Geometric Properties of Central Catadioptric Line Images and Their Application in Calibration

摘要

In central catadioptric systems, lines in a scene are projected to coniccurves in the image. This work studies the geometry of the central catadioptricprojection of lines and its use in calibration. It is shown that the conic curves wherethe lines are mapped possess several projective invariant properties. From theseproperties, it follows that any central catadioptric system can be fully calibrated froman image of three or more lines. The image of the absolute conic, the relative posebetween the camera and the mirror, and the shape of the reflective surface can berecovered using a geometric construction based on the conic loci where the linesare projected. This result is valid for any central catadioptric system and generalizesprevious results for paracatadioptric sensors. Moreover, it is proven that systemswith a hyperbolic/elliptical mirror can be calibrated from the image of two lines. Ifboth the shape and the pose of the mirror are known, then two line images areenough to determine the image of the absolute conic encoding the camera’sintrinsic parameters. The sensitivity to errors is evaluated and the approach is usedto calibrate a real camera