Source-linked AI summary
Score-Based Point Cloud Denoising
Shitong Luo, Wei Hu
TL;DR
Point clouds are noisy, which harms downstream reconstruction and analysis, while existing denoising approaches face geometric-prior and detail-preservation challenges. The paper estimates the score of a noise-convolved point distribution from noisy inputs and uses gradient ascent for denoising. Experiments report superior performance under varied noise models and potential for point cloud upsampling.
Problem
Noise perturbs point clouds and affects downstream reconstruction and analysis, while existing methods face a trade-off between geometric-prior reliance, detail preservation, and denoising effectiveness.
Method
The method estimates the score ∇x log[(p * n)(x)] of the noise-convolved distribution from noisy point clouds and denoises them by gradient ascent toward its mode.
Results
The proposed model outperforms state-of-the-art methods under a variety of noise models and shows potential for point cloud upsampling.
Takeaways & Limitations
Score-guided gradient ascent provides a denoising framework that the paper reports as robust to artifacts such as shrinkage and outliers.
Takeaways & Limitations
The analysis assumes continuous noise with a unique mode at 0, although experiments report strong performance in some cases where these assumptions do not hold.
Abstract
from arXiv · showhide
Point clouds acquired from scanning devices are often perturbed by noise, which affects downstream tasks such as surface reconstruction and analysis. The distribution of a noisy point cloud can be viewed as the distribution of a set of noise-free samples $p(x)$ convolved with some noise model $n$, leading to $(p * n)(x)$ whose mode is the underlying clean surface. To denoise a noisy point cloud, we propose to increase the log-likelihood of each point from $p * n$ via gradient ascent -- iteratively updating each point's position. Since $p * n$ is unknown at test-time, and we only need the score (i.e., the gradient of the log-probability function) to perform gradient ascent, we propose a neural network architecture to estimate the score of $p * n$ given only noisy point clouds as input. We derive objective functions for training the network and develop a denoising algorithm leveraging on the estimated scores. Experiments demonstrate that the proposed model outperforms state-of-the-art methods under a variety of noise models, and shows the potential to be applied in other tasks such as point cloud upsampling. The code is available at \url{https://github.com/luost26/score-denoise}.
1. Introduction
Point cloud denoising is important but difficult because noise deforms structures and point clouds are irregular and unordered. The paper proposes estimating the score of a noise-convolved distribution and using gradient ascent to move noisy points toward the clean surface.
- Motivation: Noise deforms underlying point-cloud structures, affecting downstream tasks such as rendering, reconstruction, and analysis.
- Motivation: Point cloud denoising is challenging because point clouds are irregularly sampled from continuous surfaces and have irregular, unordered characteristics.
- Existing approaches: Prior optimization-based methods rely heavily on geometric priors and can trade off detail preservation against denoising effectiveness.
- Proposed approach: The proposed paradigm models noisy points with the convolution (p * n)(x), whose mode corresponds to the underlying clean surface, and denoises by gradient ascent on its log-probability.
- Proposed approach: The method estimates the unknown score ∇x log[(p * n)(x)] from noisy point clouds using a neural network, then applies the estimated score for denoising.
- Contributions: Extensive experiments report performance under a variety of noise models and potential application to point cloud upsampling.
2. Related Work
Prior denoising methods use geometric priors, displacement prediction, or manifold reconstruction, while score matching motivates a distinct framework that models noisy-point distributions directly.
- Optimization-based methods rely on geometric priors and may trade detail preservation against denoising effectiveness.
- Deep-learning denoisers commonly predict each noisy point’s displacement, but inaccurate displacement estimates can produce shrinkage and outliers.
- Downsample-upsample reconstruction approaches can lose details, especially when noise levels are low.
- The proposed framework instead performs gradient ascent using an estimated noisy-distribution log-density gradient, alleviating shrinkage and outliers.
- Unlike generative score models such as ShapeGF, this method models the noise-convolved distribution and uses local score functions for arbitrary-shape generalization.
