Correct fusion of data from two sensors is not possible without an accurate estimate of their relative pose, which can be determined through the process of extrinsic calibration. When two or more sensors are capable of producing their own egomotion estimates (i.e., measurements of their trajectories through an environment), the 'hand-eye' formulation of extrinsic calibration can be employed. In this paper, we extend our recent work on a convex optimization approach for hand-eye calibration to the case where one of the sensors cannot observe the scale of its translational motion (e.g., a monocular camera observing an unmapped environment). We prove that our technique is able to provide a certifiably globally optimal solution to both the known- and unknown-scale variants of hand-eye calibration, provided that the measurement noise is bounded. Herein, we focus on the theoretical aspects of the problem, show the tightness and stability of our solution, and demonstrate the optimality and speed of our algorithm through experiments with synthetic data.

中文翻译：

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可证明的最佳单目手眼校准

如果不准确估计两个传感器的相对位姿，就不可能正确融合来自两个传感器的数据，这可以通过外部校准过程确定。当两个或多个传感器能够产生它们自己的自我运动估计（即，通过环境测量它们的轨迹）时，可以采用外在校准的“手眼”公式。在本文中，我们将我们最近关于手眼校准的凸优化方法的工作扩展到其中一个传感器无法观察其平移运动的尺度的情况（例如，单目相机观察未映射的环境）。我们证明我们的技术能够为手眼校准的已知和未知尺度变体提供可证明的全局最优解，前提是测量噪声是有界的。在这里，我们专注于问题的理论方面，展示我们解决方案的紧密性和稳定性，并通过合成数据的实验证明我们算法的最优性和速度。