基于双重覆盖的无符号距离场鲁棒零等值面提取
Robust Zero Level-Set Extraction from Unsigned Distance Fields Based on Double Covering
AI总结：
提出DoubleCoverUDF方法，通过双重覆盖策略和最小割后处理，从无符号距离场中鲁棒提取零等值面，有效避免折叠并提升网格质量。
摘要：
在本文中，我们提出了一种名为DoubleCoverUDF的新方法，用于从无符号距离场（UDFs）中提取零等值面。DoubleCoverUDF以学习到的UDF和用户指定的参数$r$（一个小的正实数）作为输入，并使用传统的marching cubes算法提取等值为$r$的等值面。我们证明，计算出的等值面是目标零等值面$S$的$r$-偏移体积的边界，无论$S$的拓扑结构如何，它都是一个可定向流形。接下来，该算法计算一个覆盖映射，将边界网格投影到$S$上，同时保持网格的拓扑结构并避免折叠。如果$S$是一个可定向流形表面，我们的算法使用鲁棒的最小割后处理步骤将双层网格分离为单层。否则，它将保留双层网格作为输出。我们通过重建开放模型的3D表面验证了我们的算法，并在合成模型和基准数据集上展示了其有效性和实用性。我们的实验结果证实，与现有的基于UDF的方法相比，我们的方法具有鲁棒性，并且在视觉评估和定量测量方面都能生成质量更好的网格。源代码可在https://github.com/jjjkkyz/DCUDF获取。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
