## 4 Methodology of Vision-Based Vehicle Weight Identification  
In the previous sections, the equations of tire-road contact force were established. In terms of the equations, the tire-road contact force could be estimated as long as the tire inflation pressure, tire vertical deflection, and other physical parameters are known. The vehicle weight can then be identified by summing the contact forces of all the tires as,  
\[G=\sum_{1}^{i}F_{i}=\sum_{1}^{i}P_{i}S_{i} \tag{13}\]  
where \(G\) is the gross weight of the vehicle; \(i\) is the total number of tires; \(F_{i}\) is the contact force of each tire; \(P_{i}\) is the inflation pressure of each tire; \(S_{i}\) is the contact area of each tire. The modified equations of the footprint for passenger car tires and truck tires refer to Equations (9) and (12), respectively.  
The main parameters to be measured for the contact force estimation include the inflation pressure \(P\), vertical deflection \(\delta\), and tire specification parameters such as \(D\), \(H\), \(B\). The authors proposed a computer vision-based method to measure those parameters. A single-lens reflex (SLR) camera is used to capture images of each tire. Then, the computer vision techniques such as the edge detection and character recognition algorithms are used to detect the edges of the tire and rim, tire vertical deflection, and tire sidewall markings from the images, as shown in Figure 15. More details can be found in [PERSON] et al. [28].  
For the captured images of the tire, the K-means clustering algorithm [42] is first used for coarse segmentation, and then the region growing segmentation algorithm (RGSA) [43] is applied for fine segmentation. Thus, a continuous, and complete tire edge can be detected from the image background. Then, the Otsu algorithm [44] and projection algorithm [45] are applied for character detection and positioning in the tire sidewall, and the window scanning algorithm is used for character segmentation. After that, the tire specification  
Figure 14: Estimation error of truck tire contact force: (**a**) different deflection, (**b**) different inflation pressure.  
label can be identified by the template matching algorithm, for instance, 235/55R18, as shown in Figure 15. That is, the section width is 235 mm, the aspect ratio is 0.55, and the rim diameter is 18 in. Since it is reasonable to assume that the rim is rigid, the scale factor of the tire image could be calculated based on the physical value and the pixel number of the rim diameter. The tire vertical deflection can then be calculated by multiplying the scale factor with the pixel number of the vertical deformation, which is the movement of the lowest point of the tire edge before and after the deformation.  
The inflation pressure can be measured remotely by pressure sensors, such as the Tire Pressure Monitor System (TPMS) equipped on most vehicles. For vehicles that do not have TPMS, such as most trucks, a computer vision-based method was proposed. Generally, the label on the tire sidewall shows the manufacturer-recommended inflation pressure value, as shown in Figure 16. Based on the statistical analysis of a large set of measured data, the ratio of the measured pressure to the manufacturer-recommended pressure is within a limited range. For heavy trucks, the ratio is in the range of 1.1-1.2 [28]. Herein, a ratio of 1.15 is assumed for a heavy truck. Thus, the inflation pressure can be estimated by multiplying the manufacturer-recommended pressure with the ratio. For example, the inflation pressure of the tire in Figure 16 is equal to 900 \(\times\) 1.15 = 1035 KPa.  
Figure 15: Flowcharts: vision-based tire force identification method.  
Once the tire vertical deflection, inflation pressure, and specification parameters are obtained, the derived contact force equations are adopted to calculate the contact force of each tire. Finally, the vehicle weight including the axle weight and gross weight can be estimated by summing the contact forces of all the tires.