Recursive Green's Function Registration

Björn Beuthien, Ali Kamen, Bernd Fischer


Non-parametric image registration is still among the most challenging problems in both computer vision and medical imaging. Here, one tries to minimize a joint functional that is comprised of a similarity measure and a regularizer in order to obtain a reasonable displacement field that transforms one image to the other. A common way to solve this problem is to formulate a necessary condition for an optimizer, which in turn leads to a system of partial differential equations (PDEs). In general, the most time consuming part of the registration task is to find a numerical solution for such a system. In this paper, we present a generalized and efficient numerical scheme for solving such PDEs simply by applying 1-dimensional recursive filtering to the right hand side of the system based on the Green's function of the differential operator that corresponds to the chosen regularizer. So in the end we come up with a general linear algorithm. We present the associated Green's function for the diffusive and curvature regularizers and show how one may efficiently implement the whole process by using recursive filter approximation. Finally, we demonstrate the capability of the proposed method on realistic examples.
Original languageEnglish
Title of host publicationMedical Image Computing and Computer-Assisted Intervention – MICCAI 2010
EditorsTianzi Jiang, Nassir Navab, Josien P. W. Pluim, Max A. Viergever
Number of pages8
Place of PublicationBerlin, Heidelberg
PublisherSpringer Berlin Heidelberg
Publication date09.2010
ISBN (Print)978-3-642-15744-8
ISBN (Electronic)978-3-642-15745-5
Publication statusPublished - 09.2010
Event13 International Conference on Medical Image Computing and Computer-Assisted Intervention - Beijing, China
Duration: 20.09.201024.09.2010


Dive into the research topics of 'Recursive Green's Function Registration'. Together they form a unique fingerprint.

Cite this