Computing Topology Preservation of RBF Transformations for Landmark-Based Image Registration

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. Mat\'{e}rn 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 Mat\'{e}rn transformations are compared with results of Gaussian, Wendland's, and Wu's functions

Soft X-ray spectromicroscopy

In recent years much progress has been made in the field of spectromicroscopy, the combination of spectroscopy with lateral resolution. This method is applicated increasingly to problems in biology, material and surface science. Different technical approaches will be outlined and discussed with respect to their imaging and spectroscopic properties.The scanning soft x-ray microscope at HASYLAB has been equipped continuously with new operating modes and has now the capability to use photoelectrons, photodesorbed ions, luminescence, fluorescence, scattered and transmitted photons for imaging and spectroscopy. Examinations of artificial structures, of luminescent ceramics and crystals and of porous silicon will be presented