# Mask R-CNN-Based Stone Detection and Segmentation for Underground Pipeline Exploration Robots
## 3 Experimental Results and Analysis
### Testing of Distance Measurement  
Our model is tested in a real environment to measure the distance between the explorer robot and the segmented stones. The explorer robot shown in Figure 1 is used for testing the real-time stone segmentation and distance measurement systems inside the underground pipeline. The robot is equipped with an L515 LiDAR camera, and the major specification details are shown in Table 3. The distance of each masked stone in the RGB frame is calculated through the depth frame by estimating their centroid point.  
In this study, object distance measurement is tested on 40 segmented objects from eight frames, and their values are recorded to estimate the average error. The experimental images with distance information are shown in Figure 11. The error difference between the actual distance and the measured distance is shown in millimeters in Table 4. A measuring tape with a precision of \(\pm\)0.5 mm is used to verify the estimated distance from our model. The experimental result shows that the average absolute error is 11.36 mm. We developed a GUI using Python to monitor the real-time pipeline inspection results using our model. In Figure 12, the system interface is presented, where segmented stones with their estimated distances are shown.  
Figure 11: _Cont._  
Figure 10: Examples of distance measurement with depth image. (a) Stones are in an empty pipe: (b) Stones are scattered on sand; and (c) Stones are dipped in water in the pipe.  
Figure 11: Measurement data. (**a**) Showing four stones and their distances inside the pipe’s hollow space; (**b**) Showing six stones and their distances inside the pipe’s hollow space; (**c**) Showing three stones and their distances inside the pipe’s hollow space; (**d**) Showing three stones and their distances inside the pipe’s hollow space; (**e**) Displaying six stones and their distances in a pipe partially filled with sand: (**f**) Displaying eight stones and their distances in a pipe partially filled with sand: (**g**) Displaying four stones and their distances in a pipe with water; and (**h**) Displaying six stones and their distances in a pipe with water.  
Figure 12: Stone segmentation and distance measurement system interface.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Trail Images Detail**} & \multicolumn{3}{c}{**Measurement Unit: mm**} \\ \hline Test Images & No. of Objects & Serial No. & Actual Distance & Measured Distance & Absolute Error \\ \hline \multirow{4}{*}{Figure 11a} & & 1 & 260.50 & 248.00 & 12.50 \\  & & 2 & 355.00 & 339.25 & 15.75 \\  & & 3 & 389.50 & 382.00 & 7.50 \\  & & 4 & 437.50 & 433.00 & 4.50 \\ \hline \multirow{4}{*}{Figure 11b} & & 1 & 270.00 & 264.00 & 6.00 \\  & & 2 & 305.00 & 294.00 & 11.00 \\  & & 3 & 326.00 & 316.25 & 9.75 \\ \cline{1-1}  & 6 & 4 & 357.00 & 363.00 & 6.00 \\ \cline{1-1}  & & 5 & 418.00 & 405.75 & 12.25 \\ \cline{1-1}  & & 6 & 460.00 & 456.75 & 3.25 \\ \hline \multirow{4}{*}{Figure 11c} & & 1 & 431.00 & 416.25 & 14.75 \\  & 3 & 2 & 537.00 & 529.25 & 7.75 \\ \cline{1-1}  & & 3 & 726.00 & 722.00 & 4.00 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Average distance measurement error.