Cross-Calibration of RGB and Thermal Cameras with a LIDAR for RGB-Depth-Thermal Mapping

We present a method for calibrating the extrinsic parameters between a RGB camera, a thermal camera, and a LIDAR. The calibration procedure we use is common to both the RGB and thermal cameras. The extrinsic calibration procedure assumes that the cameras are geometrically calibrated. To aid the geometric calibration of the thermal camera, we use a calibration target made of black-and-white melamine that looks like a checkerboard pattern in the thermal and RGB images. For the extrinsic calibration, we place a circular calibration target in the common field of view of the cameras and the LIDAR and compute the extrinsic parameters by minimizing an objective function that aligns the edges of the circular target in the LIDAR to its corresponding edges in the RGB and thermal images. We illustrate the convexity of the objective function and discuss the convergence of the algorithm. We then identify the various sources of coloring errors (after cross-calibration) as (a) noise in the LIDAR points, (b) error in the intrinsic parameters of the camera, (c) error in the translation parameters between the LIDAR and the camera and (d) error in the rotation parameters between the LIDAR and the camera. We analyze the contribution of these errors with respect to the coloring of a 3D point. We illustrate that these errors are related to the depth of the 3D point considered - with errors (a), (b), and (c) being inversely proportional to the depth, and error (d) being directly proportional to the depth.