An alternating direction method for optical flow estimation with lp regularization

We consider the optical flow estimation problem with l
_p
sub-quadratic regularization, where 0 ≤ p ≤ 1. As in other image analysis tasks based on functional minimization, sub-quadratic regularization is expected to admit discontinuities and avoid oversmoothing of the estimated optical flow field. The problem is mathematically challenging, since the regularization term is non-differentiable. It is harder than the l
₁
case, that can be addressed via Moreau proximal mapping with a closed form solution. In this paper, we propose a novel approach, based on variable splitting and the Alternating Direction Method of Multipliers (ADMM). We exemplify that our method can outperform optical flow with l
₁
regularization, but this is not the essence of this paper. The contribution is in demonstrating that state of the art optimization methods can be harnessed to solve a mathematically-challenging class of important image processing problems, and to highlight crucial numerical aspects that are often obscured in the image processing literature.