This paper presents a complete, accurate, and efficient solution for the Perspective-n-Line (PnL) problem. Generally, the camera pose can be determined from $N \geq 3$ 2D-3D line correspondences. The minimal problem ($N= 3$) and the least-squares problem ($N > 3$) are generally solved in different ways. This paper shows that a least-squares PnL problem can be transformed into a quadratic equation system that has the same form as the minimal problem. This leads to a unified solution for the minimal and least-squares PnL problems. We adopt the Gram-Schmidt process and a novel hidden variable polynomial solver to increase the numerical stability of our algorithm. Experimental results show that our algorithm is more accurate and robust than the state-of-the-art least-squares algorithms [1]–[4] and is significantly faster. Moreover, our algorithm is more stable than previous minimal solutions [3], [5], [6] with comparable runtime.

中文翻译：

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Perspective-n-Line 问题的完整、准确和有效的解决方案

本文为透视 n 线 (PnL) 问题提供了完整、准确且有效的解决方案。通常，相机位姿可以由$N \geq 3$2D-3D 线对应。最小的问题（$N= 3$) 和最小二乘问题 ($N > 3$) 通常以不同的方式解决。本文表明，最小二乘 PnL 问题可以转化为与极小问题具有相同形式的二次方程组。这导致了最小和最小二乘 PnL 问题的统一解决方案。我们采用 Gram-Schmidt 过程和一种新颖的隐藏变量多项式求解器来增加我们算法的数值稳定性。实验结果表明，我们的算法比最先进的最小二乘算法更准确和鲁棒[1]——[4]并且明显更快。此外，我们的算法比以前的最小解更稳定[3], [5], [6] 具有可比的运行时间。