The accurate estimation of camera pose using numerous line correspondences in real time is a challenging task. This paper presents a non-iterative approach to solve the Perspective-n-Line (PnL) problem. The method can provide high speed and global optimality, as well as linear complexity. A nonlinear least squares (non-LLS) objective function is first formulated by parameterizing the rotation matrix with Cayley representation. A system of three third-order equations is then derived from its optimality conditions, and then, it is solved directly based on the Gröbner basis technique. Finally, the camera pose can be easily obtained by back-substitution. A major advantage of the proposed method lies in scalability, as the size of the elimination template used in the Gröbner basis technique is independent to the number of line correspondences. Extensive and detailed experiments on synthetic data and real images are conducted, demonstrating that the proposed method achieves an accuracy that is equivalent or superior to the leading methods, but with reduced computational requirements. The source code is available at https://github.com/dannyshin1/danny/tree/master/OPnL1.

中文翻译：

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使用线特征的相机姿态估计的高效全局最优方法

实时使用大量线对应来准确估计相机姿态是一项艰巨的任务。本文提出了一种非迭代的方法来求解Perspective- n -Line（P nL）问题。该方法可以提供高速和全局最优性以及线性复杂度。首先通过用Cayley表示对旋转矩阵进行参数化来制定非线性最小二乘（non-LLS）目标函数。然后从其最优性条件中得出一个由三个三阶方程组成的系统，然后直接基于Gröbner基技术对其进行求解。最后，可以通过反替换轻松获得相机姿态。所提出的方法的主要优点在于可扩展性，因为在Gröbner基础技术中使用的消除模板的大小与行对应的数量无关。对合成数据和真实图像进行了广泛而详细的实验，证明了所提出的方法所达到的精度与领先方法相当或更高，但减少了计算需求。源代码位于https://github.com/dannyshin1/danny/tree/master/OPnL1。