Large Deformation Diffeomorphic Metric Mappings -- Theory, Numerics, and Applications

In this thesis three diffeomorphic image registration methods are proposed. ADiscretize-then-Optimize approach is used to derive these methods from optimalcontrol formulations in the Large Deformation Diffeomorphic Metric Mapping (LD-DMM) framework. We give a condensed overview of the theoretical background ofLDDMM and discuss the two major groups of algorithms: relaxation and shootingapproaches. Afterwards, we examine the connection to optimal control and derivethe relaxation and shooting models that are used for registration in this work. Aparticular focus of this dissertation is the discretization of the proposed models andthe solution of the constrained numerical optimization problem. The latter includesthe consistent solution of the arising partial differential equations (like transport andcontinuity equations) that are the constraints of the optimization problem. As we dealwith large-scale problems, explicit fourth-order Runge-Kutta methods are employed,which offer a good compromise between fast computation and small errors.Key elements of the proposed techniques are the flexible choice of arbitrary differ-entiable distance measures, the memory-efficient discretization of velocity fields andtransformations as well as the generation of diffeomorphic transformations in thediscrete setting. Experiments on computed tomography (CT) data of the lungs (com-prising large deformations and pathologies) demonstrate that our algorithms achievestate-of-the-art accuracy: The second-best of all published results on the DIR-Labchronic obstructive pulmonary disease (COPD) datasets is achieved with an averagelandmark distance after registration of 0.96 mm. Furthermore, the effectiveness of ourtailored discretization is confirmed by a reduction of memory consumption by 95 %and run times that are superior to those of related LDDMM methods. While otherauthors report run times of more than one hour for their LDDMM algorithms whenregistering two lung CT scans on powerful computer clusters, our registration takesabout 20 minutes on a standard desktop computer.The proposed methods are suitable for a wide range of clinical applications for diffeo-morphic lung CT registration like lung ventilation estimation, follow-up registration,radiotherapy, and COPD staging. Due to the flexible choice of distance measures ourmethods can be properly adapted to other data types and applications.