Application of the Levenberg-Marquardt algorithm to optimize the extrinsic parameters of LiDAR-camera joint calibration

Camera-LiDAR joint calibration is the basic requirement for data fusion of two sensors in autonomous vehicle. In order to minimize the re-projection error of the joint calibration and enhance the accuracy of the fusion of image and laser point cloud data, a Levenberg-Marquardt algorithm is designed to optimize the external parameters for the joint calibration of the camera and LiDAR. Firstly, the least square function is constructed based on the difference between image pixel coordinates and point cloud re-projection coordinates. To reduce the number of optimization parameters, we employ the Rodriges transformation, a formula that enables us to represent the rotation matrix using a vector of only 3 parameters. Then, the Levenberg-Marquardt algorithm is utilized to optimize the joint calibration parameters and solve the optimized re-projection error. The results demonstrate that the optimized re-projection error is 0.226, which is reduced by 53.5% compared with before optimization, and the accuracy of joint calibration is improved. Finally, visualization of the calibration results validates the effectiveness of the optimization algorithm.