| Medical imaging, modeling, computer graphics, and computer vision are fields that represent and manipulate three dimensional surfaces. Such surfaces are often represented by irregularly spaced points connected into a mesh of edges and faces. There are many classical signal processing techniques which would also be useful in surface representations. In particular, frequency domain representations of surfaces could be used for filtering, classification, and other tasks. We develop a frequency representation for surfaces using results and methods from nonuniform sampling theory. We then use this representation to adjust the number of samples in a surface as it is deformed to match a target object.; The general organization of this dissertation is as follows. First, we introduce the objective and describe potential applications. Next, we review relevant background material from geometry and signal processing, describe current shape analysis methods, and review useful or related results from the literature. We then present the continuous and discrete versions of our frequency representation for surfaces, including a set of procedures developed in response to specific problems with the surface representation. Next, we use these techniques to adjust the number of samples in a deformable model. Finally, we review the current status of this investigation, and outline the anticipated course of future work. |
