Render implicit surfaces as volumes for efficient light scattering
Gaussian Process Implicit Surfaces as Participating Media: Realization-Free Rendering from Level-Crossing Statistics
Graphics
Summary
Many computer graphics techniques struggle to show how light bounces on shapes that are defined by fuzzy or complex surfaces. The authors found a way to treat these shapes like cloudy or porous materials, making the way light behaves easier to predict and simulate. They connected mathematical models of surfaces (called Gaussian Process Implicit Surfaces) with how light moves through and bounces inside materials. This approach improves rendering speed and helps turn different kinds of 3D data, including uncertain shapes, into more realistic images without needing to build complicated surface models first.
What this means in practice
- •For visual effects artists: Render complex or uncertain 3D shapes more efficiently by treating them as volumes without explicit surface models.
- •For game engine developers: Integrate a volume rendering approach that supports anisotropic light scattering for improved material realism from implicit surface data.
Authors
Jack Cui, Kehan Xu, Eugene d'Eon, Wojciech Jarosz
Abstract
We present a theory of light scattering that connects Gaussian Process Implicit Surfaces (GPISes) and participating media in both directions. Applying the Kac--Rice level-crossing formula under a local-conditioning approximation yields a complete anisotropic radiative transfer equation (RTE) directly from pointwise GPIS statistics. A shared projected area couples extinction and scattering, ensuring geometric consistency between the GPIS and its volumetric representation. The framework spans rough surfaces, porous and non-height-field geometries, and participating media. From the same statistical structure, we derive full-sphere Beckmann and GGX normal distribution functions supporting in-plane and out-of-plane anisotropy. These families provably recover SGGX, Beckmann, and GGX as special cases and admit exact visible-normal importance sampling. We also derive analytic masking--shadowing functions and single-scattering surface models for specular microsurfaces, with extensions to multiple scattering. In the height-field limit, we prove that the local-conditioning approximation reduces to Smith's independence assumption. Our realization-free approach improves rendering efficiency over realization-based methods and can be implemented within a standard volume renderer. In the inverse direction, we characterize families of GPISes corresponding to compatible RTE parameters and develop practical lifts for heterogeneous density fields. Existing volumetric assets thereby become renderable as GPISes, while trained radiance-field reconstructions yield surface geometry and shading normals without mesh extraction and provide a density-based representation of geometric uncertainty.