## 3 Proposed Methods
### Obstacle Detection Method Based on Plane Normal Vector (OD-PNV)  
The OD-PNV method first performs an initial screening of the input superpixel point clouds to shield the point clouds with too little 3D information. Then, the 3D information of the point clouds contained in the superpixel is used to fit the local plane model. The probability that the superpixel belongs to an obstacle is calculated according to the differ  
Figure 2: The segmentation result of the SLIC algorithm. ence between the normal vector of the local plane model and the normal vector of the free space plane model. The flow chart of the OD-PNV method is shown in Figure 3.  
Common obstacles in traffic scenes mainly include vehicles, pedestrians, buildings and vegetation, while free space mainly includes areas such as road and parking lots. Figure 4 shows the point cloud distribution of these two types of objects (the coordinate origin in the figure is the superpixel point cloud centroid, the \(x\)-axis coincides with the optical axis and points to the front of the camera, the \(y\)-axis is perpendicular to the \(x\)-axis and points above the camera, and the \(z\)-axis is perpendicular to the \(y\)-axis and \(x\)-axis and points to the left of the camera). It can be seen from the figure that the point cloud distribution in the obstacle area tends to be vertical, while the point cloud distribution in the free space area tends to be horizontal. If a plane model is used to fit the point cloud in the superpixel, the greater the angle \(\theta\) between the normal vector of the plane model and the positive direction of the \(y\)-axis, the more the superpixel conforms to the feature of the obstacle area. The OD-PNV method distinguishes the obstacle and the free space by this feature of the point cloud. First, plane fitting is performed on the point cloud in the superpixel; then, the probability that the superpixel belongs to an obstacle is calculated according to the included angle \(\theta\). This method independently calculates the probability that each superpixel belongs to an obstacle based on the plane normal vector. Supposing that \(H_{o}\) shows that the superpixel belongs to an obstacle, and \(H_{f}\) shows the superpixel belongs to a free space, \(H_{o}\) and \(H_{f}\) are mutually exclusive events. Each local plane is represented by model \(ax+by+cz+d=0\), then \(\overrightarrow{\theta}=(a,b,c)\) represents its normal vector. In order to enhance the robustness of the algorithm, this paper uses the RANSAC algorithm [32] to estimate the local plane model. RANSAC randomly extracts the least original data that satisfy the hypothesis and expands the initial point set with the consistent data points. It is an algorithm to find the optimal  
Figure 4: Comparison of point cloud distribution between obstacle and free space area: (**a**) Typical traffic scene; (**b**) Superpixel point cloud distribution in the obstacle area; (**c**) The angle \(\theta\) between the normal vector of the obstacle area and the \(y\)-axis; (**d**) Superpixel point cloud distribution in free space area; (**e**) The angle \(\theta\) between the normal vector of the free space area and the \(y\)-axis. Figure 3: Flow chart of OD-PNV method. model to fit the data through iteration. RANSAC needs to randomly select three points in the point cloud every time, and determine the 3D plane based on these three points. Then, it calculates the distance of each point to the plane, that is, the error. According to the error threshold, it is judged whether each point belongs to the inliers. RANSAC will continue to iterate to find the plane model with the largest number of inliers, that is, the optimal model. The input of the RANSAC algorithm is the 3D point cloud data of the superpixel, and the output is the optimal local plane model parameters and the maximum consistent set. As at least three points are required to determine a plane in 3D space, the minimum subset size of the RANSAC algorithm needs to be set to three.