Nonrigid image registration with two-sided space-fractional partial differential equations

Fractional partial differential equations can be used to model super-diffusive processes. Recent research into fractional PDEs has explored their impact on nonrigid image registration, which typically uses differential operators of integer order. In this paper, we propose a nonrigid registration algorithm that involves directly and rapidly solving a discretized fractional PDE at each time step that is subject to physically realistic image boundary conditions. The proposed algorithm is validated through registration experiments on breast MR imagery with simulated biomechanical deformations, indicating that the super-diffusive model yields lower average deformation errors than standard diffusion-based registration.