Alignment of 3D point clouds without overlap

Alignment of two-dimensional (2D) or three-dimensional (3D) point clouds often requires overlapping the datasets, as the alignment algorithms utilise the data in the overlapped area to perform iterative closest point registration. However, in some applications, datasets are from different objects and have no inherent overlapping regions, making existing alignment algorithms inapplicable. In this paper, we present a novel method for aligning 2D and 3D point clouds without overlap. The distances from each point in the first dataset to all points in the second dataset are first calculated. The minimum distances can then be determined. The process is then repeated to calculate the minimum distance for all other points. The mean of the minimum distances is then calculated. An iterative optimisation process is established to minimise the mean value. As the two datasets are intended to have no overlap, a nonlinear constraint is introduced in the optimisation process to ensure that none of the points in the first dataset are within the mesh (2D) or volume (3D) of the second dataset. This constraint can ensure the optimisation process is performed within the purpose of alignment without overlap and minimising the distance. The proposed method was implemented in MATLAB using the optimisation toolbox, and its effectiveness was demonstrated through simulations (2D data) and actual 3D measurements. The results demonstrate that the proposed method is effective, offering a promising solution to align 2D and 3D point clouds without overlap.