Progressive Expectation-Maximization for Hierarchical Volumetric Photon Mapping

State‐of‐the‐art density estimation methods for rendering participating media rely on a dense photon representation of the radiance distribution within a scene. A critical bottleneck of such kernel‐based approaches is the excessive number of photons that are required in practice to resolve fine illu...

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Veröffentlicht in:Computer graphics forum Jg. 30; H. 4; S. 1287 - 1297
Hauptverfasser: Jakob, Wenzel, Regg, Christian, Jarosz, Wojciech
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford, UK Blackwell Publishing Ltd 01.06.2011
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ISSN:0167-7055, 1467-8659
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Abstract State‐of‐the‐art density estimation methods for rendering participating media rely on a dense photon representation of the radiance distribution within a scene. A critical bottleneck of such kernel‐based approaches is the excessive number of photons that are required in practice to resolve fine illumination details, while controlling the amount of noise. In this paper, we propose a parametric density estimation technique that represents radiance using a hierarchical Gaussian mixture. We efficiently obtain the coefficients of this mixture using a progressive and accelerated form of the Expectation‐Maximization algorithm. After this step, we are able to create noise‐free renderings of high‐frequency illumination using only a few thousand Gaussian terms, where millions of photons are traditionally required. Temporal coherence is trivially supported within this framework, and the compact footprint is also useful in the context of real‐time visualization. We demonstrate a hierarchical ray tracing‐based implementation, as well as a fast splatting approach that can interactively render animated volume caustics.
AbstractList State‐of‐the‐art density estimation methods for rendering participating media rely on a dense photon representation of the radiance distribution within a scene. A critical bottleneck of such kernel‐based approaches is the excessive number of photons that are required in practice to resolve fine illumination details, while controlling the amount of noise. In this paper, we propose a parametric density estimation technique that represents radiance using a hierarchical Gaussian mixture. We efficiently obtain the coefficients of this mixture using a progressive and accelerated form of the Expectation‐Maximization algorithm. After this step, we are able to create noise‐free renderings of high‐frequency illumination using only a few thousand Gaussian terms, where millions of photons are traditionally required. Temporal coherence is trivially supported within this framework, and the compact footprint is also useful in the context of real‐time visualization. We demonstrate a hierarchical ray tracing‐based implementation, as well as a fast splatting approach that can interactively render animated volume caustics.
Abstract State-of-the-art density estimation methods for rendering participating media rely on a dense photon representation of the radiance distribution within a scene. A critical bottleneck of such kernel-based approaches is the excessive number of photons that are required in practice to resolve fine illumination details, while controlling the amount of noise. In this paper, we propose a parametric density estimation technique that represents radiance using a hierarchical Gaussian mixture. We efficiently obtain the coefficients of this mixture using a progressive and accelerated form of the Expectation-Maximization algorithm. After this step, we are able to create noise-free renderings of high-frequency illumination using only a few thousand Gaussian terms, where millions of photons are traditionally required. Temporal coherence is trivially supported within this framework, and the compact footprint is also useful in the context of real-time visualization. We demonstrate a hierarchical ray tracing-based implementation, as well as a fast splatting approach that can interactively render animated volume caustics. [PUBLICATION ABSTRACT]
Author Jakob, Wenzel
Regg, Christian
Jarosz, Wojciech
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  fullname: Regg, Christian
  organization: Disney Research Zürich
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  givenname: Wojciech
  surname: Jarosz
  fullname: Jarosz, Wojciech
  organization: Disney Research Zürich
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References_xml – reference: Hasan B. A. S., Gan J.: Sequential EM for unsupervised adaptive Gaussian mixture model based classifier. In Machine Learning and Data Mining in Pattern Recognition, vol. 5632. 2009, pp. 96-106. 2.
– reference: Jarosz W., Zwicker M., Jensen H. W.: The beam radiance estimate for volumetric photon mapping. Computer Graphics Forum 27, 2 (Apr. 2008). 1, 3.
– reference: Hachisuka T., Ogaki S., Jensen H. W.: Progressive photon mapping. ACM Transactions on Graphics 27, 5 (Dec. 2008), 130:1-130:8. 2, 10.
– reference: Hanrahan P., Salzman D., Aupperle L.: A rapid hierarchical radiosity algorithm. In Computer Graphics (Proceedings of SIGGRAPH 91) (July 1991), pp. 197-206. 2.
– reference: Hachisuka T., Jarosz W., Jensen H. W.: A progressive error estimation framework for photon density estimation. ACM Transactions on Graphics. 29 (December 2010). 10.
– reference: Dutré P., Bala K., Bekaert P.: Advanced global illumination. AK Peters Ltd, 2006. 2.
– reference: Spencer B., Jones M. W.: Hierarchical photon mapping. IEEE Transactions on Visualization and Computer Graphics 15, 1 (Jan.Feb. 2009), 49-61. 2.
– reference: Zhou K., Ren Z., Lin S., Bao H., Guo B., Shum H.-Y.: Real-time smoke rendering using compensated ray marching. ACM Transactions on Graphics. 27, 3 (2008). 2, 6.
