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Frame rate up-conversion (FRUC) improves the viewing experience of a video because the motion in a FRUC-constructed high frame-rate video looks more smooth and continuous. This paper proposes a multiple hypotheses Bayesian FRUC scheme for estimating the intermediate frame with maximum a posteriori probability, in which both temporal motion model and spatial image model are incorporated into the optimization criterion. The image model describes the spatial structure of neighboring pixels while the motion model describes the temporal correlation of pixels along motion trajectories. Instead of employing a single uniquely optimal motion, multiple “optimal” motion trajectories are utilized to form a group of motion hypotheses. To obtain accurate estimation for the pixels in missing intermediate frames, the motion-compensated interpolations generated by all these motion hypotheses are adaptively fused according to the reliability of each hypothesis. We revealed by numerical analysis that this reliability (i.e., the variance of interpolation errors along the hypothesized motion trajectory) can be measured by the variation of reference pixels along the motion trajectory. To obtain the multiple motion fields, a set of block-matching sizes is used and the motion fields are estimated by progressively reducing the size of matching block. Experimental results show that the proposed method can significantly improve both the objective and the subjective quality of the constructed high frame rate video.