Closed-form solution to point- and plane-based co-registration of terrestrial LiDAR point clouds

Co-registration is required when the alignment of two or more point clouds obtained for mapping natural and built environments is needed. While closed-form solutions are suitable for co-registration, most of the existing approaches rely on unit quaternion solutions for the estimation of transformation parameters from point or plane correspondences. This paper presents a novel co-registration of terrestrial light detection and ranging point clouds solution to create globally consistent 3-D environments. Our method exploits the advantages of the dual quaternion solution combining both points and plane correspondences. The role of our relaxation labeling technique in 3-D matching (3PRL) is investigated, and its efficiency to find the best plane correspondences is shown. The paper also presents a method to treat degenerate plane configurations with corresponding virtual points. Experimental results reveal that our 3PRL technique can update and improve the 3-D matching probabilities using binary relations. At the same time, the proposed dual quaternions point- and plane-based optimization indicated that the mathematical optimization might represent a valid model for co-registration of point clouds. A closer inspection of co-registration accuracy revealed that the translation and rotation error mean decreased drastically, with margins between 0.10 m and 0.17 m and 0.01° and 0.33°, respectively. Experiments have shown that our method generally achieves better results than existing methods.