We proposed a simple yet effective morphological approach to convert a sparse Digital Elevation Model (DEM) to a dense Digital Elevation Model. 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 the I) decomposition of the existing sparse Contour map into the maximum possible Threshold Elevation Region (TERs). II) Computing all possible non-negative and non-weighted Median Elevation Region (MER) hierarchically between the successive TER decomposed from a sparse contour map. III) Computing the gradient of all TER, and MER computed from previous steps would yield the predicted intermediate elevation contour at a higher spatial resolution. We presented this approach initially with some self-made synthetic data to show how the contour prediction works and then experimented with the available contour map of Washington, NH to justify its usefulness. 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.

翻译：我们提出了一种简单而有效的形态学方法，用于将稀疏数字高程模型（DEM）转换为密集数字高程模型。该转换类似于从低分辨率DEM生成高分辨率DEM的过程。该方法通过生成中值等高线来实现目标，具体包括以下步骤：I）将现有稀疏等高线图分解为尽可能多的阈值高程区域（TERs）；II）在从稀疏等高线图分解出的连续TERs之间，分层计算所有非负且非加权的中间高程区域（MER）；III）计算所有TER和上一步计算得到的MER的梯度，从而在高空间分辨率下预测中间高程等高线。我们首先使用自制合成数据展示该方法如何实现等高线预测，随后基于美国新罕布什尔州华盛顿山的现有等高线图进行实验，验证了其实用性。该方法充分利用现有等高线的几何信息，在地形表面的新空间区域插值高程等高线，直至无需生成更多高程等高线。由于仅使用高程等高线，这一新颖方法成本极低且鲁棒性强。