PLK-Calib: Single-shot and Target-less LiDAR-Camera Extrinsic Calibration using Pl""ucker Lines

2025-03-11

AI Summary

To address the limitations of conventional LiDAR–camera extrinsic calibration—namely, reliance on artificial calibration targets and multiple data acquisitions—this paper proposes a single-shot, targetless, line-feature-driven calibration method. Leveraging geometric constraints of common perpendicularity and parallelism among 3D lines represented in Plücker coordinates, we achieve, for the first time, theoretical decoupling of rotational and translational parameter estimation. We rigorously prove that only three non-parallel corresponding 3D–2D line pairs are sufficient for unique solution recovery, overcoming the traditional dependence on point- or plane-based features. The method formulates and minimizes line reprojection error, incorporates degeneracy analysis, and validates robustness via Monte Carlo simulations. Evaluated on a custom multi-scene dataset, our approach achieves mean rotational and translational errors of 0.12° and 1.8 cm, respectively—substantially outperforming existing targetless methods.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Multi-modal Vision
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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 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.

Problem

• Accurate LiDAR-Camera calibration for autonomous systems.
• Single-shot, target-less algorithms using line features.
• Minimal three nonparallel line pairs for calibration.

Innovation

• Single-shot, target-less LiDAR-camera calibration
• Uses Plücker lines for geometric constraints
• Decouples rotation and translation for accuracy