A shape adapted motion model based on thin-plate splines and point clustering for point set registration

This paper focuses on the problem of ill-posedness of deformable point set registration and we propose anew approach to restrict the solution space using shape information. The basic elements of the investigated kind of registration algorithm are a cost functional, an optimization strategy and a motion model. The motion model determines the kind of motions and deformations that are allowed and how they are restricted. The motion model itself is mainly determined by the kind of parameterized transformation used to express the motion/deformation. Here, we observe that matching with more degrees of freedom (the parameters of the transformation) than necessary can introduce mismatches due to a higher sensitivity to noise or by destroying local shape information. In this paper we propose a cost functional which is robust to noise and we introduce a new method to specify a shape adapted deformation model based on thin-plate splines and initial control point placing using point clustering. We show that these initial positions have a strong impact on the match and we define them as cluster centers where we cluster on one of the point sets (weighting each point of this set with its distance to the other point set). Our experiments with known ground truth show that the shape adapted model recovers constantly very accurately corresponding points. In our evaluation with more than 1200 single experiments we showed that, compared to a conventional octree based scheme, we could save more than 60% of degrees of freedom while preserving matching quality.