Guo Kai, Ye Hu, Chen Honglin, Gao Xin
Northwest Institute of Nuclear Technology, Xi'an 710024, China.
Sensors (Basel). 2022 Feb 25;22(5):1841. doi: 10.3390/s22051841.
Estimating the absolute pose of a camera is one of the key steps for computer vision. In some cases, especially when using a wide-angle or zoom lens, the focal length and radial distortion also need to be considered. Therefore, in this paper, an efficient and robust method for a single solution is proposed to estimate the absolute pose for a camera with unknown focal length and radial distortion, using three 2D-3D point correspondences and known camera position. The problem is decomposed into two sub-problems, which makes the estimation simpler and more efficient. The first sub-problem is to estimate the focal length and radial distortion. An important geometric characteristic of radial distortion, that the orientation of the 2D image point with respect to the center of distortion (i.e., principal point in this paper) under radial distortion is unchanged, is used to solve this sub-problem. The focal length and up to four-order radial distortion can be determined with this geometric characteristic, and it can be applied to multiple distortion models. The values with no radial distortion are used as the initial values, which are close to the global optimal solutions. Then, the sub-problem can be efficiently and accurately solved with the initial values. The second sub-problem is to determine the absolute pose with geometric linear constraints. After estimating the focal length and radial distortion, the undistorted image can be obtained, and then the absolute pose can be efficiently determined from the point correspondences and known camera position using the undistorted image. Experimental results indicate this method's accuracy and numerical stability for pose estimation with unknown focal length and radial distortion in synthetic data and real images.
估计相机的绝对位姿是计算机视觉的关键步骤之一。在某些情况下，尤其是使用广角或变焦镜头时，还需要考虑焦距和径向畸变。因此，本文提出了一种高效且鲁棒的单解方法，利用三组二维-三维点对应关系和已知相机位置，来估计焦距和径向畸变未知的相机的绝对位姿。该问题被分解为两个子问题，这使得估计更简单、更高效。第一个子问题是估计焦距和径向畸变。利用径向畸变的一个重要几何特性，即径向畸变下二维图像点相对于畸变中心（即本文中的主点）的方向不变，来解决这个子问题。利用这个几何特性可以确定焦距和高达四阶的径向畸变，并且它可以应用于多种畸变模型。将无径向畸变的值用作初始值，这些初始值接近全局最优解。然后，利用这些初始值可以高效、准确地解决该子问题。第二个子问题是利用几何线性约束确定绝对位姿。在估计了焦距和径向畸变后，可以得到去畸变后的图像，然后利用去畸变后的图像从点对应关系和已知相机位置高效地确定绝对位姿。实验结果表明了该方法在合成数据和真实图像中对未知焦距和径向畸变进行位姿估计的准确性和数值稳定性。
