 2006","author":"Raab Matthias","year":"2006","unstructured":"Matthias Raab, Daniel Seibert, and Alexander Keller. 2006. Unbiased global illumination with participating media. In Monte Carlo and Quasi-Monte Carlo Methods 2006."},{"issue":"4","key":"e_1_3_3_70_1","article-title":"Merf: Memory-efficient radiance fields for real-time view synthesis in unbounded scenes","volume":"42","author":"Reiser Christian","year":"2023","unstructured":"Christian Reiser, Rick Szeliski, Dor Verbin, Pratul Srinivasan, Ben Mildenhall, Andreas Geiger, Jon Barron, and Peter Hedman. 2023. Merf: Memory-efficient radiance fields for real-time view synthesis in unbounded scenes. ACM Trans. Graph. 42, 4, Article No.: 89 (2023), 1\u201312.","journal-title":"ACM Trans. Graph."},{"issue":"6","key":"e_1_3_3_71_1","article-title":"Point-based rendering techniques","volume":"28","author":"Sainz Miguel","year":"2004","unstructured":"Miguel Sainz and Renato Pajarola. 2004. Point-based rendering techniques. Comput. Graph. 28, 6 (2004), 869\u2013879.","journal-title":"Comput. Graph."},{"issue":"4","key":"e_1_3_3_72_1","article-title":"A volumetric approach to predictive rendering of fabrics","volume":"30","author":"Schr\u00f6der Kai","year":"2011","unstructured":"Kai Schr\u00f6der, Reinhard Klein, and Arno Zinke. 2011. A volumetric approach to predictive rendering of fabrics. Comput. Graph. Forum 30, 4 (2011), 1277\u20131286.","journal-title":"Comput. Graph. Forum"},{"issue":"4","key":"e_1_3_3_73_1","article-title":"Two pairs of families of estimators for transport problems","volume":"14","author":"Spanier Jerome","year":"1966","unstructured":"Jerome Spanier. 1966. Two pairs of families of estimators for transport problems. SIAM J. Appl. Math. 14, 4 (1966), 702\u2013713.","journal-title":"SIAM J. Appl. Math."},{"key":"e_1_3_3_74_1","volume-title":"Monte Carlo Principles and Neutron Transport Problems","author":"Spanier Jerome","year":"2008","unstructured":"Jerome Spanier and Ely M. Gelbard. 2008. Monte Carlo Principles and Neutron Transport Problems. Courier Corporation."},{"issue":"4","key":"e_1_3_3_75_1","article-title":"Geometry-aware scattering compensation for 3D printing","volume":"38","author":"Sumin Denis","year":"2019","unstructured":"Denis Sumin, Tobias Rittig, Vahid Babaei, Tim Weyrich, Thomas Nindel, Piotr Didyk, Bernd Bickel, Jaroslav K\u0159iv\u00e1nek, Alexander Wilkie, and Karol Myszkowski. 2019. Geometry-aware scattering compensation for 3D printing. ACM Trans. Graph. 38, 4, Article No.: 111 (2019), 1\u201314.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_3_76_1","doi-asserted-by":"publisher","unstructured":"T. M. Sutton F. B. Brown F. G. Bischoff D. B. MacMillan C. L. Ellis J. T. Ward C. T. Ballinger D. J. Kelly and L. Schindler. 1999. The physical models and statistical procedures used in the RACER Monte Carlo code. DOI:10.2172\/767449","DOI":"10.2172\/767449"},{"issue":"2","key":"e_1_3_3_77_1","article-title":"Unbiased light transport estimators for inhomogeneous participating media","volume":"36","author":"Szirmay-Kalos L\u00e1szl\u00f3","year":"2017","unstructured":"L\u00e1szl\u00f3 Szirmay-Kalos, Iliyan Georgiev, Mil\u00e1n Magdics, Bal\u00e1zs Moln\u00e1r, and D\u00e1vid L\u00e9gr\u00e1dy. 2017. Unbiased light transport estimators for inhomogeneous participating media. Comput. Graph. Forum 36, 2 (2017), 9\u201319.","journal-title":"Comput. Graph. Forum"},{"issue":"1","key":"e_1_3_3_78_1","article-title":"Free path sampling in high resolution inhomogeneous participating media","volume":"30","author":"Szirmay-Kalos L\u00e1szl\u00f3","year":"2011","unstructured":"L\u00e1szl\u00f3 Szirmay-Kalos, Bal\u00e1zs T\u00f3th, and Mil\u00e1n Magdics. 