Using Rigid Constraints to Analyse Motion Parameters from Two Sets of 3D Corresponding Point Pattern

Abstract

Given a rigid body motion expressed by a set of 2D or 3D correspondences, the distance between feature points and angular information can be used as rigid constraints to calibrate motion parameters. In this paper, we first present a novel geometrical analysis of properties of reected correspondence vectors. The analysis provides explicit expressions for distance between feature points and angle measurement synthesised into a single coordinate frame providing the closed form solutions to all motion parameters of interest. A novel calibration algorithm is proposed and compared with an algorithm based on the least squares method. The algorithm demonstrates the importance of the geometrical properties of reflected correspondence vectors to motion parameter estimation and that it is generally more accurate than algorithms based on the least squares method.