An enhanced method in optimization rooted in direct collocation is formulated to treat the finite set optimal control problem. This is motivated by applications in which a hybrid dynamical system is subject to ordinary differential continuity constraints, but control variables are contained within finite spaces. Resulting solutions display control discontinuities as variables switch between one feasible value to another. Solutions derived are characterized as optimal switching schedules between feasible control values. The methodology allows control switches to be determined over a continuous spectrum, overcoming many of the limitations associated with discretized solutions. Implementation details are presented and several applications demonstrate the method’s utility and capability. Simple applications highlight the effectiveness of the methodology, while complicated dynamic systems showcase its relevance. A key example considers the challenges associated with libration point formations. Extensions are proposed for broader classes of hybrid systems. / text

Nonrigid image registration has received much attention in the medical imaging and computer vision research communities, because it enables a wide variety of applications. Feature tracking, segmentation, classification, temporal image differencing, tumour growth estimation, and pharmacokinetic modeling are examples of the many tasks that are enhanced by the use of aligned imagery. Over the years, the medical imaging and computer vision communties have developed and refined image registration techniques in parallel, often based on similar assumptions or underlying paradigms. This thesis focuses on variational registration, which comprises a subset of nonrigid image registration. It is divided into chapters that are based on fundamental aspects of the variational registration problem: image dissimilarity measures, changing overlap regions, regularizers, and computational solution strategies. Key contributions include the development of local versions of standard dissimilarity measures, the handling of changing overlap regions in a manner that is insensitive to the amount of non-interesting background information, the combination of two standard taxonomies of regularizers, and the generalization of solution techniques based on Fourier methods and the Demons algorithm for use with many regularizers. To illustrate and validate the various contributions, two sets of example imagery are used: 3D CT, MR, and PET images of the brain as well as 3D CT images of lung cancer patients.