Northwest Institute of Nuclear Technology, Xi'an 710024, China.
Sensors (Basel). 2023 Apr 3;23(7):3694. doi: 10.3390/s23073694.
This paper proposes a new pose and focal length estimation method using two vanishing points and a known camera position. A vanishing point can determine the unit direction vector of the corresponding parallel lines in the camera frame, and as input, the unit direction vector of the corresponding parallel lines in the world frame is also known. Hence, the two units of direction vectors in camera and world frames, respectively, can be transformed into each other only through the rotation matrix that contains all the information of the camera pose. Then, two transformations can be obtained because there are two vanishing points. The two transformations of the unit direction vectors can be regarded as transformations of 3D points whose coordinates are the values of the corresponding unit direction vectors. The key point in this paper is that our problem with vanishing points is converted to rigid body transformation with 3D-3D point correspondences, which is the usual form in the PnP (perspective-n-point) problem. Additionally, this point simplifies our problem of pose estimation. In addition, in the camera frame, the camera position and two vanishing points can form two lines, respectively, and the angle between the two lines is equal to the angle between the corresponding two sets of parallel lines in the world frame. When using this geometric constraint, the focal length can be estimated quickly. The solutions of pose and focal length are both unique. The experiments show that our proposed method has good performances in numerical stability, noise sensitivity and computational speed with synthetic data and real scenarios and also has strong robustness to camera position noise.
本文提出了一种新的使用两个消失点和一个已知相机位置的姿势和焦距估计方法。一个消失点可以确定相机帧中对应平行线的单位方向向量，作为输入，世界帧中对应平行线的单位方向向量也是已知的。因此，相机和世界帧中两个方向向量的单位分别可以通过包含相机姿势所有信息的旋转矩阵相互转换。然后，因为有两个消失点，所以可以得到两个变换。两个单位方向向量的变换可以看作是坐标为相应单位方向向量值的 3D 点的变换。本文的关键点在于，我们的消失点问题转化为具有 3D-3D 点对应关系的刚体变换，这是 PnP（透视-n-点）问题中的常见形式。此外，这一点简化了我们的姿势估计问题。此外，在相机帧中，相机位置和两个消失点可以分别形成两条线，并且两条线之间的角度等于世界帧中对应两组平行线之间的角度。当使用此几何约束时，可以快速估计焦距。姿势和焦距的解都是唯一的。实验表明，我们提出的方法在合成数据和真实场景中具有良好的数值稳定性、噪声敏感性和计算速度性能，并且对相机位置噪声具有很强的鲁棒性。
