无需神经网络，用沃罗诺伊几何优化点云法向，高效生成3D形状的无符号距离场。
Voronoi-Assisted Optimization for Diffusing Unsigned Distance Fields from Unoriented Points
- 基于沃罗诺伊几何设计能量函数，自动对齐无方向点云的法向。
- 通过扩散法向生成梯度场并积分，恢复出稳定的无符号距离场。
- 适合处理开放、非流形和不可定向等复杂几何结构，计算高效稳定。
无符号距离场（UDFs）能灵活表示任意拓扑的3D形状，包括开闭曲面、可定向与不可定向几何以及非流形结构。尽管近期神经方法在学习UDFs方面展现出潜力，但常面临数值不稳定、计算成本高和控制性差的问题。本文提出一种轻量级、无需网络的直接方法——沃罗诺伊辅助扩散优化（VAD），从无方向点云中计算UDFs。该方法首先根据两个基于沃罗诺伊的几何准则，在能量函数指导下为输入点分配双向法向；随后将对齐后的法向扩散形成近似UDF梯度场，并通过积分恢复最终的UDF。实验表明，VAD能稳健处理封闭与开放表面，以及复杂的非流形和不可定向几何，同时保持计算高效与数值稳定。
原文摘要 · Abstract (English)
Unsigned Distance Fields (UDFs) provide a flexible representation for 3D shapes with arbitrary topology, including open and closed surfaces, orientable and non-orientable geometries, and non-manifold structures. While recent neural approaches have shown promise in learning UDFs, they often suffer from numerical instability, high computational cost, and limited controllability. We present a lightweight, network-free method, Voronoi-Assisted Optimization for Diffusing (VAD), to compute UDFs directly from unoriented point clouds. Our approach begins by assigning bi-directional normals to input points, guided by two Voronoi-based geometric criteria encoded in an energy function for optimal alignment. The aligned normals are then diffused to form an approximate UDF gradient field, which is subsequently integrated to recover the final UDF. Experiments demonstrate that VAD robustly handles watertight and open surfaces, as well as complex non-manifold and non-orientable geometries, while remaining computationally efficient and stable.
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