A Generalized Factored Stochastic Model for Optimal Registration of LIDAR Range Images

Surveying complex shapes or very large entities by laser scanners often requires the registration of a sufficient number of partial 3-D range images in order to completely reproduce the model of the real object. If redundancy exists among the partial models composing the measured entity, a global adjustment of the model components improves the final accuracy with respect to a simple pairwise registration. To this regard, a new solution for the optimal least squares registration of range images, based on the Generalised Procrustes Analysis techniques, has been recently developed by the authors and can be found in the literature. The method, using the classical tie point correspondence, has proven to be very efficient since it does not require any prior information of the geometrical relationship existing among the particular reference frames in which the different partial 3-D models are expressed. Considering its computational advantages, it does not involve linearisation of equation systems nor matrix inversions, the only requirement is the singular value decomposition (SVD) of matrices of order 3 x 3. In this paper a significant analytical enhancement of the Procrustean method is presented, to manage the stochastic properties of the tie point coordinates in a more complete and exhaustive way. In the previous formulation the possibility to assign a different isotropic weighting factor to the single tie points, according to their specific accuracy, was considered. With the new proposed method, also the positional components, i.e. each coordinate, can be weighted separately. In this way a complete anisotropic and inhomogeneous factored stochastic model can be introduced in the Procrustes procedure. The generalisation of the stochastic model is recommended for certain practical applications, particularly for joining aerial laserscanners strips produced with low sampling density. In these cases, matching correspondence points of low resolution range images generates poorly accurate tie point coordinate estimation. Indeed, this event introduces an uncertainty in the 3-D position that must be considered anisotropic, i.e. not affecting the three components of the same amount. In fact, considering one tie-point laying on a surface perpendicular to the laser beam, the effective position of the laser footprint on the correspondence element affects the planimetric position more than the related altimetric component. In these situations, the different quality of the tie points position components must be correctly and advantageously preserved, performing the global registration adopting the anisotropic model here presented. A suitable application is discussed in the paper to illustrate the registration problem and the expected advantages of the method proposed.