Direct passive navigation : analytical solution for planes

"This paper derives a closed form sloution for recovering the motion of an observer relative to a planar surface directly from image brightness gradients. The optical flow is not computed as an intermediate step, only the spatial and temporal intensity gradients at a minimum of eight points. A linear matrix equation is solved for the elements of a 3x3 matrix. The eigenvalue decomposition of its symmetric part is then used to compute the motion parameters and the plane orientation. Keywords Passive navigation; Optical flor; Structure and motion; Planar surfaces; Least squares method."@en
"Abstract: "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 3x3 matrix. The eigenvalue decomposition of its symmetric part is then used to compute the motion parameters and the plane orientation.""@en