Mirror Localization for a Catadioptric Imaging System by Projecting Parallel Lights

This paper describes a method of mirror localization to calibrate a catadioptric imaging system. Even though the calibration of a catadioptric system includes the estimation of various parameters, in this paper we focus on the localization of the mirror. Since some previously proposed methods assume a single view point system, they have strong restrictions on the position and shape of the mirror. We propose a method that uses parallel lights to simplify the geometry of projection for estimating the position of the mirror, thereby not restricting the position or shape of the mirror. Further, we omit the translation process between the camera and calibration objects from the parameters to be estimated by observing some parallel lights from a different direction. We obtain the constraints on the projection and compute the error between the model of the mirror and the measurements. The position of the mirror is estimated by minimizing the error. We also test our method by simulation and real experiments, and finally we evaluate the accuracy of our method.