仅用一个3D点云样本实现无训练异常检测，解决工业制造中数据稀缺难题。

Anomaly detection based on 3D point cloud data is an important research problem and receives more and more attention recently. Untrained anomaly detection based on only one sample is an emerging research problem motivated by real manufacturing industries such as personalized manufacturing where only one sample can be collected without any additional labels and historical datasets. Identifying anomalies accurately based on one 3D point cloud sample is a critical challenge in both industrial applications and the field of machine learning. This paper aims to provide a formal definition of the untrained anomaly detection problem based on 3D point cloud data, discuss the differences between untrained anomaly detection and current unsupervised anomaly detection problems. Unlike trained unsupervised learning, untrained unsupervised learning does not rely on any data, including unlabeled data. Instead, they leverage prior knowledge about the surfaces and anomalies. We propose three complementary methodological frameworks: the Latent Variable Inference Framework that employs probabilistic modeling to distinguish anomalies; the Decomposition Framework that separates point clouds into reference, anomaly, and noise components through sparse learning; and the Local Geometry Framework that leverages neighborhood information for anomaly identification. Experimental results demonstrate that untrained methods achieve competitive detection performance while offering significant computational advantages, demonstrating up to a 15-fold increase in execution speed. The proposed methods provide viable solutions for scenarios with extreme data scarcity, addressing critical challenges in personalized manufacturing and healthcare applications where collecting multiple samples or historical data is infeasible.