On the estimation of optical flow: A novel robust estimation based in fractional derivatives with kernel exponential

A fractional operator for optical flow estimation is presented in this research paper. The formulation of this operator is carried out by the Caputo–Fabrizio derivative and the Horn–Schunck method. In this way, our operator generalizes the traditional Horn–Schunck technique. The Caputo–Fabrizio fractional-order derivative is introduced for its high capability to enhance and preserve both texture detail and image edges, making it more suitable for optical flow estimation in images with weak edges caused by low contrast or noise. A fractional-order multiscale strategy is also considered to deal with large displacements. This fractional-order approach produces a dense flow and greatly increases robustness at outliers. Experimental comparisons with the conventional multiscale Horn–Schunck algorithm and some integer- and fractional-order methods existing on the MPI Sintel and Middlebury Stereo datasets demonstrate that our operator provides significantly lower average endpoint error and average angular error. The firefly algorithm is used to get the optimal order for all the stereoscopic image sequences.