This thesis tackles the visual tracking problem as a target contour estimation problem in the face of corrupted measurements. The major aim is to design robust recursive curve filters for accurate contour-based tracking. The state-space representation adopted comprises of a group component and a shape component describing the rigid motion and the non-rigid shape deformation respectively; filtering strategies on each component are then decoupled. The thesis considers two implicit curve descriptors, a classification probability field and the traditional signed distance function, and aims to develop an optimal probabilistic contour observer and locally optimal curve filters. For the former, introducing a novel probabilistic shape description simplifies the filtering problem on the infinite-dimensional space of closed curves to a series of point-wise filtering tasks. The definition and justification of a novel update model suited to the shape space, the derivation of the filtering equations and the relation to Kalman filtering are studied. In addition to the temporal consistency provided by the filtering, extensions involving distributed filtering methods are considered in order to maintain spatial consistency. For the latter, locally optimal closed curve filtering strategies involving curve velocities are explored. The introduction of a local, linear description for planar curve variation and curve uncertainty enables the derivation of a mechanism for estimating the optimal gain associated to the curve filtering process, given quantitative uncertainty levels. Experiments on synthetic and real sequences of images validate the filtering designs.
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