A Mathematical Framework for Optical Flow Computation

Abstract

In this paper, we propose a mathematical framework under which we present the necessary condition of the minimization of the optical flow problem. The framework is a straightforward spatiotemporal extension, which can be used to accommodate most of the known differential-based optical flow computation. In addition, this paper presents an alternative formulation of the optical flow problem that relies on spline functionals. With the framework, we describe some typical optical flow methods.