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A well-known theoretical result for motion estimation using the generalized camera model is that 17 corresponding image rays can be used to solve linearly for the motion of a generalized camera. However, this paper shows that for many common configurations of the generalized camera models (e.g., multi-camera rig, catadioptric camera etc.), such a simple 17-point algorithm does not exist, due to some previously overlooked ambiguities. We further discover that, despite the above ambiguities, we are still able to solve the motion estimation problem effectively by a new algorithm proposed in this paper. Our algorithm is essentially linear, easy to implement, and the computational efficiency is very high. Experiments on both real and simulated data show that the new algorithm achieves reasonably high accuracy as well.