# Deep Point Set Resampling via Gradient Fields

arXiv: https://arxiv.org/abs/2111.02045 · HTML: https://mlsanity.com/paper/2111.02045/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 63 references that are in the map.
- First posted on arXiv 3 Nov 2021.

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

- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [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)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [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)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Learning Gradient Fields for Shape Generation](https://mlsanity.com/paper/2008.06520/) (2020)
- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [PU-GAN: a Point Cloud Upsampling Adversarial Network](https://mlsanity.com/paper/1907.10844/) (2019)
- [DensePoint: Learning Densely Contextual Representation for Efficient Point Cloud Processing](https://mlsanity.com/paper/1909.03669/) (2019)
- [Patch-based Progressive 3D Point Set Upsampling](https://mlsanity.com/paper/1811.11286/) (2018)
- [PointCleanNet: Learning to Denoise and Remove Outliers from Dense Point Clouds](https://mlsanity.com/paper/1901.01060/) (2019)
- [EC-Net: an Edge-aware Point set Consolidation Network](https://mlsanity.com/paper/1807.06010/) (2018)
- [Score-Based Point Cloud Denoising](https://mlsanity.com/paper/2107.10981/) (2021)
- [Point Cloud Upsampling via Disentangled Refinement](https://mlsanity.com/paper/2106.04779/) (2021)
- [PUGeo-Net: A Geometry-centric Network for 3D Point Cloud Upsampling](https://mlsanity.com/paper/2002.10277/) (2020)
- [Repulsion Loss: Detecting Pedestrians in a Crowd](https://mlsanity.com/paper/1711.07752/) (2017)
- [Total Denoising: Unsupervised Learning of 3D Point Cloud Cleaning](https://mlsanity.com/paper/1904.07615/) (2019)
- [Differentiable Manifold Reconstruction for Point Cloud Denoising](https://mlsanity.com/paper/2007.13551/) (2020)
- [3D Point Cloud Denoising using Graph Laplacian Regularization of a Low Dimensional Manifold Model](https://mlsanity.com/paper/1803.07252/) (2018)
- [Learning Graph-Convolutional Representations for Point Cloud Denoising](https://mlsanity.com/paper/2007.02578/) (2020)
- [Feature Graph Learning for 3D Point Cloud Denoising](https://mlsanity.com/paper/1907.09138/) (2019)
- [Graph-Based Blind Image Deblurring From a Single Photograph](https://mlsanity.com/paper/1802.07929/) (2018)
- [Graph Signal Processing for Geometric Data and Beyond: Theory and Applications](https://mlsanity.com/paper/2008.01918/) (2020)
- [3D Point Cloud Denoising via Deep Neural Network based Local Surface Estimation](https://mlsanity.com/paper/1904.04427/) (2019)
- [Random Walk Graph Laplacian based Smoothness Prior for Soft Decoding of JPEG Images](https://mlsanity.com/paper/1607.01895/) (2016)
- [Dynamic Point Cloud Denoising via Manifold-to-Manifold Distance](https://mlsanity.com/paper/2003.08355/) (2020)
- [Graph-based denoising for time-varying point clouds](https://mlsanity.com/paper/1511.04902/) (2015)

