Nonlocal sparse and low-rank regularization for optical flow estimation.

Designing an appropriate regularizer is of great importance for accurate optical flow estimation. Recent works exploiting the nonlocal similarity and the sparsity of the motion field have led to promising flow estimation results. In this paper, we propose to unify these two powerful priors. To this end, we propose an effective flow regularization technique based on joint low-rank and sparse matrix recovery. By grouping similar flow patches into clusters, we effectively regularize the motion field by decomposing each set of similar flow patches into a low-rank component and a sparse component. For better enforcing the low-rank property, instead of using the convex nuclear norm, we use the log det(·) function as the surrogate of rank, which can also be efficiently minimized by iterative singular value thresholding. Experimental results on the Middlebury benchmark show that the performance of the proposed nonlocal sparse and low-rank regularization method is higher than (or comparable to) those of previous approaches that harness these same priors, and is competitive to current state-of-the-art methods.