Low-Cost Method for the Estimation of the Shape of Quadric Mirrors and Calibration of Catadioptric Cameras

Abstract

This paper tackles the problem of the quadric mirror estimation of omnidirectional imaging systems, as well as the poses of the camera relative to the mirror and to the world reference system. These estimates are obtained for quadric-shaped mirrors (including elliptic, parabolic, hyperbolic and spherical mirrors) where the position of the camera and mirror is unconstrained (fully non central configurations). The apparent contour of the mirror can be used to reduce the uncertainty in the estimation. Although it can enhance both the accuracy of the estimation (allowing the method to converge from farther initial configurations) and also its performance, its use is not strictly required. The intrinsic parameters of the camera model (pinhole or orthographic) are assumed to be known as well as the structure of a calibration object in local coordinates. The method is nonlinear and we use a genetic algorithm in conjunction with the Nelder-Mead simplex algorithm to minimize the objective function. Experimental results using real data are presented demonstrating the accuracy of this calibration method, comparing accuracy with and without the apparent contour and computing the reprojection error. As the mirror quadric is estimated, this method can also be used to identify and classify the mirror.