- The paper introduces UGD, an unsupervised geometric metric that evaluates noisy point cloud denoising without requiring paired ground-truth data.
- It employs a self-supervised Point Cloud Transformer and a GMM-based prior to extract patch-level descriptors, achieving 99.29% ranking accuracy across various noise types.
- UGD reliably benchmarks denoising methods on real-world LiDAR scans, correlating well with human visual assessments and exposing limitations of traditional metrics.
UGD: An Unsupervised Geometric Distance for Evaluating Real-world Noisy Point Cloud Denoising
Introduction and Problem Statement
Point cloud denoising is critical in 3D vision, graphics, and downstream tasks such as registration and reconstruction, yet robust evaluation remains a bottleneck due to limited access to ground-truth clean data in real-world scenarios. Traditional metrics like Hausdorff Distance, Chamfer Distance, and PSNR necessitate paired ground-truth and denoised point clouds, making them unsuitable outside curated synthetic datasets. Subjective or qualitative assessments are the dominant practice on real-world data, limiting comparability and quantitative benchmarking. Prior works on No-Reference (NR) PCQA provide score prediction for colored, perceptually-distorted points, yet are not directly applicable to the geometry-only, structure-focused denoising evaluation required in many practical scenarios.
This paper addresses the absence of an unsupervised, reference-free geometric metric for real-world noisy point cloud denoising by introducing UGD (Unsupervised Geometric Distance). UGD is computed solely from denoised or noisy point clouds and a set of pristine reference models, allowing objective, quantitative analysis without requiring ground-truth counterparts.
UGD Methodology
The UGD pipeline comprises offline prior modeling and online evaluation phases.
Offline Phase: A large, diverse collection of clean point clouds is segmented into overlapping local patches via farthest point sampling and grouping. Patch-level, geometry-aware descriptors are then extracted using a self-supervisedly trained Point Cloud Transformer (PCT) backbone. These descriptors populate the clean patch feature space, over which a multivariate Gaussian Mixture Model (GMM) is trained. This GMM serves as a surrogate, statistical reference encoding the "natural" geometry distribution of clean, uncorrupted data.
Online Phase: Patches are extracted from a denoised point cloud, and descriptors are computed using the same feature extractor. For each descriptor, UGD calculates a weighted Mahalanobis distance to the reference GMM components. Patch-wise scores are aggregated, weighted by learned patch importance via a secondary network (WPNet). The final UGD score reflects the consistency of the evaluated point cloud with the learned manifold of clean geometry.
(Figure 1)
Figure 1: Visualization of results of the proposed UGD, the point-to-point (po2po), and the Chamfer Distance (CD) metrics (Figure 2).
The self-supervised feature extractor is trained via a multi-task objective combining pair-wise ranking (relative quality), distortion classification, and distortion distribution prediction, leveraging synthesized distortions (Gaussian, uniform, impulse, exponential, and mixtures) across a range of strengths.
Experimental Evaluation
Synthetic Noise Discrimination and Ranking
Extensive experiments are conducted using a 150-shape clean dataset built from ModelNet and the Stanford 3D Scanning Repository. Quantitative results demonstrate that UGD achieves 99.29% mean pair-wise ranking accuracy across five distortion types and several noise levels, closely matching or surpassing most supervised full-reference metrics (po2po, po2pl, CD), with the exception of anomalous performance in normal-based metrics (pl2pl).
Denoising Algorithm Benchmarking
Benchmarking typical denoising pipelines (e.g., PointFilter, PD-LTS, IterativePFN) on G-PCD, UGD's ranking is consistent with supervised metrics and aligns well with subjective visual quality. Notably, UGD penalizes over-smoothed outputs that degrade important geometric features, capturing detrimental denoising artifacts that traditional metrics often miss.
Real-world Scan Assessment
In the absence of ground-truth, UGD enables discrimination among denoising algorithms on real LiDAR datasets (TerraMobilita, LiDAR-Net). Visualizations confirm that UGD positively correlates with human-perceived geometric fidelity in complex, large-scale, and highly noisy scenes, where supervised metrics are not feasible.
Ablation and Sensitivity Analysis
Ablations show the critical impact of patch weight prediction and feature backbone. Removing patch weights drops the ranking accuracy from 99.29% to 85.77%. Switching PCT to DGCNN reduces mean accuracy to 91.67%. The multi-task supervision in feature extraction also yields significant gains over single-task setups, supporting the effectiveness of robust, distortion-aware representations.
Theoretical and Practical Implications
The core theoretical contribution is the shift from ground-truth-based geometric quality assessment to prior-based, distributional self-supervision. UGD enables unsupervised benchmarking of denoising techniques, increasing reproducibility and scalability in real-world applications. Its GMM-based prior implicitly encodes the geometry manifold of clean surfaces and can adapt with dataset diversity.
One limitation is a potential bias towards regular, smooth structures if the "clean prior" lacks adequate complexity. UGD may sometimes elevate over-smoothed denoising artifacts if the prior is unbalanced, highlighting the need for structurally diverse training data and potentially adaptive or hierarchical GMMs. Furthermore, UGD is inherently a relative metric—meaningful mainly for model selection or intra-set comparisons under fixed priors.
Future Directions
- Extending prior modeling to encompass more intricate geometries, increasing robustness on highly detailed or non-uniform scans.
- Integrating perceptual cues (when available) and exploring fusion with color or attribute-aware features.
- Adapting GMM priors in a semi-supervised or domain-adaptive fashion to reduce bias toward over-represented structural types.
- Benchmarking UGD on downstream, task-critical applications to assess correlation with ultimate system performance metrics.
Conclusion
UGD provides a scalable, unsupervised, and objective geometric metric for evaluating point cloud denoising algorithms under real-world conditions. Its GMM-based prior bridges the quantitative assessment gap for denoising in the absence of ground-truth, effectively correlating with traditional metrics and human judgments, while exposing new avenues for research in unsupervised, distributional quality analysis of geometric data.
