This paper presents a robust stereo-vision-based drivable road detection and tracking system that was designed to navigate an intelligent vehicle through challenging traffic scenarios and increment road safety in such scenarios with advanced driver-assistance systems (ADAS). This system is based on a formulation of stereo with homography as a maximum a posteriori (MAP) problem in a Markov random held (MRF). Under this formulation, we develop an alternating optimization algorithm that alternates between computing the binary labeling for road/nonroad classification and learning the optimal parameters from the current input stereo pair itself. Furthermore, online extrinsic camera parameter reestimation and automatic MRF parameter tuning are performed to enhance the robustness and accuracy of the proposed system. In the experiments, the system was tested on our experimental intelligent vehicles under various real challenging scenarios. The results have substantiated the effectiveness and the robustness of the proposed system with respect to various challenging road scenarios such as heterogeneous road materials/textures, heavy shadows, changing illumination and weather conditions, and dynamic vehicle movements.