Rate-Distortion Theory for Simplified Affine Motion Compensation Used in Video Coding

In this work, we derive the rate-distortion function for video coding using the simplified affine, 4-parameter motion compensation model as it is used in the Joint Exploration Model (JEM) by the Joint Video Exploration Team (JVET) on Future Video coding. We model the displacement estimation error during motion estimation and obtain the bit rate by applying the rate-distortion theory. We assume that the displacement estimation error is caused by perturbed parameters of the simplified affine model. These transformation parameters are assumed statistically independent, with each of them having a zero-mean Gaussian distributed estimation error. The joint probability density function (p.d.f.) of the displacement estimation errors is derived and related to the prediction error. We calculate the bit rate as a function of the accuracy of the parameter estimation for the simplified affine motion model. Finally, we compare our results with a translational motion model as used in video coding standards like HEVC as well as with a full affine motion model with 6 degrees of freedom. For aerial sequences containing distinct affine motion, the minimum required bit rate to encode the prediction error can be significantly reduced from 2.5 ^bit / sample to 0.02 bit/sample for a reasonable operating point and a block size of 64×64 pel ² .