For accurate registration of overlapping free form shapes, different points in one shape must select different points in another as their most sensible correspondents. To reach this ideal state, in this paper we develop a novel algorithm to penalize those points in one shape that select the same closest point in another as their tentative correspondents. The novel algorithm then models the relative weight change over time of a tentative correspondence as the difference between the negative functions of the numbers of points in one shape that actually and ideally select the same closest point in another. Such modeling results in an optimal estimation of the weights of different tentative correspondences, in the sense of deterministic annealing, that lead the camera motion parameters to be estimated in the weighted least squares sense. The proposed algorithm is initialized using the pure translational motion derived from the centroids difference of the overlapping free form shapes being registered. Experimental results show that it outperforms three selected state-of-the-art algorithms on the whole for the accurate and robust registration of real overlapping free form shapes captured using two different laser scanners under typical imaging conditions.