Multi-camera systems are widely applied in the three dimensional (3D) computer vision, especially when multiple cameras are distributed on both sides of the measured object. The calibration methods of multi-camera systems are critical to the accuracy of vision measurement and the key is to find an appropriate calibration target. In this paper, a high-precision camera calibration method for multi-camera systems based on transparent glass checkerboards and ray tracing is described, and is used to calibrate multiple cameras distributed on both sides of the glass checkerboard. Firstly, the intrinsic parameters of each camera are obtained by Zhang’s calibration method. Then, multiple cameras capture several images from the front and back of the glass checkerboard with different orientations, and all images contain distinct grid corners. As the cameras on one side are not affected by the refraction of glass checkerboard, extrinsic parameters can be directly calculated. However, the cameras on the other side are influenced by the refraction of glass checkerboard, and the direct use of projection model will produce a calibration error. A multi-camera calibration method using refractive projection model and ray tracing is developed to eliminate this error. Furthermore, both synthetic and real data are employed to validate the proposed approach. The experimental results of refractive calibration show that the error of the 3D reconstruction is smaller than 0.2 mm, the relative errors of both rotation and translation are less than 0.014%, and the mean and standard deviation of reprojection error of the four-camera system are 0.00007 and 0.4543 pixels, respectively. The proposed method is flexible, highly accurate, and simple to carry out.
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