Plane-Based Calibration of Central Catadioptric Cameras

We present a novel calibration technique for all central catadioptric cameras using images of planar grids. We adopted the well-known sphere camera model to describe the catadioptric projection. We show that, using the so-called lifted coordinates, a linear relation mapping the grid points to the corresponding points on the image plane can be written as a 6 x 6 matrix H-cata, which acts like the classical 3 x 3 homography for perspective cameras. We show how to compute the image of the absolute conic (IAC) from at least 3 homographies and how to recover from it the intrinsic parameters of the catadioptric camera. In the case of paracatadioptric cameras one such homography is enough to estimate the IAC, thus allowing the calibration from a single image.