# An Integrated Algorithm for Extracting Terrain Feature-Point Clusters Based on DEM Data
## 3 Results and Discussion
### Point Cluster Properties and Geomorphological Regionalization  
The relationship between the HDPS and mountain control area size and mountain undulation was analyzed above, and their fitting coefficients were found to be highly correlated with geomorphic zones. Therefore, further analyses were performed to validate the relationships between the point cluster properties and geomorphological zones. This paper's study area is dominated by loess landforms [56]. There are many parameters that can measure the characteristics in the terrain analysis, but from another perspective, we could consider evaluating the cutting of the saddles and compare the differences between landscape types on this basis. [PERSON] pointed out that the commonly used relative height is not a very good index, because even if the relative height was the same, the absolute height difference might also be different [57]. Likewise, when the relative height between the peak and the outlet is the same, the height difference between the saddles and peaks may also be different. Thus, here we define the Saddle Dissection Index:  
\[SDI=(H_{peak}-H_{saddle})/(H_{peak}-H_{discharge}) \tag{9}\]  
where \(H_{peak}\), \(H_{saddle}\) and \(H_{discharge}\) are defined as peak height, saddle height and the outlet height relative to the peak; thus, the SDI can be interpreted as the ratio between the HDPS and the degree of ups and downs. Based on the terrain feature-point clusters extracted from the 0.5\({}^{\circ}\)\(\times\) 0.5\({}^{\circ}\) grids of Shaanxi Province in Section 3.2, the HDPS and SDI of each peak are calculated. Then, the statistical attributes of each peak are interpolated using the natural neighborhood  
Figure 13: Relationship between the HDPS and mountain control area size and mountain undulation in each sample area of Shaanxi Province: (**a,b**) the coefficient distribution histogram of the exponential regression between the HDPS and the mountain control area size; (**c,d**) the coefficient distribution histogram of the linear regression between the HDPS and the mountain undulation, while coefficient \(c\) and \(d\) are the gradient and intercept of the regression line, respectively; six colors in the figures correspond to six geomorphological zones in Shaanxi Province. method to obtain the spatial distribution of the HDPS and SDI at 1 km spatial resolution in Shaanxi Province (Figure 14). As shown in Figure 14, the statistical attributes of point clusters better reflect the overall characteristics of the terrain in Shaanxi Province, i.e., the topographic undulation shows an overall increasing trend from north to south. The topographic undulation in the Wind and Sand Transition Zone and Guanzhong Plain is low, the topographic undulation in Qinling and Daba Mountains is large, and the Loess Plateau is between them. In addition, the spatial distribution trend of the HDPS can be well distinguished from the Wind and Sand Transition Zone, the Loess Plateau, Guanzhong Plain and Qinling Mountain. The relatively weak portrayal appears between Guanzhong Plain and Qinling Mountain and Daba Mountain, which may be related to this region's narrow distribution and complex topographic conditions. Figure 14 shows that the erosion in Shaanxi Province increases from south to north as a whole, and the northern part of the Loess Plateau is seriously eroded, showing a strong fragmentation trend, while the topography of the southern Loess Plateau and Guanzhong Plain is the most complete. The SDI can better distinguish the Loess Plateau, Guanzhong Plain and Qinling Mountains and the poorly carved area is the Hanzhong Basin. This may be due to the interaction of mountains around the basin, which leads to a certain fragmentation trend in the spatial trend of this region [58; 59]. To sum up, the terrain feature-point clusters and their statistical attributes can reflect the fragmentation of the plane and mountains, and the stereoscopic undulation to a certain extent.