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In this paper we present a new method for tracking rigid objects using a modified version of the Active Appearance Model. Unlike most of the other appearance-based methods in the literature, our method allows for both partial and self occlusion of the objects. We use ground-truth to demonstrate the accuracy of our tracking algorithm. We show that our method can be applied to track moving objects over wide variations in position and orientation of the object - one meter in translation and 140 degrees in rotation - with an accuracy of a few millimeters.