A method for calibrating the central catadioptric camera via Homographic matrix

In this paper, we present a homography-based method for calibrating the central catadioptric vision system. We consider two cases, i.e. orthographic camera with parabolic mirror and perspective camera with hyperbolic mirror. In both cases, the parameters of the mirror and the extrinsic parameters of the camera are estimated simultaneously, assuming that the intrinsic parameters of the camera are known. We formulate the calibration task into a polynomial eigenvalue problem and obtain a closed-form solution for all the variables using the plane-based homography matrix. Our results show that five pairs of corresponding points for the first case and fourteen for the second case are sufficient to calibrate the vision system. Finally, some experiments are performed to validate the proposed algorithm.