– reference: Papas M., Jarosz W., Jakob W., Rusinkiewicz S., Matusik W., Weyrich T.: Goal-based caustics. Computer Graphics Forum (Proceedings of Eurographics '11) 30, 2 (June 2011). 2.
– reference: Walter B., Fernandez S., Arbree A., Bala K., Donikian M., Greenberg D. P.: Lightcuts: a scalable approach to illumination. ACM Transactions on Graphics. 24, 3 (Aug. 2005). 2.
– reference: Cerezo E., Pérez F., Pueyo X., Seron F. J., Sillion F. X.: A survey on participating media rendering techniques. The Visual Computer 21, 5 (2005). 1.
– reference: Sillion F. X.: A unified hierarchical algorithm for global illumination with scattering volumes and object clusters. IEEE Transactions on Visualization and Computer Graphics 1, 3 (1995). 2.
– reference: Walter B., Arbree A., Bala K., Greenberg D. P.: Multidimensional lightcuts. ACM Transactions on Graphics. 25, 3 (2006). 1, 2.
– reference: Zwicker M., Pfister H., Van Baar J., Gross M.: EWA splatting. IEEE Transactions on Visualization and Computer Graphics 8, 3 (JulySept. 2002), 223-238. 2.
– reference: Schjøth L., Sporring J., Olsen O. F.: Diffusion based photon mapping. Computer Graphics Forum 27, 8 (Dec. 2008), 2114-2127. 2.
– reference: Goldberger J., Roweis S.: Hierarchical clustering of a mixture model. Advances in Neural Information Processing Systems 17, 505-512 (2005), 2-4. 2, 7.
– reference: Spencer B., Jones M. W.: Into the blue: Better caustics through photon relaxation. Computer Graphics Forum 28, 2 (Apr. 2009), 319-328. 2.
– reference: Tan P., Lin S., Quan L., Guo B., Shum H.-Y.: Multiresolution reflectance filtering. In Proceedings Eurographics Symposium on Rendering 2005 (2005), pp. 111-116. 2, 9.
– reference: Dempster A., Laird N., Rubin D., et al.: Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society. 39, 1 (1977), 1-38. 2.
– reference: Neal R., Hinton G.: A view of the EM algorithm that justifies incremental, sparse, and other variants. Learning in graphical models 89 (1998), 355-368. 2, 4.
– reference: Lehtinen J., Zwicker M., Turquin E., Kontkanen J., Durand F., Sillion F. X., Aila T.: A meshless hierarchical representation for light transport. ACM Transactions on Graphics 27, 3 (Aug. 2008), 37:1-37:9. 2.
– reference: Hopf M., Luttenberger M., Ertl T.: Hierarchical splatting of scattered 4d data. IEEE Computer Graphics and Applications 24 (July 2004), 64-72. 2.
– reference: Han C., Sun B., Ramamoorthi R., Grinspun E.: Frequency domain normal map filtering. ACM Transactions on Graphics. 26, 3 (2007). 2, 9.
– reference: Jarosz W., Nowrouzezahrai D., Sadeghi I., Jensen H. W.: A comprehensive theory of volumetric radiance estimation using photon points and beams. ACM Transactions on Graphics 30, 1 (Jan. 2011), 5:1-5:19. 3, 9.
– reference: Verbeek J. J., Nunnink J. R., Vlassis N.: Accelerated EM-based clustering of large data sets. Data Mining and Knowledge Discovery 13, 3 (November 2006), 291-307. 2, 4.
– reference: Chandrasekhar S.: Radiative Transfer. Dover Publications, New York , 1960. 2.
– volume: 29
  year: December 2010
  article-title: A progressive error estimation framework for photon density estimation
  publication-title: ACM Transactions on Graphics.
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– volume: 5632
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  year: 2009
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  article-title: Sequential EM for unsupervised adaptive Gaussian mixture model based classifier
  publication-title: Machine Learning and Data Mining in Pattern Recognition
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  year: July 1991
  end-page: 206
  article-title: A rapid hierarchical radiosity algorithm
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Snippet State‐of‐the‐art density estimation methods for rendering participating media rely on a dense photon representation of the radiance distribution within a...
Abstract State-of-the-art density estimation methods for rendering participating media rely on a dense photon representation of the radiance distribution...
State-of-the-art density estimation methods for rendering participating media rely on a dense photon representation of the radiance distribution within a...
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StartPage 1287
SubjectTerms Algorithms
Atoms & subatomic particles
Caustics
Computer graphics
Density
Gaussian
I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism-Ray Tracing
I.6.8 [Simulation and Modeling]: Simulation-Monte Carlo
Illumination
Mapping
Photons
Radiance
Rendering
Studies
Title Progressive Expectation-Maximization for Hierarchical Volumetric Photon Mapping
URI https://api.istex.fr/ark:/67375/WNG-HHK6P52S-W/fulltext.pdf
https://onlinelibrary.wiley.com/doi/abs/10.1111%2Fj.1467-8659.2011.01988.x
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https://www.proquest.com/docview/914624204
Volume 30
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