Mathematical Analysis of the Multisolution Phenomenon in the P3P Problem
Mathematical Analysis of the Multisolution Phenomenon in the P3P Problem
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DOI：
10.1007/s10851-014-0525-0
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发表时间：
2015-02
影响因子：
2
通讯作者：
M. Vynnycky;K. Kanev
中科院分区：
文献类型：
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作者：
M. Vynnycky;K. Kanev
视角三点问题，也被称为姿态估计，起源于相机校准，在许多领域都很重要：例如，计算机动画，自动化，图像分析和机器人。其中一项活动涉及到用数学方法将其表述为寻找四次方程的解。然而，一般来说，方程没有唯一解，在某些情况下根本没有解。在这里，我们提出了一种解决问题的新方法；这需要更仔细地检查多项式的系数，以便了解给定的一组问题参数有多少个解。我们发现，如果控制点间距相等，则在控制点组合的所有可用空间位置的25%处有四个正解，在其余75%处有两个正解。
The perspective 3-point problem, also known as pose estimation, has its origins in camera calibration and is of importance in many fields: for example, computer animation, automation, image analysis and robotics. One line of activity involves formulating it mathematically in terms of finding the solution to a quartic equation. However, in general, the equation does not have a unique solution, and in some situations there are no solutions at all. Here, we present a new approach to the solution of the problem; this involves closer scrutiny of the coefficients of the polynomial, in order to understand how many solutions there will be for a given set of problem parameters. We find that, if the control points are equally spaced, there are four positive solutions to the problem at 25 % of all available spatial locations for the control-point combinations, and two positive solutions at the remaining 75 %.