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The application of advanced motion compensation techniques-control grid interpolation (CGI) and overlapped block motion compensation (OBMC)-to video coding systems provides significant performance advantages, terms of compression ratio and visual quality, over traditional block-matching motion compensation. However, the two-dimensional (2-D) interdependence among motion vectors introduced by these compensation frameworks makes the problem of finding rate-distortion optimal motion vectors, computationally prohibitive. Thus, iterative optimization techniques are often used to achieve good compensation performance. While most reported optimization algorithms adopt an approach that uses a block-matching algorithm to obtain an initial estimate and then successively optimize each motion vector, the over-relaxed motion-vector dependency relations often result in considerable performance degradation. In view of this problem, we present a new optimization scheme for dependent motion-vector optimization problems, one based on dynamic programming. Our approach efficiently decomposes 2-D dependency problems into a series of one-dimensional (1-D) dependency problems. We show that a reliable initial estimate of motion vectors can be obtained efficiently by only considering the dependency in the rate term. We also show that at the iterative optimization stage an effective logarithmic search strategy can be used with dynamic programming to reduce the necessary complexity involved in distortion computation. Compared to conventional iterative approaches, our experimental results demonstrate that our algorithm provides superior rate and distortion performance while maintaining reasonable complexity