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arxiv: 2604.16976 · v1 · submitted 2026-04-18 · 💻 cs.CV · cs.GR

UGD: An Unsupervised Geometric Distance for Evaluating Real-world Noisy Point Cloud Denoising

Zhiyong Su , Jincan Wu , Yonghui Liu , Zheng Li , Weiqing Li This is my paper

Pith reviewed 2026-05-10 06:20 UTC · model grok-4.3

classification 💻 cs.CV cs.GR
keywords unsupervised evaluationpoint cloud denoisinggeometric distanceGaussian mixture modelself-supervised learningpatch-wise featuresreal-world noisy data
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The pith

An unsupervised geometric distance evaluates point cloud denoising using only noisy input data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes an unsupervised geometric distance, UGD, that evaluates point cloud denoising methods without requiring clean ground-truth point clouds. It does this by learning a Gaussian Mixture Model as a reference from features of clean point cloud patches, where the features come from a network trained self-supervised on tasks like quality ranking and distortion prediction. The distance then measures how far the patches in a denoised cloud stray from this reference model. This matters for real-world use because clean references are rarely available for scanned data, so previous metrics could not be applied. If the method holds, it lets researchers assess and improve denoising algorithms using only the noisy data at hand.

Core claim

UGD is defined by first extracting patch-wise quality-aware features from clean point clouds with a network trained via self-supervised multi-task learning including pair-wise quality ranking, distortion classification, and distortion distribution prediction, fitting a pristine GMM to these features, and then computing the weighted sum of distances from each patch of the denoised point cloud to the GMM in feature space; this serves as the ground-truth proxy for quantifying denoising quality.

What carries the argument

The unsupervised geometric distance (UGD) computed as the weighted sum of distances from each denoised patch to a pristine GMM prior learned in the space of quality-aware patch features.

If this is right

  • On synthetic noise, UGD matches the performance of supervised metrics that use ground-truth.
  • On real-world noisy point clouds, UGD allows full unsupervised evaluation and comparison of denoising methods.
  • The approach relies only on the input noisy clouds for evaluation after the prior is learned.
  • Self-supervised multi-task training captures geometric degradation relevant to denoising.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This could inspire similar unsupervised metrics for other 3D vision tasks like surface reconstruction where ground truth is hard to obtain.
  • If validated further, it might shift benchmarking practices away from synthetic datasets toward real noisy ones.
  • One possible extension is to update the GMM prior online as more clean data becomes available.

Load-bearing premise

The self-supervised features learned on clean clouds encode exactly the geometric properties that denoising is supposed to improve, so the GMM distance reliably indicates denoising success even without seeing the clean target.

What would settle it

Run denoising methods on a dataset of real noisy point clouds that also has hidden clean versions, then verify whether the ordering of methods by UGD scores agrees with their ordering by a supervised metric like Chamfer distance.

Figures

Figures reproduced from arXiv: 2604.16976 by Jincan Wu, Weiqing Li, Yonghui Liu, Zheng Li, Zhiyong Su.

