Speaker:  Lars Ruthotto, Department of Earth and Ocean Sciences, UBC

Location:  ESB 4133

Intended Audience:  Public

Finding geometrical correspondences between two images, called image registration, is one of the numerous challenging problems in image processing. Commonly,  image registration is phrased as a variational problem that is known to be ill-posed. Thus, regularization is used to ensure existence of solutions, introduce prior knowledge about the expected solution, and/or increase the robustness against noise. This talk gives a comprehensive overview of theory, numerical methods, and applications of regularization energies based on hyperelasticity.

The first part of this talk transfers existence results for polyconvex functionals from variational calculus to image registration. Thereby it is shown that solutions to hyperelastic registration problems are one-to-one, which is a necessary condition in most practical applications. Further it is shown that the regularizer is well-suited for handling volume constraints.

The second part briefly describes a numerical method based on a standard finite element method and the registration toolbox Flexible Algorithms for Image Registration (FAIR). As the variational problem is solved in the space of continuous and piecewise linear transformations numerical solutions can be ensured to be one-to-one as guaranteed by the theory.

The final part outlines the great potential of hyperelastic registration methods based on three applications from Positron Emission Tomography (PET), Echo-Planar Imaging (EPI) and Dynamic Contrast Enhanced Magnetic Resonance Imaging (MRI).