Linear Subspace Methods for Recovering Translational Direction

The image motion eld for an observer moving through a static environment de pends on the observer s translational and rotational velocities along with the distances to surface points Given such a motion eld as input we have recently introduced sub space methods for the recovery of the observer s motion and the depth structure of the scene This class of methods involve splitting the equations describing the motion eld into separate equations for the observer s translational direction the rotational veloc ity and the relative depths The resulting equations can then be solved successively beginning with the equations for the translational direction Here we concentrate on this rst step In earlier work a linear method was shown to provide a biased estimate of the translational direction We discuss the source of this bias and show how it can be e ectively removed The consequence is that the observer s velocity and the relative depths to points in the scene can all be recovered by successively solving three linear