Image motion in computer vision: Variational analysis and experimental verification

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The purpose of this research is to provide a unified algorithmic framework under the variational paradigm of the fundamental subjects of image motion processing in computer vision. The subjects are motion estimation, detection, tracking, and three-dimensional interpretation. Motion estimation evaluates the optical velocity field from the image spatiotemporal variations. Motion detection determines the region in an image covered by the moving objects, i.e., it segments the image into a foreground of moving objects and its complement. Tracking is the process of following moving objects through an image sequence, and three-dimensional (3D) interpretation recovers the shape and motion of the objects in space which produced the image motion. Variational methods formulate problems from an optimization viewpoint, i.e., as the optimization of an objective functional which expresses all of the constraints that characterize the desired solution. As a result, they can compute very accurate solutions and do so efficiently. In spite of their manifest advantage, variational methods have not been systematically investigated in motion analysis as there are currently many important problems that have been addressed by traditional heuristic processing schemes. This research will investigate problems currently treated by non-variational methods but will also address important open problems. The investigations will consist of a variational analysis of each problem, which includes the design of the objective functional and an inquiry about efficient means of its optimization, such as parametric graph cuts and the calculus of variations via level sets. The resulting formulations will be verified by detailed comparative experimentation using image sequences from freely accessible databases dedicated to the validation of image motion processing algorithms. The anticipated outcome of this research is a unified body of efficient, easily usable, and well documented algorithms for motion analysis.