Global Registration of Non Static 3D LiDAR Point Clouds: SVD Factorization and Robust GPA Methods

The paper reports two analytical methods capable to reliably perform the simultaneous global registration of non static 3D LiDAR point clouds, and investigates their applicability by analysing the results of some preliminary numerical examples. The first method, proposed by Xiao (2005), and Xiao et al. (2006), apply a direct SVD factorisation to non static 3D fully overlapping point clouds characterised by target points. The factorisation is applied to a matrix, sequentially containing by rows the coordinates of the corresponding targets present in the cloud scenes. Besides the rigid transformation parameters, a number of shape bases is determined for each point cloud, whose linear combination describes the dynamic component of the scenes. A linear closed-form solution is finally obtained, enforcing linear constraints on orthonormality of the rigid rotations and on uniqueness of the linear bases. The second method analysed is the so called “Robust Generalised Procrustes Analysis”, recently proposed by the authors. To overcome the lack of robustness of Generalised Procrustes Analysis, a progressive sequence inspired to the “forward search” was developed. Starting from an initial partial point cloud configuration satisfying the LMS principle, the configuration is updated, point by point, till a significant variation of the registration parameters occur. This reveals the presence of non stationary points among the new elements just inserted, that are therefore not included in the registration process. Both methods are capable to correctly determine the registration parameters, when compared to the commonly applied “two steps method”, where the registration of deformable shapes is biased by non - rigid deformation components.