Camera intrinsic calibration based on an improved exponential-trigonometric optimizer

Abstract

Accurate camera intrinsic calibration is essential for high-quality three-dimensional measurement, but the nonlinear refinement stage in classic planar calibration can converge to local minima when the reprojection objective is high-dimensional and non-convex. This paper presents an improved exponential-trigonometric optimizer (IETO) for monocular intrinsic calibration. Zhang's closed-form solution is first used to obtain the initial intrinsic matrix and feasible parameter bounds. Focal lengths, principal point coordinates, and radial and tangential distortion coefficients are then jointly refined by minimizing the root-mean-square reprojection error. To improve both global search and local refinement, IETO combines SPM chaotic initialization, a smooth exploration-exploitation transition function, greedy selection, and Lévy-flight perturbation. Experiments on 25 checkerboard images acquired with a 4-megapixel color camera show that IETO converges within about 20 iterations and achieves a reprojection error of 0.0401 pixels, outperforming Levenberg-Marquardt, particle swarm optimization, grey wolf optimization, and the original exponential-trigonometric optimizer. Repeated calibration and Gaussian-noise experiments further demonstrate lower error dispersion and stronger robustness. The proposed offline optimizer provides a reliable calibration strategy for high-precision machine-vision measurement.