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This paper proposes fast sub-pixel motion estimation techniques having lower computational complexity. The proposed methods are based on mathematical models of the motion-compensated prediction errors in compressing moving pictures. Unlike conventional hierarchical motion estimation techniques, the proposed methods avoid sub-pixel interpolation and subsequent secondary search after the integer-precision motion estimation, resulting in reduced computational time. In order to decide the coefficients of the models, the motion-compensated prediction errors of the neighboring pixels around the integer-pixel motion vector are utilized. The prediction errors, here, were already obtained during the pixel accuracy motion search. Once the coefficients are determined, the models estimate motion compensated prediction errors at sub-pixel locations surrounding the integer-pixel motion vector, yielding the sub-pixel motion vector. The performance of the proposed methods, despite substantially lower computational complexity, is close to that of the conventional interpolation-and-search method.