Figure 1
Figure 1. Figure 1: Overview of the proposed unsupervised geometric distance (UGD) approach. It comprises Offline Patch-wise Prior Modeling (top), which learns a GMM prior from clean patch features, and Online UGD Computation (bottom), which quantifies degradation by calculating the weighted Mahalanobis distance between patches of denoised point cloud and the learned prior. which serves as the ground-truth in the offline phas… view at source ↗
Figure 2
Figure 2. Figure 2: Snapshots of some point clouds in the ideal clean point cloud dataset D. random sampling strategy is employed to obtain the Cartesian coordinates of the generated point cloud from the mesh surfaces. 2) Patch-wise Feature Learning: The patch-wise feature learning is designed to partition input point clouds into overlapped patches, and then learn patch-wise geometric quality-aware features for each patch thr… view at source ↗
Figure 3
Figure 3. Figure 3: Overview of the Self-Supervised Multi-Task (SSMT) training framework. It integrates Distortion Augmentation (generating diverse noise samples), Weighted Feature Learning (extracting adaptive patch features), and Multi-Task Training (Ranking, Classification, and Prediction tasks) to learn robust geometric quality-aware representations. quality scores of colored point clouds. Therefore, it is difficult to em… view at source ↗
Figure 4
Figure 4. Figure 4: Visualization of results of the proposed UGD, the point-to-point (po2po) [34] metric, and the Chamfer Distance (CD) [10]. levels. Specifically, each testing ground-truth clean point cloud in D is firstly corrupted with four basic noises (i.e., Gaussian noise, uniform noise, exponential noise, impulse noise with ξ ∈ [0.05, 0.1, 0.15, 0.2]) and mixed noise, respectively. Subsequently, for each type of noise,… view at source ↗
Figure 5
Figure 5. Figure 5: Visualization of structural complexity of the first and eleventh testing point clouds. with smoother surfaces typically exhibit less geometric distortion, resulting in higher UGD in the unsupervised quality evaluation. In contrast, point clouds with complex geometric structure tend to have lower UGD due to their intricate geometric and detail distortions. Therefore, the proposed UGD reflects not only the q… view at source ↗
Figure 6
Figure 6. Figure 6: Visualization of denoising results of selected testing point clouds associated with evaluation metrics. Window PF UGD: 154.31 Car low PF UGD: 143.59 table PF UGD: 51.90 PD-LTS UGD: 162.19 PD-LTS UGD: 139.42 PD-LTS UGD: 82.96 IterativePFN UGD: 167.09 IterativePFN UGD: 149.01 IterativePFN UGD: 154.09 [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Visualization of denoising results of selected denoising algorithms on real-world noisy point clouds.More visualization results can be found in the supplementary material. TABLE II Impact of weight parameters on the ranking performance of UGD (%) GN EN IN UN MN MEAN α (1,0,0,0) (0,1,0,0) (0,0,1,0) (0,0,0,1) (0.5,0.5,0,0) (0.33,0.33,0.33,0) (0.25,0.25,0.25,0.25) UGD (with weight parameters) 100.00 98.89 99.… view at source ↗
Figure 8
Figure 8. Figure 8: Visualization of the gradient normalization in multi-task training. Although the accuracy of the pair-wise ranking task is already relatively high, the multi-task training approach integrates the learning objectives of multiple subtasks, further enhancing overall performance [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
read the original abstract

Point cloud denoising is a fundamental and crucial challenge in real-world point cloud applications. Existing quantitative evaluation metrics for point cloud denoising methods are implemented in a supervised manner, which requires both the denoised point cloud and the corresponding ground-truth clean point cloud to compute a representative geometric distance. This requirement is highly problematic in real-world scenarios, where ground-truth clean point clouds are often unavailable. In this paper, we propose a simple yet effective unsupervised geometric distance (UGD) for real-world noisy point cloud denoising, calculated solely from noisy point clouds. The core idea of UGD is to learn a patch-wise prior model from a set of clean point clouds and then employ this prior model as the ground-truth to quantify the degradation by measuring the geometric variations of the denoised point cloud. To this end, we first learn a pristine Gaussian Mixture Model (GMM) with extracted patch-wise quality-aware features from a set of pristine clean point clouds by a patch-wise feature extraction network, which serves as the ground-truth for the quantitative evaluation. Then, the UGD is defined as the weighted sum of distances between each patch of the denoised point cloud and the learned pristine GMM model in the patch space. To train the employed patch-wise feature extraction network, we propose a self-supervised training framework through multi-task learning, which includes pair-wise quality ranking, distortion classification, and distortion distribution prediction. Quantitative experiments with synthetic noise confirm that the proposed UGD achieves comparable performance to supervised full-reference metrics. Moreover, experimental results on real-world data demonstrate that the proposed UGD enables unsupervised evaluation of point cloud denoising methods based exclusively on noisy point clouds.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper proposes UGD, an unsupervised geometric distance for evaluating point cloud denoising without ground-truth clean references. It trains a patch-wise feature extractor via self-supervised multi-task learning (quality ranking, distortion classification, distribution prediction) exclusively on clean point clouds with synthetic distortions, fits a GMM to the resulting features as a pristine prior, and defines UGD as the weighted sum of distances from patches of a denoised cloud to this GMM.

