Slipping Objects in Image Registration: Improved Motion Field Estimation with Direction-dependent Regularization

The computation of accurate motion fields is a crucial aspect in 4D medical imaging. It is usually done using a non-linear registration without further modeling of physiological motion properties. However, a globally homogeneous smoothing (regularization) of the motion field during the registration process can contradict the characteristics of motion dynamics. This is particularly the case when two organs slip along each other which leads to discontinuities in the motion field. In this paper, we present a diffusion-based model for incorporating physiological knowledge in image registration. By decoupling normal- and tangential-directed smoothing, we are able to estimate slipping motion at the organ borders while ensuring smooth motion fields in the inside and preventing gaps to arise in the field. We evaluate our model focusing on the estimation of respiratory lung motion. By accounting for the discontinuous motion of visceral and parietal pleurae, we are able to show a significant increase of registration accuracy with respect to the target registration error (TRE).