# Dynamic Point Cloud Denoising via Manifold-to-Manifold Distance

arXiv: https://arxiv.org/abs/2003.08355 · HTML: https://mlsanity.com/paper/2003.08355/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Mar 2020.

## Built on by (most cited first, 12 of 12)

- [Score-Based Point Cloud Denoising](https://mlsanity.com/paper/2107.10981/) (2021)
- [Deep Point Set Resampling via Gradient Fields](https://mlsanity.com/paper/2111.02045/) (2021)
- [PUFA-GAN: A Frequency-Aware Generative Adversarial Network for 3D Point Cloud Upsampling](https://mlsanity.com/paper/2203.00914/) (2022)
- [GQE-Net: A Graph-based Quality Enhancement Network for Point Cloud Color Attribute](https://mlsanity.com/paper/2303.13764/) (2023)
- [MODNet: Multi-offset Point Cloud Denoising Network Customized for Multi-scale Patches](https://mlsanity.com/paper/2208.14160/) (2022)
- [High Efficiency Wiener Filter-based Point Cloud Quality Enhancement for MPEG G-PCC](https://mlsanity.com/paper/2503.17467/) (2025)
- [Dynamic Point Cloud Denoising via Gradient Fields](https://mlsanity.com/paper/2204.08755/) (2022)
- [NoiseTrans: Point Cloud Denoising with Transformers](https://mlsanity.com/paper/2304.11812/) (2023)
- [Gradient-based Point Cloud Denoising with Uniformity](https://mlsanity.com/paper/2207.10279/) (2022)
- [Incomplete Gamma Kernels: Generalizing Locally Optimal Projection Operators](https://mlsanity.com/paper/2205.01087/) (2022)
- [NSANet: Noise Seeking Attention Network](https://mlsanity.com/paper/2302.13392/) (2023)
- [Rotation Perturbation Robustness in Point Cloud Analysis: A Perspective of Manifold Distillation](https://mlsanity.com/paper/2411.01748/) (2024)

## Abstract (arXiv)

3D dynamic point clouds provide a natural discrete representation of real-world objects or scenes in motion, with a wide range of applications in immersive telepresence, autonomous driving, surveillance, etc. Nevertheless, dynamic point clouds are often perturbed by noise due to hardware, software or other causes. While a plethora of methods have been proposed for static point cloud denoising, few efforts are made for the denoising of dynamic point clouds, which is quite challenging due to the irregular sampling patterns both spatially and temporally. In this paper, we represent dynamic point clouds naturally on spatial-temporal graphs, and exploit the temporal consistency with respect to the underlying surface (manifold). In particular, we define a manifold-to-manifold distance and its discrete counterpart on graphs to measure the variation-based intrinsic distance between surface patches in the temporal domain, provided that graph operators are discrete counterparts of functionals on Riemannian manifolds. Then, we construct the spatial-temporal graph connectivity between corresponding surface patches based on the temporal distance and between points in adjacent patches in the spatial domain. Leveraging the initial graph representation, we formulate dynamic point cloud denoising as the joint optimization of the desired point cloud and underlying graph representation, regularized by both spatial smoothness and temporal consistency. We reformulate the optimization and present an efficient algorithm. Experimental results show that the proposed method significantly outperforms independent denoising of each frame from state-of-the-art static point cloud denoising approaches, on both Gaussian noise and simulated LiDAR noise.