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On the Effect of Control-Point Spacing on the Multisolution Phenomenon in the P3P Problem

机译：P3P问题中控制点间距对多解决方案现象的影响

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摘要

The perspective 3-point (P3P) 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 possibility is to formulate it mathematically in terms of finding the solution to a quartic equation. However, there is yet no quantitative knowledge as to how control-point spacing affects the solution structure-in particular, the multisolution phenomenon. Here, we consider this problem through an algebraic analysis of the quartic's coefficients and its discriminant and find that there are significant variations in the likelihood of two or four solutions, depending on how the spacing is chosen. The analysis indicates that although it is never possible to remove the occurrence of the four-solution case completely, it could be possible to choose spacings that would maximize the occurrence of two real solutions. Moreover, control-point spacing is found to impact significantly on the reality conditions for the solution of the quartic equation.
机译：透视3点（P3P）问题（也称为姿势估计）起源于相机校准，并且在许多领域都很重要：例如，计算机动画，自动化，图像分析和机器人技术。一种可能性是根据找到四次方程的解进行数学公式化。但是，关于控制点间距如何影响解决方案结构（特别是多解决方案现象），尚无定量知识。在这里，我们通过对四次方系数及其判别式进行代数分析来考虑这个问题，并且发现根据间隔的选择方式，两个或四个解的可能性存在显着差异。分析表明，尽管永远不可能完全消除四解情况的出现，但有可能选择使两个实际解的出现最大化的间隔。此外，发现控制点间距对四次方程解的现实条件有很大影响。

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  • 来源
    《Mathematical Problems in Engineering》 |2018年第7期|5932508.1-5932508.13|共13页
  • 作者

    Vynnycky M.; Reddy G. M. M.;

  • 作者单位

    Royal Inst Technol KTH, Dept Mat Sci & Engn, Brinellvagen 23, S-10044 Stockholm, Sweden;

    Univ Sao Paulo Sao Carlos, Inst Math & Comp Sci, Dept Appl Math & Stat, POB 668, BR-13560970 Sao Carlos, SP, Brazil;

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