In our work, the traditional sub-pixel application and its new development are explored. First, prior use of sub-pixel techniques in video coding are demonstrated. Then we introduce a new form of advanced sub-pixel interpolation---Lagrangian interpolation. This new approach to interpolate sub-pixel grids increases the video coding quality. To simplify the motion estimation process, we introduce fast subpixel motion-search algorithm and successfully utilize it to reduce the computational complexity. We also use Lagrangian interpolation to build a displacement error surface which allows us to use numerical optimization method to find the global minimum of the displacement error. It is demonstrated that sequential quadratic programming (SQP) maintains the coding quality and reduces the computational time in a number of video sequences.; Our algorithms are designed for the spatial and wavelet-based video coding architectures. We present the results in both experimental systems. (Abstract shortened by UMI.)
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