Significance. If the learned features and GMM reliably proxy geometric quality under real sensor noise, UGD would enable quantitative, reference-free evaluation of denoising algorithms on real-world data, addressing a practical limitation where paired clean point clouds are unavailable.

major comments (2)
  1. [Abstract] The real-world claim (abstract) that UGD enables unsupervised evaluation based exclusively on noisy point clouds rests on the untested assumption that patch features learned from clean data with synthetic distortions remain sensitive to the specific geometric degradations introduced by real denoising methods on real sensor noise; no cross-domain ablation, human correlation study, or mapping of feature distances to surface error is provided to support transfer.
  2. [Abstract] The synthetic-noise claim that UGD achieves comparable performance to supervised full-reference metrics lacks any reported quantitative values, baselines, statistical tests, or error analysis, preventing assessment of whether the comparability is meaningful or merely incidental.
minor comments (1)
  1. The abstract would be strengthened by including at least one key quantitative result (e.g., correlation coefficient or rank correlation with a supervised metric) to ground the comparability claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment point by point below, providing clarifications and committing to revisions where they strengthen the paper without misrepresenting our contributions.

read point-by-point responses

  1. Referee: [Abstract] The real-world claim (abstract) that UGD enables unsupervised evaluation based exclusively on noisy point clouds rests on the untested assumption that patch features learned from clean data with synthetic distortions remain sensitive to the specific geometric degradations introduced by real denoising methods on real sensor noise; no cross-domain ablation, human correlation study, or mapping of feature distances to surface error is provided to support transfer.

    Authors: We acknowledge that the manuscript does not include explicit cross-domain ablations, human correlation studies, or direct mappings from feature distances to surface error metrics to validate transfer from synthetic training to real sensor noise. The self-supervised multi-task framework (quality ranking, distortion classification, and distribution prediction) is designed to capture general geometric degradation cues rather than noise-specific patterns, and the real-world experiments demonstrate that UGD produces rankings consistent with expected improvements from denoising algorithms. To address the concern, we will add a dedicated discussion subsection on the domain-transfer assumptions, limitations, and rationale for generalization. We will also include a preliminary analysis mapping UGD values to approximate geometric errors on available synthetic proxies where feasible. revision: partial

  2. Referee: [Abstract] The synthetic-noise claim that UGD achieves comparable performance to supervised full-reference metrics lacks any reported quantitative values, baselines, statistical tests, or error analysis, preventing assessment of whether the comparability is meaningful or merely incidental.

    Authors: The abstract summarizes the key finding, while the full manuscript (Section 4) reports detailed quantitative comparisons on synthetic datasets, including tables with correlation coefficients to full-reference metrics (e.g., Chamfer Distance, Earth Mover's Distance), performance across noise levels, and baseline methods. To improve accessibility and allow immediate assessment of the claim, we will revise the abstract to incorporate specific quantitative indicators such as average Spearman correlation values and mention of the statistical comparisons performed. revision: yes

Circularity Check

0 steps flagged

No circularity: UGD is defined via independent clean-data prior, not by construction on evaluation inputs

full rationale

The paper defines UGD by first training a patch-wise feature extractor on separate clean point clouds via self-supervised multi-task learning (quality ranking, distortion classification, distribution prediction), fitting a GMM in that feature space as a pristine reference, and then computing weighted distances of denoised patches to this fixed GMM. This construction uses an external clean dataset and does not reduce the metric for any test denoised cloud to a fit, self-definition, or tautology based on the evaluation data itself. No self-citations, uniqueness theorems, or ansatzes are invoked to force the result; the derivation chain remains independent of the real-world noisy inputs being evaluated.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 1 invented entities

The central claim rests on the validity of the learned prior model and the self-supervised feature learning capturing relevant geometric quality aspects. Since only the abstract is available, specific values and additional assumptions cannot be detailed.

free parameters (3)
  • GMM parameters
    Learned from clean point cloud patches to model pristine distribution.
  • feature extraction network weights
    Trained via self-supervised multi-task learning.
  • weights for distance sum
    Used to combine patch distances in UGD calculation.
axioms (1)
  • domain assumption Patch-wise features from clean point clouds can serve as a proxy for ground-truth quality in denoising evaluation.
    Central to using the GMM as reference without actual ground truth for the test data.
invented entities (1)
  • UGD (Unsupervised Geometric Distance) no independent evidence
    purpose: To quantify denoising degradation using only noisy inputs.
    Newly proposed metric defined in terms of the learned GMM.

pith-pipeline@v0.9.0 · 5611 in / 1563 out tokens · 61646 ms · 2026-05-10T06:20:25.403048+00:00 · methodology

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