从三视图单应矩阵中恢复焦距，提升精度与速度。
Three-view Focal Length Recovery From Homographies
- 利用两单应矩阵法向一致性推导焦距约束
- 三视图可解出1或2个未知焦距，精度更高
- 适用于相机焦距相同或部分已知场景
本文提出一种从三视图单应矩阵中恢复焦距的新方法。通过分析两个单应矩阵间法向量的一致性，采用消元技术推导出焦距与单应矩阵间的显式约束。结果表明，三视图可提供两个额外约束，从而实现一个或两个焦距的恢复。我们讨论了四种可能情形：三相机焦距未知且相等、三相机有两个不同未知焦距、一相机焦距已知其余两个相等或不等。所有问题均可转化为求解一个或两个未知数的多项式方程，可通过Sturm序列或隐变量法高效求解。合成数据与真实数据的评估显示，所提求解器比依赖双视图求解的方法更快更准确。代码与数据已在https://github.com/kocurvik/hf公开。
原文摘要 · Abstract (English)
In this paper, we propose a novel approach for recovering focal lengths from three-view homographies. By examining the consistency of normal vectors between two homographies, we derive new explicit constraints between the focal lengths and homographies using an elimination technique. We demonstrate that three-view homographies provide two additional constraints, enabling the recovery of one or two focal lengths. We discuss four possible cases, including three cameras having an unknown equal focal length, three cameras having two different unknown focal lengths, three cameras where one focal length is known, and the other two cameras have equal or different unknown focal lengths. All the problems can be converted into solving polynomials in one or two unknowns, which can be efficiently solved using Sturm sequence or hidden variable technique. Evaluation using both synthetic and real data shows that the proposed solvers are both faster and more accurate than methods relying on existing two-view solvers. The code and data are available on https://github.com/kocurvik/hf
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