Calibration of Cameras with Radially Symmetric Distortion

Résumé

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 [5], fisheyes and most central or non-central 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 an 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 [12], which however can not handle such a broad variety of camera configurations, showing similar performance.

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