A Segmentation Based Robust Fractional Variational Model for Motion Estimation

Abstract

In this paper, we introduce a nonlinear robust fractional order varia-tional framework for motion estimation from image sequences (video). Particu-larly, the presented model provides a generalization of integer order derivative based variational functionals and offers an enhanced robustness against outliers while preserving the discontinuity in the dense flow field. The motion is esti-mated in the form of optical flow. For this purpose, a level set segmentation based fractional order variational functional composed of a non-quadratic Char-bonnier norm and a regularization term is propounded. The non-quadratic Char-bonnier norm introduces a noise robust character in the model. The fractional order derivative demonstrates non-locality that makes it competent to deal with discontinuous information about edges and texture. The level set segmentation is carried on the flow field instead of images, which is a union of disjoint and independently moving regions such that each motion region contains objects of equal flow velocity. The resulting fractional order partial differential equations are numerically discretized using Grunwald-Letnikov fractional derivative. The nonlinear formulation is transformed into a linear system which is solved with the help of an efficient numerical technique. The results are evaluated by conducting experiments over a variety of datasets. The accuracy and efficiency of the propounded model is also depicted against recently published works.