Mirror Localization for Catadioptric Imaging System by Observing Parallel Light Pairs

Abstract

This paper describes a method of mirror localization to calibrate a catadioptric imaging system. While the calibration of a catadioptric system includes the estimation of various parameters, we focus on the localization of the mirror. The proposed method estimates the position of the mirror by observing pairs of parallel lights, which are projected from various directions. Although some earlier methods for calibrating catadioptric systems assume that the system is single viewpoint, which is a strong restriction on the position and shape of the mirror, our method does not restrict the position and shape of the mirror. Since the constraint used by the proposed method is that the relative angle of two parallel lights is constant with respect to the rigid transformation of the imaging system, we can omit both the translation and rotation between the camera and calibration objects from the parameters to be estimated. Therefore, the estimation of the mirror position by the proposed method is independent of the extrinsic parameters of a camera. We compute the error between the model of the mirror and the measurements, and then estimate the position of the mirror by minimizing this error. We test our method using both simulation and real experiments, and evaluate the accuracy thereof.