Journal of Mathematical Imaging and Vision

We introduce a new point-based elastic registration scheme for medical images which is based on elastic body splines (EBS). Since elastic body splines result from a physical model in form of analytical solutions of the Navier equation these splines describe elastic deformations of physical objects. This property is advantageous in medical registration applications, in which the geometric differences between the images are often caused by physical deformations of human tissue due to surgical interventions or pathological processes. In this contribution we introduce a new class of elastic body splines which is based on Gaussian forces (GEBS). By varying the standard deviation of the Gaussian forces our new approach is well suited to cope with local as well as global differences in the images. This is in contrast to the previous EBS approach where polynomial and rational forces have been used. We demonstrate the performance of our new approach by presenting two different kinds of experiments. First, we demonstrate that this approach well approximates deformations given by an analytic solution of the Navier equation. Second, we apply our approach to pre- and postsurgical tomographic images of the human brain. It turns out that the new EBS approach well models the physical deformation behavior of tissues and in the case of local deformations performs significantly better than the previous EBS.