Radial basis functions with compact support for elastic registration of medical images

摘要

Common elastic registration schemes based on landmarks and radial basis functions (RBFs) such as thin-plate splines or multiquadrics are global. Here, we introduce radial basis functions with compact support for elastic registration of medical images which have an improved locality, i.e. which allow to constrain elastic deformations to image parts where required. We give the theoretical background of these basis functions and compare them with other basis functions w.r.t. locality, solvability, and efficiency. A detailed comparison with the Gaussian as well as conditions for preserving topology is given. An important property of the used RBFs (Wendland's ψ-functions) is that they are positive definite. Therefore, in comparison to the use of the truncated Gaussian, the solvability of the resulting system of equations is always guaranteed. We demonstrate the applicability of our approach for synthetic as well as for 2D and 3D tomographic images.