Using minimum covariance determinant for simultaneous noise removal and robust planar surface fitting in coordinate metrology

Integrated inspection system (IIS) enriches digital metrology by decreasing uncertainty due to closed-loop implementation of the cyber-components of digital metrology including planning the measurement of points, fitting the best Substitute Geometry (SGE) and evaluating the actual geometry of the surface. Optical devices are favored over contact metrology devices as they offer faster, fuller, and non-invasive measurement, but they are also susceptible to noise and outliers that may affect the accuracy and quality of the inspection. Principal Component Analysis (PCA) has been presenting high efficiency in attaining transformation matrix of the large number of discrete points given by the optical devices based on the point’s distribution; however, it is not robust to noise. Noise removal prior to SGE provides pure information feedbacked to the other cyber-components of IIS, and finally correctly identifies the actual geometry of the inspected surface. In this paper, in order to obtain the robust principal component of the unorganized point cloud of the planar surfaces, a subset of the data, which is least affected by noise, is found with Minimum Covariance Determinant (MCD), and then PCA is conducted on the obtained MCD-subset. Due to the MCD’s robustness, the noises can be detected by their large robust distances based on the MCD location and scatter matrix. The results of implementation on two case studies show the efficiency of MCD in simultaneous noise removal and robust surface fitting. Variety of inspection tools can utilize the methodology for point cloud filtration.