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Obstacle detection is the primary task of the Advanced Driving Assistance System (ADAS). However, it is very difficult to achieve accurate obstacle detection in complex traffic scenes. To this end, this paper proposes an obstacle detection method based on the local spatial features of point clouds. Firstly, the local spatial point cloud of a superpixel is obtained through stereo matching and the SLIC image segmentation algorithm. Then, the probability of the obstacle in the corresponding area is estimated from the spatial feature information of the local plane normal vector and the superpixel point-cloud height, respectively. Finally, the detection results of the two methods are input into the Bayesian framework in the form of probabilities for the final decision. In order to describe the traffic scene efficiently and accurately, the detection results are further transformed into a multi-layer stixel representation. We carried out experiments on the KITTI dataset and compared several obstacle detection methods. The experimental results indicate that the proposed method has advantages in terms of its Pixel-wise True Positive Rate (PTPR) and Pixel-wise False Positive Rate (PFPR), particularly in complex traffic scenes, such as uneven roads.