# Point Cloud Measurement of Rubber Tread Dimension Based on RGB-Depth Camera
## 4 Results and Analysis
### Analysis of Rubber Tread Size Measurement Results  
The actual size of the rubber tread of \(200.28\times 150.17\times 25.98\) mm is selected for the experiment for 3D inspection. The parameters of the RANSAC algorithm are set as follows: Each iteration requires estimation based on three data points, and the algorithm iterates 500 times. Extract the reference surface of the workbench, recorded as \(\alpha_{1}\) (\(\{A_{1},B_{1},C_{1},D_{1}\}\)); remove the point cloud that does not belong to the plane, as shown in Figure 12; and then extract the upper surface of the tread from the remaining point cloud data, recorded as \(\alpha_{2}\) (\(\{A_{2},B_{2},C_{2},D_{2}\}\)), as shown in Figure 13.  
The planar expressions for the table datum and the upper surface of the tread can be obtained by fitting the planes to them, respectively, as shown in Equation (9):  
\[\left\{ \begin{array}{l}\alpha_{1}:0.03x-0.00y+1.00z-0.798384=0\\ \alpha_{2}:0.01x-0.00y+1.00z-0.771813=0\end{array} \right. \tag{9}\]  
Referring to Figure 7 and the two-plane representation, it is evident that the reference plane of the workbench aligns parallel to the upper surface of the tread. According to Equation (9), the distance from the workbench to the upper surface of the tread measures 0.026571 m, indicating a tread thickness of 26.571 mm. This value deviates by 0.591 mm from the actual tread product thickness of 25.98 mm, resulting in an error of 2.3%. Figure 12: Workbench reference plane point cloud. Figure 13: Point cloud of the upper surface of the tread. Using the OBB enclosing box to detect the edge collision on the upper surface of the tread [39], connecting the vertices of the OBB enclosing box yields the enclosing result of the upper surface of the tread, as shown in Figure 14.  
After filtering the enclosing box coordinates to the maximum value, the matrix of coordinates of each vertex of the enclosing box is shown in Equation (10):  
\[E^{\prime}=\left[ \begin{array}{cccc}-0.013&-0.132&0.773\\ 0.185&-0.123&0.771\\ -0.041&0.019&0.774\\ -0.013&-0.132&0.769\\ 0.139&0.050&0.768\\ -0.041&0.019&0.770\\ 0.185&-0.123&0.767\\ 0.139&-0.050&0.772\\ \end{array} \right] \tag{10}\]  
Combined with Figure 14 and according to Equation (10), encircling box vertex matrix calculations can be solved on the upper surface of the tire surface OBB encircling box side length of \(198.3\times 152.9\) mm, that is, an upper tire surface length and width of 198.3 mm and 152.9 mm, respectively, and the actual size of the tire surface of \(200.28\times 150.17\) mm of the products of the difference in the length of 1.7 mm, the difference in the width of 2.9 mm, the error of the length of 0.85%, and the error of the width of 1.9%. Comprehensive measurement results, the actual measured size, and the error level control relationship are shown in Table 7.  
Table 7 illustrates the measurement errors in thickness, length, and width, conforming to national standards and meeting the accuracy requirements of ST1 (\(\pm 3.5\%\)) and SW1 (\(\pm 2\%\)). The comparison results of the tread size inspection based on pixel metrics are depicted in Figure 15.  
In Figure 15, SXx represents the error level (ST for thickness; SW for width/length) within the display range. The depth of the point cloud measurement results adheres to the upper and lower limits of error specified by national standards. A comparison between two inspection methods reveals the accuracy of measuring the length of the tread's three dimensions relative to the true value. The visual measurement accuracy using the RGB-D \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Measured Value/** & **Actual Value/** & **Error/** & **ST1/** & **ST2/** & **ST3/** \\  & **(mm)** & **(mm)** & **(\%)** & **SW1 (\%)** & **SW2 (\%)** & **SW3 (\%)** \\ \hline Thickness & 26.57 & 25.98 & 2.27 & 3.5 & 5.0 & 7.0 \\ Width & 152.90 & 150.17 & 1.82 & 2.0 & 2.5 & 3.0 \\ Length & 198.30 & 200.28 & 0.99 & 2.0 & 2.5 & 3.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison results.