Non-local Graph-Based Regularization for Deformable Image Registration

Deformable image registration aims to deliver a plausible spatial transformation between two or more images by solving a highly dimensional, ill-posed optimization problem. Covering the complexity of physiological motion has so far been limited to either generic physical models or local motion regularization models. This paper presents an alternative, graphical regularization model, which captures well the non-local scale of motion, and thus enables to incorporate complex regularization models directly into deformable image registration. In order to build the proposed graph-based regularization, a Minimum Spanning Tree (MST), which represents the underlying tissue physiology in a perceptually meaningful way, is computed first. This is followed by a fast non-local cost aggregation algorithm that performs regularization of the estimated displacement field using the precomputed MST. To demonstrate the advantage of the presented regularization, we embed it into the widely used Demons registration framework. The presented method is shown to improve the accuracy for exhale-inhale CT data pairs.