## 2 Related Work  
Early obstacle detection methods based on stereo vision usually map the depth information into 2D or 3D occupancy grids [15], and locate obstacle regions by finding the occupied grids. As in reference [16], a stochastic occupancy grid was constructed to solve the detection problem of free space area. It applied dynamic programming to the stochastic occupancy grid to finally find the optimal dividing line between the obstacle area and the free space area. However, it could not provide the specific location information of the obstacles. Some references obtain obstacle location information by creating and analyzing a \"v-disparity\" image. In the \"v-disparity\" image, roads are projected as approximately horizontal lines, and vertical obstacles are projected as approximately vertical lines. Reference [17] used this principle to detect roads and obstacles, and judged the location of the obstacles by projection difference. This approach reduces the effects of vehicle dynamic pitching. Reference [18] proposed a method that can localize scene elements through sparse 3D point clouds. It first used the \"v-disparity\" image to detect the depth values of obstacles and extracted the consecutive points corresponding to these depth values from the point cloud. Then, these points were clustered, and finally, the obstacles were located through the clustering results. Although these early methods can detect most obstacles, their detection accuracy is generally low and the amount of information that can be provided is small. Therefore, it is often only suitable for some simple scenes. From the perspective of vehicle trafficability, traffic scenes can be divided into two classes: obstacle and free space. Free space refers to the part of the road surface that does not contain any obstacle, i.e., the area where the vehicle may enter. In order to segment these two areas, some references first establish a global road surface model, and then detect obstacles by comparing other parts of the scene with the road surface model. For example, reference [19] proposed a road obstacle detection method based on height. The method used point clouds to fit the road plane and calculated the height of the point clouds, and finally detected the obstacles according to the height information of the point clouds. The stixel method, proposed in reference [20], mapped the road surface to a straight line in the v-disparity space, and detected the straight line through Hough transform to determine the road surface model. Then, adjacent rectangular sticks of a certain width and height were used to describe obstacles. Reference [10] proposed the multi-layer stixel on the basis of reference [20]. This method lifted the constraint of the stixel to touch the ground surface and allowed for multiple stixels along every column of the image, thus enabling a more comprehensive description of the traffic scene. Reference [5] proposed an obstacle detection method combining the v-disparity image and stixel method. This method computationally reduced the complexity of making an effective Hough space and improved the accuracy of the road surface extraction results. The digital elevation map method proposed in reference [21] converted the 3D point cloud into a digital elevation map, and combined the quadratic road surface model to detect and represent different types of obstacles. Reference [22] first identified the free space to segment the drivable area, and then used the pixels in the free space to estimate the digital elevation map to improve the estimation accuracy of the road profile. Compared with the original image, the data size of the stixel and digital elevation map is greatly reduced, and the influence of outliers on the detection results is weakened. Therefore, these two scene representation methods are widely used in the current research field of obstacle detection. The road surface models established by the above methods are relatively simple, and they are difficult to fit to the real road surface well.