The detection of multiple curved lane markings on a non-flat road surface is still a challenging task for vehicular systems. To make an improvement, depth information can be used to enhance the robustness of the lane detection systems. In this paper, a proposed lane detection system is developed from our previous work where the estimation of the dense vanishing point is further improved using the disparity information. However, the outliers in the least squares fitting severely affect the accuracy when estimating the vanishing point. Therefore, in this paper we use random sample consensus to update the parameters of the road model iteratively until the percentage of the inliers exceeds our pre-set threshold. This significantly helps the system to overcome some suddenly changing conditions. Furthermore, we propose a novel lane position validation approach which computes the energy of each possible solution and selects all satisfying lane positions for visualisation. The proposed system is implemented on a heterogeneous system which consists of an Intel Core i7-4720HQ CPU and an NVIDIA GTX 970M GPU. A processing speed of 143 fps has been achieved, which is over 38 times faster than our previous work. Moreover, in order to evaluate the detection precision, we tested 2495 frames including 5361 lanes. It is shown that the overall successful detection rate is increased from 98.7% to 99.5%.