Mobile Camera Localization Using Apollonius Circles and Virtual Landmarks

We investigate the localization of a camera subject to a planar motion with horizontal optical axis in the presence of known vertical landmarks. Under these assumptions, a calibrated camera can measure the distance to the viewed landmarks. We propose to replace the trilateration method by intersecting a pair of Chasles-Apollonius circles. In the case of square pixels but unknown focal length we introduce a new method to recover the camera position from one image with three vertical landmarks. To this end we consider virtual landmarks and Apollonius-like circles. We extend this method in order to deal with an unknown principal point by using four landmarks.