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

2025-12-16

AI Summary

Existing radiance field methods (e.g., 3D Gaussian Splatting) rely on spherical harmonics (SH) for appearance modeling, which struggle to represent high-frequency details, suffer from Gibbs ringing artifacts, and lack explicit specular reflection modeling. This paper introduces differentiable spherical Voronoi partitioning—the first integration of spherical Voronoi diagrams into differentiable appearance modeling. Given the reflection direction as input, our method adaptively partitions the directional domain to construct learnable reflection probes that jointly model diffuse and specular components. It enables differentiable spherical geometric partitioning, direction-adaptive region division, and reflection-vector-driven probe querying, and is jointly optimized end-to-end with 3D Gaussian Splatting. Evaluated on both synthetic and real-world datasets, our approach achieves state-of-the-art performance, significantly improving specular detail reconstruction, enhancing optimization stability, and eliminating the need for strong regularization.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Learning with Manifolds
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Improves appearance modeling in radiance fields
• Overcomes Spherical Harmonics' limitations for reflections
• Simplifies optimization for view-dependent effects

Innovation

• Spherical Voronoi partitions sphere into learnable directional regions
• SV serves as learnable reflection probes for specular effects
• Provides efficient alternative to Spherical Harmonics in Gaussian Splatting