Estimation of slipping organ motion by registration with direction-dependent regularization

Accurate estimation of respiratory motion is essential for many applications in medical 4D imaging, for example for radiotherapy of thoracic and abdominal tumors. It is usually done by non-linear registration of image scans at different states of the breathing cycle but without further modeling of specific physiological motion properties. In this context, the accurate computation of respiration-driven lung motion is especially challenging because this organ is sliding along the surrounding tissue during the breathing cycle, leading to discontinuities in the motion field. Without considering this property in the registration model, common intensity-based algorithms cause incorrect estimation along the object boundaries.In this paper, we present a model for incorporating slipping motion in image registration. Extending the common diffusion registration by distinguishing between normal- and tangential-directed motion, we are able to estimate slipping motion at the organ boundaries while preventing gaps and ensuring smooth motion fields inside and outside. We further present an algorithm for a fully automatic detection of discontinuities in the motion field, which does not rely on a prior segmentation of the organ.We evaluate the approach for the estimation of lung motion based on 23 inspiration/expiration pairs of thoracic CT images. The results show a visually more plausible motion estimation. Moreover, the target registration error is quantified using manually defined landmarks and a significant improvement over the standard diffusion regularization is shown.