The surface quality inspection of manufacturing parts based on 3D point cloud data has attracted increasing attention in recent years. The reason is that the 3D point cloud can capture the entire surface of manufacturing parts, unlike the previous practices that focus on some key product characteristics. However, achieving accurate 3D anomaly detection is challenging, due to the complex surfaces of manufacturing parts and the difficulty of collecting sufficient anomaly samples. To address these challenges, we propose a novel untrained anomaly detection method based on 3D point cloud data for complex manufacturing parts, which can achieve accurate anomaly detection in a single sample without training data. In the proposed framework, we transform an input sample into two sets of profiles along different directions. Based on one set of the profiles, a novel segmentation module is devised to segment the complex surface into multiple basic and simple components. In each component, another set of profiles, which have the nature of similar shapes, can be modeled as a low-rank matrix. Thus, accurate 3D anomaly detection can be achieved by using Robust Principal Component Analysis (RPCA) on these low-rank matrices. Extensive numerical experiments on different types of parts show that our method achieves promising results compared with the benchmark methods.

翻译：基于三维点云数据的制造零件表面质量检测近年来受到越来越多的关注。其原因是三维点云能够捕获制造零件的完整表面，而传统方法仅关注部分关键产品特征。然而，由于制造零件表面形状复杂且异常样本难以充分采集，实现精确的三维异常检测颇具挑战性。针对这些问题，我们提出了一种基于三维点云数据的无训练异常检测方法，该方法无需训练数据即可在单样本条件下实现精确的异常检测。在所提出的框架中，我们将输入样本沿不同方向转换为两组轮廓。基于其中一组轮廓，我们设计了一种新型分割模块，将复杂表面分割为多个基础且简单的组件。在每个组件中，另一组具有相似形状特征的轮廓可被建模为低秩矩阵。因此，通过在这些低秩矩阵上应用稳健主成分分析方法（RPCA），即可实现精确的三维异常检测。针对不同类型零件的广泛数值实验表明，与基准方法相比，我们的方法取得了优异的结果。