# Panoramic Digital Image Correlation for 360-Deg Full-Field Displacement Measurement
## 3 Experiments and Discussions
### Evaluation of Separate Camera Parameters Calibration Method
#### 3.2.3 Scale Factor Details  
Although the translation vector calculated by the above method is the result of normalization, it can be restored to its original dimension so long as there is a known dimension in the view. In this study, the laser point cloud data of the log specimen was used as the know dimensions in the view, and Algorithm 3 was used to calculate the scale factor of each stereo camera pair. Through iterations of the ICP algorithm, not only the optimal scale factor for each stereo camera pair was obtained, but also the rotation matrix and translation vector of each reconstructed real scale point cloud with respect to the laser point cloud are obtained simultaneously, which are listed in Table 3. In this step, each pair of corresponding image points was converted from image coordinates to three-dimensional coordinates by a linear triangulation algorithm [46] using the camera-related calibration parameters. The local three-dimensional shape of the log was optimized to the real scale during the ICP iteration, as shown in Figure 5. The three local reconstructed shapes contain all the information of the 360-deg contour features of the log. Although the edges were defective, there were overlapping regions in the edges of the three reconstructed shapes, and an overlap was observed between the data. In order to quantitatively assess the accuracy of the three-dimensional reconstruction results based on reliable scale information, the  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{6}{c}{**Camera**} \\ \cline{2-7}  & \(\mathbf{C_{1-L}}\) & \(\mathbf{C_{1-R}}\) & \(\mathbf{C_{2-L}}\) & \(\mathbf{C_{2-R}}\) & \(\mathbf{C_{3-L}}\) & \(\mathbf{C_{3-R}}\) \\ \hline \(f_{x}\)(pixel) & 2399.27 & 2411.09 & 2400.38 & 2410.89 & 2399.49 & 2412.82 \\ \(f_{y}\)(pixel) & 2399.28 & 2411.28 & 2400.76 & 2410.97 & 2399.83 & 2413.62 \\ \(c_{x}\)(pixel) & 647.961 & 636.759 & 651.751 & 630.942 & 625.272 & 645.155 \\ \(c_{y}\)(pixel) & 493.472 & 506.526 & 489.522 & 510.861 & 511.794 & 492.031 \\ \(k_{1}\) & \(-0.073\) & \(-0.053\) & \(-0.065\) & \(-0.053\) & \(-0.048\) & \(-0.055\) \\ \(k_{2}\) & 1.834 & 0.034 & 1.612 & 0.085 & \(-0.112\) & 0.147 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Intrinsic parameters determined by planar target.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{4}{c}{**Camera Pair**} \\ \cline{2-5}  & \(\mathbf{C_{1}}\) & \(\mathbf{C_{2}}\) & \(\mathbf{C_{3}}\) \\ \hline \multirow{2}{*}{Rotation angle (\(\circ\))} & \(\theta_{1}\) & 0.2105 & 1.4844 & 4.6002 \\  & \(\theta_{2}\) & 11.5137 & 9.5123 & 13.4627 \\  & \(\theta_{3}\) & 0.6432 & 0.5387 & 0.7070 \\ \hline \multirow{2}{*}{Translation vector (normalized)} & \(t_{1}\) & \(-0.9790\) & \(-0.3548\) & \(-0.9677\) \\  & \(t_{2}\) & \(-0.1282\) & \(-0.0143\) & 0.2204 \\ \(t_{2}\) & \(0.0838\) & \(-0.8895\) & 0.1119 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Extrinsic parameters determined by proposed method.  
reconstructed three-dimensional points were overlaid on the reference position of the laser point cloud. The root mean square error (RMSE) between the original laser point cloud and the constructed point cloud represents the stereo calibration error. The RMSEs in the three reconstructions were 0.61 mm, 0.75 mm, and 0.93 mm, respectively, indicating good reconstruction results.