Iterative Fine Point-Set Matching of a Free-Form Surface Based on the Point-to-Sphere Distance

Abstract

Three-dimensional point-set matching that aligns the moving point set with the fixed design model is an increasingly popular technique in manufacturing automation, which also increases the demand for matching performance. In this article, an iterative fine matching algorithm based on point-to-sphere distance is proposed to balance convergence accuracy, stability, and speed. By considering the neighborhood of a fixed point as a spherical surface, a point-to-sphere distance from a moving point to the design model is derived to improve the distance calculation accuracy with respect to unknown motion parameters. A point-to-sphere iterative closest point (ICP) matching method is presented, which translates the matching into a nonlinear optimization problem. Using the Newton method, a second-order Taylor expansion is applied to iteratively solve the motion parameters. Theoretical analysis verifies the advantages in convergence performance. It is proven that the proposed method can show faster convergence speed than point-to-point ICP and better convergence stability than point-to-plane ICP in large initial poses. Experiments implementing five models verify the feasibility of the point-to-sphere distance and the corresponding matching method.