# NeUDF: Leaning Neural Unsigned Distance Fields with Volume Rendering

arXiv: https://arxiv.org/abs/2304.10080 · HTML: https://mlsanity.com/paper/2304.10080/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 67 references that are in the map.
- First posted on arXiv 20 Apr 2023.

## Builds on (most cited first, 30 of 42)

- [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)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (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)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [GIRAFFE: Representing Scenes as Compositional Generative Neural Feature Fields](https://mlsanity.com/paper/2011.12100/) (2020)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (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)
- [NICE-SLAM: Neural Implicit Scalable Encoding for SLAM](https://mlsanity.com/paper/2112.12130/) (2021)
- [NeRV: Neural Reflectance and Visibility Fields for Relighting and View Synthesis](https://mlsanity.com/paper/2012.03927/) (2020)
- [BlendedMVS: A Large-scale Dataset for Generalized Multi-view Stereo Networks](https://mlsanity.com/paper/1911.10127/) (2019)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [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)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Multi-Garment Net: Learning to Dress 3D People from Images](https://mlsanity.com/paper/1908.06903/) (2019)
- [DONeRF: Towards Real-Time Rendering of Compact Neural Radiance Fields using Depth Oracle Networks](https://mlsanity.com/paper/2103.03231/) (2021)
- [Geo-Neus: Geometry-Consistent Neural Implicit Surfaces Learning for Multi-view Reconstruction](https://mlsanity.com/paper/2205.15848/) (2022)
- [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)
- [NASA: Neural Articulated Shape Approximation](https://mlsanity.com/paper/1912.03207/) (2019)
- [Improving neural implicit surfaces geometry with patch warping](https://mlsanity.com/paper/2112.09648/) (2021)
- [HF-NeuS: Improved Surface Reconstruction Using High-Frequency Details](https://mlsanity.com/paper/2206.07850/) (2022)

## Built on by (most cited first, 30 of 41)

- [SC-GS: Sparse-Controlled Gaussian Splatting for Editable Dynamic Scenes](https://mlsanity.com/paper/2312.14937/) (2023)
- [Recent Advances in 3D Gaussian Splatting](https://mlsanity.com/paper/2403.11134/) (2024)
- [SparseFlex: High-Resolution and Arbitrary-Topology 3D Shape Modeling](https://mlsanity.com/paper/2503.21732/) (2025)
- [DeferredGS: Decoupled and Editable Gaussian Splatting with Deferred Shading](https://mlsanity.com/paper/2404.09412/) (2024)
- [Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection](https://mlsanity.com/paper/2308.11441/) (2023)
- [Mesh-based Gaussian Splatting for Real-time Large-scale Deformation](https://mlsanity.com/paper/2402.04796/) (2024)
- [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)
- [VRP-UDF: Towards Unbiased Learning of Unsigned Distance Functions from Multi-view Images with Volume Rendering Priors](https://mlsanity.com/paper/2407.16396/) (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)
- [GridPull: Towards Scalability in Learning Implicit Representations from 3D Point Clouds](https://mlsanity.com/paper/2308.13175/) (2023)
- [MultiPull: Detailing Signed Distance Functions by Pulling Multi-Level Queries at Multi-Step](https://mlsanity.com/paper/2411.01208/) (2024)
- [DMesh++: An Efficient Differentiable Mesh for Complex Shapes](https://mlsanity.com/paper/2412.16776/) (2024)
- [3D Shape Tokenization via Latent Flow Matching](https://mlsanity.com/paper/2412.15618/) (2024)
- [Diffusion Knows Transparency: Repurposing Video Diffusion for Transparent Object Depth and Normal Estimation](https://mlsanity.com/paper/2512.23705/) (2025)
- [DUDF: Differentiable Unsigned Distance Fields with Hyperbolic Scaling](https://mlsanity.com/paper/2402.08876/) (2024)
- [DMesh: A Differentiable Mesh Representation](https://mlsanity.com/paper/2404.13445/) (2024)
- [Surf-D: Generating High-Quality Surfaces of Arbitrary Topologies Using Diffusion Models](https://mlsanity.com/paper/2311.17050/) (2023)
- [NU-MCC: Multiview Compressive Coding with Neighborhood Decoder and Repulsive UDF](https://mlsanity.com/paper/2307.09112/) (2023)
- [A Lightweight UDF Learning Framework for 3D Reconstruction Based on Local Shape Functions](https://mlsanity.com/paper/2407.01330/) (2024)
- [MeshFlow: Efficient Artistic Mesh Generation via MeshVAE and Flow-based Diffusion Transformer](https://mlsanity.com/paper/2606.04621/) (2026)
- [Unsigned Orthogonal Distance Fields: An Accurate Neural Implicit Representation for Diverse 3D Shapes](https://mlsanity.com/paper/2403.01414/) (2024)
- [AniSDF: Fused-Granularity Neural Surfaces with Anisotropic Encoding for High-Fidelity 3D Reconstruction](https://mlsanity.com/paper/2410.01202/) (2024)
- [Coordinate Quantized Neural Implicit Representations for Multi-view Reconstruction](https://mlsanity.com/paper/2308.11025/) (2023)
- [4DRecons: 4D Neural Implicit Deformable Objects Reconstruction from a single RGB-D Camera with Geometrical and Topological Regularizations](https://mlsanity.com/paper/2406.10167/) (2024)
- [DCUDF2: Improving Efficiency and Accuracy in Extracting Zero Level Sets from Unsigned Distance Fields](https://mlsanity.com/paper/2408.17284/) (2024)
- [Differentiable Light Transport with Gaussian Surfels via Adapted Radiosity for Efficient Relighting and Geometry Reconstruction](https://mlsanity.com/paper/2509.18497/) (2025)
- [From Transparent to Opaque: Rethinking Neural Implicit Surfaces with α-NeuS](https://mlsanity.com/paper/2411.05362/) (2024)

## Abstract (arXiv)

Multi-view shape reconstruction has achieved impressive progresses thanks to the latest advances in neural implicit surface rendering. However, existing methods based on signed distance function (SDF) are limited to closed surfaces, failing to reconstruct a wide range of real-world objects that contain open-surface structures. In this work, we introduce a new neural rendering framework, coded NeUDF, that can reconstruct surfaces with arbitrary topologies solely from multi-view supervision. To gain the flexibility of representing arbitrary surfaces, NeUDF leverages the unsigned distance function (UDF) as surface representation. While a naive extension of an SDF-based neural renderer cannot scale to UDF, we propose two new formulations of weight function specially tailored for UDF-based volume rendering. Furthermore, to cope with open surface rendering, where the in/out test is no longer valid, we present a dedicated normal regularization strategy to resolve the surface orientation ambiguity. We extensively evaluate our method over a number of challenging datasets, including DTU}, MGN, and Deep Fashion 3D. Experimental results demonstrate that nEudf can significantly outperform the state-of-the-art method in the task of multi-view surface reconstruction, especially for complex shapes with open boundaries.