## 4 Conclusions  
In this paper, a simple and effective single-shot 3D reconstruction approach, using the grid pattern-based structured-light vision method, was proposed. The system consisted of a camera and a low-cost LED projector.  
The grid pattern-based structured-light model was combined with the camera pinhole model and the multiple light plane constraint. The tangential distortion and radial distortion were compensated for. Without the use of the epipolar constraint, the error propagation of the low calibration accuracy of the stereo vision model was avoided. The grid pattern consisted of a number of intersecting light stripes. The common algorithms for stripe center extraction are inaccurate. However, the intersections of the grid lines could be precisely extracted. Following the topological distribution of the intersections, an effective extraction method was investigated to gather the sub-pixel centers on the grid strips. The white circles on the calibration board could disturb the extraction. To solve the problem, the gray value of the ellipse region on the input image was properly and automatically attenuated. A calibration method, based on the coplanar constraint, was presented, which could be implemented in one step.  
Displacement measurement experiments were conducted to evaluate the performance of the proposed method. The displacements measured by the grating ruler with 1 \(\upmu\)m accuracy were regarded as the ground truth. The maximum relative error between the measurement results and the corresponding ground truth values was 0.840%. The 3D reconstruction of a sphere object was implemented in single-shot by using the grid pattern-based structured-light vision system. By comparing this with the reconstruction of the sphere from the commercial RGB-D camera, the proposed method was verified. Following the development of deep learning techniques, the detection and correspondence retrieval techniques of the grid pattern could achieve several innovations in the future.  
Conceptualization, G.W. and B.L.; methodology, G.W. and B.L.; software, F.Y. and Y.H.; validation, G.W., B.L. and F.Y.; formal analysis, B.L. and Y.Z.; investigation, B.L. and Y.Z.; resources, B.L. and Y.Z.; data curation, B.L., Y.H. and F.Y.; writing--original draft preparation, B.L. and F.Y.; writing--review and editing, G.W. and B.L.; visualization, F.Y. and Y.H.; supervision,  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Nominal Radius (mm)** & **Our Approach (mm)** & **D455 (mm)** \\ \hline
85.000 & 84.652 & 88.937 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The measured radius of our approach and D455.  
Figure 17: The 3D reconstruction of the sphere object using D455. (**a**) Depth map; (**b**) Three-dimensional reconstruction result.  
G.W.; project administration, G.W.; funding acquisition, G.W., B.L. and F.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (51835007), Natural Science Foundation of Tianjin (21 JCZDJC00760), \"Project + Team\" Key Training Fund of Tianjin (XC202054), Tianjin Graduate Scientific Research Innovation Project (2020 YJSS013).  
Not applicable.  
The data presented in this research are available on request from the corresponding author.  
The authors declare no conflict of interest.