We propose two minimal solvers to the problem of relative pose estimation for a camera with known relative rotation angle. In practice, such angle can be derived from the readings of a 3D gyroscope. Different from other relative pose formulations fusing a camera and a gyroscope, the use of relative rotation angle does not require extrinsic calibration between the two sensors. The first proposed solver is formulated for a calibrated regular camera and requires four-point correspondences from two views. The second solver extends the problem to a generalized camera and requires five-point correspondences. We represent the rotation part of the motion in terms of unit quaternions in order to construct polynomial equations encoding the epipolar constraints. The Gröbner basis technique is then used to efficiently derive the polynomial solutions. Our first solver for regular cameras significantly improves the existing state-of-the-art solution. The second solver for generalized cameras is novel. The presented minimal solvers can be used in a hypothesize-and-test architecture such as RANSAC for reliable pose estimation. Experiments on synthetic and real datasets confirm that our algorithms are numerically stable, fast, and robust.

中文翻译：

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已知相对旋转角度情况下相机和广义相机的有效相对姿态估计

对于已知相对旋转角度的相机的相对姿态估计问题，我们提出了两个最小求解器。实际上，这种角度可以从3D陀螺仪的读数中得出。与将相机和陀螺仪融合在一起的其他相对姿态公式不同，使用相对旋转角度不需要在两个传感器之间进行外部校准。首先提出的求解器是为校准的常规摄像机制定的，需要从两个视图进行四点对应。第二个求解器将问题扩展到通用摄像机，并且需要五点对应关系。我们用单位四元数表示运动的旋转部分，以便构造编码对极约束的多项式方程。然后使用Gröbner基技术来有效地导出多项式解。我们的第一个常规摄像机求解器大大改善了现有的最新解决方案。通用相机的第二个求解器是新颖的。提出的最小解算器可用于假设和测试架构（如RANSAC）中，以进行可靠的姿态估计。在合成数据集和真实数据集上进行的实验证实，我们的算法在数值上稳定，快速且可靠。