Filtering for Closed Curves
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This thesis deals with the problem of tracking highly deformable objects in the presence of noise, clutter and occlusions. The contributions of this thesis are threefold: A novel technique is proposed to perform filtering on an infinite dimensional space of curves for the purpose of tracking deforming objects. The algorithm combines the advantages of particle filter and geometric active contours to track deformable objects in the presence of noise and clutter. Shape information is quite useful in tracking deformable objects, especially if the objects under consideration get partially occluded. A nonlinear technique to perform shape analysis, called kernelized locally linear embedding, is proposed. Furthermore, a new algebraic method is proposed to compute the pre-image of the projection in the context of kernel PCA. This is further utilized in a parametric method to perform segmentation of medical images in the kernel PCA basis. The above mentioned shape learning methods are then incorporated into a generalized tracking algorithm to provide dynamic shape prior for tracking highly deformable objects. The tracker can also model image information like intensity moments or the output of a feature detector and can handle vector-valued (color) images.