# 3D Point Cloud Denoising using Graph Laplacian Regularization of a Low Dimensional Manifold Model

arXiv: https://arxiv.org/abs/1803.07252 · HTML: https://mlsanity.com/paper/1803.07252/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2018.

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

- [Neural Scene Flow Prior](https://mlsanity.com/paper/2111.01253/) (2021)
- [Score-Based Point Cloud Denoising](https://mlsanity.com/paper/2107.10981/) (2021)
- [Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --](https://mlsanity.com/paper/2301.03362/) (2023)
- [Look Inside for More: Internal Spatial Modality Perception for 3D Anomaly Detection](https://mlsanity.com/paper/2412.13461/) (2024)
- [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)
- [Boosting 3D Adversarial Attacks with Attacking On Frequency](https://mlsanity.com/paper/2201.10937/) (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)
- [GQE-Net: A Graph-based Quality Enhancement Network for Point Cloud Color Attribute](https://mlsanity.com/paper/2303.13764/) (2023)
- [Geometric Graph Filters and Neural Networks: Limit Properties and Discriminability Trade-offs](https://mlsanity.com/paper/2305.18467/) (2023)
- [Advancing 3D Point Cloud Understanding through Deep Transfer Learning: A Comprehensive Survey](https://mlsanity.com/paper/2407.17877/) (2024)
- [MODNet: Multi-offset Point Cloud Denoising Network Customized for Multi-scale Patches](https://mlsanity.com/paper/2208.14160/) (2022)
- [Enhancing Diffusion-based Point Cloud Generation with Smoothness Constraint](https://mlsanity.com/paper/2404.02396/) (2024)
- [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)
- [Convolutional Filtering on Sampled Manifolds](https://mlsanity.com/paper/2211.11058/) (2022)
- [GraphReg: Dynamical Point Cloud Registration with Geometry-aware Graph Signal Processing](https://mlsanity.com/paper/2302.01109/) (2023)
- [GeodesicPSIM: Predicting the Quality of Static Mesh with Texture Map via Geodesic Patch Similarity](https://mlsanity.com/paper/2308.04928/) (2023)
- [Noise2Score3D: Tweedie's Approach for Unsupervised Point Cloud Denoising](https://mlsanity.com/paper/2503.09283/) (2025)
- [Self-Supervised Multi-Frame Neural Scene Flow](https://mlsanity.com/paper/2403.16116/) (2024)
- [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)
- [Towards Uniform Point Distribution in Feature-preserving Point Cloud Filtering](https://mlsanity.com/paper/2201.01503/) (2022)
- [NoiseTrans: Point Cloud Denoising with Transformers](https://mlsanity.com/paper/2304.11812/) (2023)
- [Retinex-based Image Denoising / Contrast Enhancement using Gradient Graph Laplacian Regularizer](https://mlsanity.com/paper/2307.02625/) (2023)
- [Graph-Based Depth Denoising & Dequantization for Point Cloud Enhancement](https://mlsanity.com/paper/2111.04946/) (2021)
- [Gradient-based Point Cloud Denoising with Uniformity](https://mlsanity.com/paper/2207.10279/) (2022)
- [Linear optimal transport subspaces for point set classification](https://mlsanity.com/paper/2403.10015/) (2024)

## Abstract (arXiv)

3D point cloud - a new signal representation of volumetric objects - is a discrete collection of triples marking exterior object surface locations in 3D space. Conventional imperfect acquisition processes of 3D point cloud - e.g., stereo-matching from multiple viewpoint images or depth data acquired directly from active light sensors - imply non-negligible noise in the data. In this paper, we adopt a previously proposed low-dimensional manifold model for the surface patches in the point cloud and seek self-similar patches to denoise them simultaneously using the patch manifold prior. Due to discrete observations of the patches on the manifold, we approximate the manifold dimension computation defined in the continuous domain with a patch-based graph Laplacian regularizer and propose a new discrete patch distance measure to quantify the similarity between two same-sized surface patches for graph construction that is robust to noise. We show that our graph Laplacian regularizer has a natural graph spectral interpretation, and has desirable numerical stability properties via eigenanalysis. Extensive simulation results show that our proposed denoising scheme can outperform state-of-the-art methods in objective metrics and can better preserve visually salient structural features like edges.