Digital elevation model (DEM) provides information of geographic landscapes at multiple scales. However, the study on the scales of DEM is not sufficient and there still remain many issues in DEM scaling. Generating DEMs of different scales has to consider terrain skeletons and terrain structural details for preserving terrain feature hierarchies. Existing literatures (e.g., maximum Z-tolerance approach) generate coarse scales of DEM mainly concentrating on selecting elevation points with minimum elevation error to reconstruct TIN (triangulated irregular network). However, many structural details (e.g., slope and local terrain features) can still be neglected in this process. In order to preserve all the structural details in DEM hierarchy, we should first identify the whole structures of terrain surface and then preserve relevant ones according to the coarse-scale hierarchy. For this process, we propose to apply the graph model to capture structural relations of elevation points. In this way, the Laplacian downsample technique can then be implemented to generate multi-scale representations of DEM with terrain structural features preserved. Specifically, the proposed Integrated Graph Laplacian downsample (IGLD)-based method firstly extracts DEM skeletons (i.e., ridge and valley) with the classical D8 technique. Then, we apply the Graph Laplacian downsample method to select the terrain structural features between DEM skeletons. Therefore, the restructured coarse-scale TIN surfaces are able to preserve both the terrain skeletons and structural details (i.e., peak, slope, and curvature). Through experiments compared with existing methods, our proposed method can preserve more DEM structural details and keep the slope and roughness more consistent with origin DEM data.

数字高程模型（DEM）可提供多种尺度的地理景观信息。但是，对DEM规模的研究还不够，在DEM规模方面仍然存在许多问题。生成不同比例的DEM必须考虑地形骨架和地形结构细节，以保留地形特征层次结构。现有文献（例如，最大的Z容差方法）生成DEM的粗略尺度，主要集中在选择具有最小仰角误差的仰角来重建TIN（三角不规则网络）。但是，在此过程中，许多结构细节（例如坡度和局部地形特征）仍然可以忽略。为了保留DEM层次结构中的所有结构细节，首先应识别地形表面的整体结构，然后根据粗尺度层次结构保留相关的结构。对于此过程，我们建议应用图模型来捕获高程点的结构关系。通过这种方式，拉普拉斯下采样技术可以被实现以生成保留了地形结构特征的DEM的多尺度表示。具体而言，所提出的基于集成图拉普拉斯下采样（IGLD）的方法首先使用经典D8技术提取DEM骨架（即山脊和山谷）。然后，我们应用图拉普拉斯图下采样方法选择DEM骨架之间的地形结构特征。因此，经过重组的TIN粗面能够保留地形骨架和结构细节（即峰，坡度，和曲率）。通过与现有方法进行对比实验，我们提出的方法可以保留更多的DEM结构细节，并使坡度和粗糙度与原始DEM数据更加一致。