Uncertainty of extreme fit evaluation for three-dimensional measurement data analysis

Abstract Three-dimensional measurement is the process of obtaining information about a measured object in the form of surface coordinates. Of course this information must be accompanied by a data analysis procedure that evaluates geometric dimensions from the measured data. Currently extreme fits, that are based on an L∞ norm estimation, are widely applied to analyze these data. The extreme fit results reflect the functionality of the part, and they are more consistent with standard definitions. However, they are subject to sampling uncertainty as they are sensitive to measurement sampling density. Previous studies focused on the evaluation methodology of the extreme fits; however, the uncertainty of the extreme fits has not been thoroughly addressed. In this paper, we investigate the uncertainty of extreme fits, and propose a statistical approach to evaluate it. We employ the bootstrap method to determine the confidence interval of the extreme fit evaluations. The proposed method is independent of the geometry and evaluation method; thus, it can be easily generalized for various extreme fit evaluations and geometries.