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Title: Constrained PDE Optimization Methods for Motion Segmentation and Layer Extraction
Committee:
Dr. Yezzi, Advisor
Dr. Vela, Chair
Dr. AlRegib
Dr. Kang
Abstract:
The objective of the proposed research is to present a variational approach to building generative layered models that have flexibility in modeling shape, appearance, motion and occlusion structure (for objects in a set of images). Such a layered representation allows us to capture the motion, shape, appearance and occlusion structure without going into the complexity of a full 3D representation of the scene. We approach this problem in the framework of PDEs and calculus of variations. Our proposed technique links to the simplification of an earlier variational approach to layering that used diffeomorphic maps (for modeling shape) and Mumford Shah style appearance models. We simplify the shape modeling component by replacing the diffeomorphic maps with active contours. This significantly reduces the computational complexity of the model, allows for an easier implementation and yet still provides a generous amount of flexibility in modeling shape. A novelty of this modeling technique is that it relaxes the brightness constancy constraint for pixels associated with a particular moving object which is likely to be the case when tracking moving objects in real life and therefore makes the model a better fit for most real life scenes. Furthermore we discovered that a joint (appearance and shape) optimization for the layers in such a model induced a surprising shrinking bias on the regions covered by the foreground layers as images with a more heterogeneous appearance were used (which is where the model was designed to excel). We were able to trace the cause for this effect to a bias in the formulation in the original model that unintentionally penalized the amount of layer occlusion thereby producing the effect. We resolve this problem by replacing the joint optimization with an alternative constrained shape optimization subject to PDE based appearance constraints. In doing so we bring out the true potential of the proposed technique.
