Bilateral Regularization in Reproducing Kernel Hilbert Spaces for Discontinuity Preserving Image Registration

The registration of abdominal images is an increasing field in research and forms the basis for studying the dynamic motion of organs. Particularly challenging therein are organs which slide along each other. They require discontinuous transform mappings at the sliding boundaries to be accurately aligned. In this paper, we present a novel approach for discontinuity preserving image registration. We base our method on a sparse kernel machine (SKM), where reproducing kernel Hilbert spaces serve as transformation models. We introduce a bilateral regularization term, where neighboring transform parameters are considered jointly. This regularizer enforces a bias to homogeneous regions in the transform mapping and simultaneously preserves discontinuous magnitude changes of parameter vectors pointing in equal directions. We prove a representer theorem for the overall cost function including this bilateral regularizer in order to guarantee a finite dimensional solution. In addition, we build direction-dependent basis functions within the SKM framework in order to elongate the transformations along the potential sliding organ boundaries. In the experiments, we evaluate the registration results of our method on a 4DCT dataset and show superior registration performance of our method over the tested methods.