On the Accuracy of Dense Fisheye Stereo

Fisheye cameras offer a large field of view, which is important for several robotics applications as a larger field of view allows for covering a large area with a single image. In contrast to classical cameras, however, fisheye cameras cannot be approximated well using the pinhole camera model and this renders the computation of depth information from fisheye stereo image pairs more complicated. In this work, we analyze the combination of an epipolar rectification model for fisheye stereo cameras with existing dense methods. This has the advantage that existing dense stereo systems can be applied as a black-box even with cameras that have field of view of more than 180° to obtain dense disparity information. We thoroughly investigate the accuracy potential of such fisheye stereo systems using image data from our UAV. The empirical analysis is based on image pairs of a calibrated fisheye stereo camera system and two state-of-the-art algorithms for dense stereo applied to adequately rectified image pairs from fisheye stereo cameras. The canonical stochastic model for sensor points assumes homogeneous uncertainty and we generalize this model based on an empirical analysis using a test scene consisting of mutually orthogonal planes. We show that: (1) the combination of adequately rectified fisheye image pairs and dense methods provides dense 3D point clouds at 6-7 Hz on our autonomous multicopter UAV; (2) the uncertainty of points depends on their angular distance from the optical axis; (3) how to estimate the variance component as a function of that distance; and (4) how the improved stochastic model improves the accuracy of the scene points.