# NeuralUDF: Learning Unsigned Distance Fields for Multi-view Reconstruction of Surfaces with Arbitrary Topologies

arXiv: https://arxiv.org/abs/2211.14173 · HTML: https://mlsanity.com/paper/2211.14173/

## Key facts

- Cited by 63 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 58 references that are in the map.
- First posted on arXiv 25 Nov 2022.

## Builds on (most cited first, 30 of 36)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [MVSNet: Depth Inference for Unstructured Multi-view Stereo](https://mlsanity.com/paper/1804.02505/) (2018)
- [GIRAFFE: Representing Scenes as Compositional Generative Neural Feature Fields](https://mlsanity.com/paper/2011.12100/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [BARF: Bundle-Adjusting Neural Radiance Fields](https://mlsanity.com/paper/2104.06405/) (2021)
- [Cascade Cost Volume for High-Resolution Multi-View Stereo and Stereo Matching](https://mlsanity.com/paper/1912.06378/) (2019)
- [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)
- [Recurrent MVSNet for High-resolution Multi-view Stereo Depth Inference](https://mlsanity.com/paper/1902.10556/) (2019)
- [NeuralRecon: Real-Time Coherent 3D Reconstruction from Monocular Video](https://mlsanity.com/paper/2104.00681/) (2021)
- [Learning a Multi-View Stereo Machine](https://mlsanity.com/paper/1708.05375/) (2017)
- [DIST: Rendering Deep Implicit Signed Distance Function with Differentiable Sphere Tracing](https://mlsanity.com/paper/1911.13225/) (2019)
- [SparseNeuS: Fast Generalizable Neural Surface Reconstruction from Sparse Views](https://mlsanity.com/paper/2206.05737/) (2022)
- [SDFDiff: Differentiable Rendering of Signed Distance Fields for 3D Shape Optimization](https://mlsanity.com/paper/1912.07109/) (2019)
- [Improving neural implicit surfaces geometry with patch warping](https://mlsanity.com/paper/2112.09648/) (2021)
- [SurfaceNet: An End-to-end 3D Neural Network for Multiview Stereopsis](https://mlsanity.com/paper/1708.01749/) (2017)
- [Neural Lumigraph Rendering](https://mlsanity.com/paper/2103.11571/) (2021)
- [Deep Fashion3D: A Dataset and Benchmark for 3D Garment Reconstruction from Single Images](https://mlsanity.com/paper/2003.12753/) (2020)
- [Learning Signed Distance Field for Multi-view Surface Reconstruction](https://mlsanity.com/paper/2108.09964/) (2021)

## Built on by (most cited first, 30 of 63)

- [Delicate Textured Mesh Recovery from NeRF via Adaptive Surface Refinement](https://mlsanity.com/paper/2303.02091/) (2023)
- [SparseFlex: High-Resolution and Arbitrary-Topology 3D Shape Modeling](https://mlsanity.com/paper/2503.21732/) (2025)
- [Neural Signed Distance Function Inference through Splatting 3D Gaussians Pulled on Zero-Level Set](https://mlsanity.com/paper/2410.14189/) (2024)
- [DeferredGS: Decoupled and Editable Gaussian Splatting with Deferred Shading](https://mlsanity.com/paper/2404.09412/) (2024)
- [Towards Better Gradient Consistency for Neural Signed Distance Functions via Level Set Alignment](https://mlsanity.com/paper/2305.11601/) (2023)
- [Single-view 3D Scene Reconstruction with High-fidelity Shape and Texture](https://mlsanity.com/paper/2311.00457/) (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)
- [Unsupervised Inference of Signed Distance Functions from Single Sparse Point Clouds without Learning Priors](https://mlsanity.com/paper/2303.14505/) (2023)
- [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)
- [VRP-UDF: Towards Unbiased Learning of Unsigned Distance Functions from Multi-view Images with Volume Rendering Priors](https://mlsanity.com/paper/2407.16396/) (2024)
- [Inverse Rendering of Glossy Objects via the Neural Plenoptic Function and Radiance Fields](https://mlsanity.com/paper/2403.16224/) (2024)
- [Fast Learning of Signed Distance Functions from Noisy Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2407.14225/) (2024)
- [GaussianUDF: Inferring Unsigned Distance Functions through 3D Gaussian Splatting](https://mlsanity.com/paper/2503.19458/) (2025)
- [Geometry Field Splatting with Gaussian Surfels](https://mlsanity.com/paper/2411.17067/) (2024)
- [3D Neural Edge Reconstruction](https://mlsanity.com/paper/2405.19295/) (2024)
- [Neural Radiance Fields for the Real World: A Survey](https://mlsanity.com/paper/2501.13104/) (2025)
- [Digging into Depth Priors for Outdoor Neural Radiance Fields](https://mlsanity.com/paper/2308.04413/) (2023)
- [CF-NeRF: Camera Parameter Free Neural Radiance Fields with Incremental Learning](https://mlsanity.com/paper/2312.08760/) (2023)
- [DMesh++: An Efficient Differentiable Mesh for Complex Shapes](https://mlsanity.com/paper/2412.16776/) (2024)
- [NeuDA: Neural Deformable Anchor for High-Fidelity Implicit Surface Reconstruction](https://mlsanity.com/paper/2303.02375/) (2023)
- [NeTO:Neural Reconstruction of Transparent Objects with Self-Occlusion Aware Refraction-Tracing](https://mlsanity.com/paper/2303.11219/) (2023)
- [DUDF: Differentiable Unsigned Distance Fields with Hyperbolic Scaling](https://mlsanity.com/paper/2402.08876/) (2024)
- [Neural-ABC: Neural Parametric Models for Articulated Body with Clothes](https://mlsanity.com/paper/2404.04673/) (2024)
- [DMesh: A Differentiable Mesh Representation](https://mlsanity.com/paper/2404.13445/) (2024)
- [Bridging 3D Anomaly Localization and Repair via High-Quality Continuous Geometric Representation](https://mlsanity.com/paper/2505.24431/) (2025)
- [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)
- [Surf-D: Generating High-Quality Surfaces of Arbitrary Topologies Using Diffusion Models](https://mlsanity.com/paper/2311.17050/) (2023)

## Abstract (arXiv)

We present a novel method, called NeuralUDF, for reconstructing surfaces with arbitrary topologies from 2D images via volume rendering. Recent advances in neural rendering based reconstruction have achieved compelling results. However, these methods are limited to objects with closed surfaces since they adopt Signed Distance Function (SDF) as surface representation which requires the target shape to be divided into inside and outside. In this paper, we propose to represent surfaces as the Unsigned Distance Function (UDF) and develop a new volume rendering scheme to learn the neural UDF representation. Specifically, a new density function that correlates the property of UDF with the volume rendering scheme is introduced for robust optimization of the UDF fields. Experiments on the DTU and DeepFashion3D datasets show that our method not only enables high-quality reconstruction of non-closed shapes with complex typologies, but also achieves comparable performance to the SDF based methods on the reconstruction of closed surfaces.