Drivable area detection is one of the essential functions of autonomous vehicles. However, due to the complexity and diversity of unknown environments, it remains a challenge specifically on rough roads. In this paper, we propose a systematical framework for drivable area detection, including ground segmentation and road labelling. For each scan, the point cloud is projected onto two different planes simultaneously, generating an elevation map and a range map. Different from the existing methods based on mathematical models, we accomplish the ground segmentation using image processing methods. Subsequently, road points will be filtered out from ground points and used to generate the road area with the assistance of a range map. Meanwhile, a two-step search method is utilized to create the reachable area from an elevation map. For the robustness of drivable area detection, Bayesian decision theory is introduced in the final step to fuse the road area and the reachable area. Since we explicitly avoid complex three-dimensional computation, our method, from both empirical and theoretical perspectives, has a high real-time capability, and experimental results also show it has promising detection performance in various traffic situations.