Spherical Voronoi: Directional Appearance as a Differentiable Partition of the Sphere

Abstract

Radiance field methods (e.g. 3D Gaussian Splatting) have emerged as a powerful paradigm for novel view synthesis, yet their appearance modeling often relies on Spherical Harmonics (SH), which impose fundamental limitations. SH struggle with high-frequency signals, exhibit Gibbs ringing artifacts, and fail to capture specular reflections - a key component of realistic rendering. Although alternatives like spherical Gaussians offer improvements, they add significant optimization complexity. We propose Spherical Voronoi (SV) as a unified framework for appearance representation in 3D Gaussian Splatting. SV partitions the directional domain into learnable regions with smooth boundaries, providing an intuitive and stable parameterization for view-dependent effects. For diffuse appearance, SV achieves competitive results while keeping optimization simpler than existing alternatives. For reflections - where SH fail - we leverage SV as learnable reflection probes, taking reflected directions as input following principles from classical graphics. This formulation attains state-of-the-art results on synthetic and real-world datasets, demonstrating that SV offers a principled, efficient, and general solution for appearance modeling in explicit 3D representations.