A fractional order variational model for the robust estimation of optical flow from image sequences

In this paper, a fractional order variational model for estimating the optical flow is presented. In particular, the proposed model generalizes the integer order variational optical flow models. The fractional order derivative describes discontinuous information about texture and edges, and therefore a more suitable in estimating the optical flow. The proposed variational functional is a combination of a global model of Horn and Schunck and the classical model of Nagel and Enkelmann. This formulation yields a dense flow and preserves discontinuities in the flow field and also provides a significant robustness against outliers. The Grünwald-Letnikov derivative is used for solving complex fractional order partial differential equations. The corresponding linear system of equations is solved by an efficient numerical scheme. A detailed stability and convergence analysis is given in order to show the mathematical applicability of the numerical algorithm. Experimental results on various datasets verify the validity of the proposed model.