Closed-form solutions for estimating a rigid motion from plane correspondences extracted from point clouds

Registration is often a prerequisite step in processing point clouds. While planar surfaces are suitable features for registration, most of the existing plane-based registration methods rely on iterative solutions for the estimation of transformation parameters from plane correspondences. This paper presents a new closed-form solution for the estimation of a rigid motion from a set of point–plane correspondences. The role of normalization is investigated and its importance for accurate plane fitting and plane-based registration is shown. The paper also presents a thorough evaluation of the closed-form solutions and compares their performance with the iterative solution in terms of accuracy, robustness, stability and efficiency. The results suggest that the closed-form solution based on point–plane correspondences should be the method of choice in point cloud registration as it is significantly faster than the iterative solution, and performs as well as or better than the iterative solution in most situations. The normalization of the point coordinates is also recommended as an essential preprocessing step for point cloud registration. An implementation of the closed-form solutions in MATLAB is available at: http://people.eng.unimelb.edu.au/kkhoshelham/research.html#directmotion.