Guo Kai, Ye Hu, Zhao Zinian, Gu Junhao
Northwest Institute of Nuclear Technology, Xi'an 710024, China.
Sensors (Basel). 2021 Sep 28;21(19):6480. doi: 10.3390/s21196480.
In this paper we propose an efficient closed form solution to the absolute orientation problem for cameras with an unknown focal length, from two 2D-3D point correspondences and the camera position. The problem can be decomposed into two simple sub-problems and can be solved with angle constraints. A polynomial equation of one variable is solved to determine the focal length, and then a geometric approach is used to determine the absolute orientation. The geometric derivations are easy to understand and significantly improve performance. Rewriting the camera model with the known camera position leads to a simpler and more efficient closed form solution, and this gives a single solution, without the multi-solution phenomena of perspective-three-point (P3P) solvers. Experimental results demonstrated that our proposed method has a better performance in terms of numerical stability, noise sensitivity, and computational speed, with synthetic data and real images.
在本文中，我们针对焦距未知的相机，从两组二维-三维点对应关系以及相机位置出发，提出了一种高效的绝对定向问题闭式解。该问题可分解为两个简单子问题，并可通过角度约束求解。求解一个一元多项式方程来确定焦距，然后采用几何方法确定绝对定向。几何推导易于理解且显著提高了性能。利用已知相机位置重写相机模型可得到更简单、高效的闭式解，且该解为单一解，不存在透视三点（P3P）求解器的多解现象。实验结果表明，我们提出的方法在数值稳定性、噪声敏感性和计算速度方面，对于合成数据和真实图像均具有更好的性能。
