A new flexible method to calibrate the external parameters of two cameras with no-overlapping field of view (<i>FOV</i>) is proposed in our paper. A flexible target with four spheres and a 1<i>D</i> bar is designed. All spheres can move freely along the bar to make sure that each camera can capture the image of two spheres clearly. As the radius of each sphere is known exactly, the center of each sphere under its corresponding camera coordinate system can be confirmed from each sphere projection. The centers of the four spheres are collinear in the process of calibration, so we can express the relationship of the four centers only by external parameters of the two cameras. When the expressions in different positions are obtained, the external parameters of two cameras can be determined. In our proposed calibration method, the center of the sphere can be determined accurately as the sphere projection is not concerned with the sphere orientation, meanwhile, the freely movement of the spheres can ensure the image of spheres clearly. Experiment results show that the proposed calibration method can obtain an acceptable accuracy, the calibrated vision system reaches 0.105 mm when measuring a distance section of 1040 mm. Moreover, the calibration method is efficient, convenient and with an easy operation.
Homography matrix is a matric representation of the projective relation between the space plane and its corresponding
image plane in computer vision. It is widely used in visual metrology, camera calibration, 3D reconstruction and etc.
Therefore, the accurate estimation of the homography matrix is significant. Here, the quantum-behaved particle swarm
optimization method, which is global convergent, is first introduced into the estimation of homography matrix. When suited
cost function is chosen, enough point correspondences can be utilized to search the optimal homography matrix, which can
make the estimation accurately. For the purpose of evaluating the proposed method, simulations and experiments are
conducted to confirm the feasibility and robustness. The points obtained from the deviated homography matrix are reprojected
to the image plane to evaluate the accuracy. To compare with the proposed method, the Levenberg-Marquardt
method, which is a typical iterative minimization method, is utilized to obtain the homography matrix. Simulations and
experimental results show that the proposed method is reasonable, accurate, and with an excellent robustness. When 10
correspondences and 20 particles are utilized, the root mean square error of the re-projected points can reach about 0.019 mm.
Furthermore, our proposed method is not related with the initialization and less correlated with the chosen cost function,
which is the deficiency of the common estimation methods.