# MIND: Material Interface Generation from UDFs for Non-Manifold Surface Reconstruction

arXiv: https://arxiv.org/abs/2506.02938 · HTML: https://mlsanity.com/paper/2506.02938/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 65 references that are in the map.
- First posted on arXiv 3 Jun 2025.

## Builds on (most cited first, 30 of 35)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [CLAY: A Controllable Large-scale Generative Model for Creating High-quality 3D Assets](https://mlsanity.com/paper/2406.13897/) (2024)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Geo-Neus: Geometry-Consistent Neural Implicit Surfaces Learning for Multi-view Reconstruction](https://mlsanity.com/paper/2205.15848/) (2022)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [HF-NeuS: Improved Surface Reconstruction Using High-Frequency Details](https://mlsanity.com/paper/2206.07850/) (2022)
- [Deep Fashion3D: A Dataset and Benchmark for 3D Garment Reconstruction from Single Images](https://mlsanity.com/paper/2003.12753/) (2020)
- [POCO: Point Convolution for Surface Reconstruction](https://mlsanity.com/paper/2201.01831/) (2022)
- [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)
- [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)
- [Towards Better Gradient Consistency for Neural Signed Distance Functions via Level Set Alignment](https://mlsanity.com/paper/2305.11601/) (2023)
- [Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection](https://mlsanity.com/paper/2308.11441/) (2023)
- [NeAT: Learning Neural Implicit Surfaces with Arbitrary Topologies from Multi-view Images](https://mlsanity.com/paper/2303.12012/) (2023)
- [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)
- [Ghost on the Shell: An Expressive Representation of General 3D Shapes](https://mlsanity.com/paper/2310.15168/) (2023)
- [UDiFF: Generating Conditional Unsigned Distance Fields with Optimal Wavelet Diffusion](https://mlsanity.com/paper/2404.06851/) (2024)
- [Robust Zero Level-Set Extraction from Unsigned Distance Fields Based on Double Covering](https://mlsanity.com/paper/2310.03431/) (2023)
- [Surface Extraction from Neural Unsigned Distance Fields](https://mlsanity.com/paper/2309.08878/) (2023)
- [VRP-UDF: Towards Unbiased Learning of Unsigned Distance Functions from Multi-view Images with Volume Rendering Priors](https://mlsanity.com/paper/2407.16396/) (2024)
- [Unsupervised Occupancy Learning from Sparse Point Cloud](https://mlsanity.com/paper/2404.02759/) (2024)
- [Deep Medial Fields](https://mlsanity.com/paper/2106.03804/) (2021)
- [Reach For the Spheres: Tangency-Aware Surface Reconstruction of SDFs](https://mlsanity.com/paper/2308.09813/) (2023)
- [DUDF: Differentiable Unsigned Distance Fields with Hyperbolic Scaling](https://mlsanity.com/paper/2402.08876/) (2024)
- [2S-UDF: A Novel Two-stage UDF Learning Method for Robust Non-watertight Model Reconstruction from Multi-view Images](https://mlsanity.com/paper/2303.15368/) (2023)

## Abstract (arXiv)

Unsigned distance fields (UDFs) are widely used in 3D deep learning due to their ability to represent shapes with arbitrary topology. While prior work has largely focused on learning UDFs from point clouds or multi-view images, extracting meshes from UDFs remains challenging, as the learned fields rarely attain exact zero distances. A common workaround is to reconstruct signed distance fields (SDFs) locally from UDFs to enable surface extraction via Marching Cubes. However, this often introduces topological artifacts such as holes or spurious components. Moreover, local SDFs are inherently incapable of representing non-manifold geometry, leading to complete failure in such cases. To address this gap, we propose MIND (Material Interface from Non-manifold Distance fields), a novel algorithm for generating material interfaces directly from UDFs, enabling non-manifold mesh extraction from a global perspective. The core of our method lies in deriving a meaningful spatial partitioning from the UDF, where the target surface emerges as the interface between distinct regions. We begin by computing a two-signed local field to distinguish the two sides of manifold patches, and then extend this to a multi-labeled global field capable of separating all sides of a non-manifold structure. By combining this multi-labeled field with the input UDF, we construct material interfaces that support non-manifold mesh extraction via a multi-labeled Marching Cubes algorithm. Extensive experiments on UDFs generated from diverse data sources, including point cloud reconstruction, multi-view reconstruction, and medial axis transforms, demonstrate that our approach robustly handles complex non-manifold surfaces and significantly outperforms existing methods. The source code is available at https://github.com/jjjkkyz/MIND.