# CAP-UDF: Learning Unsigned Distance Functions Progressively from Raw Point Clouds with Consistency-Aware Field Optimization

arXiv: https://arxiv.org/abs/2210.02757 · HTML: https://mlsanity.com/paper/2210.02757/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 94 references that are in the map.
- First posted on arXiv 6 Oct 2022.

## Builds on (most cited first, 30 of 54)

- [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)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [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)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Neural RGB-D Surface Reconstruction](https://mlsanity.com/paper/2104.04532/) (2021)
- [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)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (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)
- [SDFDiff: Differentiable Rendering of Signed Distance Fields for 3D Shape Optimization](https://mlsanity.com/paper/1912.07109/) (2019)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [HF-NeuS: Improved Surface Reconstruction Using High-Frequency Details](https://mlsanity.com/paper/2206.07850/) (2022)
- [SALD: Sign Agnostic Learning with Derivatives](https://mlsanity.com/paper/2006.05400/) (2020)
- [Deep Geometric Prior for Surface Reconstruction](https://mlsanity.com/paper/1811.10943/) (2018)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [POCO: Point Convolution for Surface Reconstruction](https://mlsanity.com/paper/2201.01831/) (2022)
- [PatchNets: Patch-Based Generalizable Deep Implicit 3D Shape Representations](https://mlsanity.com/paper/2008.01639/) (2020)
- [MeshUDF: Fast and Differentiable Meshing of Unsigned Distance Field Networks](https://mlsanity.com/paper/2111.14549/) (2021)

## Built on by (most cited first, 30 of 47)

- [Advances in 3D Generation: A Survey](https://mlsanity.com/paper/2401.17807/) (2024)
- [DiffGS: Functional Gaussian Splatting Diffusion](https://mlsanity.com/paper/2410.19657/) (2024)
- [Binocular-Guided 3D Gaussian Splatting with View Consistency for Sparse View Synthesis](https://mlsanity.com/paper/2410.18822/) (2024)
- [Towards Better Gradient Consistency for Neural Signed Distance Functions via Level Set Alignment](https://mlsanity.com/paper/2305.11601/) (2023)
- [Differentiable Registration of Images and LiDAR Point Clouds with VoxelPoint-to-Pixel Matching](https://mlsanity.com/paper/2312.04060/) (2023)
- [NeuSurf: On-Surface Priors for Neural Surface Reconstruction from Sparse Input Views](https://mlsanity.com/paper/2312.13977/) (2023)
- [Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection](https://mlsanity.com/paper/2308.11441/) (2023)
- [Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian](https://mlsanity.com/paper/2309.01793/) (2023)
- [Zero-Shot Scene Reconstruction from Single Images with Deep Prior Assembly](https://mlsanity.com/paper/2410.15971/) (2024)
- [GeoUDF: Surface Reconstruction from 3D Point Clouds via Geometry-guided Distance Representation](https://mlsanity.com/paper/2211.16762/) (2022)
- [Unsupervised Inference of Signed Distance Functions from Single Sparse Point Clouds without Learning Priors](https://mlsanity.com/paper/2303.14505/) (2023)
- [Learning Signed Distance Functions from Noisy 3D Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2306.01405/) (2023)
- [MaterialRefGS: Reflective Gaussian Splatting with Multi-view Consistent Material Inference](https://mlsanity.com/paper/2510.11387/) (2025)
- [Robust Zero Level-Set Extraction from Unsigned Distance Fields Based on Double Covering](https://mlsanity.com/paper/2310.03431/) (2023)
- [MAtCha Gaussians: Atlas of Charts for High-Quality Geometry and Photorealism From Sparse Views](https://mlsanity.com/paper/2412.06767/) (2024)
- [Learning Continuous Implicit Field with Local Distance Indicator for Arbitrary-Scale Point Cloud Upsampling](https://mlsanity.com/paper/2312.15133/) (2023)
- [VRP-UDF: Towards Unbiased Learning of Unsigned Distance Functions from Multi-view Images with Volume Rendering Priors](https://mlsanity.com/paper/2407.16396/) (2024)
- [Neural Vector Fields: Implicit Representation by Explicit Learning](https://mlsanity.com/paper/2303.04341/) (2023)
- [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)
- [NeRFPrior: Learning Neural Radiance Field as a Prior for Indoor Scene Reconstruction](https://mlsanity.com/paper/2503.18361/) (2025)
- [GridPull: Towards Scalability in Learning Implicit Representations from 3D Point Clouds](https://mlsanity.com/paper/2308.13175/) (2023)
- [Learning Neural Implicit through Volume Rendering with Attentive Depth Fusion Priors](https://mlsanity.com/paper/2310.11598/) (2023)
- [Learning Signed Hyper Surfaces for Oriented Point Cloud Normal Estimation](https://mlsanity.com/paper/2305.05873/) (2023)
- [Robustifying Generalizable Implicit Shape Networks with a Tunable Non-Parametric Model](https://mlsanity.com/paper/2311.12967/) (2023)
- [SparseRecon: Neural Implicit Surface Reconstruction from Sparse Views with Feature and Depth Consistencies](https://mlsanity.com/paper/2508.00366/) (2025)
- [Spurfies: Sparse Surface Reconstruction using Local Geometry Priors](https://mlsanity.com/paper/2408.16544/) (2024)
- [Learning Bijective Surface Parameterization for Inferring Signed Distance Functions from Sparse Point Clouds with Grid Deformation](https://mlsanity.com/paper/2503.23670/) (2025)
- [GAP: Gaussianize Any Point Clouds with Text Guidance](https://mlsanity.com/paper/2508.05631/) (2025)
- [Retro-FPN: Retrospective Feature Pyramid Network for Point Cloud Semantic Segmentation](https://mlsanity.com/paper/2308.09314/) (2023)

## Abstract (arXiv)

Surface reconstruction for point clouds is an important task in 3D computer vision. Most of the latest methods resolve this problem by learning signed distance functions from point clouds, which are limited to reconstructing closed surfaces. Some other methods tried to represent open surfaces using unsigned distance functions (UDF) which are learned from ground truth distances. However, the learned UDF is hard to provide smooth distance fields due to the discontinuous character of point clouds. In this paper, we propose CAP-UDF, a novel method to learn consistency-aware UDF from raw point clouds. We achieve this by learning to move queries onto the surface with a field consistency constraint, where we also enable to progressively estimate a more accurate surface. Specifically, we train a neural network to gradually infer the relationship between queries and the approximated surface by searching for the moving target of queries in a dynamic way. Meanwhile, we introduce a polygonization algorithm to extract surfaces using the gradients of the learned UDF. We conduct comprehensive experiments in surface reconstruction for point clouds, real scans or depth maps, and further explore our performance in unsupervised point normal estimation, which demonstrate non-trivial improvements of CAP-UDF over the state-of-the-art methods.