Model-based Lane Detection

Model-based methods represent the lane lines through a few geometric parameters. According to the shapes of lane lines, the lane line models can be defined as a straight line model [12][14][15][28] or a parabolic model (that is, curve) [10][30], even a spline model [4][13][29]. Moreover, how to find the best parameters for the model is the core problem to be solved. Compared with the feature-based methods, the model-based methods are less sensitive to weak lane line appearance features and noise.

To acquire the best parameters of lane line model, the likelihood function [10][25], the Hough transform [11][28], and curve fitting [30], had been applied into the lane line detection. However, the model-based methods require a complex modeling process involving much prior knowledge. Constructing a simple model for

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one scene can get better efficiency, but this model may not work well in another scene because it cannot describe arbitrary shape of lane lines. So, the simple models are less adaptive. But for the complex models, although they can adapt to multiple scenes and describe arbitrary shape of lane lines, an iterative error minimization algorithm should be applied for the estimation of best model parameters, which is comparatively time-consuming. The process would take much time and would not satisfy the real time requirement of the driving applications. Next, we discuss some representative works of model-based lane line detection.

In [25], Kluge and Lakshmanan present a deformable template model of lane line structure, called Likelihood Of Image Shape (LOIS), to locate the lane lines by optimizing a likelihood function. It is assumed that the left and right lane lines are modeled as two parallel parabolas on the flat ground plane. For each pixel, this algorithm uses a Canny edge detector [26] to obtain the gradient magnitude and orientation. The parameters of perspective projection model are then estimated by applying the Maximum A Posteriori (MAP) estimation [27] and the Metropolis algorithm based on the image gradient. Figure 2-6 shows some results of LOIS’ lane detection under the various road environmental conditions.

Figure 2-6 : Examples of LOIS’ lane line detection [25].

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The LANA system [10], proposed by Kreucher and Lakshmanan, is similar to the LOIS system [25] at the detection stage. But LANA combines the frequency domain features of the lane lines with a deformable template for finding the lane line edges. The feature vectors are used to compute the likelihood probability through fitting the detected features to a lane line model. Li et al. [11] develop the Springrobot system by using the color and edge gradient as the lane line features and the adaptive randomized Hough transform (ARHT) to locate the curve lane lines on the feature map. A multi-resolution strategy is applied to achieve an accurate solution rapidly and to decrease the running time to meet the real-time requirement. As illustrated in Figure 2-7, they first reduce the size of the original image to 1/2^z, where z = 1, 2, by bicubic interpolation. The reduced images are called “half image” and “quarter image”, respectively. In these images with lower resolution, they apply the ARHT with fixed quantized accuracy to roughly and efficiently locate the global optima of lane lines without regarding the accuracy. The parameters resulting from the previous step can be used as starting values of another ARHT for more accurate location of lane lines. Therefore, the parameter search can be restricted to a small area around the previous solution, saving time and storage complexities. This coarse-to-fine location speeds up the process of lane line detection, thus it offers an acceptable solution at an affordable computational cost. Figure 2-7 shows the results of multi-resolution algorithm in Springrobot system.

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Figure 2-7 : Multiresolution algorithm for detecting the lane line rapidly and accurately [11], which uses the size reducing at first, then applies the ARHT to detect the parameters of lane lines roughly, and finally uses coarse-to-fine location method to offer the better position of lane lines.

Park et al. [30] use the lane-curve function (LCF) for lane line detection. The whole process of algorithm is shown in Figure 2-8. The LCF is obtained by transforming the defined parabolic function from the world coordinates into the image coordinates. Moreover, this algorithm needs no transformation of the image pixels into the world coordinates. The main idea of this algorithm is to search for the best-described LCF of the lane-curve on an image. In advance, several LCFs are assumed by changing the curvature and for each LCF, it defines its lane line region of interest. Then, the comparison is carried out between the slope of an assumed LCF and the phase angle of the edge pixels in the lane line region of interest. The LCF with the minimal difference in the comparison becomes the true LCF corresponding to the lane-curve.

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Figure 2-8 : The process overview of LCF [30].

Wang et al. [29] propose a Catmull-Rom spline [32] based lane line model. Their algorithm uses a maximum likelihood approach in detecting the lane lines. As Catmull-Rom spline model can form arbitrary shapes by control points, it can describe a wider range of lane line structures than the straight or parabolic model. Figure 2-9 shows the estimation of lane lines to real road image by implementing the Catmull-Rom spline algorithm. In [13], Wang et al. propose a B-Snake based lane line detection and tracking algorithm without any camera parameters. The main characteristics of this method are as follows. (1) The Canny/Hough Estimation of Vanishing Point (CHEVP) is presented for providing a good initial position for the B-Snake. (2) The Minimum Mean-Square Error (MMSE) is proposed to determine the control points of the B-Snake model by the overall image forces on two sides of the

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lane. (3) The Gradient Vector Flow (GVF) [31] field is used to let the B-Snake move to its optimal solution. The estimation of lane lines by B-Snake is shown in Figure 2-10.

Figure 2-9 : An example of lane line detection by Catmull-Rom spline. (a) Original road image. (b) The result of lane line detection by Catmull-Rom splines. ( PL0, PL1, PL2) and ( PR0, PR1, PR2) are the control points for left and right side of lane line. PL0

and PR0 are the same control point, which supposes to be vanishing point. [29]

Figure 2-10 : Examples of lane line detection using the B-Snake. [13]