Optimizing motion-vector accuracy in block-based video coding

In classical block-based video coding, one motion vector per image block is used to improve the prediction of the frame to be coded. These motion vectors and the resulting motion-compensated difference frame must be encoded with bits. All motion vectors are encoded with the same fixed accuracy, typically m-pixel accuracy, but the best motion-vector accuracies are not known. In this paper, we present a theoretical framework to find the motion vector accuracies that minimize the total encoding rate with this type of coder, for the classical case where all motion vectors are encoded with the same accuracy, and for new cases where the accuracy is adapted on a frame-by-frame or block-by-block basis. To do this, we analytically model the effect of motion vector accuracy and show that the energy in a block of the difference frame is approximately quadratic in the accuracy of the block's motion vector. This energy-accuracy model is then used to obtain expressions for the total bit rate (motion rate plus difference-frame rate) in terms of the blocks' motion accuracies and other key parameters. Minimizing these expressions leads to simple formulas that indicate how to choose the best motion-vector accuracies for this type of coder. These formulas also show that the motion accuracy must increase where more texture is present and decrease when there is much scene noise or when the level of compression is high. We implement several entropy and MPEG-like video coders based on our analysis and present experimental results on synthetic and real video sequences. These results suggest that our formulas are accurate and that significant bit rate savings can be achieved when our optimization procedures are used.