3. Method
The method estimates local scores of the noise-convolved point-cloud distribution and denoises by gradient ascent, using neighborhood-aware training and ensemble scores.
- The noisy point-cloud distribution is modeled as p ∗ n, whose mode corresponds to the underlying clean surface.
- A neural network estimates point-wise scores ∇x log[(p ∗ n)(xi)] from only the noisy input point cloud.
- Local score functions focus estimation on neighborhoods around each point, supporting generalization by learning basic 3D shape fragments.
- The score estimation unit combines each point’s feature with a nearby coordinate and predicts its localized score using an MLP.
- Training matches predicted and ground-truth scores throughout each point’s neighborhood, so scores remain available as points move during gradient ascent.
- An ensemble score aggregates neighboring local scores to improve robustness and reduce estimation bias before updating points by gradient ascent.
- The step-size sequence decreases toward zero, with an initial value below 1 to support convergence and avoid over-denoising.
- The method reports no shrinkage-induced artifacts, eliminating the need for post-processing used by some prior deep-learning denoisers.
4. Analysis
The paper models noisy point clouds as samples from a convolution of a clean-surface distribution and a noise distribution, whose mode recovers the underlying surface under mild assumptions. It then denoises by gradient ascent using an estimated score rather than the unknown density itself.
- A noise-free point cloud is modeled as samples from a 3D distribution p supported on 2D manifolds.
- A noisy point cloud adds noise samples to clean points, with a continuous noise density assumed to have a unique mode at 0.
- The noisy-point distribution is the convolution of the clean distribution p and noise distribution n.
- When the noise mode is 0 and the distribution is unimodal, the clean manifold is the mode of the noisy distribution q.
- Denoising maximizes the log-density of each point through gradient ascent, requiring only the score ∇x log q(x).Because q is unknown at test time, the method estimates its score from noisy point clouds using a detail-preserving neural network and trains it with a score-matching objective.
5. Experiments
Experiments evaluate the method on synthetic and real-world point clouds against deep-learning and optimization-based denoisers. The method performs strongly across noise types, preserves details qualitatively, and also supports point-cloud upsampling.
- Setup: Training uses 20 meshes sampled at 10K–50K points and perturbed with Gaussian noise at 0.5%–2% of the bounding-sphere radius.
- Setup: Evaluation uses PU-Net and PointCleanNet test sets, multiple synthetic noise models, and the real-world Paris-rue-Madame laser-scanner dataset.
- Setup: The method is compared with deep-learning denoisers PointCleanNet and DMRDenoise and optimization-based denoisers including bilateral filtering, jet fitting, MRPCA, and GLR.
- Quantitative Results: Under isotropic Gaussian noise, the model significantly outperforms previous deep-learning methods in all settings and surpasses optimization-based methods in most cases.Noise standard deviations range from 1% to 3% of the shape’s bounding-sphere radius; evaluation uses Chamfer distance and point-to-mesh distance.
- Quantitative Results: Despite Gaussian-only training, the denoiser generalizes to unseen simulated LiDAR noise and outperforms previous methods.
- Quantitative Results: Across non-isotropic Gaussian, uni-directional, Laplace, uniform, and discrete noise, the model outperforms competing baselines in most settings.
- Qualitative Results: Visual comparisons report cleaner results, better detail preservation, and greater outlier robustness than competing methods under Gaussian and simulated LiDAR noise.On Paris-rue-Madame, the result is cleaner and smoother than PCNet while preserving details better than DMRDenoise; the trajectory shows convergence toward the mode of p ∗n.
- Ablation Studies: All three main design components contribute positively to denoising performance in ablation studies.The components are the score-based update, neighborhood-covering training objective, and ensemble score function.
6. Conclusions
The paper presents point cloud denoising as score-guided gradient ascent on a noise-convolved distribution. Its results also indicate potential beyond denoising, including point cloud upsampling.
- The method models noisy point clouds as samples from a noise-convolved distribution.
- A neural network estimates the distribution score, which guides gradient-ascent denoising.
- The model shows potential for other point cloud tasks such as upsampling.