A general approach for egomotion estimation with omnidirectional images

Computing a camera´s ego-motion from an image sequence is easier to accomplish when a spherical retina is used, as opposed to a standard retinal plane. On a spherical field of view both the focus of expansion and contraction are visible, whereas for a planar retina that is not necessarily the case. Recent research has shown that omnidirectional systems can be used to emulate spherical retinas by mapping image velocity vectors from the omnidirectional image to the spherical retina. That has been done by using the Jacobian of the transformation between the image formation model and the spherical coordinate system. As a consequence, the Jacobian matrix must be derived for each specific omnidirectional camera, to account for the different mirror shapes. Instead, in this paper we derive the Jacobian matrix using of a general projection model, that can describe all single projection center cameras by suitable parameterization. Hence, both the back-projection of an image point to the unit sphere, as well as the mapping of velocities through the transformation Jacobian remains general for all cameras with a single center of projection. We have conducted a series of experimental tests to illustrate the validity of our approach which lead to encouraging results.