## 3 Results and Discussion
### Vision Module Simulation and Testing Performance  
Figure 13 shows the sample detection of the vision module. Results showed that using a TensorRT-optimized SSD MobileNetV1 to detect plants in 1280 \(\times\) 720 images on an NVIDIA Jetson Nano 4 GB had an average inferencing speed of 45 _fps_. This average inferencing speed only represented the elapsed time to inference on an already loaded frame. However, due to calculation overheads caused by additional data processing and transmission, the average effective inferencing speed of the vision module was only 16 _fps_, as shown in Figure 13. The effective speed was the average time difference for the vision module to complete a single loop, including grabbing a frame from the camera, inferencing, calculating detection parameters, image processing, and transmitting data.  
The results using the theoretical approach and simulation for the vision module are shown in Table 6. Using Equation (2), the configuration of the laboratory setup falls under Case 2 since \(r_{o}>1\). Then, using Equation (4), \(r_{d,th}\) was calculated to be equal to 1.00. Applying Equation (5) yields \(\widetilde{v}_{max}=12.64\) m/s, which was highly sufficient for the target 0.3 m/s and inferred that multiple vision modules were not required to prevent missed detections. Theoretical prediction of the performance of the vision module showed that the configuration was sufficient to prevent missed detection. Likewise, the theoretical result  
Figure 12: The range of plant hill indices detected per frame along the first 10 m of the simulated field at _fps_ = 2.4, \(S=0.5\) m, and \(d_{h}=0.2\) m: (a) detections at 1.3 m/s using two cameras where broken red lines represent plant hills undetected by the first camera but detected by the second camera; and (b) detections at 2.5 m/s and three cameras where broken orange lines represent plant hills undetected by the first and second cameras but detected by the third camera.  
was confirmed by the simulation results that showed no missed detections (\(r_{d,sim}=1.00\)) for both crops and weeds among the simulated \(\overrightarrow{v}\).  
Table 7 summarizes the precision and recall of the trained CNN model in detecting potted plants at different relative travel velocities of the conveyor. Results showed that the combination of an optimized SSD MobileNetV1 in TensorRT running in a Jetson Nano 4 GB have robust detection performance, and incorrect or missed detections were absent despite increasing travel velocity. Comparing the value of \(r_{actual}\) to \(r_{d,th}\) and \(r_{d,sim}\), results showed that the detection rates were equal. The recall was used for comparison instead of precision since the former is the ratio of the correctly detected plants to the total sample plants. This definition of \(r_{actual}\) in Equation (16) is equivalent to the definition of \(r_{d,sim}\) in Equation (14). Since the \(r_{actual}\), \(r_{d,th}\) and \(r_{d,sim}\) were equal, these results proved the validity of the theoretical concepts and simulation methods presented in this study. Hence, \(r_{d,th}\) and \(r_{d,sim}\) can be used to theoretically determine the detection rate of a vision system in capturing plant images as a function of \(\overrightarrow{v}\) and \(fps\) with known \(S\).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \(\overrightarrow{v}\), **m/s** & \(d_{f}\)**m/Frame** & \(r_{o}\) & **Case** & \(r_{g}\) & \(r_{d,th}\) & \(r_{d,sim}\) \\ \hline
0.1 & 0.0063 & 126.40 & 2 & 0.00 & 1.00 & 1.00 \\
0.2 & 0.0125 & 63.20 & 2 & 0.00 & 1.00 & 1.00 \\
0.3 & 0.0188 & 42.13 & 2 & 0.00 & 1.00 & 1.00 \\ \hline \end{tabular}
\end{table}
Table 6: Theoretical and simulation performance of the CNN-based vision module for plant detection at \(S=0.79\) m, \(16\)\(fps\), and at three-levels of travel velocity (\(\overrightarrow{v}\) ).  
Figure 13: Sample real-time inferencing using trained SSD MobileNetV1 model and optimized in TensorRT. The vision system utilized Jetson Inference API.