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

TL;DR

This work tackles precise LiDAR–camera extrinsic calibration using circular targets by addressing the Circle Center Problem through two innovations: a CGA-based 3D circle center estimator integrated with RANSAC, and a chord-length variance method to recover the true 2D projection center, resolved via homography validation or a quasi-RANSAC fallback. The authors demonstrate that jointly optimizing 3D and 2D centers yields significantly improved calibration accuracy, outperforming state-of-the-art decoupled methods in synthetic and real-world settings. The approach is robust to noise, partial and sparse data, and outliers, and extends to diverse sensor-target configurations, with open-source code to ensure reproducibility and broad applicability.

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.

Figures (10)

• Figure 1: Comparison of 3D circle fitting approaches. Decoupled fitting Rusu_ICRA2011_PCL estimates a plane first, then fits a 2D circle on projected points. Joint optimization Fremontdorst simultaneously minimizes point-to-plane and point-to-circle distances.
• Figure 2: Locating the true center of a 3D circle from its 2D image. (a) A circle in 3D space projects to an ellipse in the 2D image plane. (b) The key challenge: the point corresponding to the true 3D center (red cross) is displaced from the ellipse's geometric center (yellow circle) and its center of mass (cyan diamond) due to perspective. (c) Our proposed score map optimization locates the true center (green star) and successfully disambiguates it from a false positive candidate (green triangle).
• Figure 3: Overview of the LiDAR-Camera calibration pipeline. The primary contributions--robust 3D circle fitting via CGA and perspective-aware 2D center refinement--enable accurate 3D-2D correspondences for high-precision extrinsic calibration.
• Figure 4: Geometric constrint under projection
• Figure 5: Comparison results of Accuracy Under Challenging Geometric Conditions.