Modern sensing technologies have enabled the collection of unstructured point cloud data (PCD) of varying sizes, which are used to monitor the geometric accuracy of 3D objects. PCD are widely applied in advanced manufacturing processes, including additive, subtractive, and hybrid manufacturing. To ensure the consistency of analysis and avoid false alarms, preprocessing steps such as registration and mesh reconstruction are commonly applied prior to monitoring. However, these steps are error-prone, time-consuming and may introduce artifacts, potentially affecting monitoring outcomes. In this paper, we present a novel registration-free approach for monitoring PCD of complex shapes, eliminating the need for both registration and mesh reconstruction. Our proposal consists of two alternative feature learning methods and a common monitoring scheme designed to handle hundreds of features. Feature learning methods leverage intrinsic geometric properties of the shape, captured via the Laplacian and geodesic distances. In the monitoring scheme, thresholding techniques are used to further select intrinsic features most indicative of potential out-of-control conditions. Numerical experiments and case studies highlight the effectiveness of the proposed approach in identifying different types of defects.

翻译：现代传感技术使得能够采集不同规模的非结构化点云数据，这些数据被用于监测三维物体的几何精度。点云数据广泛应用于增材制造、减材制造及混合制造等先进制造工艺中。为确保分析的一致性并避免误报，在监测前通常需进行点云配准与网格重建等预处理步骤。然而，这些步骤易引入误差、耗时较长且可能产生伪影，进而影响监测结果。本文提出一种针对复杂形状点云数据的新型免配准监控方法，该方法无需进行配准与网格重建。本方案包含两种可替代的特征学习方法及一个能处理数百个特征的通用监控框架。特征学习方法通过拉普拉斯算子与测地距离提取形状的固有几何特性。在监控框架中，采用阈值技术进一步筛选最能表征潜在失控状态的固有特征。数值实验与案例研究验证了所提方法在识别多种类型缺陷方面的有效性。