A Stepwise Self-Calibration Method for Binocular Cameras in Pin Shaft Production Lines Based on the Kruppa Equation

Binocular camera calibration is the core foundation of 3D vision technology, and its performance directly determines the accuracy of subsequent tasks. Zhang’s checkerboard method relies on calibration targets and suffers from poor scene adaptability, whereas conventional Kruppa self-calibration is prone to parameter divergence, low accuracy, and slow convergence. To address these issues, this paper proposes a boardless stepwise self-calibration method for binocular cameras based on an improved Kruppa equation. The method introduces (1) a stepwise decoupled optimization strategy that alternates between intrinsic and distortion parameters, combined with a SIFT + bidirectional FLANN + RANSAC + Census feature pipeline; (2) a multi-constraint regularization framework that enforces focal-length consistency, principal-point bounds, and a distortion penalty; and (3) an entropy-based feature-coverage criterion with inheritance-based batch tuning for streaming production-line images. Experiments on 800 binocular pairs from a laboratory-simulated pin-shaft production line show that the proposed method achieves an average reprojection error of 0.52 px, an 83.6% reduction over the traditional Kruppa method, approaching Zhang’s calibration. The stepwise solver converges within 7.4 inner iterations per batch, versus 23.31 iterations for the Kruppa baseline. In an end-to-end pin-shaft length measurement task, the mean absolute error is 3.01 mm, on par with Zhang’s calibration and well within the ±5 mm industrial tolerance; even under strong vibration-blur interference, the error remains 3.32 mm.