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We propose block-based motion estimation algorithms based on the pixelwise classification of the motion compensation error: (1) displaced frame difference (DFD) and (2) brightness constraint constancy term (BCCT). Block-based motion estimation has disadvantages such as unreliable motion vectors and block artifacts, especially in object boundaries. The proposed algorithms attempt to reduce artifacts in boundary blocks caused by incorrect assumption of a single rigid (translational) motion. They yield more appropriate motion vectors in boundary blocks under the assumption that there exist up to three different regions with different motions. Experimental results with several test sequences show the effectiveness of the proposed algorithms.