Refractive Projection and Ray Tracing

Multi-cameras system is widely applied in 3D computer vision especially when multiple 11 cameras are distributed on both sides of the measured object. The calibration methods of multi12 cameras system are critical to the accuracy of vision measurement and the key is to find an 13 appropriate calibration target. In this paper, a high-precision camera calibration method for multi14 cameras system based on transparent glass checkerboard and ray tracing is described, which is used 15 to calibrate multiple cameras distributed on both sides of the glass checkerboard. Firstly, the 16 intrinsic parameters of each camera is obtained by Zhang’s calibration method. Then, multiple 17 cameras capture several images from the front and back of the glass checkerboard with different 18 orientations, and all images contain distinct grid corners. As the cameras on one side are not affected 19 by the refraction of glass checkerboard, extrinsic parameters can be directly calculated. However, 20 the cameras on another side are influenced by the refraction of glass checkerboard, and the direct 21 use of projection model will produce calibration error. A multi-cameras calibration method using 22 refractive projection model and ray tracing is developed to eliminate this error. Furthermore, both 23 synthetic and real data are employed to validate the proposed approach. The experimental results 24 of refractive calibration show that the error of the 3D reconstruction is smaller than 0.2 mm, the 25 relative errors of both rotation and translation are less than 0.014%, and the mean and standard 26 deviation of reprojection error of 4-cameras system are 0.00007 and 0.4543 pixel. The proposed 27 method is flexible, high accurate, and simple to carry out. 28