Calibrating internal and external parameters of multi-cameras by moving freely rigid ball bar

According to the requirements of calibrating multi-cameras in motion parameter optoelectronic measurement systems used in big space motion analysis, a novel approach of calibrating the internal and external parameters of multi-cameras is proposed. Firstly, a principal point is assumed at a certain location around the image plane center, and the fundamental matrix is found out by Hartley's eight-point-algorithm. Then, different focal lengths of different cameras are obtained linearly through a epipolar geometry and it's constraint. After educing the essential matrix, the singular-value-decomposition is carried out to obtain the rotation matrix and translation vector with a scale factor. Moreover, the coordinates and the distances of the ball bar are computed by a triangulation method, and the scale factor is found out through the true distance of the ball bar. Finally, the estimation of internal and external parameters of the multi-cameras is transformed to a nonlinear minimization problem by a cost function, and the optimal principal points of two cameras are found out iteratively by using the improved simulated annealing evolution strategy. The experimental results show that the precision of focal length and principal point is up to 0.1 pixel and the stardard deviation bar length is 0.046 mm. Compared with traditional methods, the novel calibration approach expands the applications of the multi cameras and can find out the internal and external parameters simultaneously without the constraint for the ball bar movement. These results prove that the improved simulated annealing evolution strategy accelerates the convergence speed and improves the global convergence performance.