J Intell Robot Syst (2010) 58:287–308 DOI 10.1007/s10846-009-9375-1 Mobile Camera Localization Using Apollonius Circles and Virtual Landmarks Rudi Penne · Luc Mertens · Jelle Veraart Received: 16 October 2007 / Accepted: 14 September 2009 / Published online: 25 September 2009 © Springer Science + Business Media B.V. 2009 Abstract 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. Keywords Ego-motion · Camera localization · Planar geometry 1 Introduction There is a large interest in finding the position of the camera from which a given photograph has been taken [2, 3, 5, 7, 11, 13]. Often we also need to know the orientation of this camera, in order to reconstruct the complete camera pose. There can be several motivations for solving this problem. For instance, for building up (geographic) maps or reconstructing the environment (probably by means of several images) one might be interested in finding the position of the viewed objects with respect to some absolute world reference. In this context the data from the images must be complemented by information about the camera pose. But perhaps the most frequent application of camera localization is supplied in the field of robotics. When navigating an autonomously guided vehicle, the current position R. Penne (B ) · L. Mertens · J. Veraart Department of Engineering, Karel de Grote-Hogeschool, Antwerp, Belgium e-mail: rudi.penne@kdg.be