A nonlinear modeling of fractional order based variational model in optical flow estimation

Abstract

In this paper, a nonlinear fractional order variational (NFOV) model is introduced to estimate the optical flow. In particular, the presented model can be scaled to the existing integer order variational models. The proposed variational functional is designed by combining a non-quadratic Charbonnier norm based data term and Marchaud fractional derivative based regularization term. This non-quadratic penalty is robust against outliers, whereas the non-local character of Marchaud fractional derivative leads the model to deal with the discontinuous information about texture and edges, and yields a dense flow field. The numerical discretization of the Marchaud fractional derivative is carried out with the help of Grünwald–Letnikov fractional derivative. The discretized nonlinear system is further reduced to a linear system of equations by employing an outer fixed point iteration scheme, and finally solved with an efficient iteration technique. The experiments are performed over a variety of datasets. The performance of the model is tested using different error measures (AAE, AEE, AENG, WE) depending upon the availability of the ground truth (GT) flow. The robustness of the NFOV model is shown under different amounts of noise along with the variation of smoothing parameter. A detailed comparison with the recently published works is presented to demonstrate the efficiency and accuracy of the proposed model.