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In this paper, we look at the issue of accurate estimation of the three-dimensional motion parameters of a rigid body from a sequence of synthetic images, and relate the effect of some parameters to the shape of an error function. We first consider the case where only a small set of corresponding points is identified and suggest that a technique called regularization improves the quality and stability of a solution. We then observe that, if more pairs of corresponding points are available, the error function becomes smooth and the solution stable. Finally, we try to improve the quality of estimation by considering more than two consecutive frames for a moving camera looking at a stationary scene, and summing the error functions obtained for any two consecutive frames. Surprisingly enough, this technique does not improve stability unless we use regularization again.