高斯过程隐式曲面作为参与介质：基于水平穿越统计的无实现渲染
Gaussian Process Implicit Surfaces as Participating Media: Realization-Free Rendering from Level-Crossing Statistics
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中文总结 AI 辅助
本文提出一种光散射理论，从高斯过程隐式曲面的水平穿越统计中直接推导出各向异性辐射传输方程，实现无实现渲染，并支持多种表面与介质，同时可逆向提升体积资产为GPIS。
中文摘要 AI 辅助
我们提出了一种光散射理论，该理论在双向连接了高斯过程隐式曲面（GPISes）与参与介质。在局部条件近似下应用Kac-Rice水平穿越公式，直接从逐点GPIS统计中推导出完整的各向异性辐射传输方程（RTE）。一个共享的投影面积耦合了消光和散射，确保了GPIS与其体积表示之间的几何一致性。该框架涵盖了粗糙表面、多孔和非高度场几何体以及参与介质。从相同的统计结构中，我们推导出支持面内和面外各向异性的全球面Beckmann和GGX法线分布函数。这些函数族可证明地恢复SGGX、Beckmann和GGX作为特例，并允许精确的可见法线重要性采样。我们还推导了解析的掩蔽-阴影函数和用于镜面微表面的单次散射表面模型，并扩展到多次散射。在高度场极限下，我们证明了局部条件近似简化为Smith独立性假设。我们的无实现方法相比基于实现的方法提高了渲染效率，并且可以在标准体积渲染器中实现。在逆方向上，我们描述了与兼容RTE参数对应的GPIS函数族，并为异质密度场开发了实用的提升方法。因此，现有的体积资产可以作为GPIS进行渲染，而训练好的辐射场重建无需网格提取即可产生表面几何和着色法线，并提供基于密度的几何不确定性表示。
英文摘要
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.
发表机构
- Dartmouth College（达特茅斯学院）
- NVIDIA（英伟达）
机构由 AI 辅助整理，请以论文原文为准。
