Computing optical flow from an overconstrained system of linear algebraic equations

A method is presented for the recovery of optical flow. The key idea is that the local spatial structure of optical flow, with the exception of surface boundaries, is usually rather coherent and can thus be appropriately approximated by a linear vector field. According to the proposed method, the optical flow components and their first order spatial derivatives are computed at the central points of rather large and overlapping patches which cover the image plane as the solution to a highly overconstrained system of linear algebraic equations. The equations, which are solved through the use of standard least mean square techniques, are derived from the assumptions that the changing image brightness is stationary everywhere over time and that optical flow is, locally, a linear vector field. The method has been tested on many sequences of synthetic and real images and the obtained optical flow has been used to estimate three-dimensional motion parameters with very good results