Neural Centroidal Voronoi Tessellations

2026-09-08

AI Summary

该研究通过引入基于学习的神经CVT方法，加速了计算图形中表面CVT的优化过程，同时保持了几何精度。

Abstract

Centroidal Voronoi tessellation (CVT) is a fundamental primitive for high-quality surface sampling and isotropic remeshing in computer graphics. However, computing surface CVTs with classical solvers remains expensive: each optimization step repeatedly constructs restricted Voronoi diagrams (RVDs) and integrates quantities over their surface cells. We introduce Neural CVT, a learning-based surface-CVT solver that replaces these costly geometric computations with a recurrent neural optimizer, accelerating CVT optimization by one to two orders of magnitude in our benchmarks while preserving geometric fidelity. Given an input surface, we sample a dense point cloud and extract multi-scale geometric descriptors with a graph neural encoder. A lightweight recurrent optimizer then refines seed positions over a small number of iterations, aggregating interpolated surface features and optimization history to predict per-seed displacements. The framework is trained self-supervised using CVT objectives that promote uniform distributions and, when desired, feature alignment. Across diverse organic and CAD-like shapes, Neural CVT generalizes to unseen geometry, initialization strategies, and seed densities, producing isotropic, feature-preserving remeshes comparable to state-of-the-art offline optimization methods at a fraction of the computational cost. Code and trained models will be released.

Problem

• Centroidal Voronoi Tessellation
• surface sampling
• isotropic remeshing
• computational cost

Innovation

• Neural CVT
• recurrent neural optimizer
• surface-CVT solver
• multi-scale geometric descriptors
• self-supervised training