In this paper, we propose a new method, called DoubleCoverUDF, for extracting the zero level-set from unsigned distance fields (UDFs). DoubleCoverUDF takes a learned UDF and a user-specified parameter $r$ (a small positive real number) as input and extracts an iso-surface with an iso-value $r$ using the conventional marching cubes algorithm. We show that the computed iso-surface is the boundary of the $r$-offset volume of the target zero level-set $S$, which is an orientable manifold, regardless of the topology of $S$. Next, the algorithm computes a covering map to project the boundary mesh onto $S$, preserving the mesh's topology and avoiding folding. If $S$ is an orientable manifold surface, our algorithm separates the double-layered mesh into a single layer using a robust minimum-cut post-processing step. Otherwise, it keeps the double-layered mesh as the output. We validate our algorithm by reconstructing 3D surfaces of open models and demonstrate its efficacy and effectiveness on synthetic models and benchmark datasets. Our experimental results confirm that our method is robust and produces meshes with better quality in terms of both visual evaluation and quantitative measures than existing UDF-based methods. The source code is available at https://github.com/jjjkkyz/DCUDF.

翻译：本文提出了一种新方法DoubleCoverUDF，用于从无符号距离场中提取零水平集。该方法以学习得到的UDF和用户指定参数$r$（小正实数）为输入，通过传统移动立方体算法提取等值为$r$的等值面。我们证明，计算得到的等值面是目标零水平集$S$的$r$偏移体边界，该边界为可定向流形，且与$S$的拓扑无关。随后，算法计算覆盖映射将边界网格投影至$S$，从而保持网格拓扑并避免折叠。若$S$为可定向流形曲面，算法通过鲁棒最小切割后处理步骤将双层网格分离为单层；否则保留双层网格作为输出。我们通过重建开放模型的三维曲面验证算法有效性，并在合成模型与基准数据集上展示了其优异性能。实验结果表明，与现有基于UDF的方法相比，本方法在视觉评估和定量指标上均能生成更高质量的网格。源代码见https://github.com/jjjkkyz/DCUDF。