Variance-Minimization Iterative Matching Method for Free-Form Surfaces-Part I: Theory and Method

摘要

Free-form surface matching that aligns measured points with a design model is a common problem in manufacturing automation. In this paper, an iterative variance-minimization matching (VMM) method is proposed to address measured points that have measuring defects, such as uneven/open point distributions and measuring noise. The basic idea is that the objective function is defined as the variance of the closest distance from each measured point to the design model, and the measuring defects are considered by incorporating an average distance item into the objective function. Using the defined average distance item, a strategy for analyzing the effect of measuring defects on VMM and existing methods is presented. It is shown that the VMM method does not easily become trapped in a local optimum when measuring defects exist. To consider convergence speed and convergence stability, a new distance based on the first-order point-to-point distance and point-to-tangent distance is developed and used in the objective function. To demonstrate the availability of the proposed method, quadratic convergence and positive definiteness are theoretically analyzed. The proposed method is efficient and insensitive to measuring defects and is useful for shape matching tasks involving free-form surface features.