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

arXiv: https://arxiv.org/abs/2604.16976 · HTML: https://mlsanity.com/paper/2604.16976/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 70 references that are in the map.
- First posted on arXiv 18 Apr 2026.

## Builds on (most cited first, 30 of 31)

- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [RankIQA: Learning from Rankings for No-reference Image Quality Assessment](https://mlsanity.com/paper/1707.08347/) (2017)
- [PointCleanNet: Learning to Denoise and Remove Outliers from Dense Point Clouds](https://mlsanity.com/paper/1901.01060/) (2019)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [Score-Based Point Cloud Denoising](https://mlsanity.com/paper/2107.10981/) (2021)
- [dipIQ: Blind Image Quality Assessment by Learning-to-Rank Discriminable Image Pairs](https://mlsanity.com/paper/1904.06505/) (2019)
- [Total Denoising: Unsupervised Learning of 3D Point Cloud Cleaning](https://mlsanity.com/paper/1904.07615/) (2019)
- [Inferring Point Cloud Quality via Graph Similarity](https://mlsanity.com/paper/2006.00497/) (2020)
- [Point Cloud Quality Assessment: Dataset Construction and Learning-based No-Reference Metric](https://mlsanity.com/paper/2012.11895/) (2020)
- [Differentiable Manifold Reconstruction for Point Cloud Denoising](https://mlsanity.com/paper/2007.13551/) (2020)
- [Pointfilter: Point Cloud Filtering via Encoder-Decoder Modeling](https://mlsanity.com/paper/2002.05968/) (2020)
- [Perceptual Quality Assessment of Colored 3D Point Clouds](https://mlsanity.com/paper/2111.05474/) (2021)
- [No-Reference Point Cloud Quality Assessment via Domain Adaptation](https://mlsanity.com/paper/2112.02851/) (2021)
- [Reduced Reference Perceptual Quality Model and Application to Rate Control for 3D Point Cloud Compression](https://mlsanity.com/paper/2011.12688/) (2020)
- [IterativePFN: True Iterative Point Cloud Filtering](https://mlsanity.com/paper/2304.01529/) (2023)
- [GPA-Net:No-Reference Point Cloud Quality Assessment with Multi-task Graph Convolutional Network](https://mlsanity.com/paper/2210.16478/) (2022)
- [GMS-3DQA: Projection-based Grid Mini-patch Sampling for 3D Model Quality Assessment](https://mlsanity.com/paper/2306.05658/) (2023)
- [PD-Flow: A Point Cloud Denoising Framework with Normalizing Flows](https://mlsanity.com/paper/2203.05940/) (2022)
- [Subjective Quality Database and Objective Study of Compressed Point Clouds With 6DoF Head-Mounted Display](https://mlsanity.com/paper/2008.02501/) (2020)
- [A generalized Hausdorff distance based quality metric for point cloud geometry](https://mlsanity.com/paper/2003.13669/) (2020)
- [Contrastive Pre-Training with Multi-View Fusion for No-Reference Point Cloud Quality Assessment](https://mlsanity.com/paper/2403.10066/) (2024)
- [Contrastive Learning for Joint Normal Estimation and Point Cloud Filtering](https://mlsanity.com/paper/2208.06811/) (2022)
- [TCDM: Transformational Complexity Based Distortion Metric for Perceptual Point Cloud Quality Assessment](https://mlsanity.com/paper/2210.04671/) (2022)
- [StraightPCF: Straight Point Cloud Filtering](https://mlsanity.com/paper/2405.08322/) (2024)
- [Reduced-Reference Quality Assessment of Point Clouds via Content-Oriented Saliency Projection](https://mlsanity.com/paper/2301.07681/) (2023)
- [MODNet: Multi-offset Point Cloud Denoising Network Customized for Multi-scale Patches](https://mlsanity.com/paper/2208.14160/) (2022)
- [Perception-Guided Quality Metric of 3D Point Clouds Using Hybrid Strategy](https://mlsanity.com/paper/2407.03885/) (2024)

## Abstract (arXiv)

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.