An Image Registration Framework for Sliding Motion with Piecewise Smooth Deformations

We present a novel variational framework for image registration with explicit modeling of sliding motion, as it occurs, e.g., in the medical context at organ boundaries. The key of our method is a piecewise smooth deformation model that allows for discontinuities at the sliding interfaces while keeping the sliding domain in contact with its surrounding. The presented approach is generic and can be used with a large class of both image similarity measures and regularizers for the deformations. A useful byproduct of the proposed method is an automatic propagation of a given segmentation from one image to the other. We proof existence of minimizers under rather mild assumptions and present an efficient scheme for computing a numerical solution. The minimization is based on a splitting approach with alternating derivative based Gauss-Newton and fast first order convex optimization. Finally, we evaluate the proposed method on synthetic and real data.