  Estimating optical flows is one of the most interesting problems in computer
vision, which estimates the essential information about pixel-wise
displacements between two consecutive images. This work introduces an efficient
dual optimization framework with accelerated preconditioners to the challenging
nonsmooth optimization problem of total-variation regularized optical-flow
estimation. In theory, the proposed dual optimization framework brings an
elegant variational analysis on the given difficult optimization problem, while
presenting an efficient algorithmic scheme without directly tackling the
corresponding nonsmoothness in numeric. By introducing efficient
preconditioners with a multi-scale implementation, the proposed accelerated
dual optimization approaches achieve competitive estimation results of image
motion, comparing to the state-of-the-art methods. Moreover, we show that the
proposed preconditioners can guarantee convergence of the implemented numerical
schemes with high efficiency.
