## Abstract

Multi-camera systems are widely applied in many fields, but the camera calibration is particularly important and difficult. In the application of a multi-camera system, it is very common for multiple cameras to be distributed on both sides of the measured object with overlapping field of view. In this paper, we present a novel calibration method for a multi-camera system based on flat refractive geometry. All cameras in the system can acquire calibration images of a transparent glass calibration board (TGCB) at the same time. The application of TGCB leads to a refractive phenomenon that can generate calibration error. The theory of flat refractive geometry is employed to eliminate the error. The proposed method combines the camera projection model with flat refractive geometry to determine the intrinsic and extrinsic camera parameters. The bundle adjustment method is employed to minimize the reprojection error and obtain optimized calibration results. The simulation is performed with zero-mean Gaussian noise of the standard deviation changes from 0 to 0.4 pixels, and the results show that the error of rotation angle is less than $5.6\mathrm{e}-3\text{\hspace{0.17em}}\mathrm{deg}$, and the error of translation is less than $4.6\mathrm{e}-3\text{\hspace{0.17em}}\mathrm{mm}$. The four-camera calibration results of real data show that the mean value and standard deviation of the reprojection error of our method are $4.3411\mathrm{e}-05$ and 0.4553 pixels, respectively. Both the simulative and real experiments show that the proposed method is accurate and feasible.

© 2017 Optical Society of America

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