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 transformations, in particular on the topology preservation of compactly supported radial basis functions transformations. In Cavoretto and De Rossi (Appl Math Inf Sci 7:2113–2121, 2013), 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 Yang et al. (Pattern Recognit Lett 32:1162–1177, 2011), where Wendland's andWu's functions are considered.