# DUDF: Differentiable Unsigned Distance Fields with Hyperbolic Scaling

arXiv: https://arxiv.org/abs/2402.08876 · HTML: https://mlsanity.com/paper/2402.08876/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 52 references that are in the map.
- First posted on arXiv 14 Feb 2024.

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

- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (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)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [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)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [Deep Fashion3D: A Dataset and Benchmark for 3D Garment Reconstruction from Single Images](https://mlsanity.com/paper/2003.12753/) (2020)
- [MeshUDF: Fast and Differentiable Meshing of Unsigned Distance Field Networks](https://mlsanity.com/paper/2111.14549/) (2021)
- [Deep Implicit Moving Least-Squares Functions for 3D Reconstruction](https://mlsanity.com/paper/2103.12266/) (2021)
- [NeuralUDF: Learning Unsigned Distance Fields for Multi-view Reconstruction of Surfaces with Arbitrary Topologies](https://mlsanity.com/paper/2211.14173/) (2022)
- [Curriculum DeepSDF](https://mlsanity.com/paper/2003.08593/) (2020)
- [Deep Level Sets: Implicit Surface Representations for 3D Shape Inference](https://mlsanity.com/paper/1901.06802/) (2019)
- [GIFS: Neural Implicit Function for General Shape Representation](https://mlsanity.com/paper/2204.07126/) (2022)
- [NeUDF: Leaning Neural Unsigned Distance Fields with Volume Rendering](https://mlsanity.com/paper/2304.10080/) (2023)
- [Deep Implicit Surface Point Prediction Networks](https://mlsanity.com/paper/2106.05779/) (2021)
- [Towards Better Gradient Consistency for Neural Signed Distance Functions via Level Set Alignment](https://mlsanity.com/paper/2305.11601/) (2023)
- [Learning Anchored Unsigned Distance Functions with Gradient Direction Alignment for Single-view Garment Reconstruction](https://mlsanity.com/paper/2108.08478/) (2021)

## Built on by (most cited first, 9 of 9)

- [Details Enhancement in Unsigned Distance Field Learning for High-fidelity 3D Surface Reconstruction](https://mlsanity.com/paper/2406.00346/) (2024)
- [A Lightweight UDF Learning Framework for 3D Reconstruction Based on Local Shape Functions](https://mlsanity.com/paper/2407.01330/) (2024)
- [Inferring Neural Signed Distance Functions by Overfitting on Single Noisy Point Clouds through Finetuning Data-Driven based Priors](https://mlsanity.com/paper/2410.19680/) (2024)
- [Monge-Ampere Regularization for Learning Arbitrary Shapes from Point Clouds](https://mlsanity.com/paper/2410.18477/) (2024)
- [Geometric implicit neural representations for signed distance functions](https://mlsanity.com/paper/2511.07206/) (2025)
- [High Resolution UDF Meshing via Iterative Networks](https://mlsanity.com/paper/2509.17212/) (2025)
- [MIND: Material Interface Generation from UDFs for Non-Manifold Surface Reconstruction](https://mlsanity.com/paper/2506.02938/) (2025)
- [Human Knowledge Integrated Multi-modal Learning for Single Source Domain Generalization](https://mlsanity.com/paper/2603.12369/) (2026)
- [DiffGI: Differentiable Geometry Images for High-Fidelity Thin-Shell 3D Generation](https://mlsanity.com/paper/2607.13365/) (2026)

## Abstract (arXiv)

In recent years, there has been a growing interest in training Neural Networks to approximate Unsigned Distance Fields (UDFs) for representing open surfaces in the context of 3D reconstruction. However, UDFs are non-differentiable at the zero level set which leads to significant errors in distances and gradients, generally resulting in fragmented and discontinuous surfaces. In this paper, we propose to learn a hyperbolic scaling of the unsigned distance field, which defines a new Eikonal problem with distinct boundary conditions. This allows our formulation to integrate seamlessly with state-of-the-art continuously differentiable implicit neural representation networks, largely applied in the literature to represent signed distance fields. Our approach not only addresses the challenge of open surface representation but also demonstrates significant improvement in reconstruction quality and training performance. Moreover, the unlocked field's differentiability allows the accurate computation of essential topological properties such as normal directions and curvatures, pervasive in downstream tasks such as rendering. Through extensive experiments, we validate our approach across various data sets and against competitive baselines. The results demonstrate enhanced accuracy and up to an order of magnitude increase in speed compared to previous methods.