Estimation method of homography matrix based on the quantum-behaved particle swarm optimization

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.