Smartphones, tablets and camera systems used, e.g., in cars and UAVs, are typically equipped with IMUs (inertial measurement units) that can measure the gravity vector accurately. Using this additional information, the $y$-axes of the cameras can be aligned, reducing their relative orientation to a single degree-of-freedom. With this assumption, we propose a novel globally optimal solver, minimizing the algebraic error in the least-squares sense, to estimate the relative pose in the over-determined case. Based on the epipolar constraint, we convert the optimization problem into solving two polynomials with only two unknowns. Also, a fast solver is proposed using the first-order approximation of the rotation. The proposed solvers are compared with the state-of-the-art ones on four real-world datasets with approx. 50000 image pairs in total. Moreover, we collected a dataset, by a smartphone, consisting of 10933 image pairs, gravity directions, and ground truth 3D reconstructions.

翻译：智能手机、平板电脑和相机系统,例如汽车和无人驾驶航空器中使用的智能手机、平板电脑和相机系统,一般都配备了能够准确测量引力矢量的IMU(惯性测量单位)系统。使用这一附加信息,相机的美元轴可以对齐,将其相对方向降低到单一的自由度。有了这一假设,我们提议了一个新的全球最佳解答器,将最小方位的代数错误最小化,以估计超定案的相对构成。根据上层限制,我们将优化问题转换为解决两个仅有两种未知因素的多面体问题。此外,还提议使用第一阶的旋转近似法快速解答器。提议的解答器与四个真实世界数据集中的最高级解答器进行了比较,四组为近似5万对图像。此外,我们用智能手机收集了一个数据集,由10933对图像、重力方向和地面真相3D重建组成。