# 3PSDF: Three-Pole Signed Distance Function for Learning Surfaces with Arbitrary Topologies

arXiv: https://arxiv.org/abs/2205.15572 · HTML: https://mlsanity.com/paper/2205.15572/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 42 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 30 of 32)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (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)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [4D Spatio-Temporal ConvNets: Minkowski Convolutional Neural Networks](https://mlsanity.com/paper/1904.08755/) (2019)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [3D Semantic Segmentation with Submanifold Sparse Convolutional Networks](https://mlsanity.com/paper/1711.10275/) (2017)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [3D-FRONT: 3D Furnished Rooms with layOuts and semaNTics](https://mlsanity.com/paper/2011.09127/) (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)
- [Octree Generating Networks: Efficient Convolutional Architectures for High-resolution 3D Outputs](https://mlsanity.com/paper/1703.09438/) (2017)
- [Learning a Predictable and Generative Vector Representation for Objects](https://mlsanity.com/paper/1603.08637/) (2016)
- [3D Point Cloud Generative Adversarial Network Based on Tree Structured Graph Convolutions](https://mlsanity.com/paper/1905.06292/) (2019)
- [Deep Mesh Reconstruction from Single RGB Images via Topology Modification Networks](https://mlsanity.com/paper/1909.00321/) (2019)
- [Learning to Infer Implicit Surfaces without 3D Supervision](https://mlsanity.com/paper/1911.00767/) (2019)
- [SiCloPe: Silhouette-Based Clothed People](https://mlsanity.com/paper/1901.00049/) (2018)
- [Curriculum DeepSDF](https://mlsanity.com/paper/2003.08593/) (2020)
- [Scan2Mesh: From Unstructured Range Scans to 3D Meshes](https://mlsanity.com/paper/1811.10464/) (2018)
- [Deep Implicit Surface Point Prediction Networks](https://mlsanity.com/paper/2106.05779/) (2021)
- [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, 27 of 27)

- [SparseFlex: High-Resolution and Arbitrary-Topology 3D Shape Modeling](https://mlsanity.com/paper/2503.21732/) (2025)
- [NeuralUDF: Learning Unsigned Distance Fields for Multi-view Reconstruction of Surfaces with Arbitrary Topologies](https://mlsanity.com/paper/2211.14173/) (2022)
- [NeUDF: Leaning Neural Unsigned Distance Fields with Volume Rendering](https://mlsanity.com/paper/2304.10080/) (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)
- [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)
- [ALTO: Alternating Latent Topologies for Implicit 3D Reconstruction](https://mlsanity.com/paper/2212.04096/) (2022)
- [ShadowNeuS: Neural SDF Reconstruction by Shadow Ray Supervision](https://mlsanity.com/paper/2211.14086/) (2022)
- [Neural Radiance Fields for the Real World: A Survey](https://mlsanity.com/paper/2501.13104/) (2025)
- [Surf-D: Generating High-Quality Surfaces of Arbitrary Topologies Using Diffusion Models](https://mlsanity.com/paper/2311.17050/) (2023)
- [Unsigned Orthogonal Distance Fields: An Accurate Neural Implicit Representation for Diverse 3D Shapes](https://mlsanity.com/paper/2403.01414/) (2024)
- [Adaptive Local Basis Functions for Shape Completion](https://mlsanity.com/paper/2307.08348/) (2023)
- [Neural Surface Detection for Unsigned Distance Fields](https://mlsanity.com/paper/2407.18381/) (2024)
- [DCUDF2: Improving Efficiency and Accuracy in Extracting Zero Level Sets from Unsigned Distance Fields](https://mlsanity.com/paper/2408.17284/) (2024)
- [Faithful Contouring: Near-Lossless 3D Voxel Representation Free from Iso-surface](https://mlsanity.com/paper/2511.04029/) (2025)
- [FullFormer: Generating Shapes Inside Shapes](https://mlsanity.com/paper/2303.11235/) (2023)
- [3D-WAG: Hierarchical Wavelet-Guided Autoregressive Generation for High-Fidelity 3D Shapes](https://mlsanity.com/paper/2411.19037/) (2024)
- [LoG3D: Ultra-High-Resolution 3D Shape Modeling via Local-to-Global Partitioning](https://mlsanity.com/paper/2511.10040/) (2025)
- [AnySurf: Any Surface Generation with Directed Edge](https://mlsanity.com/paper/2605.26149/) (2026)
- [IPVNet: Learning Implicit Point-Voxel Features for Open-Surface 3D Reconstruction](https://mlsanity.com/paper/2311.02552/) (2023)
- [Gradient Distance Function](https://mlsanity.com/paper/2410.22422/) (2024)
- [Neural Shortest Path for Surface Reconstruction from Point Clouds](https://mlsanity.com/paper/2502.06047/) (2025)
- [MIND: Material Interface Generation from UDFs for Non-Manifold Surface Reconstruction](https://mlsanity.com/paper/2506.02938/) (2025)
- [SHARC: Reference point driven Spherical Harmonic Representation for Complex Shapes](https://mlsanity.com/paper/2604.01894/) (2026)
- [Functionalization via Structure Completion and Motion Rectification](https://mlsanity.com/paper/2605.18010/) (2026)
- [DiffGI: Differentiable Geometry Images for High-Fidelity Thin-Shell 3D Generation](https://mlsanity.com/paper/2607.13365/) (2026)

## Abstract (arXiv)

Recent advances in learning 3D shapes using neural implicit functions have achieved impressive results by breaking the previous barrier of resolution and diversity for varying topologies. However, most of such approaches are limited to closed surfaces as they require the space to be divided into inside and outside. More recent works based on unsigned distance function have been proposed to handle complex geometry containing both the open and closed surfaces. Nonetheless, as their direct outputs are point clouds, robustly obtaining high-quality meshing results from discrete points remains an open question. We present a novel learnable implicit representation, called the three-pole signed distance function (3PSDF), that can represent non-watertight 3D shapes with arbitrary topologies while supporting easy field-to-mesh conversion using the classic Marching Cubes algorithm. The key to our method is the introduction of a new sign, the NULL sign, in addition to the conventional in and out labels. The existence of the null sign could stop the formation of a closed isosurface derived from the bisector of the in/out regions. Further, we propose a dedicated learning framework to effectively learn 3PSDF without worrying about the vanishing gradient due to the null labels. Experimental results show that our approach outperforms the previous state-of-the-art methods in a wide range of benchmarks both quantitatively and qualitatively.