Simplex minimization for single- and multiple-reference motion estimation

Block-matching motion estimation (BMME) can be formulated as a 2-D constrained minimization problem. This problem can, therefore, be solved with reduced complexity using optimization techniques. This paper proposes a novel fast BMME algorithm called the simplex minimization search (SMS). The algorithm is based on the simplex minimization (SM) optimization method. The initialization procedure, termination criterion, and constraints on the independent variables of the search are designed to take advantage of the characteristics of the BMME problem and the properties of the block motion fields of typical video sequences. Simulation results show that the proposed algorithm outperforms other fast BMME algorithms, providing better prediction quality, a smoother motion field, and higher speed-up ratio. This paper also investigates the properties of the multiple-reference (MR) block motion field. Guided by the results of this investigation, the paper extends the SMS algorithm to the MR case. Three MR SMS algorithms are proposed, providing different degrees of compromise between prediction quality and computational complexity. Simulation results using 50 reference frames indicate that the proposed MR algorithms have a computational complexity comparable to that of single-reference full-search while still maintaining the prediction gain of MR motion estimation.