Matching Misaligned Two-Resolution Metrology Data

Multiresolution metrology devices coexist in today's manufacturing environment, producing coordinate measurements complementing each other. Typically, the high-resolution (HR) device produces a scarce but accurate data set, whereas the low-resolution (LR) one produces a dense but less accurate data set. Research has shown that combining the two data sets of different resolutions makes better predictions of the geometric features of a manufactured part. A challenge, however, is how to effectively match each HR data point to an LR counterpart that measures approximately the same physical location. A solution to this matching problem appears a prerequisite to a good final prediction. We solved this problem by formulating it as a quadratic integer program, aiming at minimizing the maximum interpoint distance difference among all potential correspondences. Due to the combinatorial nature of the optimization model, solving it to optimality is computationally prohibitive even for a small problem size. We therefore propose a two-stage matching framework capable of solving real-life-sized problems within a reasonable amount of time. This two-stage framework consists of downsampling the full-size problem, solving the downsampled problem to optimality, extending the solution of the downsampled problem to the full-size problem, and refining the solution using iterative local search. Numerical experiments show that the proposed approach outperforms two popular point set registration alternatives, the iterative closest point and coherent point drift methods, using different performance metrics. The numerical results also show that our approach scales much better as the instance size increases, and is robust to the changes in initial misalignment between the two data sets.