A Variational Formulation for Discrete Registration

We present a novel variational formulation of discrete deformable registration as the minimization of a convex energy functional that involves diffusion regularization. We show that a finite difference solution (FD) of the variational formulation is equivalent to a continuous-valued Gaussian Markov random field (MRF) energy minimization formulation previously proposed as the random walker deformable registration method. A computationally efficient solution using the finite element method (FEM) method has been proposed to solve the variational minimization problem. Our proposed method obtained competitive results when compared with 14 other deformable registration methods on the CUMC12 MRI dataset.