Automatic surface localization by defining weighted-iteration distance function and Lyapunov-test statistic

Abstract

Automatic localization, aligning the measured points with the design model, is a basic task in free-form surface inspection. The main difficulty of current localization algorithms is how to define effective distance function and localization reliability index. This paper proposes a new method of calculating motion parameters and evaluating localization reliability. First, improved modified coefficient is defined and applied to weighted-iteration distance function, which better approximates the point-to-surface closest distance. It can control the contribution ratios of different measured points by considering the curvature feature and iterative residual. Second, the mapping relationship between localization error and geometric error is analyzed, from which a Lyapunov-test statistic is derived to define a frame-independence index. Then, the determination of localization reliability changes into a supposition examination problem. This can avoid rejecting correct motion parameters, which exists in the traditional judgment of absolute root-mean-square distance. In addition, two test experiments are implemented to demonstrate the proposed localization algorithm.