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<p><b>Abstract</b>—Multiple moving objects, partially occluded objects, or even a single object moving against the background gives rise to discontinuities in the optical flow field in corresponding image sequences. While uniform global regularization based moderately fast techniques cannot provide accurate estimates of the discontinuous flow field, statistical optimization based accurate techniques suffer from excessive solution time. A 'weighted anisotropic' smoothness based numerically robust algorithm is proposed that can generate discontinuous optical flow field with high speed and linear computational complexity. Weighted sum of the first-order spatial derivatives of the flow field is used for regularization. Less regularization is performed where strong gradient information is available. The flow field at any point is interpolated more from those at neighboring points along the weaker intensity gradient-component. Such intensity gradient weighted regularization leads to Euler-Lagrange equations with strong anisotropies coupled with discontinuities in their coefficients. A robust multilevel iterative technique, that recursively generates coarse-level problems based on intensity gradient weighted smoothing weights, is employed to estimate discontinuous optical flow field. Experimental results are presented to demonstrate the efficacy of the proposed technique.</p>
Discontinuous optical flow estimation, weighted anisotropic smoothness, partial differential equation (PDE), scalable algorithm, multilevel iterative methods.

S. Ghosal and P. Vanek, "A Fast Scalable Algorithm for Discontinuous Optical Flow Estimation," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 18, no. , pp. 181-194, 1996.
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