Accurate Measurement of 3D and 2D Circular Centers With Application to LiDAR–Camera Extrinsic Calibration

Accurate measurement of circular centers is a fun-damental geometric sensing problem in instrumentation and measurement tasks involving cameras, LiDARs, and other spa-tial sensors. In circular-target-based LiDAR-camera extrinsic calibration, a 3D circular center measured from LiDAR and its corresponding 2D projected center measured in the image serve as cross-modal geometric observations for estimating the rigid transformation between the two sensor frames. Conven-tional pipelines can bias both measurements: the 3D center is often obtained by sequential plane fitting, point projection, and 2D circle fitting, while the image ellipse center is frequently treated as the projected circle center even though the two generally differ under perspective projection. This paper focuses on accurate 3D and 2D circular-center measurement and uses LiDAR-camera extrinsic calibration as a representative applica-tion. A conformal-geometric-algebra estimator is integrated with RANSAC to jointly recover the 3D center, normal, and radius from noisy or partially observed LiDAR points. A chord-length-variance criterion then estimates the 2D projected center, with its twofold ambiguity resolved by homography validation or a quasi-RANSAC fallback. Synthetic and real-sensor experiments show that the proposed method improves circular-center measurement accuracy and reduces extrinsic calibration error across different target and sensor configurations.