# Fast Cylinder Shape Matching Using Random Sample Consensus in Large Scale Point Cloud
## 5 Experiments and Discussions
There are many cases where the pipe of the plant is constructed vertically/horizontally on the ground, but there are also cases where it is installed in a diagonal line, which means that additional calculation is necessary when constraints exist [9]. In addition, the bend area is calculated by finding the intersection point by extending the length from the result of finding the straight pipe and the \(90^{\circ}\) or T-shaped area. On the other hand, the proposed method can find not only vertical and horizontal regions, but also oblique regions, and S-shaped region estimation is also possible. The execution time is equal to \(O(n(P)\cdot\epsilon\cdot n(L)\cdot n(E)\cdot c)\), where \(n(P)\) is the total number of data points, \(\epsilon\) is the sphere fitting search increment, \(n(L)\) is the number of linear candidates/estimators, \(n(E)\) is the number of curved region candidates/estimators, and \(n(E)\) is the number of curved region candidates/estimators. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Figure 12a**} & \multicolumn{2}{c}{**Figure 12b**} & \multicolumn{2}{c}{**Figure 12c**} \\ \cline{2-7}  & **Line** & **Curve** & **Line** & **Curve** & **Line** & **Curve** \\ \hline
**Real No.** & 30 & 21 & 200 & 200 & 170 & 88 \\ \hline
**Correct No.** & 25 & 13 & 157 & 129 & 128 & 56 \\ \hline
**Ratio** & 0.833 & 0.619 & 0.785 & 0.645 & 0.752 & 0.636 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results in Figure 12 (unit: number). Figure 12: Estimation from nonsegmented data with \(\epsilon\). From top: point cloud/bent area, center axis/bent area, center axis, straight/final result mapping: (**a**) simple data; (**b**) complicated data 1; (**c**) complicated data 2.  
and c is the evaluation cost. Eventually the appropriate \(\epsilon\) value needs to be set in order to reduce execution time. In other words, the number of central axis data points determined by \(\epsilon\) affects the amount of computation of \(n(L)\), \(n(E)\), and c. Therefore, the proper setting of \(\epsilon\) has a great influence on overall performance. In order to verify its efficiency, the proposed method using the data in Figure 12b compares/ verifies the Hough transform method [10]. Figure 13 shows the left side of Figure 12b. Figure 13a shows the pipe estimation through the Hough transform [10], and Figure 13b shows no significant difference in the pipe estimation results by the proposed method. Figure 13a shows an execution time of 591 s. Figure 13b shows that step 1 took 16 s and step 2 took 10 s. Therefore, it was \(591/(16+10)=22.73\) times faster to estimate the pipe. A total of 89 left (C\({}_{\text{E}}\)) pipes exist in the left data, and the proposed method estimated 130 straight lines (C\({}_{\text{D}}\)) and 90 curves (C\({}_{\text{C}}\)). This seems to be better than the comparison of 60 C\({}_{\text{D}}\). However, since the comparison object is estimated to have detected only the area of the top image of Figure 13a, the result of linear/curve estimation of the right area added in the top image of Figure 13b should be removed. The added right-hand region has about 50 straight lines and 15 curved lines. As a result, a straight line/curve of 80 (C\({}_{\text{D}}\)) and 75 (C\({}_{\text{C}}\)) was estimated. Here, the error is 10 (C\({}_{\text{F}}\)). This is a result of estimating a strict standard (constant length/position/angle). C\({}_{\text{D}}\)/C\({}_{\text{E}}\) is 0.9 and C\({}_{\text{T}}\)/C\({}_{\text{D}}\) is 0.88, which is somewhat greater than the 0.67 and 0.87 of the comparison subjects. Figure 13: Cont. In Table 2, \(\mathrm{R_{r}}\) (recall rate) is \(\mathrm{C_{T}}/\mathrm{C_{E}}\), \(\mathrm{E_{r}}\) (error rate) is \(\mathrm{C_{F}}/\mathrm{C_{E}}\), and \(\mathrm{P_{r}}\) (precision rate) is \(\mathrm{C_{T}}/\mathrm{C_{D}}\). The proposed method has a relatively high \(\mathrm{R_{r}}\) because it limits the minimum radius of the pipe to 8 inches. There are more pipes in the actual data. \(\mathrm{E_{r}}\) shows that the comparison method has better results.