A Variational Image Registration Approach Based on Curvature Scale Space

Abstract

This paper presents a novel scale space approach to obtain a deformation which matches two images acquired from the same or from different medical imaging modalities. The image registration problem is known to be mathematically ill-posed due to the fact that determining the unknown components of the displacements merely from the images is an underdetermined problem. The approach presented here utilizes an auxiliary regularization term, which favors displacements with minimal curvature surface. One of the important aspects of this approach is that the kernel of the Euler-Lagrange equation is spanned by all rigid motions. Hence, the presented approach includes a rigid alignment. A minimizer is determined as the steady-state solution of the Euler-Lagrange equation namely by the biharmonic diffusion equation with higher order boundary conditions. In this framework we give a new interpretation of the underlying regularization parameter α. Finally, we present experimental results for registration problems of a Magnetic Resonance Imaging (MRI) (monomodal) registration and for a real computer tomography (CT)–magnetic resonance imaging (multimodal) registration.