Single-Image Calibration of Off-Axis Catadioptric Cameras Using Lines

We present a novel calibration method for off-axis catadioptric cameras, i.e. standard perspective cameras placed in a generic position w.r.t. an axial-symmetric mirror of unknown shape. The proposed method estimates the intrinsic parameters of the natural perspective camera, the 3D shape of the mirror and its pose w.r.t. the camera. The peculiarity of our approach is that, unlike several other calibration methods, we do not require any cross section of the mirror to be visible in the image. Instead, we require that the catadioptric image contains at least the image of one generic space line. We then derive some constraints that, combined with the harmonic homology relating the apparent contours of the mirror, allow us to calibrate the off-axis camera. We provide experimental results both on synthetic and camera images that prove the validity of the technique.