# Surface Extraction from Neural Unsigned Distance Fields

arXiv: https://arxiv.org/abs/2309.08878 · HTML: https://mlsanity.com/paper/2309.08878/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2023.

## Built on by (most cited first, 17 of 17)

- [GaussianUDF: Inferring Unsigned Distance Functions through 3D Gaussian Splatting](https://mlsanity.com/paper/2503.19458/) (2025)
- [PoNQ: a Neural QEM-based Mesh Representation](https://mlsanity.com/paper/2403.12870/) (2024)
- [Coverage Axis++: Efficient Inner Point Selection for 3D Shape Skeletonization](https://mlsanity.com/paper/2401.12946/) (2024)
- [Deep3DSketch+: Rapid 3D Modeling from Single Free-hand Sketches](https://mlsanity.com/paper/2309.13006/) (2023)
- [Design2Cloth: 3D Cloth Generation from 2D Masks](https://mlsanity.com/paper/2404.02686/) (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)
- [OffsetOPT: Explicit Surface Reconstruction without Normals](https://mlsanity.com/paper/2503.15763/) (2025)
- [High Resolution UDF Meshing via Iterative Networks](https://mlsanity.com/paper/2509.17212/) (2025)
- [UltraBoneUDF: Self-supervised Bone Surface Reconstruction from Ultrasound Based on Neural Unsigned Distance Functions](https://mlsanity.com/paper/2505.17912/) (2025)
- [Voronoi-Assisted Optimization for Diffusing Unsigned Distance Fields from Unoriented Points](https://mlsanity.com/paper/2510.12524/) (2025)
- [S2MDF: A Plug-And-Play Layer for Intersection-Free Multi-Object Signed Distance Fields](https://mlsanity.com/paper/2605.29761/) (2026)
- [Gradient Distance Function](https://mlsanity.com/paper/2410.22422/) (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)
- [Neural parametric representations for thin-shell shape optimisation](https://mlsanity.com/paper/2604.06612/) (2026)

## Abstract (arXiv)

We propose a method, named DualMesh-UDF, to extract a surface from unsigned distance functions (UDFs), encoded by neural networks, or neural UDFs. Neural UDFs are becoming increasingly popular for surface representation because of their versatility in presenting surfaces with arbitrary topologies, as opposed to the signed distance function that is limited to representing a closed surface. However, the applications of neural UDFs are hindered by the notorious difficulty in extracting the target surfaces they represent. Recent methods for surface extraction from a neural UDF suffer from significant geometric errors or topological artifacts due to two main difficulties: (1) A UDF does not exhibit sign changes; and (2) A neural UDF typically has substantial approximation errors. DualMesh-UDF addresses these two difficulties. Specifically, given a neural UDF encoding a target surface barS to be recovered, we first estimate the tangent planes of barS at a set of sample points close to barS. Next, we organize these sample points into local clusters, and for each local cluster, solve a linear least squares problem to determine a final surface point. These surface points are then connected to create the output mesh surface, which approximates the target surface. The robust estimation of the tangent planes of the target surface and the subsequent minimization problem constitute our core strategy, which contributes to the favorable performance of DualMesh-UDF over other competing methods. To efficiently implement this strategy, we employ an adaptive Octree. Within this framework, we estimate the location of a surface point in each of the octree cells identified as containing part of the target surface. Extensive experiments show that our method outperforms existing methods in terms of surface reconstruction quality while maintaining comparable computational efficiency.