Estimating Parameters of Non-Central Catadioptric Systems Using Bundle Adjustment

This paper describes a new method to calibrate the intrinsic and extrinsic parameters of a generalized catadioptric camera (central or noncentral). The algorithm has two steps. The first one is the estimation of correspondences between incident lines in space and pixels (black box model calibration) in an arbitrary world reference frame. The second step is the calibration of the intrinsic parameters of the pinhole camera, the coefficients of the mirror expressed by a quadric (quadric mirror shape and the pose of the camera in relation to it), the position of the optical center of the camera in the world reference frame and its relative orientation (pose of the camera in world reference frame). A projection model relaxing Snell’s Law is derived. The deviations from Snell’s Law and the image reprojection errors are minimized by means of bundle adjustment. Information about the apparent contour of the mirror can be used to reduce the uncertainty in the estimation by introducing a new term in the cost function of the second step minimization process. Simulations and real experiments show good accuracy and robustness for this framework. However, the convergence is dependent on the initial guess as expected. A well-behaved algorithm to automatically generate the initial estimate to be used in the bundle adjustment is also presented.