Dense optical flow estimation in images is a challenging problem because the algorithm must coordinate the estimated motion across large regions in the image, while avoiding inappropriate smoothing over motion boundaries. Recent works have advocated for the use of nonlocal regularization to model long-range correlations in the flow. However, incorporating nonlocal regularization into an energy optimization framework is challenging due to the large number of pairwise penalty terms. Existing techniques either substitute intermediate filtering of the flow field for direct optimization of the nonlocal objective, or suffer substantial performance penalties when the range of the regularizer increases. In this paper, we describe an optimization algorithm that efficiently handles a general type of nonlocal regularization objectives for optical flow estimation. The computational complexity of the algorithm is independent of the range of the regularizer. We show that nonlocal regularization improves estimation accuracy at longer ranges than previously reported, and is complementary to intermediate filtering of the flow field. Our algorithm is simple and is compatible with many optical flow models.
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