# Point Cloud Measurement of Rubber Tread Dimension Based on RGB-Depth Camera
## 4 Results and Analysis
### Analysis of Rubber Tread Size Measurement Results
Figure 14: The result of building the OBB bounding box on the upper surface of the tread. camera tread point cloud data shows proximity to the actual tread dimensions, aligning closely with industrial standards for tread dimension measurement. The measurement effect is notably excellent and substantial. To further verify the stability and reliability of the measurement effect, this study aligned with the cutting conveyor belt's transportation direction and the camera's shooting frequency. The \(200.28\times 150.17\times 25.98\) mm tread is divided into five equal parts of \(150.17\times 37.00\times 25.98\) mm, screening five groups of tread point cloud data for size measurement experiments (cover layer screening, fixed width). Aliquot inspection of the tread actually takes into account the accuracy of the dimensions of the tread workpieces after cutting in the actual production line. This requires a batch inspection of the tread to ensure uniformity of the dimensional edges of the same workpiece. In this paper, five equal parts are carried out in consideration of the length of the tread samples, which can be divided into five parts to better avoid the randomness of the experimental results, and the size of its aliquot is closer to the size of the actual production. The experimental data acquisition schematic is shown in Figure 16.  
Using the Astra Pro depth camera for scanning to collect rubber tread point cloud data requires careful consideration of the object's distance from the camera and its impact on depth frame accuracy. The accuracy of the collected tread distance is inversely proportional to the distance from the camera; closer distances yield a higher accuracy in the scanned point cloud data but limit the scanning range. Table 1 specifies that the optimal distance between the Astra Pro camera and the object should range from 0.6 to 8.0 m. The camera provides a vertical viewing angle of \(40.2^{\circ}\) degrees and a horizontal viewing angle of \(58.4^{\circ}\) degrees, facilitating the simultaneous acquisition of RGB color maps and depth information [40]. The camera's acquisition range is illustrated in Figure 17.  
Figure 16: Schematic diagram of data acquisition. Figure 15: Comparison of two detection methods. The object distance from the camera to the tread is \(D\) (\(D\in[0.6,8.0]\)), the horizontal viewing angle of the camera is \(\theta_{H}\) (\(\theta_{H}=58.4^{\circ}\)), the vertical viewing angle is \(\theta_{V}\) (\(\theta_{V}=40.2^{\circ}\)), and the length and width of the scanned tread are \(L\) and \(W\), respectively, which can be described by Equation (11):  
\[\left\{ \begin{array}{l}L=2\times D\times\tan\frac{\theta_{H}}{L}\\ W=2\times D\times\tan\frac{\theta_{V}}{2}\end{array} \right. \tag{11}\]  
where \(L\in[0.67,8.94]\) and \(W\in[0.44,5.86]\); that is, in the camera's recommended working distance, it can scan the tread length range of 0.67-8.94 m and tread width range of 0.44-5.86 m (the experimental tread product size of \(200.28\times 150.17\times 25.98\) mm). For uniform sections of the tread measurement area, the tread point cloud data underwent preprocessing steps, followed by measurement of 3D information using the RANSAC-OBB dimensional detection algorithm [41]. Partial processing results and five sets of tread point cloud data are depicted in Figures 18 and 19, with measurement outcomes summarized in Table 8.  
Figure 17: Astra Pro collects the rubber tread range. Figure 18: Some processing steps. Based on Table 8, the relative and absolute error distributions of the true values and measured values for the five sets of three-dimensional tread information are illustrated in Figure 20 below. Figure 19: Five sets of tread surface point cloud data.