An integrated graph Laplacian downsample (IGLD)-based method for DEM generalization

Abstract

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.