We propose a new approach for vision based road following. The approach is tailored to a well structured highway environment with lane markers. Lane markers are detected and used for dynamic update of: (i) the lateral position and orientation of the vehicle with respect to the lane markers, (ii) the estimated road curvature, and (iii) the camera parameters (height and inclination angle) in the presence of car vibration and changes in road slope. For that purpose we model the road and hence the shape of the lane markers as quadric curves. The identification of these curves is done in a 3D reference coordinate system attached to the vehicle, rather than a 3D coordinate system attached to the road. This approach allows an unified description/estimation of the road and the vehicle parameters.