# An Integrated Algorithm for Extracting Terrain Feature-Point Clusters Based on DEM Data
## 1 Introduction  
The terrain surface is composed of a series of characteristic elements (including point, line and surface elements), and its morphology and combination characteristics can be used as the symbolic carrier of the interactions among the earth's internal tectonic movements, surface processes and climate evolution [1, 2, 3]. Among them, terrain feature-point clusters, including mountain peaks, saddles and runoff nodes, are widely distributed on the terrain surface, which are the controlling links in describing the terrain's morphological structure and formation. These three kinds of terrain feature points can not only describe an aspect of terrain independently, but also have good coupling, matching quantity and topological connection relationships among them, which can be combined to describe terrain relief, distribution difference, dynamic development and change characteristics as a whole [4]. Thus, this paper proposes terrain feature-point clusters, which are organic structures withdistance, orientation and topological constraints consisting of peaks distributed along the ridgelines and their control ranges, related saddles and runoff nodes. As a high-level abstraction of natural terrain, the terrain feature-point cluster links the micro-analysis and macro-analysis of terrain, which presents the advantages of loading multi-level information. For example, the connections between peaks and saddles describe the undulation degree of ridge and fragmentation characteristics in the region, and the connections between saddles and runoff nodes describe the current topographic erosion characteristics and confluence kinetic energy characteristics. Meanwhile, topographic characteristics and spatial orientation characteristics reflect the topographic differences between different geographic regions, which are the powerful tools for geomorphological regionalization. Existing studies usually focus on a single terrain feature point [5; 6; 7; 8]. Due to the lack of considering the matching and coupling of these points from the overall and global perspective, there are many mismatches in the spatial connection relations and other aspects among different types of point cluster elements obtained by existing methods [9]. [PERSON] and [PERSON] proposed the very important points (VIP), which are important for displaying terrain surface, and implemented the VIP extraction based on digital elevation model (DEM) data [10]. On this basis, [PERSON] and [PERSON] proposed important points and edges (IPE) and their extraction method [11]. However, all of these methods focus on the TIN (Triangulated Irregular Network)'s construction, which only considers the points' importance to the terrain surface, ignoring the geomorphological significance of points and their intrinsic relations. [PERSON] developed [PERSON] and [PERSON]'s topographic models [12; 13] based on the differential topology, and applied his theory to geodesics and other critical point extraction in high-dimensional manifolds [14; 15]. Discrete Morse theory and methods were developed to extract critical points from discrete data (e.g., DEM and high-dimensional images) [16; 17]. At the same time, surface models such as Reed graph [18] and Pfaltz's graph [19] were used to organize these critical points and lines. These methods can obtain terrain feature points and lines containing topological information, providing a new idea in feature extraction and terrain representation. However, these methods focus on the gradient of manifolds from a topological perspective and lack consideration of the geomorphological significance and scale dependence [20; 21]. Therefore, it is urgent to build an integrated terrain feature-point cluster extraction method that can realize the simultaneous extraction of terrain feature-point clusters to ensure the accuracy of point cluster positions and the relative consistency within the clusters.