Moving Mesh and Image Registration in FEniCS

Image registration is about finding a transformation that warps a source image into a target image, matching gross features. It is a critical task in medical imaging. Computational anatomy (CA) is a state-of-the-art framework for image registration, founded in the theory of fluid dynamics and PDE: one seeks a time-dependent vector field that generates a continuous warp of the source image into the target image. Here we construct a finite element realisation of CA by representing the continuous warp by a moving mesh. The PDE governing the motion of the mesh is an infinitedimensional nonlinear gradient flow; a brief description is given in section 2. In essence, it is a time-stepping problem, where an elliptic PDE is solved in each time step using the FEniCS finite element package. The solution process is summarised in fig. 1. Although commonly used in medical contexts, we stress that CA has promising applications also in structural engineering, as discussed in section 4