## 3 Proposed Method
### Collision Warning  
The blind-spot detection warning was determined based on the distance to the object and the estimated time to collision. Figure 11 illustrates the defined warning zones.  
As illustrated in Figure 11, the warnings were categorized into three levels. The closer the object and the faster it approaches, the higher the warning level. Warnings are issued progressively based on the distance and time to collision. These progressive warnings are designed to provide either a driver or autonomous vehicle with information regarding the risk of collision.  
Each level is associated with specific criteria. A Level 1 warning indicates the possibility of a lane change through acceleration. A Level 2 warning permits evasive steering maneuvers to avoid a potential forward collision. A Level 3 warning signifies a scenario in which a lane change is not feasible. Table 3 presents the definitions corresponding to each warning level.  
The warning level is determined by the relative distance and estimated time to collision. Relative distance refers to the distance between your vehicle and an object. The relative distance is obtained using the y-coordinate at the bottom of the bounding box of the detected object. The position of the rearview camera on the vehicle and the distance to the object can be calculated through the difference in coordinates. To calculate the relative distance of an object, the distorted coordinates are first converted to undistorted coordinates using Equation (4). By applying the converted image coordinates to Equation (6), the real-world coordinates can be obtained. Relative speed is then calculated using the relative distance. The relative speed is computed using Equation (11).  
\[v_{rel}=(d_{n}-d_{n-1})*f_{i}. \tag{11}\]  
where \(d_{n}\) represents the distance to the object in the \(n\)-th frame, \(d_{n-1}\) represents the distance to the object in the \((n-1)\)-th frame, and \(f_{i}\) represents the frame rate of the camera.  
The time to collision is determined based on the relative distance and relative speed. Equation (12) defines the collision time [33].  
\[t_{C}=d_{rel}/v_{rel}. \tag{12}\]  
where \(d_{rel}\) represents the relative distance and \(v_{rel}\) denotes the relative speed. The warning level was determined using Equation (13).  
Figure 11: Defined warning zone.  
\begin{table}
\begin{tabular}{c c} \hline
**Level** & **Definition** \\ \hline
1 & Indicates the possibility of a lane change through acceleration \\
2 & Permits evasive steering maneuvers to avoid a potential forward collision. \\
3 & Denotes a scenario in which a lane change is not feasible. \\ \hline \end{tabular}
\end{table}
Table 3: Definitions of warning levels.  
\[W_{C}=\begin{cases}3,\;if\;t_{C}<T_{t3}\;or\;d_{rel}<T_{d3}\\ 2,\;if\;T_{t3}\leq t_{C}<T_{t2}\;or\;T_{d3}\leq d_{rel}<T_{d2}\\ 1,\;if\;T_{t2}\leq t_{C}<T_{t3}\;or\;T_{d2}\leq d_{rel}<T_{d1}\\ 0,\;else\end{cases} \tag{13}\]  
where \(W_{c}\) is the warning level, \(t_{c}\) is the time to collision, and \(d_{rel}\) is the relative distance. \(T_{t1}\), \(T_{t2}\), and \(T_{t3}\) denote the thresholds based on time to collision, whereas \(T_{d1}\), \(T_{d2}\), and \(T_{d3}\) correspond to the thresholds based on relative distance. As illustrated in Equation (13), the warning level is determined by both the time to collision and the relative distance.  
Figure 12 shows the warning results. Specifically, Figure 12a shows a Level 1 warning, Figure 12b shows a Level 2 warning, and Figure 12c shows a Level 3 warning. The warning level increases as the relative distance decreases.