Registration-Free Localization of Defects in Three-Dimensional Parts from Mesh Metrology Data Using Functional Maps

We consider a common problem occurring after using a statistical process control (SPC) method based on three-dimensional measurements: locate where on the surface of the part that triggered an out-of-control alarm there is a significant shape difference with respect to either an in-control part or its nominal (computer-aided design (CAD)) design. In the past, only registration-based solutions existed for this problem, which first orient and locate the part and its nominal design under the same frame of reference. Recently, spectral Laplacian methods have been proposed for the SPC of discrete parts and their measured surface meshes. These techniques provide an intrinsic solution to the SPC problem: that is, a solution exclusively based on data whose coordinates lie on the surfaces without making reference to their ambient space, thus avoiding registration. Registration-free methods avoid the computationally expensive, nonconvex registration step needed to align the parts as required by previous methods, eliminating registration errors, and they are important in industry because of the increasing use of portable noncontact scanners. In this paper, we first present a new registration