Direct passive navigation: Analytical solution for planes

In this paper, we derive a closed form solution for recovering the motion of an observer relative to a planar surface directly from image brightness derivatives. We do not compute the optical flow as an intermediate step, only the spatial and temporal intensity gradients at a minimum of 8 points. We solve a linear matrix equation for the elements of a 3×3 matrix. The eigenvalue decomposition of its symmetric part is then used to compute the motion parameters and the plane orientation.