On the optimal Lagrangian parameter for motion estimation: A low-cost and effective method for improving video coding performance

The most recent video coding standards are usually based on a rate-distortion optimization (RDO) process that has been formulated in terms of an unconstrained Lagrangian optimization. The RDO provides outstanding results in exchange for a high computational cost, especially for the Inter frames, which require a computationally heavy motion estimation (ME) process. In particular, for H.264/AVC, this RDO process allows selecting both the MB partition size and the motion vector. However, as the optimum procedure is not feasible for computational reasons, the ME process uses a simplified rate-distortion (RD) cost function. Therefore, two RDO processes are involved, one for selecting the MB partition size and one for ME. Both RDO processes rely on an Lagrangian formulation and, for practical purposes, the corresponding Lagrangian parameters are related by a simple, experimentally obtained relationship. In this paper, some evidences of the weaknesses of such a relationship between the two Lagrangian parameters are given and a simple effective procedure to improve the R-D encoding performance is proposed according to such weaknesses. The proposed method has been comparatively evaluated with respect to one recently published method, showing significant average performance improvements, above 0.4 dB in terms of PSNR.