Calibration of Cameras with Radially Symmetric Distortion

We present algorithms for plane-based calibration of general radially distorted cameras. By this, we understand cameras that have a distortion center and an optical axis such that the projection rays of pixels lying on a circle centered on the distortion center form a right viewing cone centered on the optical axis. The camera is said to have a single viewpoint (SVP) if all such viewing cones have the same apex (the optical center); otherwise, we speak of NSVP cases. This model encompasses the classical radial distortion model, fisheyes, and most central or noncentral catadioptric cameras. Calibration consists in the estimation of the distortion center, the opening angles of all viewing cones, and their optical centers. We present two approaches of computing a full calibration from dense correspondences of a single or multiple planes with known Euclidean structure. The first one is based on a geometric constraint linking viewing cones and their intersections with the calibration plane (conic sections). The second approach is a homography-based method. Experiments using simulated and a broad variety of real cameras show great stability. Furthermore, we provide a comparison with Hartley-Kang´s algorithm, which, however, cannot handle such a broad variety of camera configurations, showing similar performance.