# Highly Curved Lane Detection Algorithms Based on Kalman Filter
## 1 Introduction  
The development of the self-driving car is needed for the safety of driver and passenger on the vehicle [1]. Traffic accidents occur for various reasons. The majority of traffic accidents are caused by an improper speed on the road turning or unexpected lane changes when avoiding an obstacle [2]. Some modern cars are already equipped with the emergency braking system, collision warning system, lane-keeping assist system, adaptive cruise control. These systems could be used to help avert traffic accidents when driver is distracted or lost control. The two most important parts of advanced driver assistance systems are a collision avoidance system and a Lane keeping assist system, which could help to reduce the number of traffic accidents. A fundamental technique for effective collision avoidance and lane-keeping is a robust lane detection method [3]. Especially that method should detect a straight or a curve lane in the far-field of view. A car moving at a given speed will spend a certain time to stop or reduce speed while keeping stability. This means it is necessary to detect road lane in the near field as well as in far-field of view. [PERSON] et al. showed a way to detect lane in their lane detection technique [4]. The technique consists of image pre-processing steps (grayscale conversion, canny edge detection, bitwise logical operation) on the image input; it also masked the image according to the region of interest (ROI) in the image. The final stage uses the Hough transformation [5, 6] method and detects the lines. Using this method, the parameters for a straight line are achieved. However, their technique did not propose lane detection for curve lanes and can obtain parameters of curve lines (parabola and circle). A video-based land detection at night was introduced by [PERSON] et al. [7]. The method steps include the Gabor filter operator [8] for image pre-processing, adaptive splay ROI, and Hough transformto detect the marker. Lane tracking method that uses Kalman filter [9], is added after lane detection to increase the probability and real-time detection of lane markers. But, their pre-processing steps lack an adaptive auto-threshold method to detect lane in all conditions. In order to eliminate the uncertainty of lane condition, [PERSON] et al. proposed a replacement of image pre-processing [10]. Their method uses deep learning-based lane detection as a replacement for feature-based lane detection. However, the UNet [11] based encoder-decoder requires high GPU processing unit like Nvidia GPU Geforce GTX 1060 for training and testing. Also, the paper claims CNN-branch is much slower than the feature-based branch in terms of detection rate. The fast detection rate is very important in the case of the autonomous vehicle since the vehicle moves at a very high speed. Also, the result lacks to show results of lane detection in case of the curved lane. Moreover, [PERSON] et al. introduced an algorithm [12] to solve the limitation of detecting lane in light illumination change or a shadow or worn-out lanes by using a local adaptive threshold to extract important features from the lane images. Moreover, their paper proposes a feedback RANSAC [13] algorithm to avoid false lane detection by computing two scoring functions based on the lane parameters. They used the quadratic lane model for lane fitting and Kalman filter for smooth lane tracking. However, the algorithm did not provide any close-loop lane keeping control to stay in lane. Furthermore, a combination of the Hough transform and R-least square method is introduced by [PERSON] et al. [14]. They used the Kalman filter to track the lane. Their combination of this method provides results on straight lane marking. Similarly, hazed-based Kalman is used to enhance the information of the road by [PERSON] et al. [15]. Also, [PERSON] et al. introduced a straight and polynomial curve model to detect the continuity of the lane [16]. The curve fitting method was used to detect the lanes.