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

arXiv: https://arxiv.org/abs/2310.03431 · HTML: https://mlsanity.com/paper/2310.03431/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 63 references that are in the map.
- First posted on arXiv 5 Oct 2023.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [SMPLicit: Topology-aware Generative Model for Clothed People](https://mlsanity.com/paper/2103.06871/) (2021)
- [Deep Fashion3D: A Dataset and Benchmark for 3D Garment Reconstruction from Single Images](https://mlsanity.com/paper/2003.12753/) (2020)
- [MeshUDF: Fast and Differentiable Meshing of Unsigned Distance Field Networks](https://mlsanity.com/paper/2111.14549/) (2021)
- [Neural Dual Contouring](https://mlsanity.com/paper/2202.01999/) (2022)
- [A Large Dataset of Object Scans](https://mlsanity.com/paper/1602.02481/) (2016)
- [NeuralUDF: Learning Unsigned Distance Fields for Multi-view Reconstruction of Surfaces with Arbitrary Topologies](https://mlsanity.com/paper/2211.14173/) (2022)
- [Geometry-Consistent Neural Shape Representation with Implicit Displacement Fields](https://mlsanity.com/paper/2106.05187/) (2021)
- [A Survey of Non-Rigid 3D Registration](https://mlsanity.com/paper/2203.07858/) (2022)
- [Neural Marching Cubes](https://mlsanity.com/paper/2106.11272/) (2021)
- [CAP-UDF: Learning Unsigned Distance Functions Progressively from Raw Point Clouds with Consistency-Aware Field Optimization](https://mlsanity.com/paper/2210.02757/) (2022)
- [GIFS: Neural Implicit Function for General Shape Representation](https://mlsanity.com/paper/2204.07126/) (2022)
- [Deep Implicit Surface Point Prediction Networks](https://mlsanity.com/paper/2106.05779/) (2021)
- [Globally Consistent Normal Orientation for Point Clouds by Regularizing the Winding-Number Field](https://mlsanity.com/paper/2304.11605/) (2023)
- [Learning Anchored Unsigned Distance Functions with Gradient Direction Alignment for Single-view Garment Reconstruction](https://mlsanity.com/paper/2108.08478/) (2021)
- [NeAT: Learning Neural Implicit Surfaces with Arbitrary Topologies from Multi-view Images](https://mlsanity.com/paper/2303.12012/) (2023)
- [Orienting Point Clouds with Dipole Propagation](https://mlsanity.com/paper/2105.01604/) (2021)
- [Iterative Poisson Surface Reconstruction (iPSR) for Unoriented Points](https://mlsanity.com/paper/2209.09510/) (2022)
- [GeoUDF: Surface Reconstruction from 3D Point Clouds via Geometry-guided Distance Representation](https://mlsanity.com/paper/2211.16762/) (2022)
- [3PSDF: Three-Pole Signed Distance Function for Learning Surfaces with Arbitrary Topologies](https://mlsanity.com/paper/2205.15572/) (2022)
- [VectorAdam for Rotation Equivariant Geometry Optimization](https://mlsanity.com/paper/2205.13599/) (2022)

## Built on by (most cited first, 22 of 22)

- [UDiFF: Generating Conditional Unsigned Distance Fields with Optimal Wavelet Diffusion](https://mlsanity.com/paper/2404.06851/) (2024)
- [VRP-UDF: Towards Unbiased Learning of Unsigned Distance Functions from Multi-view Images with Volume Rendering Priors](https://mlsanity.com/paper/2407.16396/) (2024)
- [Details Enhancement in Unsigned Distance Field Learning for High-fidelity 3D Surface Reconstruction](https://mlsanity.com/paper/2406.00346/) (2024)
- [A Lightweight UDF Learning Framework for 3D Reconstruction Based on Local Shape Functions](https://mlsanity.com/paper/2407.01330/) (2024)
- [Monge-Ampere Regularization for Learning Arbitrary Shapes from Point Clouds](https://mlsanity.com/paper/2410.18477/) (2024)
- [Neural Surface Detection for Unsigned Distance Fields](https://mlsanity.com/paper/2407.18381/) (2024)
- [DCUDF2: Improving Efficiency and Accuracy in Extracting Zero Level Sets from Unsigned Distance Fields](https://mlsanity.com/paper/2408.17284/) (2024)
- [Occupancy-Based Dual Contouring](https://mlsanity.com/paper/2409.13418/) (2024)
- [Quasi-Medial Distance Field (Q-MDF): A Robust Method for Approximating and Discretizing Neural Medial Axes](https://mlsanity.com/paper/2410.17774/) (2024)
- [From Transparent to Opaque: Rethinking Neural Implicit Surfaces with α-NeuS](https://mlsanity.com/paper/2411.05362/) (2024)
- [3D-WAG: Hierarchical Wavelet-Guided Autoregressive Generation for High-Fidelity 3D Shapes](https://mlsanity.com/paper/2411.19037/) (2024)
- [High Resolution UDF Meshing via Iterative Networks](https://mlsanity.com/paper/2509.17212/) (2025)
- [Voronoi-Assisted Optimization for Diffusing Unsigned Distance Fields from Unoriented Points](https://mlsanity.com/paper/2510.12524/) (2025)
- [Accurate and Efficient Surface Reconstruction from Point Clouds via Geometry-Aware Local Adaptation](https://mlsanity.com/paper/2511.08233/) (2025)
- [AnySurf: Any Surface Generation with Directed Edge](https://mlsanity.com/paper/2605.26149/) (2026)
- [Neural Octahedral Field: Octahedral prior for simultaneous smoothing and sharp edge regularization](https://mlsanity.com/paper/2408.00303/) (2024)
- [Neural Shortest Path for Surface Reconstruction from Point Clouds](https://mlsanity.com/paper/2502.06047/) (2025)
- [MIND: Material Interface Generation from UDFs for Non-Manifold Surface Reconstruction](https://mlsanity.com/paper/2506.02938/) (2025)
- [Learned Radius Estimation for UDF-Based Point Cloud Reconstruction](https://mlsanity.com/paper/2606.18787/) (2026)
- [DiffGI: Differentiable Geometry Images for High-Fidelity Thin-Shell 3D Generation](https://mlsanity.com/paper/2607.13365/) (2026)
- [Projective Normal Fields: A Convex Optimization Method for Constructing Smooth UDFs](https://mlsanity.com/paper/2609.34784/) (2026)
- [Volume Rendering with Metric--Phase Fields for Thin Structures and Sign-Ambiguous Geometry](https://mlsanity.com/paper/2610.13088/) (2026)

## Abstract (arXiv)

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.