Comparison of panoramic stereoscopic sensors based on hyperboloidal mirrors

Panoramic distance maps can provide valuable information for mobile robot navigation. An approach to obtain such distance maps is to implement a stereoscopic system using two hyperboloidal catadioptric sensors. This paper analyzes the effects over distance estimation of two typical arrangements of the mirrors. In one of the arrangements the mirrors are placed along a vertical axis, while in the other configuration the sensors are located on plane. Both configurations may yield similar distance estimation errors for an adequately chosen baseline and given measurement range of interest. However, depending on the application, some aspects can make one arrangement preferable over the other. In the vertical configuration, the epipolar lines correspond to radial lines in the omnidirectional image, and hence, the stereoscopic correspondence problem can be solved in a standard and simple way, but a drawback of this arrangement is the space required, which in the case of mobile robot and vehicular application translates into a reduced vertical clearance and poorer aerodynamics. The horizontal arrangement, on the other hand, requires less space if mounted on a mobile robot, a vehicle's roof or its lateral mirrors, but involves complex parabolic, elliptic or hyperbolic epipolar curves that make the solution of the stereo correspondence problem computationally more expensive. Despite the evident implementation advantages and drawback of each approach, no rigorous quantitative information exits in the literature about which of the two configurations provides in general the most accurate 3D reconstruction of the environment.