This thesis examines and identifies the problems of shape collapse in large deformation image registration. Shape collapse occurs in image registration when a region in the moving image is transformed into a set of near zero volume in the target image space. Shape collapse may occur when the moving image has a structure that is either missing or does not sufficiently overlap the corresponding structure in the target image. We state that shape collapse is a problem in image registration because it may lead to the following consequences: (1) Incorrect pointwise correspondence between different coordinate systems; (2) Incorrect automatic image segmentation; (3) Loss of functional signal. The above three disadvantages of registration with shape collapse are illustrated in detail using several examples with both real and phantom data. Shape collapse problem is common in image registration algorithms with large degrees of freedom such as many diffeomorphic image registration algorithms. This thesis proposes a shape collapse measurement algorithm to detect the regions of shape collapse after image registration in pairwise and group-wise registrations. We further compute the shape collapse for a whole population of pairwise transformations such as occurs when registering many images to a common atlas coordinate system. Experiments are presented using the SyN diffeomorphic image registration algorithm and diffeomorphic demons algorithm. We show that shape collapse exists in both of the two large deformation registration methods. We demonstrate how changing the input parameters to the SyN registration algorithm can mitigate the collapse image registration artifacts.

This thesis compares and contrasts currents- and varifolds-based diffeomorphic image registration approaches for registering tree-like structures in the lung and surface of the lung. In these approaches, curve-like structures in the lung—for example, the skeletons of vessels and airways segmentation—and surface of the lung are represented by currents or varifolds in the dual space of a Reproducing Kernel Hilbert Space (RKHS). Currents and varifolds 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 momentum corresponds to a mesh via the coordinates of the center of the mesh and the normal direction of the mesh at the center. The magnitude of the tangent vector for the line segment and the normal vector for the mesh are the length of the line segment and the area of the mesh respectively. A varifolds-based registration approach is similar to currents except that two varifolds representations are aligned independent of the tangent (normal) 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 thesis, we examine the image registration sensitivity and accuracy of currents- and varifolds-based registration as a function of the number and location of momenta used to represent tree like-structures in the lung and the surface of the lung. The registrations presented in this thesis were generated using the Deformetrica software package, which is publicly available at www.deformetrica.org.