  In this paper, we propose a new approach to deformable image registration
that captures sliding motions. The large deformation diffeomorphic metric
mapping (LDDMM) registration method faces challenges in representing sliding
motion since it per construction generates smooth warps. To address this issue,
we extend LDDMM by incorporating both zeroth- and first-order momenta with a
non-differentiable kernel. This allows to represent both discontinuous
deformation at switching boundaries and diffeomorphic deformation in
homogeneous regions. We provide a mathematical analysis of the proposed
deformation model from the viewpoint of discontinuous systems. To evaluate our
approach, we conduct experiments on both artificial images and the publicly
available DIR-Lab 4DCT dataset. Results show the effectiveness of our approach
in capturing plausible sliding motion.
