In the past, most design and optimization work on hybrid video codecs relied mainly on experimental evidence. A proper theoretical model is always desirable, since this allows us to explain the phenomena of existing codecs and to design better ones. In this paper, we make use of the first-order Markov model to derive an approximated separable autocorrelation model for the block-based motion compensation frame difference (MCFD) signal. A major assumption of our derivation is that the net deformation of pixels is directional, in general, rather than a uniform error distribution in a block. We have also shown that the imperfect block-based motion compensation is significant to the theoretical study and the behavior of motion-compensated codecs. Results of our experimental work show that the derived model can describe the statistical characteristics of the MCFD signals accurately. The model also shows that the imperfectly formulated block-based motion compensation can result in an incorrect MCFD autocorrelation function while, conversely, it can form a better block-based motion compensation scheme.
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