Geometric Properties of Central Catadioptric Line Images

In central catadioptric systems, lines in a scene are projected to conic curves in the image. This work studies the geometry of the central catadioptric projection of lines and its use in calibration. It is shown that the conic curves where the lines are mapped possess several projective invariant properties. From these properties, it follows that any central catadioptric system can be fully calibrated from an image of three or more lines. The image of the absolute conic, the relative pose between the camera and the mirror, and the shape of the reflective surface can be recovered using a geometric construction based on the conic loci where the lines are projected. This result is valid for any central catadioptric system and generalizes previous results for paracatadioptric sensors. Moreover, it is proven that systems with a hyperbolic/elliptical mirror can be calibrated from the image of two lines. If both the shape and the pose of the mirror are known, then two line images are enough ...

• Type: Conference
• Year: 2002
• Where: ECCV
• Authors: Helder Araújo, João P. Barreto
• Keywords: Central Catadioptric Projection, Central Catadioptric Systems, Computer Vision, Conic Curves, Conic Loci, ECCV 2002, Projective Invariant Properties