To the Graduate Council: I am submitting herewith a dissertation ...

Chapter 1: Introduction 8ultimately contributed to our alignment framework, it was not as thoroughlyinvestigated in this dissertation as the others due to our different focus.1.3 Document OrganizationThe remainder of this dissertation is organized as follows:• Chapter 2 gives a literature review of the topics most relevant to our research.Namely: 3D Free-form registration, image registration, tensor voting, and shapefrom motion.• Chapter 3 describes our work on designing the feature saliency descriptorstarting from our initial efforts at camera motion recovery and presenting a firstattempt at designing a point-set registration criterion.• Chapter 4 is the core theory chapter that develops the Gaussian Fieldsframework using mollification and relaxation approaches. It argues theoreticallyfor its advantages, and gives the details of the optimization strategy used.• Chapter 5 presents Fast Gauss Transform methods and shows its usefulness forour algorithm.• Chapter 6 contains a thorough experimental analysis on synthetic and realdatasets of the 3D registration method. Included are studies of robustness tonoise, overlap, feature choice, as well as convergence properties. This chaptershows the results of IR to color registration and examples of multimodal 3Dreconstruction.• Chapter 7 will present a short summary of the dissertation’s seminal points, adiscussion with concluding remarks, and opportunities for future research.