A method of half-pixel interpolation and quarter-pixel interpolation are adapted for reducing the impact of aliasing within motion estimation. To estimate a motion vector with quarter-pixel accuracy more efficiently, the improved method is able to skip checking certain points using the uni-modal assumption. In an embodiment, a diamond based refinement is implemented. Within the diamond based refinement are half-pel refinement and quarter-pel refinements. Furthermore, within the half-pel refinement are methods for on-the-fly interpolation and pre-computed interpolation. Within quarter-pel refinement, the method depends on whether four neighbor half-pel points are checked or just one or two half-pel points. Moreover, within each of the different embodiments is the ability to focus on quality or speed wherein different methods are implemented to maximize the desired function. In another embodiment, a square based refinement is implemented.