2011. Free path sampling in high resolution inhomogeneous participating media. Comput. Graph. Forum 30, 1 (2011), 85\u201397.","journal-title":"Comput. Graph. Forum"},{"issue":"10","key":"e_1_3_3_79_1","article-title":"Direct 2-D display of 3-D objects","volume":"4","author":"Tuy Heang K.","year":"1984","unstructured":"Heang K. Tuy and Lee Tan Tuy. 1984. Direct 2-D display of 3-D objects. IEEE Comput. Graph. Appl. 4, 10 (1984), 29\u201334.","journal-title":"IEEE Comput. Graph. Appl."},{"issue":"4","key":"e_1_3_3_80_1","article-title":"A non-exponential transmittance model for volumetric scene representations","volume":"40","author":"Vicini Delio","year":"2021","unstructured":"Delio Vicini, Wenzel Jakob, and Anton Kaplanyan. 2021a. A non-exponential transmittance model for volumetric scene representations. ACM Trans. Graph. 40, 4, Article No.: 136 (2021), 1\u201316.","journal-title":"ACM Trans. Graph."},{"issue":"4","key":"e_1_3_3_81_1","article-title":"Path replay backpropagation: Differentiating light paths using constant memory and linear time","volume":"40","author":"Vicini Delio","year":"2021","unstructured":"Delio Vicini, S\u00e9bastien Speierer, and Wenzel Jakob. 2021b. Path replay backpropagation: Differentiating light paths using constant memory and linear time. ACM Trans. Graph. 40, 4, Article No.: 108 (2021), 1\u201314.","journal-title":"ACM Trans. Graph."},{"issue":"4","key":"e_1_3_3_82_1","article-title":"On-line learning of parametric mixture models for light transport simulation","volume":"33","author":"Vorba Ji\u0159\u00ed","year":"2014","unstructured":"Ji\u0159\u00ed Vorba, Ond\u0159ej Karl\u00edk, Martin \u0160ik, Tobias Ritschel, and Jaroslav K\u0159iv\u00e1nek. 2014. On-line learning of parametric mixture models for light transport simulation. ACM Trans. Graph. 33, 4, Article No.: 101 (2014), 1\u201311.","journal-title":"ACM Trans. Graph."},{"issue":"4","key":"e_1_3_3_83_1","article-title":"Image quality assessment: From error visibility to structural similarity","volume":"13","author":"Wang Zhou","year":"2004","unstructured":"Zhou Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli. 2004. Image quality assessment: From error visibility to structural similarity. IEEE Trans. Image Process. 13, 4 (2004), 600\u2013612.","journal-title":"IEEE Trans. Image Process."},{"key":"e_1_3_3_84_1","volume-title":"Proceedings of the Conference on Applications of Computing Methods to Reactor Problems","volume":"557","author":"Woodcock E.","year":"1965","unstructured":"E. Woodcock. 1965. Techniques used in the GEM code for Monte Carlo neutronics calculations in reactors and other systems of complex geometry. In Proceedings of the Conference on Applications of Computing Methods to Reactor Problems, Vol. 557."},{"issue":"6","key":"e_1_3_3_85_1","article-title":"Anisotropic spherical Gaussians","volume":"32","author":"Xu Kun","year":"2013","unstructured":"Kun Xu, Wei-Lun Sun, Zhao Dong, Dan-Yong Zhao, Run-Dong Wu, and Shi-Min Hu. 2013. Anisotropic spherical Gaussians. ACM Trans. Graph. 32, 6, Article No.: 209 (2013), 1\u201311.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_3_86_1","volume-title":"Proceedings of CVPR","author":"Xu Qiangeng","year":"2022","unstructured":"Qiangeng Xu, Zexiang Xu, Julien Philip, Sai Bi, Zhixin Shu, Kalyan Sunkavalli, and Ulrich Neumann. 2022. Point-nerf: Point-based neural radiance fields. In Proceedings of CVPR."},{"issue":"4","key":"e_1_3_3_87_1","article-title":"Position-normal distributions for efficient rendering of specular microstructure","volume":"35","author":"Yan Ling-Qi","year":"2016","unstructured":"Ling-Qi Yan, Milo\u0161 Ha\u0161an, Steve Marschner, and Ravi Ramamoorthi. 2016. Position-normal distributions for efficient rendering of specular microstructure. ACM Trans. Graph. 35, 4, Article No.: 56 (2016), 1\u20139.