Simultaneous Registration of Multiple Range

When reverse engineering a CAD model, it is necessary to integrate information from several views of an object into a common reference frame. Given a rough initial alignment of local 3-D shape data in several images, further re nement is achieved using an improved version of the recently popular Iterative Closest Point algorithm. Improved data correspondence is determined by considering the merging data sets as a whole. A potentially incorrect distance threshold for removing outlier correspondences is not needed as in previous e orts. Incremental pose adjustments are computed simultaneously for all data sets, resulting in a more globally optimal set of transformations. Individual motion updates are computed using forcebased optimization, by considering the data sets as implicitly connected by groups of springs. Experiments on both 2-D and 3-D data sets show that convergence is possible even for very rough initial positionings, and that the nal registration accuracy typically approaches less than one quarter of the interpoint sampling resolution of the images. 2 List of Symbols T view transformation set T 3-D transformation R transformation rotation matrix t transformation translation vector I identity matrix l 3-D location v linear velocity v linear velocity damping matrix a linear acceleration rotation angle ! angular velocity ! angular velocity damping matrix angular acceleration t simulation time step Np number of sampling passes SS point sampling schedule m minimal motion threshold E distance error metric sn normalization scale factor wn point normal weighting factor bvp point visibility weighting factor surface normal angle tolerance k dimension size of feature vector N number of points in a data set nv number of corresponding points in view no number of corresponding points in all other views p,q corresponding data points np,nq corresponding surface normals F spring force spring strength d distance between two points M rotational moment mv mass of points in data set I moment of inertia r radius for moment cm center of mass of data set dd depth discontinuity threshold Gaussian kernel size 3