A zoom camera can change its focal length and track moving objects with an adjustable resolution. To extract precise geometric information for the tracked objects, a zoom camera requires an accurate calibration method. High-precision camera calibration methods, however, usually require a number of control points that are not guaranteed in some practical situations. Most zoom cameras suffer radial distortion. Athough a traditional method can recover an undistorted image with known intrinsic parameters, it fails to work for a zoom camera with an unknown focal length. Motivated by these problems, we propose a two-point calibration method (TPCM). In this scheme, we first propose an approximate focal-invariant radial distortion (AFRD) model. With the AFRD model, an RGB image can be undistorted with an unknown focal length. After that, the TPCM method is presented to estimate the focal length and rotation matrix with only two control points for one image. Synthetic experiments demonstrate that the AFRD model is efficient. In the real data experiment, the mean reprojection error of the TPCM method is less than one pixel, which is smaller than current state-of-the-art methods, and we believe meets the demand for high-precision calibration.

中文翻译：

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具有近似焦点不变径向变形模型的变焦相机的两点校准方法

变焦相机可以更改其焦距并以可调的分辨率跟踪移动的对象。为了提取被跟踪物体的精确几何信息，变焦相机需要一种精确的校准方法。但是，高精度相机校准方法通常需要许多控制点，而在某些实际情况下这些控制点是无法保证的。大多数变焦相机会出现径向变形。尽管传统方法可以使用已知的固有参数恢复未失真的图像，但对于焦距未知的变焦相机却无法使用。由于这些问题，我们提出了一种两点校准方法（TPCM）。在此方案中，我们首先提出一个近似的焦点不变径向变形（AFRD）模型。使用AFRD模型，可以以未知的焦距使RGB图像失真。之后，提出了TPCM方法来估计一个图像只有两个控制点的焦距和旋转矩阵。综合实验表明，AFRD模型是有效的。在实际数据实验中，TPCM方法的平均重投影误差小于一个像素，小于当前的最新方法，我们相信可以满足高精度校准的需求。