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.

翻译：点云去噪是真实应用场景中一项基础且关键的技术挑战。现有量化评估指标均采用有监督方式实现，需同时使用去噪点云与对应的无噪声真实点云来计算具有代表性的几何距离。这一要求在真实场景中具有显著局限性——无噪声真实点云往往难以获取。本文提出一种简单有效的无监督几何距离（UGD），仅需含噪点云即可实现对真实噪声点云去噪效果的评估。其核心思想是：从一组清洁点云中学习基于块状的先验模型，并将该先验模型作为基准，通过测量去噪点云的几何变化来量化退化程度。为此，我们首先利用块状特征提取网络从一组原始清洁点云中提取与感知质量相关的块状特征，构建纯净高斯混合模型（GMM）作为量化评估的基准；进而将UGD定义为去噪点云各块与学习得到的纯净GMM模型在块空间中的加权距离之和。为训练所采用的块状特征提取网络，我们提出通过多任务学习的自监督训练框架，涵盖成对质量排序、失真分类及失真分布预测任务。基于合成噪声的定量实验表明，所提UGD可达到与有监督全参考指标相当的性能。此外，在真实数据上的实验结果证明，该UGD方法能够仅依赖含噪点云实现对点云去噪方法的无监督评估。