采用张量分解的四摄像机测量系统标定方法

摄像机标定是精密三维视觉测量的关键，为了实现对多摄像机测量系统的精确标定，首先分析了现有基于一维靶标的多摄像机标定方法的优缺点，并针对其不足，提出了一种基于张量分解的多相机标定方法，该方法主要包括以下三个方面的内容:(1) 利用透视投影成像模型和刚体变换理论建立多摄像机测量的数学模型；(2) 分析现有基于基本矩阵的多摄像机标定方法存在标定结果之间相互耦合的问题；(3) 将四摄像机测量系统的四焦张量引入标定过程中，利用一维标定靶标的成像点坐标求解的四摄像机测量系统的四焦张量，并根据四焦张量的简化求解方法来精炼获取摄像机矩阵。最后，通过实验验证了该方法的有效性和准确性，实验结果表明:(1) 四摄像机三维测量系统的标定可仅通过三组标定靶标图像即可实现，且标定操作效率相对于基本矩阵法更高；(2) 在4000 mm×4000 mm×2000 mm范围内，多摄像机测量系统的精度达到4 mm (3σ)，相比于传统方法具有更精确的标定结果。满足室内运动目标位姿精确测量的要求。

Calibration method of quad-camera measurement system based on tensor decompose

Camera calibration is essential for vision measurement. In order to realize the accurate calibration of the multi-camera measurement system, the existing multi-camera calibration methods based on 1D (one-dimensional) targets are analyzed, and a multi-camera calibration method based on tensor decomposition is proposed. The method includes three aspects: (1) A mathematical model of multi-camera calibration is established with pin-hole model and rigid body transformation theory; (2) A problem of multi-camera calibration approach based on the fundamental matrix is analyzed, which is the calibration results coupled with each other; (3) In order to address this problem, the quad-focal tensor of a quad-camera measurement system is introduced to the calibration process, which includes that the quad-tensor is solved by using the image point of 1D calibration objects, and a reduced method for the quad-focal tensor is used to refine the camera matrices. Finally, the effectiveness and accuracy of the method are verified by experiments. The results indicate that (1) The calibration of the quad-camera 3D measurement system can be realized by only 3 groups of calibration target images, and the calibration operation efficiency is higher than that of the basic matrix method, and (2) the accuracy of the multi-camera measurement system reaches 4 mm (3σ) in the range of 4000 mm×4000 mm×2000 mm, which is more accurate than traditional approaches with only 3 groups calibration images. The proposed method meets the requirements of accurate measurement of indoor moving target pose.