# Differentiable Manifold Reconstruction for Point Cloud Denoising

arXiv: https://arxiv.org/abs/2007.13551 · HTML: https://mlsanity.com/paper/2007.13551/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2020.

## Built on by (most cited first, 30 of 52)

- [Score-Based Point Cloud Denoising](https://mlsanity.com/paper/2107.10981/) (2021)
- [A Survey on Graph Neural Networks and Graph Transformers in Computer Vision: A Task-Oriented Perspective](https://mlsanity.com/paper/2209.13232/) (2022)
- [Energy-Motivated Equivariant Pretraining for 3D Molecular Graphs](https://mlsanity.com/paper/2207.08824/) (2022)
- [Orienting Point Clouds with Dipole Propagation](https://mlsanity.com/paper/2105.01604/) (2021)
- [IterativePFN: True Iterative Point Cloud Filtering](https://mlsanity.com/paper/2304.01529/) (2023)
- [Learning Signed Distance Functions from Noisy 3D Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2306.01405/) (2023)
- [Deep Point Set Resampling via Gradient Fields](https://mlsanity.com/paper/2111.02045/) (2021)
- [PD-Flow: A Point Cloud Denoising Framework with Normalizing Flows](https://mlsanity.com/paper/2203.05940/) (2022)
- [P2P-Bridge: Diffusion Bridges for 3D Point Cloud Denoising](https://mlsanity.com/paper/2408.16325/) (2024)
- [Fast Learning of Signed Distance Functions from Noisy Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2407.14225/) (2024)
- [PC2-PU: Patch Correlation and Point Correlation for Effective Point Cloud Upsampling](https://mlsanity.com/paper/2109.09337/) (2021)
- [PCDNF: Revisiting Learning-based Point Cloud Denoising via Joint Normal Filtering](https://mlsanity.com/paper/2209.00798/) (2022)
- [PointCAT: Contrastive Adversarial Training for Robust Point Cloud Recognition](https://mlsanity.com/paper/2209.07788/) (2022)
- [StraightPCF: Straight Point Cloud Filtering](https://mlsanity.com/paper/2405.08322/) (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)
- [SLiDE: Self-supervised LiDAR De-snowing through Reconstruction Difficulty](https://mlsanity.com/paper/2208.04043/) (2022)
- [Point Cloud Denoising via Momentum Ascent in Gradient Fields](https://mlsanity.com/paper/2202.10094/) (2022)
- [Dynamic Point Cloud Denoising via Gradient Fields](https://mlsanity.com/paper/2204.08755/) (2022)
- [Deep Learning for 3D Point Cloud Enhancement: A Survey](https://mlsanity.com/paper/2411.00857/) (2024)
- [Noise2Score3D: Tweedie's Approach for Unsupervised Point Cloud Denoising](https://mlsanity.com/paper/2503.09283/) (2025)
- [Fast graph-based denoising for point cloud color information](https://mlsanity.com/paper/2401.09721/) (2024)
- [Joint Point Cloud Upsampling and Cleaning with Octree-based CNNs](https://mlsanity.com/paper/2410.17001/) (2024)
- [Robust 3D Object Detection using Probabilistic Point Clouds from Single-Photon LiDARs](https://mlsanity.com/paper/2508.00169/) (2025)
- [U-CAN: Unsupervised Point Cloud Denoising with Consistency-Aware Noise2Noise Matching](https://mlsanity.com/paper/2510.25210/) (2025)
- [Rethinking Point Cloud Filtering: A Non-Local Position Based Approach](https://mlsanity.com/paper/2110.07253/) (2021)
- [NoiseTrans: Point Cloud Denoising with Transformers](https://mlsanity.com/paper/2304.11812/) (2023)
- [Point Cloud Resampling with Learnable Heat Diffusion](https://mlsanity.com/paper/2411.14120/) (2024)
- [Noise-Injected Spiking Graph Convolution for Energy-Efficient 3D Point Cloud Denoising](https://mlsanity.com/paper/2502.19660/) (2025)
- [Learning Normals of Noisy Points by Local Gradient-Aware Surface Filtering](https://mlsanity.com/paper/2507.03394/) (2025)
- [Graph-Based Depth Denoising & Dequantization for Point Cloud Enhancement](https://mlsanity.com/paper/2111.04946/) (2021)

## Abstract (arXiv)

3D point clouds are often perturbed by noise due to the inherent limitation of acquisition equipments, which obstructs downstream tasks such as surface reconstruction, rendering and so on. Previous works mostly infer the displacement of noisy points from the underlying surface, which however are not designated to recover the surface explicitly and may lead to sub-optimal denoising results. To this end, we propose to learn the underlying manifold of a noisy point cloud from differentiably subsampled points with trivial noise perturbation and their embedded neighborhood feature, aiming to capture intrinsic structures in point clouds. Specifically, we present an autoencoder-like neural network. The encoder learns both local and non-local feature representations of each point, and then samples points with low noise via an adaptive differentiable pooling operation. Afterwards, the decoder infers the underlying manifold by transforming each sampled point along with the embedded feature of its neighborhood to a local surface centered around the point. By resampling on the reconstructed manifold, we obtain a denoised point cloud. Further, we design an unsupervised training loss, so that our network can be trained in either an unsupervised or supervised fashion. Experiments show that our method significantly outperforms state-of-the-art denoising methods under both synthetic noise and real world noise. The code and data are available at https://github.com/luost26/DMRDenoise