EPnL:一种高效且精确的PnL问题求解算法

EPnL: An Efficient and Accurate Algorithm to the PnL Problem

现有Perspective-n-line (PnL)问题求解算法无法在获得高求解精度的同时保证高求解效率.为解决这个缺点,提出了同时兼具求解效率和求解精度算法EPnL.该方法首先将PnL问题转换为求二次曲面方程组交点的问题,然后利用单位四元数中变量不同时为零的特性,分类参数化PnL问题中的旋转矩阵.最后,为克服常规优化方法可靠性和效率较低的问题,同时兼具求解效率和求解精度算法利用二次曲面方程组自身的结构信息,采用低次项参数化高次项的方式将二次曲面方程组的求解问题转换为单变量多项式的求解问题.实验表明,相比于现有算法,该算法在具有高求解精度的同时也兼具有高求解效率.

The existing algorithms for solving the perspective-n-line(PnL) problem cannot achieve high accuracy as well as maintain high computational efficiency. To solve this disadvantage, the EPnL algorithm is proposed. The EPnL firstly transfers the PnL problem into the problem of finding the intersection of quadratic surface equations,and then uses a classification parametrization, which is derived from the fact that variables are not simultaneously zero in the unit-quaternion, to parameterize the rotation matrix in the PnL problem. At last, to overcome the problem of low reliability and low efficiency of conventional optimization methods, the EPnL uses the structure information of the system of quadratic surface equations, and transfers the problem of finding the intersection of quadratic surface equations into the solving problem of univariate polynomials using the strategy that the higher order terms are parameterized by the lower order terms in the system of quadratic surface equations. Experimental results show that the proposed algorithm has high accuracy as well as high efficiency compared with existing algorithms.