Implicit models of moving and static surfaces

Computer vision is a growing research area with commercial applications ranging from surveillance to database search, from industrial inspection to multimedia and computer interfaces. There has been a vast amount of research on each of these applications over the last two or three decades and challenging problems of computer vision and solutions to those problems have evolved quite a lot since then. This thesis contributes to two research areas in computer vision: shape representation and modeling and motion analysis.; The first part of this thesis presents dense estimation of motion and appearance in layers. Modeling or explaining appearance change in image sequences is one of the challenging problems of computer vision. A great deal of research has been done to understand what goes with what in the scene, separate image sequences into depth layers, and model background/foreground using temporal consistency, spatial coherence or layers. Background subtraction techniques are popular for their simplicity they typically ignore image motion which can provide a rich source of information about scene structure. Conversely, layered motion estimation techniques typically ignore the temporal persistence of image appearance and provide parametric (rather than dense) estimates of optical flow. Recent work adaptively combines motion and appearance estimation in a mixture model framework to achieve robust tracking. In this thesis, the mixture model approaches are extended to cope with dense motion and appearance estimation. A unified Bayesian framework is proposed to simultaneously estimate the appearance of multiple image layers and their corresponding dense flow fields from image sequences. Both the motion and appearance models adapt over time and the probabilistic formulation can be used to provide a segmentation of the scene into foreground/background regions. This extension of mixture models includes priors for the spatial and temporal coherence of motion and appearance. Experimental results show that the simultaneous estimation of appearance models and flow fields in multiple layers improves the estimation of optical flow at motion boundaries.; The second part of this thesis is based on shape representation and modeling using implicit polynomials. A new non-symbolic implicitization technique called the matrix annihilation method is proposed for converting parametric Fourier representations to algebraic (implicit polynomial) representations to provide a means of benefiting from the features of both. (Abstract shortened by UMI.)...