# An Integrated Algorithm for Extracting Terrain Feature-Point Clusters Based on DEM Data
## 1 Introduction
Although the peaks exist as point elements, they are essentially abstractions of the individual mountain in geographic space, occupying the corresponding spatial area, and the saddles are located at the intersections of the control areas' boundaries corresponding to these peaks. If the original terrain is divided, the control areas of each peak can be obtained, and the saddles can be obtained by intersecting the control area boundaries with the ridgelines. From the saddles, the peaks can be connected along the watershed lines, and along the ravine lines are runoff nodes. In fact, the peaks' control areas and the watershed areas can be seen as the unstable Morse complex and stable Morse complex in the Morse theory, respectively. Meanwhile, the saddles can be seen as the Morse-Smale complex [22]. The principle is shown in Figure 1.  
Then the problem becomes how to extract ridgelines and the control areas of the peak accurately. Ridgelines are a definite and objective terrain feature object as one of the typical terrain structure lines. The current research on terrain structure line extraction mainly includes the section extreme value method [23; 24], skeletonization method [2; 25] and runoff simulation method [26; 27; 28]. The terrain profile analysis method includes three major steps: candidate point extraction, pseudo candidate point elimination, and structure line construction, but the analysis process generally only considers specific directions and ignores other directions. The skeletonization method assumes that the terrain structure lines are symmetrically distributed to the left and right, which is obviously inconsistent with the fact. Currently, the runoff simulation method is widely used to extract the terrain structure lines, among which the deterministic eight-node (D8) algorithm [26; 29] is most commonly used. However, due to the lack of an explicit threshold selection instruction in the runoff simulation, the uncertainty of the threshold in this process makes the extracted terrain structure lines poorly comparable [30; 31; 32]. As for the peak control area acquisition, [PERSON] et al. proposed the space segmentation method with the height difference limitation [33]. The original terrain was turned into an anti-terrain, and a threshold-limited filling process was performed. Then, the anti-terrain watershed areas [34; 35; 36; 37] were extracted as the mountain control areas. This method draws on the hydrological viewpoint, and the obtained mountain control areas are consistent with geomorphological perception. This paper proposes an integrated method for extracting terrain feature-point clusters to overcome the above limitations. Firstly, the ridgelines are extracted by combining the morphological features with the runoff simulation method. Meanwhile, the peaks and their control areas are extracted by the spatial subdivision method [33]. Then, the ridgelines intersect with the peaks' control area boundaries to obtain the saddles, and the control area boundaries are self-intersected to obtain the runoff nodes. Finally, the integrated terrain feature-point clusters are obtained by merging these extracted point clusters. The main contributions of our work are as follows: (1) an integrated method for extracting terrain feature-point clusters is proposed, revealing the structure and intrinsic relationship of the feature points; (2) a way for determining the flow accumulation threshold for ridgeline extraction based on the runoff simulation method is put forward, representing an important attempt at digital terrain analysis; (3) the saddle dissection index is proposed and the geomorphological significance of point clusters is explored. Section 2 elaborates the materials and methods of this study, including the study area and data (Section 2.1), positive terrain-constrained ridgeline extraction method (Section 2.2.1), and terrain feature-point cluster extraction method (Section 2.2.2).