Binocular Camera External Reference Calibration Method Based on Multi-sphere Calibration with Bundle Adjustment Optimization

To address the error accumulation in traditional binocular calibration caused by limited co-visibility of checkerboards, this paper proposes an extrinsic calibration framework using spherical targets and Bundle Adjustment (BA). Exploiting the sphere's spatial symmetry, the method captures elliptical projections independently from multiple views, avoiding the need for co-visibility. Joint optimization of camera parameters and 3D structure via BA significantly reduces reprojection error-from 47.75 to 3.06 pixels (93.6%) in single-sphere mode, and further to 0.28 pixels (94.6<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">%</sup>) in triple-sphere mode, with over 90% reduction in standard deviation. Lower error improves 3D reconstruction accuracy and reduces distortion risks in applications like inspection and robotics. The multi-sphere setup enhances spatial constraints and system robustness, offering an efficient calibration solution for complex scenes.