An Estimation-Theoretic Interpretation of Video Rate Distortion Optimization with Lagrangian Formulation

Rate distortion optimization with Lagrangian formulation is widely used in video encoder control and has proved effective in achieving a good trade-off between coding efficiency and computational complexity. It is generally interpreted as a source coding problem with a fidelity criterion. However, this interpretation cannot fully explain the Lagrangian formulation for motion estimation and how to select the corresponding Lagrangian multipliers. In this paper, we provide a new perspective based on an estimation-theoretic interpretation that formulates motion estimation and mode decision as a maximum a posteriori (MAP) estimation problem. Several interesting conclusions can be drawn from this interpretation. We show that the Lagrangian formulation in video encoder control is a straightforward result under this interpretation. With this interpretation, we can further analyze the Lagrangian multiplier's dependence on the quantization parameter and motion intensity of the content.