Generation of High Spatial Resolution Terrestrial Surface From Low Spatial Resolution Elevation Contour Maps via Hierarchical Computation of Median Elevation Regions

While we agree that "not all DEMs are derived through remotely sensed data and are not equal," there is a strong need to rely on the contours plotted on surveyed topographic maps that are available at a specific spatial resolution. As we do not have such contours from all possible spatial scales, there is a need to have a framework to generate the contours at all possible spatial scales from the contours available from surveyed topographic maps available at the specific. We proposed a simple yet effective morphological approach to convert a sparse digital elevation model (DEM) to a dense DEM. The conversion is similar to that of the generation of high-resolution DEM from its low-resolution DEM. The approach involves the generation of median contours to achieve the purpose. It is a sequential step of: 1) decomposition of the existing sparse contour map into the maximum possible threshold elevation region (TER); 2) computing all possible nonnegative and nonweighted median elevation region (MER) hierarchically between the successive TERs decomposed from a sparse contour map; and 3) computing the gradient of all TERs, and MERs computed from previous steps would yield the predicted intermediate elevation contour at a higher spatial resolution. We present this approach initially with some self-made synthetic data to show how the contour prediction works and then experiment with the available contour map of Washington, NH, to justify its usefulness and compare the result with some existing methods. This approach considers the geometric information of existing contours and interpolates the elevation contour at a new spatial region of a topographic surface until no elevation contours are necessary to generate. This novel approach is also very low cost and robust as it uses elevation contours.