Effects of camera external parameters error on measurement accuracy in monocular vision

Monocular vision is widely employed in industrial measurement scenarios due to its low cost, flexibility, mature algorithms, and high reliability. However, in actual production line monocular vision measurement systems, the measured plane may be affected by motion mechanisms or device vibrations, causing it to deviate from the system calibration plane and resulting in measurement errors. Current research primarily focuses on analyzing the influence of camera internal parameters and feature extraction algorithms on measurement errors, with limited quantitative analysis of the impact of camera external parameters. To address this issue, our paper derives a mathematical expression for measurement error when rotational and translational motion occurs between the measurement and calibration planes. Theoretical analysis reveals that when the camera optical axis is perpendicular to the measurement plane, measurement error is independent of the main point coordinates of the camera's optical axis, translation component in the measurement plane, and rotation angle around the camera's optical axis. Instead, it exhibits a linear relationship with the translation component in the direction of the camera's optical axis and is inversely proportional to the normalized focal length of the camera. When the optical axis of the camera is not perpendicular to the calibration plane, the measurement error exhibits a nonlinear relationship with camera's internal and external parameters. To verify our theoretical derivation's accuracy, we conduct measurement experiments using both industrial and telecentric lenses and analyzed rotation and translation of the measured plane separately. The measurement data was evaluated by Root Mean Square Error and Pearson Correlation Coefficient, which demonstrates that experimental and theoretical function images exhibit consistent trends, verifying our theoretical derivation's correctness and providing a theoretical guide for improving actual visual measurement accuracy.