Charbonnier-Marchaud Based Fractional Variational Model for Motion Estimation in Multispectral Vision System

Abstract

As we are aware that motion estimation is an active and challenging area of vision system, which leads to the applications of computer vision. In general, motion detection and tracking in the image sequence (video) is carried out based on optical flow. In the recent-past, researchers have made a significant contribution to the estimation of optical flow through integer order-based variational models, but these are limited to integer order differentiation. In this paper, a nonlinear modeling of fractional order variational model in optical flow estimation is introduced using the Charbonnier norm, which can be scaled to integer order L 1-norm. In particular, the variational functional is formulated by the inclusion of a non-quadratic penalty term, regularization term and the Marchaud’s fractional derivative. This non-quadratic penalty provides effective robustness against outliers, whereas the Marchaud’s fractional derivative possesses a non-local character, and therefore is capable to deal with discontinuous information about texture and edges, and yields a dense flow field. The numerical discretization of the Marchaud’s fractional derivative is employed with the help of Grünwald–Letnikov fractional derivative. The resulting nonlinear system is converted into a linear system and solved by an efficient numerical technique. Several experiments are performed over a spectrum of datasets. The robustness and accuracy of the proposed model are shown under different amounts of noise and through detailed comparisons with the recently published works.