## 3 Results and Discussion
### Effects of \(\overset{\rightharpoonup}{v}\) and \(fps\)  
Table 5 summarizes the theoretical and simulation results on the combinations of \(\overset{\rightharpoonup}{v}\) and fps at \(S\) equal to 0.5-m. Comparing the \(r_{d,th}\) to \(r_{d,sim}\) for any combinations of the tested parameters showed that detection rates were equal. Results also showed that there were no missed detections at any \(\overset{\rightharpoonup}{v}\) when the inferencing speeds were at 12.2 and 22 \(fps\) (Case 2), as illustrated in Figures 8 and 9. These results infer that one-stage object detection models, such as YOLO and SSD, running on a discrete GPU such as 1070 TI, have sufficient inferencing speed to avoid detection gaps in typical ranges of travel velocities for agricultural field operations. The result was also comparable to the 92% precision of the CNN-based MVS with 22 \(fps\) inferencing speed in the study of [PERSON] et al. (2019) [11]. Therefore, these results infer that using a one-stage CNN model such as YOLOv3 on a laptop with NVIDIA 1070 TI GPU or better can provide sufficient inferencing speed to avoid gaps in different field operations. However, as mentioned in Section 1, the study did not report the travel velocity and field of view length of their setup. Thus, only an estimated performance comparison can be made. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Treatment No.** & \(\overset{\rightharpoonup}{v}\)**, **m/s** & \(fps\)** & \(d_{f}\)**, **m/Frame** & \(\boldsymbol{r_{o}}\) & **Case** & \(\boldsymbol{r_{g}}\) & \(\boldsymbol{r_{d,th}}\) & \(\boldsymbol{r_{d,sim}}\) \\ \hline
1 & 0.1 & 2.4 & 0.0417 & 12.00 & 2 & 0.00 & 1.00 & 1.00 \\
2 & 0.1 & 12.2 & 0.0082 & 61.00 & 2 & 0.00 & 1.00 & 1.00 \\
3 & 0.1 & 22 & 0.0045 & 110.00 & 2 & 0.00 & 1.00 & 1.00 \\
4 & 1.3 & 2.4 & 0.5417 & 0.92 & 3 & 0.08 & 0.92 & 0.92 \\
5 & 1.3 & 12.2 & 0.1066 & 4.69 & 2 & 0.00 & 1.00 & 1.00 \\
6 & 1.3 & 22 & 0.0591 & 8.46 & 2 & 0.00 & 1.00 & 1.00 \\
7 & 2.5 & 2.4 & 1.0417 & 0.48 & 3 & 0.52 & 0.48 & 0.48 \\
8 & 2.5 & 12.2 & 0.2049 & 2.44 & 2 & 0.00 & 1.00 & 1.00 \\
9 & 2.5 & 22 & 0.1136 & 4.40 & 2 & 0.00 & 1.00 & 1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Theoretical and simulation performance of a vision system for plant detection at \(S=0.5\) m at three-levels of travel velocity (\(\overset{\rightharpoonup}{v}\)) and inferencing speed (\(fps\)). Figure 7: Theoretical (solid) and simulated (broken-line) detection rates at 1, 10, 100, 1000, and 10,000 m field lengths at 0.2 m hill spacing, 2.5 m/s travel velocity, 2.4 fps, and 0.5 m frame capture width. The result of this study also agrees with the results of other studies with known \(S\), \(\overrightarrow{v}\), and \(fps\). In the study of [PERSON] et al. (2019) (23), their CNN-based-vision spraying system had \(S=0.55\) m, \(\overrightarrow{v}=1.11\) m/s, and \(fps=10.0\). Applying these values to Equation (2) also yields \(r_{o}>1\) (Case 2), which correctly predicted their results of full-field coverage. In the study of [PERSON] et al. (2018) (20), their vision-based spraying system had \(S=0.28\) m, \(\overrightarrow{v}=1.77\) m/s, and \(fps=6.67\) and also falls under Case 2. Similarly, the vision-based robotic fertilizer application in the study of [PERSON] et al. (2018) (20) had a \(S=0.31\) m, \(\overrightarrow{v}=0.89\) m/s, and \(fps=4.76\). Again, calculating \(r_{o}\) yielded Case 2, which also agrees with their results. At 2.4 \(fps\), the simulated MVS failed to detect some plant hills when \(\overrightarrow{v}\) was 1.3 (Treatment 4) or 2.4 m/s (Treatment 7). In contrast, missed detections were absent at 0.1 m/s (Treatment 1). As mentioned in Section 2.5, treatments 1, 4, and 7 represent typical inferencing speeds of CNN models, such as YOLOv3 running in an embedded system, such as NVIDIA TX2 (11). From these results, it can be inferred that unless CNN object de  
Figure 8: Simulated plant hill detection rates of the vision system moving at 0.1, 1.3, and 2.5 m/s at different inferencing speeds (\(fps\)).