An Optical Flow computation based on Shearlet Transform: A mathematical Formulation

Abstract

Optical flow technique describes and computes motion information between two consecutive and adjacent frames. It finds applications in myriads of fields that includes robotics, video and space applications. Various optical flow methods including Horn–Schunck (HS), Lucas–Kanade (LK), Farneback optical flows and recently, a wavelet transform based Optical Flow have been implemented. The wavelet transform was integrated into the optical flow to solve the problem related to small capture range and low accuracy (in the face of large displacement) of the existing optical flow methods. However, wavelets are deficient in dealing with multidimensional and multivariate data such as edges, contours and multidimensional singularities. By contrast, shearlet transform is highly efficient in dealing with pointwise as well as multidimensional singularities that characterize image and video data. Hence, this research proposed a mathematical formulation that showcase the integration of the shearlet transform with the optical flow method. This is with a view to achieving an improved optical flow that is efficient, robust in the motion estimation of multidimensional data.