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Calibration of Cameras with Radially Symmetric Distortion

Jean-Philippe Tardif 1 Peter Sturm 2
2 MOVI - Modeling, localization, recognition and interpretation in computer vision
GRAVIR - IMAG - Graphisme, Vision et Robotique, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
Abstract : We present a theory and algorithms for plane-based calibration and pose recovery 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 cone centered on the optical axis. The camera is said to have a singular viewpoint (SVP) if all such view cones have the same vertex (the optical center), otherwise we speak of non-SVP, and each view cone may have its own optical center on the optical axis. This model encompasses the classical radial distortion model, fisheyes, most central or non-central catadioptric cameras, but also cameras with radially symmetric caustics. Calibration consists in the estimation of the distortion center, the opening angles of all view cones and their optical center. 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 view cones and associated ellipses in the calibration plane; calibration of the view cones can be solved by determining the closest point to a set of hyperbolas. The second approach uses existing plane-based calibration methods to directly calibrate individual view cones. A simple distortion correction algorithm for calibrated SVP images is given. Preliminary experiments show convincing results.
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Jean-Philippe Tardif, Peter Sturm. Calibration of Cameras with Radially Symmetric Distortion. 6th Workshop on Omnidirectional Vision, Camera Networks and Non-Classical Cameras, Oct 2005, Beijing, China. pp.44-51. ⟨inria-00524395⟩

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