采用简化Brown模型及改进BFGS法的相机自标定

为了精确地反映相机的几何成像关系, 本文基于简化的Brown模型和改进的BFGS （Broyden-Fletcher-Goldfarb-Shanno）算法提出了一种相机自标定方法。该方法首先将线性模型和畸变模型拟合为非线性模型, 通过线性模型的基本矩阵约束非线性模型参数得到约束方程; 然后, 提出了适用于非线性内参数约束方程的基于新拟牛顿方程的改进 BFGS 算法并求解了方程内参数。利用提出的模型和算法, 该标定方法能够在较少的迭代次数和有噪声条件下保证标定结果的精度和鲁棒性。有、无噪声情况下的收敛性分析和鲁棒性分析显示: 在噪声不大于±3 pixel 的情况下, 迭代10次即能保证重投影误差小于0.4 pixel。通过标定相机内参数并计算重投影误差进行了真实图像实验, 结果表明: 标定精度误差小于0.06%, 重投影误差为0.35 pixel, 验证了提出方法的有效性。该方法适用于计算机视觉领域中的图像处理, 模式分类和场景分析等。

Abstract

To accurately reflect the geometric imaging relationship of cameras, a self-calibration method was proposed based on simplified Brown nonlinear camera model and improved BFGS (broyden-fletcher-Shanno) algorithm. In this method, the linear camera model and the distortion model were fitted into a nonlinear model, and the nonlinear model parameters were constrained by fundamental matrices of the linear model to obtain a set of nonlinear constraint equations.Then, based on new quasi-Newtonian equation, an improved BFGS algorithm suitable for nonlinear internal parametric constraint equations were presented and the internal parameters of the equation were solved. By using the proposed model and algorithm, the calibration method improves the accuracy and robustness of the calibration results in fewer iteration times and noise conditions. The convergence analysis and robust analysis in with or without noises show that the reprojection error is less than 0.4 pixel when the noise is not greater than ±3 pixel. A real image experiment was performed by calibrating camera parameters and calculating the projection error, and the results show that the calibration precision error is less than 0.06%, and the re-projection error is 0.35 pixel, which verifies the effectiveness of the proposed method. It concluds that the method is applicable to image processing, mode classification and scene analysis in computer vision field.

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高瞻宇, 顾营迎, 刘宇航, 徐振邦, 吴清文. 采用简化Brown模型及改进BFGS法的相机自标定[J]. 光学精密工程, 2017, 25(9): 2532. GAO Zhan-yu, GU Ying-ying, LIU Yu-hang, XU Zhen-bang, WU Qing-wen. Self-calibration based on simplified brown non-linear camera model and modified BFGS algorithm[J]. Optics and Precision Engineering, 2017, 25(9): 2532.

采用简化Brown模型及改进BFGS法的相机自标定

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