Motion estimation and compensation is widely used for exploiting temporal correlation within an image sequence. To find motion vectors that lead to high compression, most motion estimation approaches use a source distortion measure, such as mean-square error (MSE) or mean-absolute error (MAE), as a search criterion. When incorporated into a closed-loop motion compensated (MC) transform video coder, these schemes produce noisy motion fields which significantly increase the bit-rates required to represent motion vectors. In view of this problem, this paper presents a rate-distortion optimal motion estimation algorithm. The proposed scheme improves rate performance of the estimated motion field while maintaining the peak signal-to-noise ratio (PSNR) prediction quality of the distortion-based methods, thereby enabling an efficient bit allocation between motion information and transform-coded prediction residuals. For coders in which motion vectors are differentially encoded, the rate-distortion optimization process is formulated as a shortest-path-finding problem. Adopting this framework, we show that the optimal solution for the conventional block-based motion estimation, followed by one-dimensional (1-D) differential coding and Huffman coding, can be obtained by using dynamic programming or the Viterbi algorithm. We propose an effective fast algorithm that closely approximates the optimal performance while requiring considerably less complexity. Our experimental results demonstrate overall gains in the range of 0.3-1.5 dB.
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