Ding Yaqing, Yang Jian, Ponce Jean, Kong Hui
IEEE Trans Pattern Anal Mach Intell. 2022 Jan;44(1):196-210. doi: 10.1109/TPAMI.2020.3005373. Epub 2021 Dec 7.
In this paper, we propose a novel approach to two-view minimal-case relative pose problems based on homography with known gravity direction. This case is relevant to smart phones, tablets, and other camera-IMU (Inertial measurement unit) systems which have accelerometers to measure the gravity vector. We explore the rank-1 constraint on the difference between the euclidean homography matrix and the corresponding rotation, and propose an efficient two-step solution for solving both the calibrated and semi-calibrated (unknown focal length) problems. Based on the hidden variable technique, we convert the problems to the polynomial eigenvalue problems, and derive new 3.5-point, 3.5-point, 4-point solvers for two cameras such that the two focal lengths are unknown but equal, one of them is unknown, and both are unknown and possibly different, respectively. We present detailed analyses and comparisons with the existing 6- and 7-point solvers, including results with smart phone images.
在本文中，我们提出了一种基于已知重力方向的单应性的新颖方法，用于解决双视图最小情况相对位姿问题。这种情况与智能手机、平板电脑以及其他配备加速度计以测量重力向量的相机 - 惯性测量单元（IMU）系统相关。我们探究了欧几里得单应性矩阵与相应旋转之间差异的秩 - 1约束，并提出了一种有效的两步解决方案，用于解决校准和半校准（未知焦距）问题。基于隐变量技术，我们将这些问题转化为多项式特征值问题，并分别推导了适用于两个相机的新的3.5点、3.5点、4点求解器，使得两个焦距未知但相等、其中一个未知以及两个都未知且可能不同的情况。我们给出了与现有的6点和7点求解器的详细分析和比较，包括使用智能手机图像的结果。
