This paper presents an accurate non-iterative method for the Perspective-n-Point problem(PnP). Our main idea is to mitigate scale bias by multiplying an independent inverse average depth variable onto the object space error. The introduced variable is of order 2 in the objective function and the optimality conditions constitute a polynomial system with three third-order and one first-order unknowns. Subsequently, we employ the Dixon resultant method to compute explicit expressions of the action matrix, the eigenvalue decomposition of which determines all the roots of the problem. We further extend this scale compensation technology to sphere cameras and contribute a uniform solver to PnP problems for both camera types. Experimental results confirm that our method is reliable and more accurate than state-of-the-art PnP algorithms.

本文提出了一种精确的非迭代方法来求解n点透视问题。我们的主要思想是通过将独立的逆平均深度变量乘以对象空间误差来减轻比例偏差。引入的变量在目标函数中的阶数为2，最优条件构成具有三个三阶和一个一阶未知数的多项式系统。随后，我们使用Dixon结果方法来计算动作矩阵的显式表达式，其特征值分解确定问题的所有根源。我们进一步将这种比例补偿技术扩展到了球面摄像机，并为两种摄像机的PnP问题做出了统一的求解器。实验结果证明，该方法比最新的PnP算法可靠且准确。