Abstract:

In various imaging applications such as autonomous vehicles and drones, autofocus lenses are indispensable for capturing clear images. However, conventional camera calibration methods typically rely either on processing multiple images at a fixed focal length or on detecting multi-plane markers in a single image and then applying multi-image calibration models. This paper proposes a flexible and accurate calibration approach that extracts subpixel saddle points from a single image containing three non-coplanar calibration boards. To compute accurate homography matrices for the three boards, outliers are removed by eliminating chessboard points that deviated from the fitted grid lines according to their row and column positions. Initial estimates of the intrinsic parameters and the poses of the three planar chessboards are obtained using the three homography matrices in combination with Zhang's calibration method.

During parameter refinement, a multi-objective optimization function is constructed, incorporating three error terms:

(1) Reprojection error of the inlier grid points;

(2) Mechanism-driven error derived from the relationship between homography matrices and camera parameters;

(3) Cross-planar linearity constraint error, which preserves the pre-imaging collinearity of any five points across different planes after projection.

For weight selection in the optimization process, confidence intervals of the detected grid points are analyzed by horizontally rotating the reprojection lines to reduce bias introduced by line slope. The optimal weights are determined by minimizing the number of points whose confidence intervals does not intersect the reprojected lines. When multiple candidates yield similar reprojection performance, the parameter set with the smallest reprojection error is selected as the final result. This method efficiently estimates both intrinsic and extrinsic camera parameters. Simulations and real-world experiments validate the high precision and effectiveness of the proposed approach. Our technique is straightforward, practical, and holds significant theoretical and practical value for rapid and reliable camera calibration.

Key words: Camera calibration, Single-image calibration, Chessboard corner detection, Subpixel saddle point extraction