Structured light systems based on phase measurement profilometry (PMP) are widely used in industrial measurements because of their good reconstruction accuracy and speed. A multi-view structured light system composed of multiple single-view structured light systems can achieve real-time multi-view 3D reconstruction, but its reconstruction accuracy is affected by the overall calibration accuracy of the system. Traditional multi-view structured light calibration needs to ensure that there is a large overlap between adjacent cameras because this is the premise of the commonly used multi-camera calibration scheme. However, the calibration area of the structured-light system determines the reconstruction area, and an excessive number of overlapping visual angle shrinks the reconstruction range of the multi-view structured light system. To reconstruct more areas, the amount of equipment required must be increased. Multi-camera calibration without overlapping visual angle can be realized with the help of a stereo target, manipulator, or rotating platform. However, high-precision stereo targets are difficult to fabricate, and high-precision auxiliary equipment is difficult to obtain. To solve the above problems, a multi-view structured light 3D measurement method based on reference standard parts is proposed, and it can be used to obtain the initial values of the external parameters between multiple cameras when there is an error in the default stereo target. The error in the external parameters is optimized by reconstructing the standard parts. The system can overcome the limitations of overlapping views and realize multi-view 3D reconstruction with no or fewer overlapping views, and its reconstruction accuracy is suitable for multi-view industrial measurement scenes.

The basic idea of this study was to first use a stereo target to obtain the initial estimation of the external parameters of the multi-camera and then carry out the multi-view 3D reconstruction of the standard plate and sphere based on the external parameters. The information of the fused point cloud is used to specify the error of the rotation and translation vectors in the external parameters, and it is used as the minimization target to optimize the external parameters of the multi-camera. Before obtaining the external parameters of multiple cameras, it is necessary to calibrate the single structured light system, that is, to use a high-precision industrial calibration board to obtain the internal parameters and distortion coefficients of the equipment. Subsequently, based on the transitivity of the external parameters, the external parameters between multiple cameras are obtained using the stereo target. Finally, considering the error of the stereo target, after the standard plate was reconstructed based on the initial value of the multi-camera external parameters, one of the plane point clouds was taken as the reference plane, and the distance variance of all points on the other plane point cloud to the reference plane was calculated. This value represents the error in the rotation vector. After the rotation vector is optimized, the standard sphere is reconstructed from multiple perspectives, the center distance of two spherical point clouds is taken as the error of the translation vector, and more accurate multi-camera external parameters can be obtained.

Our proposed multi-view structured light measurement method overcomes the limitation that adjacent cameras require overlapping viewing angles and can carry out multi-view 3D reconstruction of a single object without overlapping visual angle while ensuring accuracy. Through the reconstruction of a standard plate and sphere, it is proven that the proposed error model and optimization scheme (Equations 9 and 10) can effectively reduce the error of the external parameter matrix (Fig. 10), and the entire process does not require other high-precision auxiliary equipment. The accuracy of the optimized external parameter matrix is proven through the multi-view reconstruction of spheres of other sizes (Tables 4 and 5). The spherical fitting error of a multi-view reconstruction of an 85 mm sphere is 0.26 mm. In addition, because overlapping areas are not required, the reconstruction range of the system is larger, the equipment can be placed more freely, and the method is more suitable for use in actual industrial measurement scenarios with complex working conditions.

To sum up, we propose a multi-view structured light 3D measurement method based on reference standard parts. The initial estimated values of the multi-camera external parameters are obtained using a stereo target, and a multi-view 3D reconstruction is realized. Subsequently, the standard plate and sphere are reconstructed to obtain the standard point cloud, and the errors of the rotation and shift vectors in the initial value of the external parameters are optimized based on the feedback constraint of the standard point cloud. The proposed system overcomes the limitation that the traditional multi-view structured light system requires large overlapping visual angle of adjacent cameras. The multi-view reconstruction accuracy also meets the requirements of the multi-view industrial measurement scene and can provide a feasible technical scheme in today’s industrial 3D measurement scene.