Optical Flow with Non-local Weight and Fractional Order Regularization: A Variational Model with Superpixel Algorithm for Various Application Oriented Spectrum

The motion estimation has gained significant prominence in the field of computer vision due to its wide range of applications. In general, motion estimation is performed in terms of optical flow, which is represented by a vector plot and color maps. The objective of the work is to combine the global and local optical flow, and provide the dense and discontinuity preserving robust optical flow in various application-oriented spectra. A non-local weighted fractional order variational optical flow (NLW-FOOF) model is presented using the Marchaud fractional derivative and the superpixel algorithm. The global nature of the model provides the information about the overall motion present in the scene, while the local nature focuses on the individual motion of each object within the image frame. Thus, the fusion of local–global model along with superpixel algorithm yield the dense flow field, and the Marchaud fractional derivative deals with the textures and edge discontinuities effectively and also provides a significant robustness against outliers. An ablation study is conducted to show the significance of each component of the proposed model. The variational functional is minimized using Euler-Lagrange equations. The Marchaud derivative is numerically discretized through Grünwald-Letnikov derivative method. The resulting system of equations is solved using an efficient iteration technique. The experiments are performed on heterogeneous datasets, and results are evaluated both qualitatively and quantitatively. The performance of the proposed model is shown by comparing it with existing models. The robustness of the NLW-FOOF model is elaborated by estimating optical flow under four different noises.