Equilibrated warping: Finite element image registration with finite strain equilibrium gap regularization

•Continuum finite strain formulation of the equilibrium gap regularization principle.•Consistent linearization and finite element discretization.•Efficient implementation based on FEniCS & VTK, freely available as a python library.•Equilibrium gap regularization allows the registration of highly noisy images.•Equilibrated warping can extract strains from cardiac magnetic resonance images. [Display omitted] In this paper, we propose a novel continuum finite strain formulation of the equilibrium gap regularization for image registration. The equilibrium gap regularization essentially penalizes any deviation from the solution of a hyperelastic body in equilibrium with arbitrary loads prescribed at the boundary. It thus represents a regularization with strong mechanical basis, especially suited for cardiac image analysis. We describe the consistent linearization and discretization of the regularized image registration problem, in the framework of the finite elements method. The method is implemented using FEniCS & VTK, and distributed as a freely available python library. We show that the equilibrated warping method is effective and robust: regularization strength and image noise have minimal impact on motion tracking, especially when compared to strain-based regularization methods such as hyperelastic warping. We also show that equilibrated warping is able to extract main deformation features on both tagged and untagged cardiac magnetic resonance images.