# Neural Unsigned Distance Fields for Implicit Function Learning

arXiv: https://arxiv.org/abs/2010.13938 · HTML: https://mlsanity.com/paper/2010.13938/

## Key facts

- Cited by 265 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2020.

## Built on by (most cited first, 30 of 265)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [iMAP: Implicit Mapping and Positioning in Real-Time](https://mlsanity.com/paper/2103.12352/) (2021)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [StyleSDF: High-Resolution 3D-Consistent Image and Geometry Generation](https://mlsanity.com/paper/2112.11427/) (2021)
- [BEHAVE: Dataset and Method for Tracking Human Object Interactions](https://mlsanity.com/paper/2204.06950/) (2022)
- [AutoSDF: Shape Priors for 3D Completion, Reconstruction and Generation](https://mlsanity.com/paper/2203.09516/) (2022)
- [ECON: Explicit Clothed humans Optimized via Normal integration](https://mlsanity.com/paper/2212.07422/) (2022)
- [Stereo Radiance Fields (SRF): Learning View Synthesis for Sparse Views of Novel Scenes](https://mlsanity.com/paper/2104.06935/) (2021)
- [SMPLicit: Topology-aware Generative Model for Clothed People](https://mlsanity.com/paper/2103.06871/) (2021)
- [NeRFPlayer: A Streamable Dynamic Scene Representation with Decomposed Neural Radiance Fields](https://mlsanity.com/paper/2210.15947/) (2022)
- [MV-DUSt3R+: Single-Stage Scene Reconstruction from Sparse Views In 2 Seconds](https://mlsanity.com/paper/2412.06974/) (2024)
- [LEAP: Learning Articulated Occupancy of People](https://mlsanity.com/paper/2104.06849/) (2021)
- [imGHUM: Implicit Generative Models of 3D Human Shape and Articulated Pose](https://mlsanity.com/paper/2108.10842/) (2021)
- [Neural-GIF: Neural Generalized Implicit Functions for Animating People in Clothing](https://mlsanity.com/paper/2108.08807/) (2021)
- [Grid-guided Neural Radiance Fields for Large Urban Scenes](https://mlsanity.com/paper/2303.14001/) (2023)
- [CHORE: Contact, Human and Object REconstruction from a single RGB image](https://mlsanity.com/paper/2204.02445/) (2022)
- [POCO: Point Convolution for Surface Reconstruction](https://mlsanity.com/paper/2201.01831/) (2022)
- [The Power of Points for Modeling Humans in Clothing](https://mlsanity.com/paper/2109.01137/) (2021)
- [GIRAFFE HD: A High-Resolution 3D-aware Generative Model](https://mlsanity.com/paper/2203.14954/) (2022)
- [Pose-NDF: Modeling Human Pose Manifolds with Neural Distance Fields](https://mlsanity.com/paper/2207.13807/) (2022)
- [Capturing and Animation of Body and Clothing from Monocular Video](https://mlsanity.com/paper/2210.01868/) (2022)
- [SparseFlex: High-Resolution and Arbitrary-Topology 3D Shape Modeling](https://mlsanity.com/paper/2503.21732/) (2025)
- [MeshUDF: Fast and Differentiable Meshing of Unsigned Distance Field Networks](https://mlsanity.com/paper/2111.14549/) (2021)
- [SCALE: Modeling Clothed Humans with a Surface Codec of Articulated Local Elements](https://mlsanity.com/paper/2104.07660/) (2021)
- [Neural Dual Contouring](https://mlsanity.com/paper/2202.01999/) (2022)
- [DM-NeRF: 3D Scene Geometry Decomposition and Manipulation from 2D Images](https://mlsanity.com/paper/2208.07227/) (2022)
- [Towards Implicit Text-Guided 3D Shape Generation](https://mlsanity.com/paper/2203.14622/) (2022)
- [ALSO: Automotive Lidar Self-supervision by Occupancy estimation](https://mlsanity.com/paper/2212.05867/) (2022)
- [ImFace: A Nonlinear 3D Morphable Face Model with Implicit Neural Representations](https://mlsanity.com/paper/2203.14510/) (2022)
- [NeuralUDF: Learning Unsigned Distance Fields for Multi-view Reconstruction of Surfaces with Arbitrary Topologies](https://mlsanity.com/paper/2211.14173/) (2022)

## Abstract (arXiv)

In this work we target a learnable output representation that allows continuous, high resolution outputs of arbitrary shape. Recent works represent 3D surfaces implicitly with a Neural Network, thereby breaking previous barriers in resolution, and ability to represent diverse topologies. However, neural implicit representations are limited to closed surfaces, which divide the space into inside and outside. Many real world objects such as walls of a scene scanned by a sensor, clothing, or a car with inner structures are not closed. This constitutes a significant barrier, in terms of data pre-processing (objects need to be artificially closed creating artifacts), and the ability to output open surfaces. In this work, we propose Neural Distance Fields (NDF), a neural network based model which predicts the unsigned distance field for arbitrary 3D shapes given sparse point clouds. NDF represent surfaces at high resolutions as prior implicit models, but do not require closed surface data, and significantly broaden the class of representable shapes in the output. NDF allow to extract the surface as very dense point clouds and as meshes. We also show that NDF allow for surface normal calculation and can be rendered using a slight modification of sphere tracing. We find NDF can be used for multi-target regression (multiple outputs for one input) with techniques that have been exclusively used for rendering in graphics. Experiments on ShapeNet show that NDF, while simple, is the state-of-the art, and allows to reconstruct shapes with inner structures, such as the chairs inside a bus. Notably, we show that NDF are not restricted to 3D shapes, and can approximate more general open surfaces such as curves, manifolds, and functions. Code is available for research at https://virtualhumans.mpi-inf.mpg.de/ndf/.