## 3 Results and Discussion
\(e_{hdm}\) is the relative error of \(T_{vd}\) with \(T_{vm}\). The expression of the relative error RE is shown in the following Equation (5). \[RE=\frac{X-T}{T}\times 100\% \tag{5}\]  
where \(X\) represents the measured value and \(T\) represents the actual value. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Image**} & \multicolumn{3}{c}{**Standard Deviation of \(T_{h}\)**} & \multicolumn{3}{c}{**Standard Deviation of \(T_{v}\)**} \\ \cline{2-7}  & \(\delta_{Tha}\) & \(\delta_{Thp}\) & \(\delta_{Thy}\) & \(\delta_{Tva}\) & \(\delta_{Ty\beta}\) & \(\delta_{Ty\gamma}\) \\ \hline \(F_{s2}\) & 0.044 & 0.378 & 0.081 & 0.006 & 0.286 & 0.175 \\ \(F_{r}\) & 0.069 & 0.451 & 0.167 & None & None & None \\ \(F_{s3}\) & 0.018 & 0.237 & 0.146 & 0.046 & 0.588 & 0.392 \\ \(F_{s1}\) & 0.008 & 0.164 & 0.132 & 0.052 & 0.682 & 0.458 \\ \(F_{c}\) & 0.157 & 0.533 & 0.259 & 0.098 & 0.226 & 0.181 \\ \(F_{i}\) & 0.088 & 0.576 & 0.472 & 0.038 & 0.574 & 0.282 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Standard deviation of manual measurement of period length. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Image**} & \multirow{2}{*}{\(T_{hm}\)} & \multirow{2}{*}{\(T_{hp}\)} & \multirow{2}{*}{\(T_{h2}\)} & \multirow{2}{*}{\(T_{hd}\)} & \multirow{2}{*}{\(T_{vm}\)} & \multirow{2}{*}{\(T_{vp}\)} & \multirow{2}{*}{\(T_{v2}\)} & \multirow{2}{*}{\(T_{vd}\)} \\ \hline \(F_{s2}\) & 204.8 & 203.6 & 208.3 & 206.4 & 178.6 & 177.3 & 180.1 & 176.6 \\ \(F_{r}\) & 90.2 & 90.1 & 93.4 & 95.8 & None & None & None \\ \(F_{s3}\) & 102.2 & 101.8 & 202.8 & 128.5 & 62.8 & 63.7 & 59.7 & 65.4 \\ \(F_{s1}\) & 176.0 & 177.2 & 58.7 & 168.2 & 120.6 & 120.8 & 119.0 & 121.5 \\ \(F_{c}\) & 125.7 & 125.4 & 128.8 & 130.7 & 114.8 & 114.2 & 130.0 & 120.1 \\ \(F_{i}\) & 271.4 & 270.3 & 243.5 & 256.2 & 269.8 & 267.2 & 273.5 & 264.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Period length measurement results of various methods. From Tables 3 and 4, we could conclude that the period length measured by the proposed method had higher accuracy than the autocorrelation-based and the distance-matching function-based method. There was also a smaller relative error between the proposed method and the manual measurement result. Similar to the evaluation of the period length, the standard deviation was used to suggest the reliability of the manual measurement of the angles. Table 5 shows the manual measurement standard deviation of \(\theta_{h}\) and \(\theta_{v}\) of images (\(F_{i}\), \(F_{r}\), \(F_{c}\), \(F_{s1}\), \(F_{s2}\) and \(F_{s3}\) in Figure 11), where the \(\delta_{\theta h}\), \(\delta_{\theta h\beta}\) and \(\delta_{\theta h\gamma}\) are the minimum, maximum and average standard deviation of the \(\theta_{h}\), respectively. Similarly, \(\delta_{\theta\theta\gamma}\), \(\delta_{\theta\theta\gamma}\) and \(\delta_{\theta\theta\gamma}\) are the minimum, maximum and average standard deviation of the \(\theta_{v}\), respectively. From Table 5, we could conclude that the standard deviation of the manual measurements was small. Therefore, it was reasonable to use the manual measurement results as a benchmark to evaluate the measurement accuracy of the proposed measurement method. Table 6 shows the various methods measurement results of \(\theta_{h}\) and \(\theta_{v}\) of images (\(F_{i}\), \(F_{r}\), \(F_{c}\), \(F_{s1}\), \(F_{s2}\) and \(F_{s3}\) in Figure 11), where the \(\epsilon_{\theta h\gamma}\) represents the relative error of \(\theta_{hp}\) with \(\theta_{hm}\). \(\epsilon_{\theta\gamma m}\) represents the relative error of \(\theta_{hp}\) with \(\theta_{vm}\). \(\epsilon_{\theta\gamma m}\) represents the relative error of \(\theta_{hc}\) with \(\theta_{hm}\). \(\epsilon_{\theta\gamma m}\) represents the relative error of \(\theta_{hc}\) with \(\theta_{vm}\).