We propose an optimal quadtree (QT)-based motion estimator for video compression. It is optimal in the sense that for a given bit budget for encoding the displacement vector field (DVF) and the QT segmentation, the scheme finds a DVF and a QT segmentation which minimizes the energy of the resulting displaced frame difference (DFD). We find the optimal QT decomposition and the optimal DVF jointly using the Lagrangian multiplier method and a multilevel dynamic program. We introduce a new, very fast convex search for the optimal Lagrangian multiplier /spl lambda/*, which results in a very fast convergence of the Lagrangian multiplier method. The resulting DVF is spatially inhomogeneous, since large blocks are used in areas with simple motion and small blocks in areas with complex motion. We also propose a novel motion-compensated interpolation scheme which uses the same mathematical tools developed for the QT-based motion estimator. One of the advantages of this scheme is the globally optimal control of the tradeoff between the interpolation error energy and the DVF smoothness. Another advantage is that no interpolation of the DVF is required since we directly estimate the DVF and the QT-segmentation for the frame which needs to be interpolated. We present results with the proposed QT-based motion estimator which show that for the same DFD energy the proposed estimator uses about 25% fewer bits than the commonly used block matching algorithm. We also experimentally compare the interpolated frames using the proposed motion compensated interpolation scheme with the reconstructed original frames.
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