Total Variation Regularization of Displacements in Parametric Image Registration

Spatial regularization is indispensable in image registration to avoid both physically implausible displacement fields and potential local minima in optimization methods. Typical `2-regularization is incapable of correctly recovering non-smooth displacement fields, such as at sliding organ boundaries during time-series of breathing motion. In this paper, Total Variation (TV) regularization is used to allow for accurate registration near such boundaries. We propose a novel formulation of TV-regularization for parametric displacement fields and introduce an efficient and general numerical solution scheme using the Alternating Directions Method of Multipliers (ADMM). Our method has been evaluated on two public datasets of 4D CT lung images as well as a dataset of 4D MR liver images, demonstrating accurate registrations both inside and outside moving organs. The target registration error of our method is 2.56 mm on average in the liver dataset, which indicates an improvement of over 24% in comparison to other published methods.