A level set based fractional order variational model for motion estimation in application oriented spectrum

In recent years, motion estimation has become prominent in the field of computer vision. This is due to its applications in various domains such as object detection, video surveillance, undersea navigation, fire damage control, particle image velocimetry etc. Therefore, in this paper, a nonlinear fractional order variational model is introduced for motion estimation in an image sequence (video). The motion estimation is performed in terms of optical flow. The objective of this work is to generalize the existing variational models from integer order to fractional order and provide the increased robustness against outliers, and furnish the dense and discontinuity preserving optical flow in various spectra such as synthetic, sintell, thermal, underwater, medical, fire and smoke and fluid image sequences. For this purpose, a level set segmentation based fractional order variational functional composed of a non-quadratic Charbonnier norm and a regularization term is propounded. This non-quadratic penalty provides an effective robustness against outliers, whereas the fractional derivative possesses a non-local character, and therefore is capable to deal with discontinuous information about texture and edges. The level set segmentation is performed 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 numerical discretization of the fractional partial differential equations is employed with the help of Grunwald- Letnikov fractional derivative. The resulting nonlinear formulation is converted into a linear system and solved by an efficient numerical technique. The experimental results are carried out on 10 different application oriented spectra. The performance of the model is tested using different error measures and demonstrated against several outliers. The efficiency and accuracy of the proposed model is shown against recently published works. The graphical abstract for this algorithm is illustrated under the next section.