An Approach to Camera Extrinsic Calibration Using Weighted AprilTag Detections in the Perspective-n-Point Problem

Abstract

3D computer vision systems use multiple video cameras to obtain information about the surrounding space. The spatial calibration accuracy of multi-camera systems is critical for successfully solving 3D computer vision tasks. This paper proposes a modification to the classical approach of iterative camera registration using AprilTag markers, which performs camera positioning based on the Perspective-n-Point (PnP) algorithm. To improve calibration quality, a weighted nonlinear optimization of the reprojection error is implemented. A heuristic weight function is developed to evaluate the detection reliability of each marker, taking into account its apparent size, perspective angular distortion, and distance from the image principal point. The effectiveness of the approach is validated on 20 synthetic datasets that simulate real-world imaging conditions with uncompensated optical distortion and noisy intrinsic parameters. Statistical analysis confirms that the proposed weighted PnP algorithm significantly outperforms the standard positioning method, providing higher accuracy and robustness in estimating extrinsic parameters. An approach to calibrating camera eccentrics is proposed, based on weighted detection of AprilTag markers and solving the PnP problem for positioning objects with known geometry in space using metrics of accuracy of restoring the position and orientation of cameras. The results confirm the feasibility of using this approach for accurate and robust calibration of multi-camera systems in real-world computer vision applications.