Abstract
AbstractIn 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 aims 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. [9, 13]). 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.KeywordsMatérn functionsElastic registrationRadial basis functionsTopology preservation
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