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We address some of the major issues in optical flow within a new framework assuming nonstationary statistics for the motion field and for the errors. Problems addressed include the preservation of discontinuities, model/data errors, outliers, confidence measures, and performance evaluation. In solving these problems, we assume that the statistics of the motion field and the errors are not only spatially varying, but also unknown. We, thus, derive a blind adaptive technique based on generalized cross validation for estimating an independent regularization parameter for each pixel. Our formulation is pixelwise and combines existing first- and second-order constraints with a new second-order temporal constraint. We derive a new confidence measure for an adaptive rejection of erroneous and outlying motion vectors, and compare our results to other techniques in the literature. A new performance measure is also derived for estimating the signal-to-noise ratio for real sequences when the ground truth is unknown.