Tikhonov regularization and total variation (TV) are two famous smoothing techniques used in variational image processing problems and in particular for optical flow computation. We consider a new method that combines these two approaches in order to reconstruct piecewise-smooth optical flow. More precisely, we split the flow vector into the sum of its smooth and piecewise constant components, and then regularize the smooth part by quadratic Tikhonov regularization and the piecewise constant part by total variation. We solve the new variational optical flow problem through a discretize-optimize approach by applying a fast multilevel truncated Newton method. Experiments are performed on images from the Middlebury training benchmark to show the performance of our proposed method.
We introduce the use of optimization-based multigrid techniques for dense optical flow computation. In particular, we
evaluate the performance of a multigrid optimization (MG/OPT) algorithm based on a line search strategy for large-scale
optimization like truncated Newton. Our experimental tests have shown that the algorithm outperforms the truncated
Newton method even implemented with a coarse to fine strategy.