PLK-Calib: Single-shot and Target-less LiDAR-Camera Extrinsic Calibration using Plücker Lines

Accurate LiDAR-Camera (LC) calibration is challenging but crucial for autonomous systems and robotics. In this paper, we propose two single-shot and target-less algorithms to estimate the calibration parameters between LiDAR and camera using line features. The first algorithm constructs line-to-line constraints by defining points-to-line projection errors and minimizes the projection error. The second algorithm (PLK-Calib) utilizes the co-perpendicular and co-parallel geometric properties of lines in Pl\"ucker (PLK) coordinate, and decouples the rotation and translation into two constraints, enabling more accurate estimates. Our degenerate analysis and Monte Carlo simulation indicate that three nonparallel line pairs are the minimal requirements to estimate the extrinsic parameters. Furthermore, we collect an LC calibration dataset with varying extrinsic under three different scenarios and use it to evaluate the performance of our proposed algorithms.