ROI Determination Strategy

In this subsection, two properties of changes about positions of lane boundaries are introduced. 1). Longitudinal consistency property: From the nearby position to the farther position, lane markings appear to be lines or curves which are either continuous or dashed.

Therefore, by observing the positions of the closer lane markings, the possible positions of the farther parts can be accordingly predicted. 2). Lateral consistency property: Vehicles often move in the middle of the lane, so lateral changes of a lane marking’s position are usually slight in the sequential road-scene images. Thus, the possible position of the lane marking in the next frame can be predicted according to that of the current one. The predictive area of the lane marking is the Region of Interest (ROI), also the search area of BFT. If the ROI is too large, the computation cost would increase and the ROI may be stained by noise. On the other hand, if the ROI is too small, the actual position of the lane marking may not be appropriately covered. Therefore, the ROI should be the smallest area which can still include the area of the lane markings. Strategies for determining the ROI and three determination approaches to the ROI are presented in the subsection. Choosing the best strategy for the associated case is an effective way to reduce errors and computation costs.

Fig. 3-7. The flow chart of the selection of ROI determination strategies.

{ }

( , _p) ( , ) | [ _L, _R]; _p

Roi M N = I M N M∈ M M N =N (3.13) The ROI is illustrated as (3.13), where I(M, N) represents the image coordinates; The M-coordinate and the N-coordinate respectively denote the horizontal and vertical coordinates.

Here the left bottom coordinate is defined as the origin shown in Fig. 3-8. The ROI in the Np–th row is denoted by Roi(Mp, Np); where M ∈ [ML, MR], and ML is the left border within the range, and MR the right border. Our proposed lane detection method consists of two modes:

1) Single mode: only the information of the current processed frame is considered. 2) Sequential mode: using the temporal information of the previous frames to shrink the search area of the current frame so as to accelerate the detection and reduce errors. The selection of the suitable ROI determining strategies for different models are given as follows.

z In every row, the sequence of ROI is determined following the bottom-up direction on the N-coordinate and starting from N=0 row to the preset terminal row Ne.

z In single mode, the fixed area approach, as depicted in the following subsection (3.1), is first applied to determine the front parts of two lane markings and then the coordinates of the detected lane markings are considered the start coordinates of the left and right lane markings. Afterwards, the ROI of the farther parts of lane markings is determined by the expansion approach to follow the bottom-up direction on N-coordinate to the terminal, Ne, as described in subsection (3.2).

z In sequential mode, the ROI is determined by the tracking approach as described in subsection (3.3). If the information of the previous frames does not include Ne, then the expansion approach will be conducted to continue the detection to reach Ne.

The flow chart of selecting ROI determination strategies is given in Fig. 3-7.

The following subsections will present three kinds of ROI decision approaches.

1) Fixed Area Approach: This approach is to detect the position of the nearby part of the lane marking. As shown in Fig. 3-8, the determination of the coordinates N1 and N2 was based

on their mappings onto the two Z-coordinates, respectively 8 meters and 25 meters on the ground plane because lane markings in this range are usually very clear. After determining N1

and N2, let the two hexagonal areas be the ROI, and these sections are divided by the v axis.

The BFT detected on the left side are the possible positions of the left lane markings and the ones on the right side are the possible right lane markings. The search area of this approach is larger and it is used when no temporal information of lane markings is available.

Fig. 3-8. ROI of fixed area.

2) Expansion Approach: This approach includes two phases. Phase 1 is a bi-directional expansion scheme. In this scheme, the latest detected position of the BFT is considered as a center, and then the ROI is determined by expanding row by row along the direction of the N-coordinate, as shown in (3.14) and (3.15). Fig. 3-9(a) illustrates the ROI set in this way, where the ROI is the area within the two blue dotted lines along the two sides of the lane markings. In this way, the ROI is set by linear equations as in (3.14) and (3.15). The approach is simple and rapid, but the ROI may expand when the distance between the current row and the last row is extended. Phase 2 is a tendency expansion scheme. This approach is performed by computing the slope of the lane marking to predict its trend and expanding along the direction of the N-coordinate to determine the ROI. The computation method of the slope is

shown in Fig. 3-9(b), where mb denotes the slope of the lane marking. If a BFT is detected continuously in some rows, but can not be detected in the following several consecutive rows, then let MBS(NL) be the BS on the latest BFT, and MBS1 be the BS on the BFT in the previous rows of MBS(NL). Then the slope of the lane markings can be computed using these two points.

With the slope, the ROI can be determined by (3.16) and (3.17). The ROI calculated in this way is smaller, where the lane marking is included; however, the computational cost of the slope may increase.

mBS denotes the M-coordinate of BS.

MBS1=(m1, n1) represents another MBS.

( )

( ) ^{p L}

R BT NL s

R

N N

M M D

m

= + + − (3.17)

where

( 2)

R tan s

m = β − β

(a)

(b)

Fig. 3-9. (a)Bi-directional expansion scheme; (b) Tendency expansion scheme.

3) Tracking approach: Based on the lane marking features found in previous frames, the ROI can be found by (3.18) and (3.19). The ROI area found in this way is the smallest one, so it is the best choice for the sequential prediction mode of lane detection.

( 1)

L BS t s

M =M ₋ −D (3.18) where

MBS(t-1): the M-coordinate of BS in the Np row in the previous frame.

t: the current frame. t-1:the last frame.

( 1)

R BT t s

M =M ₋ +D (3.19) where

MBT(t-1): the M-coordinate of BT in the Np row in the previous frame.

Figure 3-10 shows the acquisition of BFT in a fixed area. The detection distance is set to be about 25m. In the figure, black lines appear only when the distance between BFT on both sides approximates to wL. Figure 3-11 is the selection of the ROI and its range. In (a), (b) and (c), the two-side expansion phase and tendency expansion phase are applied in turn, while the tracking approach is adopted in (d). In Fig. 3-11, the black lines on the two sides of the lane markings respectively represent ML and MR of those rows. On the lane markings of both sides, there are totally four big black points denote P L1, P L2, P R1, and PR2 for calibratingα.

Fig. 3-10. The acquirement of BFT in a fixed area.

(a)

(b)

(c)

(d)

Fig. 3-11. The selection of ROI and its range. (a)(b)(c) The application of the expansion approach; (d) The adoption of the tracking approach.