  It is well known that classical formulations resembling the Horn and Schunck
model are still largely competitive due to the modern implementation practices.
In most cases, these models outperform many modern flow estimation methods. In
view of this, we propose an effective implementation design for an
edge-preserving $L^1$ regularization approach to optical flow. The mathematical
well-posedness of our proposed model is studied in the space of functions of
bounded variations $BV(\Omega,\mathbb{R}^2)$. The implementation scheme is
designed in multiple steps. The flow field is computed using the robust
Chambolle-Pock primal-dual algorithm. Motivated by the recent studies of Castro
and Donoho we extend the heuristic of iterated median filtering to our flow
estimation. Further, to refine the flow edges we use the weighted median filter
established by Li and Osher as a post-processing step. Our experiments on the
Middlebury dataset show that the proposed method achieves the best average
angular and end-point errors compared to some of the state-of-the-art Horn and
Schunck based variational methods.
