Analytical least-squares solution for 3D lidar-camera calibration

This paper addresses the problem of estimating the intrinsic parameters of the 3D Velodyne lidar while at the same time computing its extrinsic calibration with respect to a rigidly connected camera. Existing approaches to solve this nonlinear estimation problem are based on iterative minimization of nonlinear cost functions. In such cases, the accuracy of the resulting solution hinges on the availability of a precise initial estimate, which is often not available. In order to address this issue, we divide the problem into two least-squares sub-problems, and analytically solve each one to determine a precise initial estimate for the unknown parameters. We further increase the accuracy of these initial estimates by iteratively minimizing a batch nonlinear least-squares cost function. In addition, we provide the minimal observability conditions, under which, it is possible to accurately estimate the unknown parameters. Experimental results consisting of photorealistic 3D reconstruction of indoor and outdoor scenes are used to assess the validity of our approach.