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.