Point-set alignment using multidimensional scaling

We show how to perform point-set alignment by applying multidimensional scaling to the interpoint distance matrix. The idea is that alignment can be effected by transforming different point-sets into a common embedding space, and correspondences located on a nearest-neighbour basis. The method offers the advantage over conventional Procrustes analysis that it extends the range of rotational angles over which it is effective. Moreover it does not require separate, and explicit, centering, scaling and rotation steps. It also proves robustness under severe levels of point-set noise and corruption.