On the topology preservation of Gneiting's functions in image registration

The purpose of image registration is to determine a transformation such that the transformed version of the source image is similar to the target one. In this paper we focus on landmark-based image registration using radial basis functions (RBFs) transformations, in particular on the topology preservation of compactly supported radial basis functions (CSRBFs) transformations. In [1] the performances of Gneiting's and Wu's functions are compared with the ones of other well known schemes in image registration, as thin plate spline and Wendland's functions. Several numerical experiments and real-life cases with medical images show differences in accuracy and smoothness of the considered interpolation methods, which can be explained taking into account their topology preservation properties. Here we analyze analytically and experimentally the topology preservation performances of Gneiting's functions, comparing results with the ones obtained in [2], where Wendland's and Wu's functions are considered.