This paper addresses the camera pose estimation problem from 3D lines and their 2D projections, known as the perspective-n-line (PnL) problem. Although many successful solutions have been presented, it is still a challenging to optimize both computational complexity and accuracy at the same time. In our work, we parameterize the rotation by using the Cayley–Gibbs–Rodriguez (CGR) parameterization and formulate the PnL problem into a polynomial system solving problem. Instead of the Grobner basis method, which may encounter numeric problems, we seek for an efficient and stability technique—the hidden variable method—to solve the polynomial system and polish the solution via the Gauss–Newton method. The performance of our method is evaluated by using simulations and real images, and results demonstrate that our method offers accuracy and precision comparable or better than existing state-of-the-art methods, but with significantly lower computational cost.

中文翻译：

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用隐变量法求解盈亏问题：准确高效的解法

本文从 3D 线及其 2D 投影解决了相机姿态估计问题，称为透视 n 线 (PnL) 问题。尽管已经提出了许多成功的解决方案，但同时优化计算复杂度和准确性仍然是一个挑战。在我们的工作中，我们通过使用 Cayley-Gibbs-Rodriguez (CGR) 参数化来参数化旋转，并将 PnL 问题公式化为多项式系统求解问题。与可能遇到数值问题的格罗布纳基法不同，我们寻求一种高效且稳定的技术——隐变量法——来求解多项式系统并通过高斯-牛顿法完善解。我们的方法的性能是通过使用模拟和真实图像来评估的，