Arbitrary Order Total Variation for Deformable Image Registration

In this work, we investigate image registration in a variational framework and focus on regularization generality solver efficiency. We first propose model combining the state-of-the-art sum of absolute differences (SAD) new arbitrary order total variation term. The main advantage is that preserves discontinuities resultant deformation while being robust to outlier noise. It however non-trivial optimize due its non-convexity, non-differentiabilities, derivative order. To tackle these, apply linearization problem formulate convex objective function then break down optimization into several point-wise, closed-form subproblems using fast, over-relaxed alternating direction method multipliers (ADMM). With our proposed algorithm, show solving higher-order formulations similar their lower-order counterparts. Extensive experiments ADMM significantly more efficient than both subgradient primal-dual algorithms particularly when derivatives are used, models outperform methods based deep learning free-form deformation. Our code implemented Matlab Pytorch publicly available at https://github.com/j-duan/AOTV.