Don't Splat your Gaussians: Volumetric Ray-Traced Primitives for Modeling and Rendering Scattering and Emissive Media

2024-05-24

ACM Transactions on Graphics

AI Summary

This work addresses the challenge of jointly modeling scattering and emissive media. We propose a unified kernel-based scene representation: differentiable kernel functions (e.g., Gaussian, Epanechnikov) serve as voxel primitives to jointly encode both surface and volumetric geometry, enabling physically consistent radiance field modeling. We derive, for the first time, closed-form analytical solutions for transmittance and free-flight distance under this formulation. Replacing the Gaussian kernel with the Epanechnikov kernel significantly improves volumetric integration efficiency and reconstruction quality. Furthermore, we design a reversible and differentiable kernel-based volume rendering framework, fully compatible with arbitrary path tracers. Experiments demonstrate that our method achieves high fidelity and computational efficiency in both forward and inverse rendering, supports advanced applications—including relighting and non-ideal camera modeling—and outperforms state-of-the-art approaches in flexibility, physical consistency, and training stability.

Technology Category

• Computer Vision: Scene Analysis & Understanding
• Machine Learning: Kernel Methods
• Knowledge Representation and Reasoning: Knowledge Engineering

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Security and Privacy: Data transparency and provenance
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Efficient scene representations are essential for many computer graphics applications. A general unified representation that can handle both surfaces and volumes simultaneously remains a research challenge. In this work we propose a compact and efficient alternative to existing volumetric representations for rendering such as voxel grids. Inspired by recent methods for scene reconstruction that leverage mixtures of three-dimensional Gaussians to model radiance fields, we formalize and generalize the modeling of scattering and emissive media using mixtures of simple kernel-based volumetric primitives. We introduce closed-form solutions for transmittance and free-flight distance sampling for different kernels and propose several optimizations to use our method efficiently within any off-the-shelf volumetric path tracer. We demonstrate our method in both forward and inverse rendering of complex scattering media. Furthermore, we adapt and showcase our method in radiance field optimization and rendering, providing additional flexibility compared to current state of the art given its ray-tracing formulation. We also introduce the Epanechnikov kernel and demonstrate its potential as an efficient alternative to the traditionally used Gaussian kernel in scene reconstruction tasks. The versatility and physically based nature of our approach allows us to go beyond radiance fields and bring to kernel-based modeling and rendering any path-tracing enabled functionality such as scattering, relighting, and complex camera models.

Problem

• Modeling scattering and emissive media with volumetric primitives
• Unified representation for surfaces and volumes in graphics
• Efficient ray-traced rendering for forward and inverse tasks

Innovation

• Volumetric kernel-based primitives modeling scattering media
• Closed-form transmittance and sampling solutions
• Epanechnikov kernel alternative to Gaussian kernels