Optimal quad-tree-based motion estimator

In this paper we propose an optimal quad-tree (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. 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 present results with the proposed QT-based motion estimator which show that for the same DFD energy the proposed estimator uses about 30% fewer bits than the commonly used block matching algorithm.