Omnidirectional Perspective and Stereopsis with Conical Mirrors

Autonomous navigation, site modelling and surveillance applications all benefit from using panoramic 360◦ images. Catadioptric omnidirectional sensors, consisting of a camera and a mirror, can track objects even while the robot is making sudden and significant turns. There has been much debate and theoretical analysis recently concerning the relative merits of several possible shapes of mirrors to be used by such sensors. 1 This work explains that the conical mirror has significant advantages over other shapes of mirrors. It then shows that the true perspective projection unwarping can be produced from conical mirror images, something that has hitherto been considered possible only with elliptic, parabolic and hyperbolic mirrors that possess the single viewpoint geometry. Finally, the design of an omnidirectional stereo system with two coaxial conical mirrors is presented and the appropriate triangulation formula is derived.