Efficiency analysis of multihypothesis motion-compensated prediction for video coding

Overlapped block motion compensation or B-frames are examples of multihypothesis motion compensation where several motion-compensated signals are superimposed to reduce the bit-rate of a video codec. This paper extends the wide-sense stationary theory of motion-compensated prediction (MCP) for hybrid video codecs to multihypothesis motion compensation. The power spectrum of the prediction error is related to the displacement error probability density functions (pdfs) of an arbitrary number of hypotheses in a closed-form expression. We then study the influence of motion compensation accuracy on the efficiency of multihypothesis motion compensation as well as the influence of the residual noise level and the gain from optimal combination of N hypotheses. For the noise-free limiting case, doubling the number of (equally good) hypotheses can yield a gain of up to 1/2 bits/sample, while doubling the accuracy of motion compensation can additionally reduce the bit-rate by up to 1 bit/sample independent of N. For realistic noise levels, it is shown that the introduction of B-frames or overlapped block motion compensation can provide larger gains than doubling motion compensation accuracy. Spatial filtering of the motion-compensated candidate signals becomes less important if more hypotheses are combined. The critical accuracy beyond which the gain due to more accurate motion compensation is small moves to larger displacement error variances with increasing noise and increasing number of hypotheses N. Hence, sub-pel accurate motion compensation becomes less important with multihypothesis MCP. The theoretical insights are confirmed by experimental results for overlapped block motion compensation, B-frames, and multiframe motion-compensated prediction with up to eight hypotheses from ten previous frames.