Progressive Expectation-Maximization for Hierarchical Rendering of Participating Media

Project Members

Wenzel Jakob (Disney Research Zurich)
Christian Regg (Disney Research Zurich/ETH Zurich)
Wojciech Jarosz (Disney Research Zurich)


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 given by the excessive number of photons that are in practice required to resolve fine illumination details, while controlling the amount of noise. In this project, 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


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Progressive Expectation-Maximization for Hierarchical Rendering of Participating Media
June 27, 2011
Eurographics Symposium on Rendering (EGSR) 2011
Paper File [pdf, 6.72 MB]

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