A Robust O(n) Solution to the Perspective-n-Point Problem
A Robust O(n) Solution to the Perspective-n-Point Problem
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DOI：
10.1109/tpami.2012.41
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发表时间：
2012-07-01
影响因子：
23.6
通讯作者：
Xie, Ming
中科院分区：
文献类型：
--
作者：
Li, Shiqi;Xu, Chi;Xie, Ming
我们提出了一个非迭代的解决方案的透视n-点（PPENS）的问题，它可以鲁棒地恢复最佳的解决方案的七阶多项式。其核心思想包括三个步骤：1）将参考点分成3点子集，以获得一系列四阶多项式，2）计算多项式的平方和，以形成成本函数，以及3）找到成本函数的导数的根，以确定最佳值。该方法的优点是：首先，它可以稳定地处理平面、普通三维和拟奇异的情况，并且与现有的迭代算法一样精确，计算时间大大减少。第二，它是第一个非迭代的解，当没有多余的参考点可以使用时，它可以获得比迭代算法更精确的结果（n
We propose a noniterative solution for the Perspective-n-Point (PnP) problem, which can robustly retrieve the optimum by solving a seventh order polynomial. The central idea consists of three steps: 1) to divide the reference points into 3-point subsets in order to achieve a series of fourth order polynomials, 2) to compute the sum of the square of the polynomials so as to form a cost function, and 3) to find the roots of the derivative of the cost function in order to determine the optimum. The advantages of the proposed method are as follows: First, it can stably deal with the planar case, ordinary 3D case, and quasi-singular case, and it is as accurate as the state-of-the-art iterative algorithms with much less computational time. Second, it is the first noniterative PnP solution that can achieve more accurate results than the iterative algorithms when no redundant reference points can be used (n