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。DoubleCoverUDF以学习得到的UDF和用户指定的参数$r$（一个小的正实数）为输入，采用传统行进立方体算法提取等值为$r$的等值面。我们证明，该等值面为目标零水平集$S$的$r$-偏移体积的边界，无论$S$的拓扑结构如何，该边界均为可定向流形。随后，算法计算覆盖映射，将边界网格投影到$S$上，同时保持网格拓扑并避免折叠。若$S$为可定向流形曲面，算法通过鲁棒的最小割后处理步骤将双层网格分离为单层网格；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了算法有效性，并在合成模型和基准数据集上展示了其效能。实验结果证实，该方法具有鲁棒性，且相较于现有基于UDF的方法，能在视觉评估和量化指标两方面生成更高质量的网格。源代码已开源至https://github.com/jjjkkyz/DCUDF。