A Point Set Registration Algorithm Using a Motion Model Based on Thin-Plate Splines and Point Clustering

Abstract

This paper focuses on the problem of ill-posedness of deformable point set registration where the point correspondences are not known a priori (in our case). The basic elements of the investigated kind of registration algorithm are a cost functional, an optimization strategy and a motion model which determines the kind of motions and deformations that are allowed and how they are restricted. We propose a method to specify a shape adapted deformation model based on thin-plate splines and point clustering and oppose it to the annealing of the regularization parameter and to a regular scheme for the warping of space with thinplate splines. As criteria for the quality of the match we consider the preservation of physical/anatomical corresponding points.

Our natural deformation model is determined by placing the control points of the splines in a way adapted to the superimposed point sets during registration using a coarse-to-fine scheme. Our experiments with known ground truth show the impact of the chosen deformation model and that the shape oriented model recovers constantly very accurately corresponding points.We observed a stable improvement of this accuracy for a increasing number of control points.