仅用两个仿射对应关系，即可求解未知焦距下的相机相对位姿。
A Minimal Solver for Relative Pose Estimation with Unknown Focal Length from Two Affine Correspondences
- 利用已知垂直方向建立约束方程，仅保留焦距与旋转角两个未知量。
- 通过多项式特征值法求解，实现3自由度相对位姿与焦距的联合估计。
- 适用于车载、手机等含IMU设备的实时定位系统，精度优于现有方法。
本文研究在已知相机内参除焦距未知的情况下，仅通过两个仿射对应关系（ACs）估计两视图间的相对位姿和焦距。在自动驾驶汽车、智能手机、无人机等应用中，相机常与惯性测量单元（IMU）结合使用，可获取相机视角的垂直方向。由此，两相机间的相对位姿从5自由度降为3自由度。本文提出一种新求解器：首先基于已知垂直方向建立仿射对应关系的约束方程；然后利用方程组存在非平凡解的性质，导出四个仅含焦距与相对旋转角的方程；最后采用多项式特征值法求解该问题。在合成数据与真实数据集上的实验表明，本方法性能优于现有最先进求解器。
原文摘要 · Abstract (English)
In this paper, we aim to estimate the relative pose and focal length between two views with known intrinsic parameters except for an unknown focal length from two affine correspondences (ACs). Cameras are commonly used in combination with inertial measurement units (IMUs) in applications such as self-driving cars, smartphones, and unmanned aerial vehicles. The vertical direction of camera views can be obtained by IMU measurements. The relative pose between two cameras is reduced from 5DOF to 3DOF. We propose a new solver to estimate the 3DOF relative pose and focal length. First, we establish constraint equations from two affine correspondences when the vertical direction is known. Then, based on the properties of the equation system with nontrivial solutions, four equations can be derived. These four equations only involve two parameters: the focal length and the relative rotation angle. Finally, the polynomial eigenvalue method is utilized to solve the problem of focal length and relative rotation angle. The proposed solver is evaluated using synthetic and real-world datasets. The results show that our solver performs better than the existing state-of-the-art solvers.
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