How to generate contour tree of positive and negative topography from open contour lines

half-open contour lines and closed contour lines is proposed. Half-open contour lines and open contour lines are separated and handled respectively. Then a polygon overlay function is used to decide the spatial relation between closed contours

resulting in contour trees. Through navigating the tree of contour lines

height bounds for every grid in the research region can be deduced

which is then used with HASMROC(region optimum control) method to construct DEM of fidelity.The maximum deviation distance of derived contours is less than the width of the grid of the DEM. Two case studies are given

one is contours from mathematical surface

another is from the manually vectorizing contours lines.