Chapter 5 Lane Departure Warning System
5.2 Lane Detection
5.2.3 Lane-Finding Algorithm
Since the edge information of lane markers has been acquired by the foregoing demonstration, marking and tracking the lane trajectory within ROI can be succeed by such pixels lying on the sides of lane boundary in the image. There have been some researches for lane-model construction. Y. U. Yim and S. Y. Oh [57] use the starting position, direction, and saturation of the lanes regarded as the three features to initialize the lane vector and find the most probable lane trajectory by Hough Transform. Roland Chapuis [58] uses the statistical model to specify the detection ROI in order to narrow the searching area of lane markings. Different from the method merely about the image processing, the lane geometry is taken into the fitting of the lane model provided by A. Lopez [59]. D. J. Kang [60] combines the vanishing point of the road from the frontal camera with Hough Transform for lane tracking.
Based on the objectives for real-time tracking and low-cost computation, a piece-wise edge linking model we proposed in this chapter is effective for lane-shape marking whether the lens-distortion of camera is serious or not.
z Hough Transform
The classical type of Hough transform is to identify the edge or boundary of lines in the image. This principle is to transform the X-Y coordinate system into the r-θ parameter space, where r represents the small distance between the line and the origin of the image, and θ is the angle of the locus vector from the origin to this closest point. The relationship of the transformation about two coordinate systems is shown in Fig. 50. According to equation (39) from this figure, they can determine if the point A and B are collinear with the same r and θ. Besides, equation (40) is to
determine if the line segment formed by A and B is collinear with that formed by C and D by judging the condition that the parameter d is smaller than a threshold.
1
cos
1sin
2cos
2sin
r = ⋅ x θ + y ⋅ θ = x ⋅ θ + y ⋅ θ
(35)
( cos sin )
d
= −r x
⋅θ
+ ⋅y θ
(36)
Fig. 50: The diagram of relationship between the x-y and r-θ coordinate systems.
z Piece-Wise Edge Linking Model
Li [61] and Yeh [62] still apply the Hough transform to track the lane markers which can not be deformed in the image captured by the normal camera. However, due to the distinct curvature with the fish-eye lens, it is impossible to take Hough transform into our system. Hence, the novel approach for lane modeling needs to be considered the geometric effect of ROI and the connectivity of the lane markers with robustness and adaptation.
The flow chart of the piece-wise edge linking model is shown in Fig. 51(b).
Θ
(a) (b)
Fig. 51: (a) Seven sub-regions automatically segmented within ROI. (b) the flow chart of the piece-wise edge linking model.
(a) (b)
Fig. 52: (a) Seven sub-regions segmented within ROI. (b) the flow chart of the piece-wise edge linking model.
Fig. 52 shows the two different size of ROI is caused by the variation of the intrinsic and extrinsic setting of camera. In general, the width of ROI depends on the yaw angle of camera, and the height of that depends on the pitch angle or the distance from the mounting position near the rearview mirror to the road plane. Although those parameters can not be taken in our system, we still find the property that the lane boundary in the image must extend to the upper-left part of ROI even if the lateral position estimated from the lane marker is not the same through the image sequences.
By using the perspective effect that lane markers almost converge near the region of vanishing point, the included angle from the diagonal of the ROI to the vertical boundary of that can be determined the maximum searching range of angles for Hough transform. This mechanism will be regarded as the initial step in the piece-wise linking model as shown in Fig. 51(b). To overcome the irregular curvature of lane trajectory from the fish-eye lens distortion, the seven sub-regions automatically segmented in Fig. 51(a) contribute to fit the edge pixels of lane since its boundary information contained in it can be regarded as the line-shape. Therefore, the principle of Hough transform described in section 3.4.2 is directly used for the bottom sub-region (A) as demonstrated in Fig. 53. The details of parameters in Fig. 53 and Fig. 54 are explained as follows:
St_X, Ed_X:
The coordinate values of x-axis in the bottom and top border of the sub-region are determined by Hough transform. Ed_X situated in the bottom border of the next sub-region, such as the same location as the bottom border of sub-region (B) and the top border of sub-region (A), can become the fixed point for searching the line edge pixels only by the angle θ as the flow chart in Fig. 54.
SkipTh:
Its size depends on the vertical pixel-width of the sub-region (A) in Fig. 53. For some circumstances like the rapidly lane changing maneuver, the lane marker may
Fig. 53: The flow chart for finding the line-shape in the bottom sub-region (A).
Fig. 54: The flow chart for finding the line-shape in sub-regions from (B) to (G).
be discontinuous for each sub-region in the image. The threshold is to control when the lane modeling procedure is performed and observe if the edge pixels in the bottom sub-region (A) have adequate amounts to composite the lane trajectory.
KeyAngle, RegAngle, q
TH, q
TH2, δ, Δθ, Lw:
KeyAngle and RegAngle are the angles about appropriate orientation of line boundary in sub-regions induced by the current and previous frame. Based on the connectivity and continuity of lane markers on the road surface,
q
TH andq
TH2 are the thresholds to limit if the difference between KeyAngle and RegAngle is small enough. In addition,q
TH2 must be smaller thanq
TH since the searching angles with sub-region (B) to (G) is restricted by the previous detecting results from the bottom sub-region (A). δ and Δθ are the slight range for detection with Hough Transform from sub-region (B) to (G) where the computation power can be reduced.At last, Lw is a revised parameter to restart the seeking area in the x-axis when the number of line pixels is zero in Fig. 54.
To simply the geometric circumstance that the distance between the vehicle and lane trajectory with some curvature in the image is much different, especially the effect of fish-eye lens distortion, we use LSR (least square regression) to make the curved a lane boundary approximate a straight line. The LSR can be induced as below:
Equations (37), (38) can be simplified as
⎪⎩
Fig. 55: LSR approximation.
According to the parameter information showed in Fig. 55(a), the linear model can be constructed by the equations (39), (40). The approximating straight lane boundary is displayed in Fig. 55(b), which is directly reflected since the image contents acquired by the camera mounted on the opposite side of the vehicle are
almost the same except for the reflective property.