Georgia Institute of Technology College of Sciences

Image registration is an essential task in almost all areas involving imaging techniques. The goal of image registration is to find geometrical correspondences between two or more images. Image registration is commonly phrased as a variational problem that is known to be ill-posed and thus regularization is commonly used to ensure existence of solutions and/or introduce prior knowledge about the application in mind. Many relevant applications, e.g., in biomedical imaging, require that plausible transformations are diffeomorphic, i.e., smooth mappings with a smooth inverse. This talk will present and compare two modeling strategies and numerical approaches to diffeomorphic image registration. First, we will discuss regularization approaches based on nonlinear elasticity. Second, we will phrase image registration as an optimal control problem involving hyperbolic PDEs which is similar to the popular framework of Large Deformation Diffeomorphic Metric Mapping (LDDMM). Finally, we will consider computational aspects and present numerical results for real-life medical imaging problems.