From microfacets to participating media: A unified theory of light transport with stochastic geometry

1Dartmouth College 2NVIDIA

In ACM Transactions on Graphics (Proceedings of SIGGRAPH), 2024
SIGGRAPH 2024 Best Paper Award!

We develop a theory of light transport for scenes with stochastic implicit surfaces [Dragiev et al. 2011; Sellán and Jacobson 2022; Williams and Fitzgibbon 2006] and show that this results in an expressive range of appearance behaviors that covers microfacet surfaces, classical participating media, and a novel continuum in between. Each object shown above is completely described by a 3D volume that encodes the mean and covariance kernel of a non-stationary Gaussian process and is rendered using the same rendering algorithm, agnostic of its “appearance type”. The insets show example realizations of the process at the highlighted points in the scene. Note how the appearance of the stochastic geometry transitions from volumetric (left) to hard-surface (right) as the correlations in the process are strengthened. Increasing the variance of the process allows us to visualize uncertainty at the macro-scale (bottom).


Stochastic geometry models have enjoyed immense success in graphics for modeling interactions of light with complex phenomena such as participating media, rough surfaces, fibers, and more. Although each of these models operates on the same principle of replacing intricate geometry by a random process and deriving the average light transport across all instances thereof, they are each tailored to one specific application and are fundamentally distinct. Each type of stochastic geometry present in the scene is firmly encapsulated in its own appearance model, with its own statistics and light transport average, and no cross-talk between different models or deterministic and stochastic geometry is possible. In this paper, we derive a theory of light transport on stochastic implicit surfaces, a geometry model capable of expressing deterministic geometry, microfacet surfaces, participating media, and an exciting new continuum in between containing aggregate appearance, non-classical media, and more. Our model naturally supports spatial correlations, missing from most existing stochastic models. Our theory paves the way for tractable rendering of scenes in which all geometry is described by the same stochastic model, while leaving ample future work for developing efficient sampling and rendering algorithms.



We would like to thank Alex Evans for his valuable contributions in the early stages of this project and Silvia Sellán for helpful discussions on stochastic geometry representations. We thank Aaron LeFohn for supporting this research, and Luca Fascione, Andrea Weidlich and Tizian Zeltner for helpful comments. Additionally, this work was generously supported by NVIDIA, a Dartmouth Senior Faculty grant, and a Neukom CompX grant. Dario Seyb and Wojciech Jarosz were partially funded by NSF award 1844538. We have used assets in the public domain / licensed under CC0 in many figures of this paper and thank the original creators for providing them. The volume data for the explosion in Fig. 1 is courtesy of JangaFX, and the two statues next to it are from The “shader ball” in Figs. 7 and 9 is based on code in the SDF dataset published by Takikawa et al. [2022]. The environment map used in Fig. 11 is part of the Tungsten example assets. The dragon figurine in Fig. 19 is part of the OpenVDB example assets. The bunny model used in Fig. 22 is based on a model in the Stanford 3D Scanning Repository. Finally, the tree in Fig. 24 is from ChatGPT was utilized to iterate on early versions of the abstract and introduction—all final text was written by the authors.


Dario Seyb, Eugene d'Eon, Benedikt Bitterli, Wojciech Jarosz. From microfacets to participating media: A unified theory of light transport with stochastic geometry. ACM Transactions on Graphics (Proceedings of SIGGRAPH), 43(4), July 2024.
    author   = {Seyb, Dario and d'Eon, Eugene and Bitterli, Benedikt and Jarosz, Wojciech},
    title    = {From microfacets to participating media: {{A}} unified theory of light transport with stochastic
    journal  = {ACM Transactions on Graphics (Proceedings of SIGGRAPH)},
    year     = {2024},
    month    = jul,
    doi      = {10.1145/3658121},
    volume   = {43},
    number   = {4},
    keywords = {volumetric light transport, stochastic processes, implicit surfaces}
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