In this work, we derive the rate-distortion function for video coding using affine global motion compensation.
We model the displacement estimation error during motion estimation and obtain the bit rate after applying the rate-distortion theory.
We assume that the displacement estimation error is caused by a perturbed affine transformation.
The 6 affine transformation parameters are assumed statistically independent, with each of them having a zero-mean Gaussian distributed estimation error.
Based on that, the joint probability density function (pdf) of the displacement estimation errors is derived and related to the prediction error.
Using the rate-distortion theory, we calculate the bit rate in dependence of the perturbation of the affine transformation parameters.
Comparing with a translational motion model in video coding standards like HEVC, we determine accuracy boundaries for the affine transformation, with which a gain can be achieved.