Cameras Seeing Cameras Geometry

We study several theoretical aspects of both 2D and 3D intra multi-view geometry of calibrated cameras when all that they can reliably recognize is each other. Starting with minimal reconstructable configurations, we propose a method for obtaining the position-orientation structure of such camera ensembles, up to a global similarity. In the 3D setting we base our analysis on Rodrigues' vector techniques familiar from mechanics and robotics. We also examine the average number of visible cameras and discuss some kinematic aspects of the problem.