We address the fundamental problem of optimally splitting a video sequence into two sources of information, the displaced frame difference (DFD) and the displacement vector field (DVF). We first consider the case of a lossless motion compensated video coder (MCVC) and derive a general dynamic programming (DP) formulation which results in an optimal tradeoff between the DVF and the DFD. We then consider the more important case of a lossy MCVC and present an algorithm which solves optimally the bit allocation between the rate and the distortion. This algorithm is based on Lagrangian relaxation and the DP approach introduced for the lossless MCVC. We then present an H.263-based MCVC which uses the proposed optimal bit allocation scheme and compare its results to H.263. As expected, the proposed coder is superior in the rate-distortion sense.
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