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_3_88_1","volume-title":"Proceedings of ICCV","author":"Yu Alex","year":"2021","unstructured":"Alex Yu, Ruilong Li, Matthew Tancik, Hao Li, Ren Ng, and Angjoo Kanazawa. 2021. PlenOctrees for real-time rendering of neural radiance fields. In Proceedings of ICCV."},{"issue":"6","key":"e_1_3_3_89_1","article-title":"Unbiased, adaptive stochastic sampling for rendering inhomogeneous participating media","volume":"29","author":"Yue Yonghao","year":"2010","unstructured":"Yonghao Yue, Kei Iwasaki, Bing-Yu Chen, Yoshinori Dobashi, and Tomoyuki Nishita. 2010. Unbiased, adaptive stochastic sampling for rendering inhomogeneous participating media. ACM Trans. Graph. 29, 6, Article No.: 177 (2010), 1\u20138.","journal-title":"ACM Trans. Graph."},{"issue":"6","key":"e_1_3_3_90_1","article-title":"A differential theory of radiative transfer","volume":"38","author":"Zhang Cheng","year":"2019","unstructured":"Cheng Zhang, Lifan Wu, Changxi Zheng, Ioannis Gkioulekas, Ravi Ramamoorthi, and Shuang Zhao. 2019. A differential theory of radiative transfer. ACM Trans. Graph. 38, 6, Article No.: 227 (2019), 1\u201316.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_3_91_1","article-title":"Nerf++: Analyzing and improving neural radiance fields","author":"Zhang Kai","year":"2020","unstructured":"Kai Zhang, Gernot Riegler, Noah Snavely, and Vladlen Koltun. 2020. Nerf++: Analyzing and improving neural radiance fields. arXiv:2010.07492. Retrieved from https:\/\/arxiv.org\/abs\/2010.07492","journal-title":"arXiv:2010.07492"},{"issue":"4","key":"e_1_3_3_92_1","article-title":"Building volumetric appearance models of fabric using micro CT imaging","volume":"30","author":"Zhao Shuang","year":"2011","unstructured":"Shuang Zhao, Wenzel Jakob, Steve Marschner, and Kavita Bala. 2011. Building volumetric appearance models of fabric using micro CT imaging. ACM Trans. Graph. 30, 4, Article No.: 44 (2011), 1\u201310.","journal-title":"ACM Trans. Graph."},{"issue":"6","key":"e_1_3_3_93_1","article-title":"Downsampling scattering parameters for rendering anisotropic media","volume":"35","author":"Zhao Shaung","year":"2016","unstructured":"Shaung Zhao, Lifan Wu, Fr\u00e9do Durand, and Ravi Ramamoorthi. 2016. Downsampling scattering parameters for rendering anisotropic media. ACM Trans. Graph. 35, 6, Article No.: 166 (2016), 1\u201311.","journal-title":"ACM Trans. Graph."},{"issue":"4","key":"e_1_3_3_94_1","article-title":"Neural complex luminaires: Representation and rendering","volume":"40","author":"Zhu Junqiu","year":"2021","unstructured":"Junqiu Zhu, Yaoyi Bai, Zilin Xu, Steve Bako, Edgar Vel\u00e1zquez-Armend\u00e1riz, Lu Wang, Pradeep Sen, Milo\u0161 Ha\u0161an, and Ling-Qi Yan. 2021. Neural complex luminaires: Representation and rendering. ACM Trans. Graph. 40, 4, Article No.: 57 (2021), 1\u201312.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_3_95_1","volume-title":"Proceedings of Visualization","author":"Zwicker M.","year":"2001","unstructured":"M. Zwicker, H. Pfister, J. van Baar, and M. Gross. 2001. EWA volume splatting. In Proceedings of Visualization."}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3711853","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3711853","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T01:19:15Z","timestamp":1750295955000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3711853"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,3]]},"references-count":94,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,2,28]]}},"alternative-id":["10.1145\/3711853"],"URL":"https:\/\/doi.org\/10.1145\/3711853","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,3]]},"assertion":[{"value":"2024-07-17","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-12-02","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-02-03","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}