Single Step Optimal Block Matched Motion Estimation with Motion Vectors Having Arbitrary Pixel Precisions

Problem statement: This study derives the optimal motion vector with arbitrary pixel precisions in a single step. Approach: A non-linear block matched motion model was proposed. Based on the proposed non-linear block matched motion model, the optimal motion vector which minimizes the mean square error was solved analytically in a single step via a gradient approach. Results: The mean square error based on the proposed method was guaranteed to be lower than or equal to that based on conventional methods. The computational efforts for the proposed method were lower than that of conventional methods particularly when the required pixel precision is higher than or equal to the quarter pixel precisions. Conclusion: As integer pixel locations, half pixel locations and quarter pixel locations are particular locations represented by the proposed model, the mean square error based on the proposed method is guaranteed to be lower than or equal to that based on these conventional methods. Also, as the proposed method does not require searching from coarse pixel locations to fine pixel locations, the computational efforts for the proposed method are lower than that of the conventional methods.