# Research on Lane Detection Based on Global Search of Dynamic Region of Interest (DROI)
## 3 Design of Dynamic Region of Interest (DROI) Based on Security Vision
### Lateral Boundary Design of DROI Based on Road Curvature  
In order to reduce computation in the lateral vision and improve detection performance, the lateral ROI constraint, based on road curvature, is proposed. If the curvature of the road is too large, according to the road extension direction, the left and right lateral boundaries will be set. For example, considering a left-hand bend, the ROI boundary on the left is large while that on the right remains within the basic range. Similarly, if a car drives in a straight line, the left and right ROI boundaries remain within the basic safety range. The flow chart of the horizontal ROI constraint is shown in Figure 5.  
To obtain the road curvature, firstly, according to the road extension direction, the track equation of the lane line is obtained. Next, the curvature radius at each point of the road can be solved through the track equation of the lane line. Because the time difference between the two adjacent frames of the road image is very small, even if the car is driving at a high speed of 120 km/h, the displacement difference between the two adjacent frames is less than 1.3 m. Therefore, the boundary of the ROI, which is obtained from the lane line track of the above frame, is used as the ROI of the next frame.  
Figure 5: Horizontal constraint flow chart.  
The curve equation of lane line trajectory is as follows:  
\[y_{t}=f_{\text{cv}}(x_{t}) \tag{19}\]  
The lateral velocity of the car at each point in the lane line curve can be obtained using the following equation:  
\[v_{x}=v_{r}cos\beta \tag{20}\]  
Because the original lane line image is transformed by the aerial view, the generated aerial view is approximately equally spaced in the horizontal and vertical directions. Therefore, the horizontal pixel size of the image has a certain proportional relationship with the actual horizontal distance; its longitudinal distance also has a corresponding proportional relationship.  
In the geodetic coordinate system, the distance between the left and right lane lines is \(\lambda=3.75\) m. In the image coordinate system, \(g\)(\(u_{i},v_{j}\)) and \(g_{r}\)(\(u_{i+a},v_{j}\)) are selected at the same height of the left and right lane lines, respectively, and the lateral displacement between these two points is the distance between the left and right lane lines in the image. The lateral displacement is as follows:  
\[B=u_{i+a}-u_{i} \tag{21}\]  
The ratio of the actual distance to the rows in a horizontal pixel is represented by \(\mu\).  
\[u=\frac{B}{\lambda} \tag{22}\]  
According to the rules of safe driving, when the lane line is straight, the basic lateral safety constraint is \(0.875/u\). Eventually, the lateral boundary can be obtained by the relationship between braking distance and speed, as given by Equation (18).  
In the actual lane line detection process, in order to avoid excessive calculation errors in the lateral boundary caused by pixel differences, lane lines are detected in the aerial view in this paper as shown in Figure 6. At the same time, the ROI, which is determined by the lane line in the current frame, is used in the aerial view in the next frame.