Technical Report PHD-2007-08

Title: Topics In Motion Analysis
Authors: Tal Nir
Supervisors: Alfred Bruckstein
Abstract: In this work we cover several motion analysis topics. In the context of optical flow estimation and sequence restoration, we show that the two problems are coupled and should be solved simultaneously, we formulate a single functional which expresses this coupling. The resulting numerical scheme iteratively changes both the optical flow and the image sequence and achieves improved optical flow reconstruction under noise. In the context of the total variation denoising, we propose an over-parameterized model based approach which yields improved regularization by penalizing for deviations from the desired model. We derive the Euler-Lagrange equations in the higher dimensional over-parameterized space. The proposed over-parameterization methodology developed here is a general tool which can be used in many problems requiring the use of regularization. Then, in the context of optical flow, we express the optical flow by a general over-parameterized model which can represent models with independent coefficients for the u and v components (such as the affine case) or models with coupling between the coefficients as in the case of a rigid or pure translation motion models. Finally, we address the problem of camera motion estimation employing the CONDENSATION methodology which was originally developed for contour tracking and tools from robust statistics yielding an efficient and robust scheme for camera motion estimation.
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