  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.
