A locally quadratic model of the motion estimation error criterion function and its application to subpixel interpolations

It is observed that around the optimum point of the motion estimation process the error criterion function is well modeled as a quadratic function with respect to the motion vector offsets. This locally quadratic functional model decomposes the motion estimation optimization at subpixel resolutions into a two-stage pipelinable processes: full-search at full-pixel resolution and interpolation at any subpixel resolution. Practical approximation formulas lead to the explicit computations of both motion vectors and error criterion functional values at subpixel resolutions.