This thesis makes significant contributions to the object detection problem in computer vision. The object detection problem is, given a digital image of a scene, to detect the relevant object in the image. One technique for performing object detection, called ``active contours,' optimizes a constructed energy that is defined on contours (closed curves) and is tailored to image features.An optimization method can be used to perform the optimization of the energy, and thereby deform an initially placed contour to the relevant object. The typical optimization technique used in almost every active contour paper is evolving the contour by the energy's gradient descent flow, i.e., the steepest descent flow, in order to drive the initial contour to (hopefully) the minimum curve. The problem with this technique is that often times the contour becomes stuck in a sub-optimal and undesirable local minimum of the energy. This problem can be partially attributed to the fact that the gradient flows of these energies make use of only local image and contour information. By local, we mean that in order to evolve a point on the contour, only information local to that point is used.Therefore, in this thesis, we introduce a new class of flows that are global in that the evolution of a point on the contour depends on global information from the entire curve. These flows help avoid a number of problems with traditional flows including helping in avoidingundesirable local minima. We demonstrate practical applications of these flows for the object detection problem, including applicationsto both image segmentation and visual object tracking.
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