Background

Camera calibration is an essential step for the optical measurement method used in the experimental mechanics. Most plumb line methods focus on solving lens distortions without considering camera intrinsic and extrinsic parameters.

Objective

In this paper, we propose a full camera calibration method to estimate the camera parameters, including camera intrinsic parameters, extrinsic parameters and lens distortion parameters, from a single image with six or more non-coplanar lines.

Methods

We parameterize the 3D lines with the intersection of two planes that allow the direct linear transformation of the lines(DLT-Lines). Based on the DLT-Lines, the projection matrix is estimated linearly, and then the camera intrinsic and extrinsic parameters are extracted from the matrix. The relationship between the distorted 2D lines and the distortion coefficients is derived, based on which the distortion coefficients can be solved linearly. In the last step, a non-linear optimization algorithm is used to jointly refine all the camera parameters, including the distortion coefficients.

Results

Both synthetic and real data are used to evaluate the performance of our method, which demonstrates that the proposed method can calibrate the cameras with radial and tangential distortions accurately.

Conclusions

We propose a DLT-lines based camera calibration method for experimental mechanics. The proposed method can calibrate all the camera parameters from a single image.

中文翻译：

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具有镜头径向和切向失真的基于 DLT 线的相机校准

背景

相机校准是实验力学中使用的光学测量方法的必要步骤。大多数铅垂线方法专注于解决镜头畸变，而不考虑相机的内在和外在参数。

客观的

在本文中，我们提出了一种完整的相机标定方法，用于从具有六个或更多非共面线的单个图像中估计相机参数，包括相机内部参数、外部参数和镜头畸变参数。

方法

我们用两个平面的交叉点参数化 3D 线，允许线的直接线性变换（DLT-Lines）。基于DLT-Lines，线性估计投影矩阵，然后从矩阵中提取相机内参和外参。推导了畸变二维线与畸变系数之间的关系，在此基础上可以线性求解畸变系数。在最后一步，使用非线性优化算法联合优化所有相机参数，包括畸变系数。

结果

合成数据和真实数据都用于评估我们方法的性能，这表明所提出的方法可以准确地校准具有径向和切向失真的相机。

结论

我们提出了一种用于实验力学的基于 DLT 线的相机校准方法。所提出的方法可以从单个图像校准所有相机参数。