Robust Zero Level-Set Extraction from Unsigned Distance Fields Based on Double Covering

TL;DR

This paper introduces DoubleCoverUDF, a robust method for extracting zero level-sets from unsigned distance fields that ensures topological correctness and high-quality mesh reconstruction, applicable to various 3D models.

Contribution

The paper presents a novel algorithm that accurately extracts iso-surfaces from UDFs using a double covering approach and topology-preserving projection, improving mesh quality and robustness.

Findings

Produces higher quality meshes than existing methods.

Successfully reconstructs surfaces of open models.

Validated on synthetic and benchmark datasets.

Abstract

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.