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In this paper, we propose a new motion estimation algorithm to be used for motion-compensated frame rate up-conversion. The proposed algorithm independently carries out motion estimations in both forward and backward directions, and selects a more reliable one between forward and backward motion vectors by evaluating the motion vector reliability from the viewpoint of the interpolated frame. The proposed algorithm smooths and refines both the forward and backward motion vectors before selecting the reliable one. This procedure helps to select the reasonable motion estimation direction. In identifying the motion vector outliers, the proposed algorithm uses a circular range of which center is located at the mean of the eight neighboring motion vectors of the motion vector being processed. Experimental results using 1720 test images show that the proposed motion estimation algorithm improves the average peak signal-to-noise ratio and the average structural similarity of the interpolated frames by up to 5.31 dB and 0.053, respectively, compared to conventional motion estimation algorithms.