# GeoUDF: Surface Reconstruction from 3D Point Clouds via Geometry-guided Distance Representation

arXiv: https://arxiv.org/abs/2211.16762 · HTML: https://mlsanity.com/paper/2211.16762/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 44 references that are in the map.
- First posted on arXiv 30 Nov 2022.

## Builds on (most cited first, 30 of 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [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)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [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)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (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)
- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [PU-GAN: a Point Cloud Upsampling Adversarial Network](https://mlsanity.com/paper/1907.10844/) (2019)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [Patch-based Progressive 3D Point Set Upsampling](https://mlsanity.com/paper/1811.11286/) (2018)
- [PU-GCN: Point Cloud Upsampling using Graph Convolutional Networks](https://mlsanity.com/paper/1912.03264/) (2019)
- [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)
- [Dual Octree Graph Networks for Learning Adaptive Volumetric Shape Representations](https://mlsanity.com/paper/2205.02825/) (2022)
- [PUGeo-Net: A Geometry-centric Network for 3D Point Cloud Upsampling](https://mlsanity.com/paper/2002.10277/) (2020)
- [Deep Implicit Moving Least-Squares Functions for 3D Reconstruction](https://mlsanity.com/paper/2103.12266/) (2021)
- [Reconstructing Surfaces for Sparse Point Clouds with On-Surface Priors](https://mlsanity.com/paper/2204.10603/) (2022)
- [Neural Points: Point Cloud Representation with Neural Fields for Arbitrary Upsampling](https://mlsanity.com/paper/2112.04148/) (2021)
- [CAP-UDF: Learning Unsigned Distance Functions Progressively from Raw Point Clouds with Consistency-Aware Field Optimization](https://mlsanity.com/paper/2210.02757/) (2022)
- [GIFS: Neural Implicit Function for General Shape Representation](https://mlsanity.com/paper/2204.07126/) (2022)
- [Shape Reconstruction by Learning Differentiable Surface Representations](https://mlsanity.com/paper/1911.11227/) (2019)

## Built on by (most cited first, 29 of 29)

- [Robust Zero Level-Set Extraction from Unsigned Distance Fields Based on Double Covering](https://mlsanity.com/paper/2310.03431/) (2023)
- [MultiPull: Detailing Signed Distance Functions by Pulling Multi-Level Queries at Multi-Step](https://mlsanity.com/paper/2411.01208/) (2024)
- [Human as Points: Explicit Point-based 3D Human Reconstruction from Single-view RGB Images](https://mlsanity.com/paper/2311.02892/) (2023)
- [DynoSurf: Neural Deformation-based Temporally Consistent Dynamic Surface Reconstruction](https://mlsanity.com/paper/2403.11586/) (2024)
- [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)
- [Unsupervised 3D Point Cloud Completion via Multi-view Adversarial Learning](https://mlsanity.com/paper/2407.09786/) (2024)
- [Monge-Ampere Regularization for Learning Arbitrary Shapes from Point Clouds](https://mlsanity.com/paper/2410.18477/) (2024)
- [DDM: A Metric for Comparing 3D Shapes Using Directional Distance Fields](https://mlsanity.com/paper/2401.09736/) (2024)
- [DCUDF2: Improving Efficiency and Accuracy in Extracting Zero Level Sets from Unsigned Distance Fields](https://mlsanity.com/paper/2408.17284/) (2024)
- [RBFIM: Perceptual Quality Assessment for Compressed Point Clouds Using Radial Basis Function Interpolation](https://mlsanity.com/paper/2503.14154/) (2025)
- [High Resolution UDF Meshing via Iterative Networks](https://mlsanity.com/paper/2509.17212/) (2025)
- [Parameterize Structure with Differentiable Template for 3D Shape Generation](https://mlsanity.com/paper/2410.10399/) (2024)
- [Point Cloud Unsupervised Pre-training via 3D Gaussian Splatting](https://mlsanity.com/paper/2411.18667/) (2024)
- [Non-uniform Point Cloud Upsampling via Local Manifold Distribution](https://mlsanity.com/paper/2504.11701/) (2025)
- [A Divide-and-Conquer Approach for Global Orientation of Non-Watertight Scene-Level Point Clouds Using 0-1 Integer Optimization](https://mlsanity.com/paper/2505.23469/) (2025)
- [Voronoi-Assisted Optimization for Diffusing Unsigned Distance Fields from Unoriented Points](https://mlsanity.com/paper/2510.12524/) (2025)
- [Analysis of Sampling Strategies for Implicit 3D Reconstruction](https://mlsanity.com/paper/2304.03999/) (2023)
- [Separability Membrane: 3D Active Contour for Point Cloud Surface Reconstruction](https://mlsanity.com/paper/2503.05217/) (2025)
- [MIND: Material Interface Generation from UDFs for Non-Manifold Surface Reconstruction](https://mlsanity.com/paper/2506.02938/) (2025)
- [Self-Attention Based Multi-Scale Graph Auto-Encoder Network of 3D Meshes](https://mlsanity.com/paper/2507.05304/) (2025)
- [PVNet: Point-Voxel Interaction LiDAR Scene Upsampling Via Diffusion Models](https://mlsanity.com/paper/2508.17050/) (2025)
- [T-MLP: Tailed Multi-Layer Perceptron for Level-of-Detail Signal Representation](https://mlsanity.com/paper/2509.00066/) (2025)
- [Objective Quality Assessment of Point Clouds Using Multi-scale Implicit Structural Similarity](https://mlsanity.com/paper/2601.01200/) (2026)
- [MGP-KAD: Multimodal Geometric Priors and Kolmogorov-Arnold Decoder for Single-View 3D Reconstruction in Complex Scenes](https://mlsanity.com/paper/2602.06158/) (2026)
- [Joint Orientation and Weight Optimization for Robust Watertight Surface Reconstruction via Dirichlet-Regularized Winding Fields](https://mlsanity.com/paper/2602.13801/) (2026)
- [SAND: Spatially Adaptive Network Depth for Fast Sampling of Neural Implicit Surfaces](https://mlsanity.com/paper/2604.25936/) (2026)
- [Projective Normal Fields: A Convex Optimization Method for Constructing Smooth UDFs](https://mlsanity.com/paper/2609.34784/) (2026)
- [Volume Rendering with Metric--Phase Fields for Thin Structures and Sign-Ambiguous Geometry](https://mlsanity.com/paper/2610.13088/) (2026)

## Abstract (arXiv)

We present a learning-based method, namely GeoUDF,to tackle the long-standing and challenging problem of reconstructing a discrete surface from a sparse point cloud.To be specific, we propose a geometry-guided learning method for UDF and its gradient estimation that explicitly formulates the unsigned distance of a query point as the learnable affine averaging of its distances to the tangent planes of neighboring points on the surface. Besides,we model the local geometric structure of the input point clouds by explicitly learning a quadratic polynomial for each point. This not only facilitates upsampling the input sparse point cloud but also naturally induces unoriented normal, which further augments UDF estimation. Finally, to extract triangle meshes from the predicted UDF we propose a customized edge-based marching cube module. We conduct extensive experiments and ablation studies to demonstrate the significant advantages of our method over state-of-the-art methods in terms of reconstruction accuracy, efficiency, and generality. The source code is publicly available at https://github.com/rsy6318/GeoUDF.