# An Integrated Algorithm for Extracting Terrain Feature-Point Clusters Based on DEM Data
## 3 Results and Discussion
### Statistics of Point Cluster Properties  
The Height Difference between Peaks and Saddles (HDPS) is one of the main objects of interest in geomorphology research. The primary consideration of extracting terrain feature-point clusters using the integrated method is to determine a reasonable threshold of the HDPS. Considering the significant controversy regarding the quantitative indicators' determination of mountain undulation, this study does not attempt to put forward a new quantitative indicator, but rather explores the influence and significance of the HDPS from the perspective of attribute statistics. The HDPS has a significant influence on the extraction of peaks and their control areas, affecting the extraction of other terrain feature elements such as saddles and runoff nodes [31]. To quantitatively analyze the influence of the HDPS, taking these six typical sample areas as an example, each element in set \(T=\{10n|n\in[1,40]\&n\in\mathbb{N}\}\) (unit: m) is used as the HDPS threshold to extract the terrain feature-point clusters, and the terrain feature-point clusters and their control areas with different HDPS thresholds are obtained. It is worth noting that the maximum value of the HDPS threshold of each typical sample area is different. This is due to the different elevation undulations in each area--some sample areas will not be able to extract the desired peaks and their control areas when the HDPS threshold exceeds a certain limit. The response of the mountain control area size and mountain undulation (the height difference between the peaks and the runoff nodes)  
Figure 10: Relative localization error distribution of extracted point clusters: the different colored boxes represent different methods; the upper and lower quartiles of the data are depicted by the box’s upper and lower boundaries, respectively; the median and average values are depicted by the inner horizontal lines and the red triangles, respectively; the whiskers extending from the ends of the boxes are used to represent variables other than the upper and lower quartiles. to the HDPS changes is demonstrated using a scatter plot (Figure 11). The blue triangles in Figure 11 represent the response of the average mountain control area size to changes in the HDPS, and the blue dashed lines show the fitting relationship between them. For the typical sample areas, the HDPS and the average mountain control area size show a typical exponential relationship:  
\[y=ae^{bx} \tag{7}\]  
where \(y\) is the extracted average mountain control area size, \(x\) is the HDPS, and \(a\) and \(b\) are the fitting coefficients. Its minimum fitting coefficient of determination (\(R^{2}\)) reaches 0.97. Observing the overall trend, it can be seen that with the gradual reduction of the topographic undulation (from the Qinling middle and high mountains to the loess hilly-gually), the fitting coefficient \(a\) gradually decreases, and the coefficient \(b\) gradually increases. Meanwhile, the orange dashed line in Figure 11 indicates the response of the average mountain undulation to changes in the HDPS, which shows a typical linear relationship:  
\[y=cx+d \tag{8}\]  
where \(y\) is the extracted average mountain undulation, \(x\) is the HDPS, \(c\) and \(d\) are the gradient and intercept of the regression line, respectively, and its average fitting \(R^{2}\) reaches 0.94. Observing the overall trend, it can be seen that the regression lines' intercept \(d\) shows a gradually increasing trend as the topographic undulation decreases. The whole Shaanxi Province was used as the experimental sample area for analysis again to further verify the pattern of the fitting coefficients. The Shaanxi Province was divided into 123 grid cells according to the cell size of 0.5\({}^{\circ}\)\(\times\) 0.5\({}^{\circ}\), and each cell belonging to the geomorphological region was determined by the location for its centroid.