# An Improved Shoulder Line Extraction Method Fusing Edge Detection and Regional Growing Algorithm
## 1 Introduction  
One of the most significant recent discussions has been the study of spatial differentiation in the Loess Plateau [1; 2; 3; 4; 5]. Shoulder lines are the topographic structural lines that best depict loess landform characteristics. The shape, grade, spatial distribution, development trend, and other characteristics of shoulder lines reflect the regional variations in loess landforms, as shown in Figure 1. However, due to the complexity of the Loess Plateau, the effective extraction of shoulder lines is influenced by a variety of factors, such as the accuracy of the source data, the local discontinuity of the lines, and the applicability of the method [6; 7; 8; 9; 10]. Consequently, a more efficient and accurate shoulder line extraction method is still needed. The traditional method of extracting shoulder lines is to use the contour lines of topographic maps or aerial images to directly delineate them [11; 12; 13; 14; 15]. Although the precision is excellent, the efficiency of this method is low, and the workload is heavy. In recent years, with the support of RS and GIS technologies, the characteristic terrain elements in a landform can be automatically extracted and analyzed, and the extraction of shoulder lines has become one of the hot spots for study [16; 17; 18; 19; 20; 21]. Researchers have studied the automatic extraction of shoulder lines. The extraction methods can be classified into three types: The first method is the geometric morphological method. Terrain parameters, such as slope, slope aspect, and curvature, are used for regular judgment to obtain shoulder lines based on the given rule of shoulder lines in the geometric form. For example, [PERSON] used DEM data as the basis for extracting shoulder lines by combining areas of low difference between mean elevation and high positive plan curvature [22]. [PERSON] obtained shoulder lines by comparing the slopes of upstream and downstream grids on the same slopes [23]. [PERSON] proposed a method for extracting shoulder lines based on slope aspect orientation according to the slope-turning characteristics of loess landforms [24]. This method is simpler, faster, and easier to implement compared with the traditional approach. However, the actual effect obtained is not ideal. The second method is the hydro-geomorphologic method. The constraint and drawing of shoulder lines are achieved as a result of the interaction between the hydrological process and the landform and are based on the principle of a flow analysis of the terrain surface. For example, [PERSON] applied a surface-flow digital simulation method and a contour vertical-line-tracking method to achieve shoulder line extraction based on the principle of a terrain surface flow analysis [25]. [PERSON] used water flow paths for distributed water flow computation to extract shoulder lines [26]. [PERSON] used the direction of confluence to determine the streamline of a slope and drew a shoulder line based on the inflection point of the streamline [27]. The shoulder lines obtained by this method have a certain geological significance compared with the geometric morphological method, and the problem of shoulder line continuity is overcome to a certain extent. However, the digital simulation of surface water is influenced by several factors, including water flow direction and catchment threshold, which increase the uncertainty of a slope's flow path, making judging points on a characteristic shoulder line difficult, lacking in precision, and necessitating substantial calculations. The third method is based on an image-processing method. The edge detection method achieves the purpose of detecting sudden edge change by comparing the changing characteristics in the image brightness value and detecting the sudden change point of the image brightness. For example, [PERSON] used the supervised classification approach for the maximum likelihood classifier to classify gullies and non-gullies [28]. [PERSON] used image binarization and various edge detection operators to extract shoulder lines [29].