## 3 Experiments and Discussion
### System Calibration  
The 2D coplanar calibration board for the calibration had plenty of circular features (Figure 11). The specification of the target is shown in Table 1.  
Figure 10: The acquired images with depth variations in a target scene. (**a**) The image with all light stripes when the monotonicity constraint was satisfied; (**b**) The image with light strip loss during measuring depth changes over the upper bound.  
Figure 9: The experimental setup.  
The target was placed at six different positions in the viewing field of the camera. The contour points of the white circles were extracted and fitted to the ellipses, as shown in Figure 12a. The ellipse centers were regarded as the feature points for calibration. The ellipse centers were sorted and marked according to topological ordering, as shown in Figure 12b.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Specifications** & **Values** \\ \hline Boundary dimensions (mm) & 180 \(\times\) 150 \\ Circle diameter (mm) & 7 (L), 3.5 (S) \\ Center distance (mm) & 15 \\ Array number & 11 \(\times\) 9 \\ Precision (mm) & \(\pm\)0.01 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The specification of the target.  
Figure 11: The acquired image of the calibration board.  
Figure 12: Different pose views and extraction results. (**a**) Ellipse fitting results of the different views. (**b**) Extracted feature centers and topological ordering results of the different views.  
By utilizing [PERSON]'s method [40], the intrinsic parameters, distortion coefficients and relative poses \(\mathbf{R}_{i}\), \(\mathbf{T}_{i}\) were obtained. The intrinsic parameters and distortion coefficients are listed in Table 2. The rotation matrix \(\mathbf{R}_{i}\) was transformed into a vector formation \(\mathbf{rvec}_{i}\), consisting of Euler angles. The extrinsic parameters of the six pose views are listed in Table 3. The reprojection errors were the distances from the measured 2D points and their respective projections obtained by applying the calibrated camera model to the 3D points [41]. The mean reprojection errors of the six images were below 0.103 pixel, as shown in Figure 13.  
There were sixteen horizontal and sixteen vertical planes on the grid pattern. The parameters of the light planes are listed in Table 4. The values [\(A_{ver}\), \(B_{ver}\), \(C_{ver}\), \(D_{ver}\)] represent the coefficients of the vertical planes, while the values [\(A_{Hor}\), \(B_{Hor}\), \(C_{Hor}\), \(D_{Hor}\)] represent the coefficients of the horizontal planes. The planes in the camera coordinate system are shown in Figure 14.  
\begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Results** \\ \hline \(f_{x}\),\(f_{y}\) (pixel) & 3354.0982, 3354.8173 \\ \(u_{0}\), \(v_{0}\) (pixel) & 697.163, 478.755 \\ \(k_{1}\), \(k_{2}\) & \(-0.041\), \(-1.344\) \\ \(p_{1}\), \(p_{2}\) & \(-0.00039\), \(-0.00041\) \\ \hline \end{tabular}
\end{table}
Table 2: The intrinsic parameters and distortion coefficients.  
Figure 13: The mean reprojection errors.  
\begin{table}
\begin{tabular}{c c c} \hline
**Pose Views** & \(\mathbf{rvec}_{i}\) & \(\mathbf{T}_{i}\) \\ \hline
1 & [\(-3.020\), \(0.046\), \(-0.760\)] & [\(1.616\), \(5.987\), \(514.204\)] \\
2 & [\(-3.124\), \(0.083\), \(-0.186\)] & [\(-8.074\), \(5.674\), \(511.550\)] \\
3 & [\(-3.048\), \(0.017\), \(-0.677\)] & [\(-18.359\), \(5.856\), \(500.676\)] \\
4 & [\(-3.073\), \(-0.015\), \(-0.548\)] & [\(-25.7326\), \(0.505\), \(549.236\)] \\
5 & [\(-3.021\), \(0.031\), \(-0.023\)] & [\(-7.029\), \(5.590\), \(469.236\)] \\
6 & [\(-2.990\), \(0.909\), \(-0.355\)] & [\(-9.006\), \(2.654\), \(464.551\)] \\ \hline \end{tabular}
\end{table}
Table 3: The extrinsic parameters of the six pose views.