Block size dependent error model for motion compensation

Current video coding standards use block-based motion estimation and compensation algorithms to exploit dependencies between consecutive frames. It is a well-known fact that decreasing the block size reduces the motion-compensated frame difference, and thus reduces the data rate. However, no theoretical evaluations are available to model this relation. This paper derives a model for the prediction error variance of block-based motion compensation algorithms with respect to the block size. It is shown that the variance of the displaced frame difference of a block can be modelled with the pixel position and only three additional parameters. It can be observed that the variance increases almost linearly with the block size.