## 6 Implementation and Experiment
### Experimental Results  
Table 2 shows the results of recognition performance for each test P&ID. Approximately 50 min were taken for each case to perform the detection of continuous lines, and about 300 s to complete the detection of line signs and flow arrows, respectively. Most of the time taken for continuous line recognition was spent on the line thinning process (about 90% of the recognition time). The recognition performance for each test P&ID was assessed in terms of precision and recall. Precision is the percentage of true positives from the results the network detected. That is, it is the ratio of correctly recognized line objects among the finally recognized line objects. Recall refers to the percentage of the network predicted as true positives out of the true positives in the input. That is, it indicates the number of correctly predicted line objects among line objects existed in the image. Table 2 outlines the \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Diagram resolution & 9933 \(\times\) 7016 \\ \hline Segmentation resolution & 512 \(\times\) 512 \\ \hline Segmentation stride & 300 \\ \hline Epoch, step & 50, 2500 \\ \hline \multirow{4}{*}{Anchor} & Size & 322, 642, 1282, 2562, 5122 \\  & Stride & 8, 16, 32, 64, 128 \\ \cline{1-1}  & Ratio & 0.289, 0.581, 1.0, 1.721, 3.457 \\ \cline{1-1}  & Scale & 0.949, 1.182, 1.543 \\ \hline \multirow{2}{*}{Threshold score} & \multicolumn{2}{c}{0.5} \\ \hline IOU threshold & \multicolumn{2}{c}{0.5} \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of the deep neural network used for learning. Figure 19: Line recognition results for test P&IDs. results of measuring precision and recall for the nine sheets of test P&IDs. The average values of the precision and recall for the test P&IDs were 96.14% and 89.59%, respectively. Table 3 shows the performance evaluation results for each type of line sign and flow arrow included in the test P&IDs. As a result, the recall of Dotted_line_h, which makes up a large part of the training dataset was lower than that of other line signs and flow arrows (except Double_slash_sign_line_v and Arrow_s). And among the fewer object types in the dataset, the recall of Double_slash_sign_line_v and Arrow_s was low; their recall was lower than that of Dotted_line_h. Through this, it can be determined that the detection performance of each object type using the deep artificial neural network is affected not only by the number of training data but also by the detection difficulty of the object shape. The line recognition results for nine test P&IDs are depicted in Figure 19. In Figure 19, different colors are used for the display of different line types. The lines including continuous_line, dotted_line, double_slash_sign_line, x_sign_line, and flow arrow are presented in light green, red, pink, light blue, and dark blue, respectively. Figure 19a shows the result of recognizing lines incorporated with flow arrows. Figure 19b shows the recognition results of continuous_line and dotted_line. Figure 19c shows the recognition result of continuous_line, dotted_line, double_slash_sign_line, and lines with flow arrows. Figure 19d shows the recognition result of continuous_line, dotted_line, and x_sign_line. Figure 19e shows the recognition result of continuous_line and dotted_line. The following is the outline of example cases where the line recognition was not performed correctly. First, there was a case where the line sign was not recognized (error case 1 in Figure 20). If the line sign was not identified, the line type could not be correctly determined. Second, there was a case where the diagonal line was not recognized (error case 2 in Figure 20). Third, a continuous line included in an object other than a line in the diagram was detected (error case 3 in Figure 20). It is considered that the problem of not recognizing the line signs or flow arrows (error case 1) is to be solved by increasing the number of training data or applying the latest network. The problem of not recognizing