Extrinsic Calibration of 2-D Laser Rangefinder and Camera From Single Shot Based on Minimal Solution

A 2-D laser rangefinder (LRF) and a camera are widely applied in various mobilized systems, such as autonomous robot and unmanned ground vehicle. Integration of these two types of sensors promotes a new measurement technology. Extrinsic calibration is crucial and basically the first step to fuse image and laser data. The chessboard-plane-based method is one of the most popular ones, which requires at least five plane-input (five shots). Vasconcelos et al. recently reduced the number of shots from five to three and derived the minimal solution. However, it requires solving a sophisticated perspective-three-point (P3P) problem with eight solutions. This paper first introduces a virtual trihedron from three plane-input and reformulates the P3P problem directly in 3-D space rather than in 3-D dual space to derive the minimal solution for extrinsic calibration. Based on this, we propose a novel and flexible method for extrinsic calibration of an LRF-camera with a trirectangular trihedron (or a cube). One unique feature is that the method requires only a single shot of the target, which can greatly simplify the calibration procedure. The proposed calibration method involves solving simplified P3P and perspective-three-line (P3L) problems separately. In particular, computation of LRF pose is formulated as a simplified P3P problem, which is easily solved and has unique solution from single-shot laser data only. It also avoids the degeneration problem. Camera pose computation is formulated as a simplified P3L problem from image data. The proposed calibration method has been tested with both simulation and real data. The results show that the method is both accurate and flexible for extrinsic calibration of a 2-D LRF and a camera.