Evaluation of the Unified Model of the Sphere for Fisheye Cameras in Robotic Applications

Abstract

A wide field of view is required for many robotic vision tasks. Such an aperture may be acquired by a fisheye camera, which provides a full image compared to catadioptric visual sensors, and does not increase the size and the weakness of the imaging system with respect to perspective cameras. While a unified model exists for all central catadioptric systems, many different models, approximating the radial distortions, exist for fisheye cameras. It is shown in this paper that the unified projection model proposed for central catadioptric cameras is also valid for fisheye cameras in the context of robotic applications. This model consists of a projection onto a virtual unitary sphere followed by a perspective projection onto an image plane. This model is shown equivalent to almost all the fisheye models. Calibration with four cameras and partial Euclidean reconstruction are done using this model, and lead to persuasive results. Finally, an application to a mobile robot navigation task is proposed and correctly executed along a 200-m trajectory.