Elastic registration of medical images using radial basis functions with compact support

We introduce radial basis functions with compact support for elastic registration of medical images. With these basis functions the influence of a landmark on the registration result is limited to a circle in 2D and, respectively, to a sphere in 3D. Therefore, the registration can be locally constrained which especially allows to deal with rather local changes in medical images due to, e.g., tumor resection. An important property of the used RBFs is that they are positive definite. Thus, the solvability of the resulting system of equations is always guaranteed. We demonstrate our approach for synthetic as well as for 2D and 3D tomographic images.