A New CMM Based Method of Camera Calibration and Distortion Compensation

Abstract

Abstract.To improve the accuracy of vision measuring system, high-precision camera calibration and distortion compensation are essential. A new CMM based method of camera calibration and distortion compensation, and a new index for evaluating the residual distortion after compensation are presented in this paper. A three-dimensional reference with a large number of feature points is provided by a high accurate CMM. Such a 3D reference is flexible in terms of the spacing and distribution of feature points and is able to cover the entire image plane of the camera. The internal and external parameters of the camera are obtained through nonlinear optimization. A distortion database is established based on the calibrated data to compensate the residual errors. Experiments show that the new method has higher accuracy and flexibility in comparison with commonly used methods, and can be applied for calibrating cameras in various vision measuring systems. IntroductionCamera calibration is essential in vision measuring systems. The accuracy of camera calibration and distortion compensation directly affects the accuracy of vision measuring system. The research on camera lens distortion can be traced back to 1919, when A. Conrady first introduced the decentering distortion [4], and afterwards many effective methods have been proposed. These methods can be roughly classified into three categories: linear methods, nonlinear methods and combined methods.Linear methods involve the determination of transformation parameters by solving linear equations, whose main advantages are simple and fast in data processing. However lens distortion is not considered and the solution is noise sensitive [11]. Direct linear transformation was introduced by Abdal-Aziz and Karara in 1970's, nevertheless its accuracy is not high enough.Nonlinear methods establish a nonlinear mathematical model with a large number of unknowns. These methods may achieve high accuracy through nonlinear optimization. However the algorithm is complicated and a bad initial guess may lead to unstable results. References [8], [9], [10], [15], [16] belong to such methods. Self-calibration methods are based on the corresponding relationship among a large number of pictures taken [12,13]. They are flexible and can be used in a variety of cases. But they are not so robust.Methods which combine linear and nonlinear transformations are widely used currently. The RAC method introduced by Tsai [7] is a typical approach. Its algorithm is relatively simple, and each parameter can be solved through an iterative optimization. However only the radial distortion is taken into account and it leads to unsatisfactory results in distortion compensation in many cases. A flexible camera calibration method [14] [14]. These techniques improved the accuracy of distortion compensation to a certain extent. However the large scale vision measuring systems ask for even