Analysing the geometric properties of reflected correspondence vectors for the registration of free form shapes

The paper presents a novel algorithm for the registration of free-form shapes represented by two sets of points before and after a rigid body motion. First, the geometric properties of reflected correspondence vectors are analysed, yielding a number of rigid motion constraints bridging the points described in different coordinate frames before and after the rigid motion. Then, a novel algorithm is developed for the registration of free-form shapes, making full use of the rigid motion constraints to cope with false matches that occur in almost every iteration of the ICP algorithm. In order to improve the accuracy of the motion parameter estimation and computational efficiency, the Monte Carlo resampling technique and a median filter are employed. A number of experiments based on both synthetic data and real images demonstrate that the proposed algorithm is accurate and robust.