# Fast Cylinder Shape Matching Using Random Sample Consensus in Large Scale Point Cloud
## 5 Experiments and Discussions
However, if the error is assumed to be the number not found in the whole of \(\mathrm{C_{E}}\), \(\mathrm{E_{r}}=\left(\mathrm{C_{E}}\mathrm{-C_{T}}\right)/\left.\mathrm{C_{E}}\right\), the proposed method will be 0.21 and 0.22, and the comparison method will be 0.42 and 0.41. This is because the \(\mathrm{C_{T}}\) in the proposed method is larger than the comparison method. Also, if 8 inches of cylinders are not excluded, \(\mathrm{C_{E}}\) will be greater \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline
**Model** & \(\mathrm{C_{E}}\) & \multicolumn{8}{c}{**Proposed**} & \multicolumn{8}{c}{**Compared [10]**} \\ \hline  & & \(\mathrm{C_{D}}\) & \(\mathrm{C_{T}}\) & \(\mathrm{C_{F}}\) & \(\mathrm{R_{r}}\) & \(\mathrm{E_{r}}\) & \(\mathrm{P_{r}}\) & \(\mathrm{t}\) & \(\mathrm{C_{D}}\) & \(\mathrm{C_{T}}\) & \(\mathrm{C_{F}}\) & \(\mathrm{R_{r}}\) & \(\mathrm{E_{r}}\) & \(\mathrm{P_{r}}\) & \(\mathrm{t}\) \\ \hline
**Figure 13 (Left)** & 89 & 80 & 70 & 10 & 0.79 & 0.11 & 0.88 & 25 s & 60 & 52 & 8 & 0.58 & 0.09 & 0.86 & 591 s \\ \hline
**Figure 14 (Right)** & 107 & 97 & 83 & 14 & 0.78 & 0.13 & 0.85 & 37 s & 72 & 63 & 9 & 0.59 & 0.08 & 0.88 & 637 s \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison verification. \(\mathrm{C_{E}}\), actual pipe number; \(\mathrm{C_{D}}\), estimated pipe number; \(\mathrm{C_{T}}\), estimated success number; \(\mathrm{C_{F}}\), estimated failure number; \(\mathrm{t}\), run time; \(\mathrm{R}\), recall rate; \(\mathrm{E}\), error rate; \(\mathrm{P_{r}}\), precision rate. Figure 14: Comparison of proposed method with actual data (right side of Figure 12b). From top to bottom: point cloud/cylinder matching/center axis/final result. (**a**) Estimation by Hough transform [10]; (**b**) estimation by proposed method. than 89, which will affect \(R_{r}\) and \(E_{r}\). The more pipes it is searched, the better way, so the new \(E_{r}\) may be meaningful. A cylinder of 8 inches or less is shown in Figure 13b (yellow circle A). These areas are cylinders with a radius of about 2 to 6 inches. Cylinders with small radii are difficult to estimate because their accuracy is low in sensor error and normal estimation. While the comparison method does not estimate the cylinder of this region, the proposed method shows some degree of cylinder estimation even though there are broken and missing parts. If \(C_{E}\) contains less than 8 inches of cylinders, the proposed method will give better results in new \(E_{r}\). \(C_{E}\) in Table 2 is in accordance with [10]. In the experiment of the proposed method, data is sampled by setting \(\epsilon=25\) as the first line of pseudo code a. The central axis candidates can be obtained by repeatedly sphere fitting (error 1 cm) on the sampled 25% data (pseudo code a 2-4 lines). When the \(D_{CL}\) is completed, average filtering is performed (Pseudo code a 5 lines). Once the filtered center axis candidates \(D_{FLT}\) is computed, it is sampled 40% and the PCA is used to calculate the directionality of the local point cloud (pseudo code a 6-8 lines). The pseudo code b estimates the complete cylinders in the directional set \(V_{PCA}^{\rightarrow}\). First, algorithm searches for a straight line candidate \(D_{EST}\) that matches the angle (<15 degrees) and the distance (<15 cm) between the two vectors as shown in the third row. Since the retrieved \(D_{EST}\) means one cylinder, the cylinder is completed using PCA as shown in the line 7. This process is repeated (pseudo code b 1-8 lines) to estimate all the cylinders. The pseudo code c is a code fitting the curve region. The \(D_{CYL}\) is the estimated set of cylinders, and curves are retrieved from the \(V_{PCA}^{\rightarrow}\) based on the end points of each cylinder in the \(D_{CYL}\). The line 2 checks whether the discriminant is within a certain range through the surrounding points in the \(\overset{\rightarrow}{V_{i}}\). When the discriminant value in the experiment is 0.02 \(\sim\) 0.06, it is determined as a curve. The straight line is 0.02 or less.