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Methods for estimating motion in video sequences that are based on the optical flow equation (OFE) assume that the scene illumination is uniform and that the imaging optics are ideal. When these assumptions are appropriate, these methods can be very accurate, but when they are not, the accuracy of the motion field drops off accordingly. This paper extends the models upon which the OFE methods are based to include irregular, time-varying illumination models and models for imperfect optics that introduce vignetting, gamma, and geometric warping, such as are likely to be found with inexpensive PC cameras. The resulting optimization framework estimates the motion parameters, illumination parameters, and camera parameters simultaneously. In some cases these models can lead to nonlinear equations which must be solved iteratively; in other cases, the resulting optimization problem is linear. For the former case an efficient, hierarchical, iterative framework is provided that can be used to implement the motion estimator.