On Accurate and Robust Estimation of 3D and 2D Circular Center: Method and Application to Camera-Lidar Calibration

TL;DR

This paper introduces a new geometrically grounded method for accurately estimating 3D and 2D circular centers, improving LiDAR-camera calibration robustness and precision across various sensors and targets.

Contribution

It presents a novel framework combining conformal geometric algebra with RANSAC and a chord-length variance minimization technique for better circular center estimation.

Findings

Significantly outperforms existing methods in accuracy.

Reduces extrinsic calibration errors.

Enables robust calibration with diverse sensors and targets.

Abstract

Circular targets are widely used in LiDAR-camera extrinsic calibration due to their geometric consistency and ease of detection. However, achieving accurate 3D-2D circular center correspondence remains challenging. Existing methods often fail due to decoupled 3D fitting and erroneous 2D ellipse-center estimation. To address this, we propose a geometrically principled framework featuring two innovations: (i) a robust 3D circle center estimator based on conformal geometric algebra and RANSAC; and (ii) a chord-length variance minimization method to recover the true 2D projected center, resolving its dual-minima ambiguity via homography validation or a quasi-RANSAC fallback. Evaluated on synthetic and real-world datasets, our framework significantly outperforms state-of-the-art approaches. It reduces extrinsic estimation error and enables robust calibration across diverse sensors and target types, including natural circular objects. Our code will be publicly released for reproducibility.