Diffeomorphic Image Registration Using Lipschitz Continuous Residual Networks

Image registration is an essential task in medical image analysis. We propose two novel unsupervised diffeomorphic image registration networks, which use deep Residual Networks (ResNets) as numerical approximations of the underlying continuous diffeomorphic setting governed by ordinary differential equations (ODEs), viewed as an Eulerian discretization scheme. While considering the ODE-based parameterizations of diffeomorphisms, we consider both stationary and non-stationary (time varying) velocity fields as the driving velocities to solve the ODEs, which gives rise to our two proposed architectures for diffeomorphic registration. We also employ Lipschitz-continuity on the Residual Networks in both architectures to define the admissible Hilbert space of velocity fields as a Reproducing Kernel Hilbert Spaces (RKHS) and regularize the smoothness of the velocity fields. We apply both registration networks to align and segment the OASIS brain MRI dataset. Experimental results demonstrate that our models are computation efficient and achieve comparable registration results with a smoother deformation field.