Computing Topology Preservation of RBF Transformations for Landmark-Based Image Registration
This work addresses the problem of ensuring topology-preserving transformations in image registration for medical or computational imaging applications, but it appears incremental as it focuses on comparing existing RBFs.
The paper analyzes the topology preservation properties of Radial Basis Functions (RBFs), specifically Matérn functions, in landmark-based image registration, comparing them with Gaussian, Wendland's, and Wu's functions through numerical results.
In image registration, a proper transformation should be topology preserving. Especially for landmark-based image registration, if the displacement of one landmark is larger enough than those of neighbourhood landmarks, topology violation will be occurred. This paper aim to analyse the topology preservation of some Radial Basis Functions (RBFs) which are used to model deformations in image registration. Matérn functions are quite common in the statistic literature (see, e.g. \cite{Matern86,Stein99}). In this paper, we use them to solve the landmark-based image registration problem. We present the topology preservation properties of RBFs in one landmark and four landmarks model respectively. Numerical results of three kinds of Matérn transformations are compared with results of Gaussian, Wendland's, and Wu's functions.