## Built on by (most cited first, 24 of 24)

- [Deep Imbalanced Learning for Multimodal Emotion Recognition in Conversations](https://mlsanity.com/paper/2312.06337/) (2023)
- [RangeLDM: Fast Realistic LiDAR Point Cloud Generation](https://mlsanity.com/paper/2403.10094/) (2024)
- [PCDNF: Revisiting Learning-based Point Cloud Denoising via Joint Normal Filtering](https://mlsanity.com/paper/2209.00798/) (2022)
- [StraightPCF: Straight Point Cloud Filtering](https://mlsanity.com/paper/2405.08322/) (2024)
- [CasSR: Activating Image Power for Real-World Image Super-Resolution](https://mlsanity.com/paper/2403.11451/) (2024)
- [Dynamic Point Cloud Denoising via Gradient Fields](https://mlsanity.com/paper/2204.08755/) (2022)
- [Efficient Point Clouds Upsampling via Flow Matching](https://mlsanity.com/paper/2501.15286/) (2025)
- [Noise2Score3D: Tweedie's Approach for Unsupervised Point Cloud Denoising](https://mlsanity.com/paper/2503.09283/) (2025)
- [Joint Point Cloud Upsampling and Cleaning with Octree-based CNNs](https://mlsanity.com/paper/2410.17001/) (2024)
- [Point Cloud Resampling with Learnable Heat Diffusion](https://mlsanity.com/paper/2411.14120/) (2024)
- [Learning Normals of Noisy Points by Local Gradient-Aware Surface Filtering](https://mlsanity.com/paper/2507.03394/) (2025)
- [Gradient-based Point Cloud Denoising with Uniformity](https://mlsanity.com/paper/2207.10279/) (2022)
- [Point Cloud Denoising With Fine-Granularity Dynamic Graph Convolutional Networks](https://mlsanity.com/paper/2411.14158/) (2024)
- [Hybrid Long and Short Range Flows for Point Cloud Filtering](https://mlsanity.com/paper/2508.08542/) (2025)
- [Deep Learning For Point Cloud Denoising: A Survey](https://mlsanity.com/paper/2508.11932/) (2025)
- [Adaptive and Iterative Point Cloud Denoising with Score-Based Diffusion Model](https://mlsanity.com/paper/2509.14560/) (2025)
- [From Part to Whole: 3D Generative World Model with an Adaptive Structural Hierarchy](https://mlsanity.com/paper/2603.21557/) (2026)
- [Incomplete Gamma Kernels: Generalizing Locally Optimal Projection Operators](https://mlsanity.com/paper/2205.01087/) (2022)
- [Noise2Score3D:Unsupervised Tweedie's Approach for Point Cloud Denoising](https://mlsanity.com/paper/2502.16826/) (2025)
- [Point upsampling networks for single-photon sensing](https://mlsanity.com/paper/2508.12986/) (2025)
- [A Survey of Deep Learning-based Point Cloud Denoising](https://mlsanity.com/paper/2508.17011/) (2025)
- [View-Consistent 3D Scene Editing via Dual-Path Structural Correspondense and Semantic Continuity](https://mlsanity.com/paper/2604.17801/) (2026)
- [SIMPC: Learning Self-Induced Mirror-Point Consistency for Unsupervised Point Cloud Denoising](https://mlsanity.com/paper/2605.26894/) (2026)
- [RODR: Riemannian Orthogonally Decoupled Regularization for Disentangled Manifold Representation](https://mlsanity.com/paper/2607.23958/) (2026)

## Abstract (arXiv)

3D point clouds acquired by scanning real-world objects or scenes have found a wide range of applications including immersive telepresence, autonomous driving, surveillance, etc. They are often perturbed by noise or suffer from low density, which obstructs downstream tasks such as surface reconstruction and understanding. In this paper, we propose a novel paradigm of point set resampling for restoration, which learns continuous gradient fields of point clouds that converge points towards the underlying surface. In particular, we represent a point cloud via its gradient field -- the gradient of the log-probability density function, and enforce the gradient field to be continuous, thus guaranteeing the continuity of the model for solvable optimization. Based on the continuous gradient fields estimated via a proposed neural network, resampling a point cloud amounts to performing gradient-based Markov Chain Monte Carlo (MCMC) on the input noisy or sparse point cloud. Further, we propose to introduce regularization into the gradient-based MCMC during point cloud restoration, which essentially refines the intermediate resampled point cloud iteratively and accommodates various priors in the resampling process. Extensive experimental results demonstrate that the proposed point set resampling achieves the state-of-the-art performance in representative restoration tasks including point cloud denoising and upsampling.