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

TL;DR

Accurate LiDAR-Camera extrinsic calibration is essential for sensor fusion but remains challenging in single-shot, target-less setups. The authors present two LC calibration algorithms based on line features, with PLK-Calib exploiting Plücker line geometry to decouple rotation and translation, requiring at least three nonparallel lines. They provide a degenerate analysis, Monte Carlo validation, and a new LC calibration dataset collected under varying extrinsics to benchmark performance. Results show PLK-Calib achieves comparable orientation accuracy to state-of-the-art single-shot methods and superior translation accuracy, highlighting its robustness across diverse scenes for autonomous driving and robotics applications.

Abstract

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 Plücker (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.

Figures (5)

• Figure 1: Geometric description of PLK line and constraints. (a) The red solid line represents a 3D line in the LiDAR coordinate with two endpoints ${}^{L}\mathbf{p}_{f1}$ and ${}^{L}\mathbf{p}_{f2}$. The vector ${}^{L}\mathbf{v}_l$ denotes the line direction, while ${}^{L}\mathbf{n}_l$ is a vector that is perpendicular to the line plane, which consists of two endpoints and the origin. (b) The green solid line corresponds to the same line depicted in (a), and $l^\prime$ represents the 2D line measurements in the camera frame. The red line is back-projected from $l^\prime$. Due to camera measurement noise, there are some rotation and translation discrepancies between red and green solid lines, although they indicate the same line. Our algorithm minimizes this residual by optimizing the extrinsic parameters.
• Figure 2: (a) Normal, (b) Coplanar, (c) Parallel, (d) Coplanar and parallel.
• Figure 3: Hardware setup. An Ouster OS1-128 LiDAR and a Kinova Gen3 lite mechanical arm are mounted on a sensor tower, and placed on the roof of a vehicle. The end effector holds a Zed 2i camera, and can navigate to different poses in 3D. The red arrows denote the coordinates of camera, LiDAR, and base frames.
• Figure 4: Dataset examples and experiment results across three different scenarios: parking lot, gym, and yard. The first two columns show dataset examples captured at various poses. The third and fourth columns display line detection results from images before and after applying combination and removal strategies. The final column illustrates line detection from the point clouds.
• Figure 5: The boxplot of $L_2$ norm of the orientation / translation (degrees / meters) errors using four algorithms in three different scenarios.