Calibration of mirror position and extrinsic parameters in axial non-central catadioptric systems

•We propose a novel calibration method for non-central catadioptric systems.•We assume an axial symmetrical mirror and a pinhole camera placed on the mirror axis.•The calibration estimates the camera/mirror position and the extrinsic parameters.•The procedure requires a single image of a (possibly planar) calibration object.•The Direct-Linear-Transformation algorithm and cross-ratio are used.

We propose a novel calibration method for catadioptric systems made up of an axial symmetrical mirror and a pinhole camera with its optical center located at the mirror axis. The calibration estimates the relative camera/mirror position and the extrinsic rotation and translation w.r.t. the world frame. The procedure requires a single image of a (possibly planar) calibration object. We show how most of the calibration parameters can be estimated using linear methods (Direct-Linear-Transformation algorithm) and cross-ratio. Two remaining parameters are obtained by using non-linear optimization. We present experimental results on simulated and real images.