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Binary motion estimation algorithms reduce the computational complexity of motion estimation, but, sometimes generate an inaccurate motion vector. This paper proposes a novel two-bit representation, called twobit transform-second derivatives (2BT-SD) which improves the efficiency of image binarization and the accuracy of motion estimation by making use of the positive and negative second derivatives independently in the derivation of the second bit plane. The second derivatives are also used to detect flat or background regions, avoiding expensive motion vector search operations for macroblocks in these areas, and deriving the motion vectors by prediction from neighboring blocks. In applying the proposed 2BT-SD in the H.264/AVC standard, a further reduction of motion estimation complexity with a minor accuracy reduction is achieved by using 2BT-SD representation for secondary motion estimation while using the full resolution representation for the primary motion estimation. A hardware cost analysis shows that about 209 K gates of hardware logics and 2.7 K bytes of memory are reduced by 2BT-SD for motion estimation of 1280times720 size videos when compared with the full resolution motion estimation. Experiments show that the proposed 2BT-SD achieves better motion estimation accuracy than other binary motion estimations and provides faster processing time in flat or background regions with an acceptable bit-rate increase.