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Reliable tracking of multiple moving objects in video is an interesting challenge, made difficult in real-world video by various sources of noise and uncertainty. We propose a Bayesian approach to find correspondences between moving objects over frames. By using color values and position information of the moving objects as observations, we probabilistically assign tracks to those objects. We allow for tracks to be lost and then recovered when they resurface. The probabilistic assignment method, along with the ability to recover lost tracks, adds robustness to the tracking system. We present results that show that the Bayesian method performs well in difficult tracking cases and compare the probabilistic results to a Euclidean distance based method.