A simplification method for grid-based DEM using topological hierarchies

Abstract

Terrain simplification is the basis of constructing multi-scale digital elevation models. However, a definite corresponding relationship between the scales and the hierarchy of terrain skeleton lines cannot be established easily. In this paper, a novel method is designed based on multiresolution Morse complex. First, a universal improved algorithm for the original terrain Morse complex is proposed to prevent artificial intersections. Second, significant points are adaptively selected in the hierarchical skeleton lines through topological simplification. Finally, an experimental companion is created. Results indicate that the proposed simplification method can not only retain the main terrain structural characteristics, but also offer better simplification precision.

Polygonal simplification and its use in DEM generalization for land surface segmentation

“…The basic iterative algorithm starts with only two triangles and then inserts point(s) of highest error on each pass to reconstruct the TIN, until no point with higher error than the predetermined threshold remains (Zhou & Chen, 2011). There are numerous implementations of the maxZT algorithm, and it is used as a basis for further variations and enhancements (e.g., Chen & Zhou, 2013; Sun et al., 2018; Wu et al., 2019; Zhang et al., 2016; Zhou & Chen, 2011) (and many others), which use the maxZT method as a reference. Therefore, we selected the maxZT method for quantitative comparison with the QEMS simplification method.…”

“…(2016), Sun et al. (2018), Wu et al. (2019), and Gökgöz and Hacar (2020) use various techniques to find the most suitable (important) points to describe landscape surfaces.…”

“…Hierarchical land surface segmentation requires a DEM generalization technique that also preserves the main topographic features at high levels of generalization. Polygonal simplification methods enable this without explicit (and at least partially subjective) searching or insertion of a terrain skeleton, characteristic of grid‐based methods (e.g., Sun, Wang, & Zhao, 2018; Zakšek & Podobnikar, 2005). These methods use the polygonal model (polyhedron with irregular faces) to represent the shape of a modeled object.…”

“…This is true for the vast majority of methods used in land surface modeling, including the traditional, yet still popular, Fowler and Little algorithm (Fowler & Little, 1979) and the very important points algorithm (Chen & Guevara, 1987). Similarly, other algorithms presented in Zakšek and Podobnikar (2005), Fei and He (2009), Chen and Zhou (2013), Chen et al ( 2016), Sun et al (2018), Wu et al (2019), and Gökgöz and Hacar (2020) use various techniques to find the most suitable (important) points to describe landscape surfaces. However, from a broader perspective, we can find diverse approaches to generalization, many of them based on modifications of the detailed polygonal model (generally, polygonal simplification methods).…”

Line simplification with sidedness relationship consistency using the constrained total least squares method

“…Substantial research has been devoted to line feature simplification, with algorithms such as Douglas–Peucker (DP), Visvalingam‐Whyatt (VW), and Li‐Openshaw methods primarily concentrating on keypoint detection and selection (Douglas & Peucker, 1973; Dyken et al., 2009; Li & Openshaw, 1992; Sun et al., 2018; Visvalingam & Whyatt, 1993). However, line simplification can lead to positional errors between simplified and original line features (Lin et al., 2021; Veregin, 2000).…”