We introduce a simplification method based on irregular triangular networks to create a generalized digital elevation model (DEM) for land surface segmentation. The quadric error metrics simplification (QEMS) algorithm was used to generalize the DEM as a method that follows the theory of optimal triangle for (land) surface representation. Its use for land surface modeling is novel, however, it is well known in computer graphics. Comparison of QEMS with the maximum z-tolerance method shows priority in terms of root mean square error. Numerical expression of the value concentration of the third-order variables (curvature changes) around zero (K₀) was used as an indicator of elementary form representation in generalized DEMs. K₀ was calculated for a set of DEMs at several generalization levels in two different territories, as well as for comparably generalized artificial surfaces. K₀ values of real DEMs vary significantly with generalization levels and character of the landforms, and their maxima point to the generalization levels that best preserve the information about elementary forms of various hierarchical levels. Differences between K₀ of real DEMs and artificial surfaces confirm the same.

中文翻译：

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多边形简化及其在地表分割的 DEM 泛化中的应用

我们引入了一种基于不规则三角形网络的简化方法，以创建用于地表分割的广义数字高程模型 (DEM)。的二次误差测度简化（QEMS）算法被用来概括DEM作为如下最佳三角形为（陆地）表面表示理论的方法。它用于地表建模是新颖的，然而，它在计算机图形学中是众所周知的。比较QEMS与最大z容差在根均方误差方面方法示出的优先级。三阶变量值集中度（曲率变化）在零附近的数值表达式（K ₀) 被用作广义 DEM 中基本形式表示的指标。K ₀是针对两个不同领域中多个泛化级别的一组 DEM 以及相对泛化的人工表面计算的。真实 DEM 的K ₀值随地貌的泛化程度和特征而显着变化，其最大值指向最能保存各层次基本形态信息的泛化程度。真实 DEM 和人造表面的K ₀之间的差异证实了相同。