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Abstract: This paper is concerned with the problem of estimating the relative orientation between an inertial measurement unit (IMU) and a camera. Unlike most existing IMU-camera calibrations, the main challenge in this paper is that the information output from the IMU is incomplete. For example, only two tilt information can be read from the gravity sensor of a smart phone. Despite incomplete inertial information, there are strong restrictions between the IMU and camera coordinate systems. This paper addresses the incomplete information based IMU-camera calibration problem by exploiting the intrinsic restrictions among the coordinate transformations. First, the IMU transformation between two poses is formulated with the unknown IMU information. Then the defective IMU information is restored using the complementary visual information. Finally, the Levenberg-Marquardt (LM) algorithm is applied to estimate the optimal calibration result in noisy environments. Experiments on both synthetic and real data show the validity and robustness of our algorithm.

基于部分惯性传感器信息的惯性传感器–摄像机标定方法

对于低端惯性传感器与摄像机组合设备惯性传感器Yaw角输出误差较大或无Yaw输出的情况，进行惯性传感器与摄像机之间的精确标定。 分析经典手眼标定方法，利用标定方程中有关矩阵的相似性质，使得在缺少惯性传感器Yaw角测量信息的情况下，仍然能够精确标定惯性传感器与摄像机之间的相对姿态。 首先，使惯性传感器和摄像机一起运动两次（图3）。根据摄像机拍摄标定板的视频图像求出摄像机两次相对位置姿态，同时记录两次惯性传感器的Roll角和Pitch角的输出。然后，通过分析经典手眼标定方程RX=XR（公式4），得出矩阵R与矩阵R为相似矩阵，且二者迹相等。据此，恢复两次惯性传感器运动的相对旋转矩阵R（算法1）。最后，为获得精准标定结果，记录惯性传感器-摄像机设备的多次运动数据，并利用Levenberg-Marquardt（LM）算法进行优化，以减小噪声影响，获得惯性传感器和摄像机之间的相对旋转（图5）。 利用相似矩阵的性质，可以恢复两次运动之间惯性传感器间的旋转矩阵，利用LM算法，可以优化标定结果。
标定；计算机视觉；惯性传感器；智能手机；部分信息

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