Current-and Varifold-Based Registration of Lung Vessel and Airway Trees

Registering lung CT images is an important problem for many applications including tracking lung motion over the breathing cycle, tracking anatomical and function changes over time, and detecting abnormal mechanical properties of the lung. This paper compares and contrasts current-and varifold-based diffeomorphic image registration approaches for registering tree-like structures of the lung. In these approaches, curve-like structures in the lung - for example, the skeletons of vessels and airways segmentation - are represented by currents or varifolds in the dual space of a Reproducing Kernel Hilbert Space (RKHS). Current and varifold representations are discretized and are parameterized via of a collection of momenta. A momenta corresponds to a line segment via the coordinates of the center of the line segment and the tangent direction of the line segment at the center. A varifold-based registration approach is similar to currents except that two varifold representations are aligned independent of the tangent vector orientation. An advantage of varifolds over currents is that the orientation of the tangent vectors can be difficult to determine especially when the vessel and airway trees are not connected. In this paper, we examine the image registration sensitivity and accuracy of current-and varifold-based registration as a function of the number and location of momentum used to represent tree like-structures in the lung. The registrations presented in this paper were generated using the Deformetrica software package ([Durrleman et al. 2014]).