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We present a theory for the optimal bit allocation among quadtree (QT) segmentation, displacement vector field (DVF), and displaced frame difference (DFD). The theory is applicable to variable block size motion-compensated video coders (VBSMCVC), where the variable block sizes are encoded using the QT structure, the DVF is encoded by first-order differential pulse code modulation (DPCM), the DFD is encoded by a block-based scheme, and an additive distortion measure is employed. We derive an optimal scanning path for a QT that is based on a Hilbert curve. We consider the case of a lossless VBSMCVC first, for which we develop the optimal bit allocation algorithm using dynamic programming (DP). We then consider a lossy VBSMCVC, for which we use Lagrangian relaxation, and show how an iterative scheme, which employs the DP-based solution, can be used to find the optimal solution. We finally present a VBSMCVC, which is based on the proposed theory, which employs a DCT-based DFD encoding scheme. We compare the proposed coder with H.263. The results show that it outperforms H.263 significantly in the rate distortion sense, as well as in the subjective sense.
Schuster et al. (Sat,) studied this question.