Uncalibrated video compass for mobile robots from paracatadioptric line images

Due to their panoramic field of view, catadioptric cameras are becoming ubiquitous in many robotics and computer vision applications. Catadioptric cameras with a unique viewpoint are of primary interest, among these is the case where the reflective surface is a parabolic mirror and the camera satisfies the orthographic projection model and which we call paracatadioptric. We here present a new geometrical property (called disparity-circles property) for paracatadioptric cameras and use it to design a video compass algorithm that can compute the 1-axis rotation angle between two views of at least two parallel lines, without any need of internal camera calibration parameters. We present a linear closed form solution suitable for real-time implementation. We then study the performances of our algorithm, its sensitivity to image noise and propose also experimental results with a paracatadioptric camera mounted on a mobile robotic platform.