A direct method for the simultaneous and optimal multidimensional models registration

An innovative solution of the global multidimensional registration problem for a set of partial object models is introduced and explained. The method, based on the classical tie-point concept, is capable to directly and optimally align models indefinitely rotated, translated and scaled. The pre-registration is carried out in an automatic way without the need of initial manual superimposition nor of approximate starting values of the transformation parameters. Registration algorithms implementing the singular value decomposition of matrix products of limited size are used in every step of the process. The procedure is based on the algorithms of the Procrustes analysis. One consequent advantage is that there are no space dimensions restrictions. This is particularly helpful for laser scanning and digital photogrammetry applications, where a set of attributes associated to the different tie-points (i.e. CYMK or RGB color components and intensity) can be used in conjunction with the corresponding Cartesian coordinate values. This connection can improve the registration reliability of range-colored images, matching simultaneously geometry, nature and aspect. The numerical experiments carried out confirm the advantages of the multidimensional approach proposed.