A Method for Extracting Some Key Terrain Features from Shaded Relief of Digital Terrain Models

Abstract

Detection of terrain features (ridges, spurs, cliffs, and peaks) is a basic research topic in digital elevation model (DEM) analysis and is essential for learning about factors that influence terrain surfaces, such as geologic structures and geomorphologic processes. Detection of terrain features based on general geomorphometry is challenging and has a high degree of uncertainty, mostly due to a variety of controlling factors on surface evolution in different regions. Currently, there are different computational techniques for obtaining detailed information about terrain features using DEM analysis. One of the most common techniques is numerically identifying or classifying terrain elements where regional topologies of the land surface are constructed by using DEMs or by combining derivatives of DEM. The main drawbacks of these techniques are that they cannot differentiate between ridges, spurs, and cliffs, or result in a high degree of false positives when detecting spur lines. In this paper, we propose a new method for automatically detecting terrain features such as ridges, spurs, cliffs, and peaks, using shaded relief by controlling altitude and azimuth of illumination sources on both smooth and rough surfaces. In our proposed method, we use edge detection filters based on azimuth angle on shaded relief to identify specific terrain features. Results show that the proposed method performs similar to or in some cases better (when detecting spurs than current terrain features detection methods, such as geomorphon, curvature, and probabilistic methods.

1. Introduction

Detection of terrain features plays a key role in learning about land surface, geologic structures, and geomorphological processes. Terrain features are also utilized in several spatial applications such as land control [1], land use [2], hazard management [3], hydrology [4], and environmental setting analysis [5]. One of the early terrain feature detection methods has been field investigation. However, this method is not practical because conducting field investigations over vast areas requires enormous time and money and poses a risk to field investigators in particularly rugged and uneven terrains. For this, remote sensing (RS) data acquired from satellites, airplanes, unmanned aerial vehicles (UAVs), and ground vehicles [6], especially in remote areas, have become the preferred method of detecting field data including terrain features. RS data can be used to derive digital elevation models (DEMs) through photogrammetry, laser scanning (LiDAR or Terrestrial Laser Scanning), radar interferometry, among others [7]. Terrain feature detection is one of the primary research topics in DEM analysis [8]. DEM datasets of different resolutions are available through varying programs [9,10,11].

LiDAR collects point cloud data that can be used to characterize terrain surfaces and has properties of points such as intensity, density, and elevation [12]. In comparison to analysis based on point cloud, raster or DEMs analysis has been used and improved for decades, leading to a comprehensive set of methodologies to support this analysis. Hence, the creation of DEMs and subsequent derivatives from point cloud data is broadly used. However, DEMs provide a description of the terrain that only include values of elevation [13,14]. For this reason, it is not a full 3D representation of the terrain and cannot represent vertical surfaces such as walls and cliffs [14] where one pixel (X,Y location) requires several values.

Detection of terrain features based on geomorphometry and DEMs analysis has three major challenges. First, terrain features are structured as an outcome of geologic and geomorphic processes that can be represented by several geomorphologically associated terrains, resulting in a high degree of uncertainty when classifying and identifying terrain features [15]. The second challenge involves drawing a boundary between terrain features using sample data from a spatially continuous surface [16]. The third challenge is detection of terrain features at various spatial scales [17].

In this work, we focus on the detection of specific terrain features, i.e., ridges, spurs, vertical cliffs (cliffs), and peaks. There are several computational techniques for obtaining valuable morphological information from given terrain using DEMs analysis. One technique is to numerically identify or classify a terrain into its constituent terrain features [18,19]. Using this technique, regional typologies of the terrain are created by using statistical methods or pattern recognition and differential geometry principles, and by using DEMs, or combining several derivatives of DEMs, as a dataset. However, with this technique, it is hard to differentiate global and local features [20]. For example, both ridges and spurs have a similar characteristic where usually low relief in three azimuthal directions and high relief in one azimuthal direction with varying degrees of slope appear. The difference is that spurs are a continuous sloping line, commonly jutting out from the side of the ridge [21]. In other words, a spur is a line continuously declining in slope and appearing from the side of another landform such as ridges. Spurs are usually a product of rills (small channels excavated by water on slopes), and are the emerging ridge formed in the space between where two rills have excavated surface material [21]. This issue led to the development of an object-based terrain feature detection method by Zhou et al. [22]. The method proposed by Zhou et al. [22] solves the problem with local optima by using multiple neighbors, by comparing target pixels with several neighboring pixels instead of one neighboring pixel, and by applying probabilistic visual descriptors to get edge pixels in only hilly terrains. Another terrain feature detection method is geomorphon, based on the principle of pattern recognition, which was proposed by Jasiewicz et al. [23]. Geomorphon is widely used and available in various geospatial libraries [24]. However, during experimentation, geomorphon detected false positive spurs for some terrains. Another technique is to calculate a shaded relief that can provide a visual representation of topography [25] that an analyst manually examines and identifies terrain features from. Even though shaded relief is a derivative of DEMs, this technique is mostly used for manual analysis, making it inefficient and impractical, particularly for large areas of interest; however, manual detection of terrain features is still considered one of the most accurate approaches. Given the limitations in manual detection efficiency and application to large datasets, automated or semi-automated methods that resemble manual detection are needed, which may also serve as a way to reduce human bias or mistakes in manual detection [26].

Humans perceive and interpret information about terrain features using perceptual cues such as light angles, shadows, patterns, and textures (elements of image interpretation) [26,27]. Such perceptual cues on shaded relief, as a visual representation of real-world terrain, can be used to identify terrain features—particularly linear features. For example, in the satellite image of Wizard Island (Figure 1a), the crater boundaries on the center of the island and rough terrain on the sides of the island can be identified from natural shadows and textures. Similarly, crater boundaries and rough terrain can be identified using shaded relief of the island in Figure 1b, with much higher confidence, since data not associated with elevation is removed.

Of interest to researchers is the automatic detection of terrain features such as ridges, spurs, cliffs, and peaks directly from a DEM, or its derivatives, based on elements of human image analysis. Even though methods to detect terrain features using elements of image analysis on shaded relief have been investigated, there is a void in literature in the efficient and automated methods that produce accurate results. Our contribution in this paper is a new method to automatically detect terrain features from shaded relief by controlling the altitude and azimuth of an illumination source and implementing an edge detection algorithm with specified filters. We addressed the following research question: What would be a method for automatically detecting terrain features using shaded relief by controlling altitude and azimuth of an illumination source and implementing an edge detection algorithm with a specific filter on shaded relief? The structure of the paper is as follows. In Section 2, background on terrain detection using DEM, shaded relief, and edge detection are given. Section 3 is devoted to a detailed description of the proposed method. In Section 4, the datasets and evaluation matrices in the experimentation are discussed. The evaluation results are presented in Section 5 and discussed in Section 6. The conclusion is given in Section 7.

2. Background and Related Works

For several decades, many researchers have been working on automatic or semi-automatic, supervised or unsupervised, object-based or pixel-based terrain feature detection using DEMs at different scales. The advances of RS technologies and geographic information systems (GIS) have made the detection of terrain features for large geographic areas with high-pixel resolution possible. DEMs have allowed topography to be automatically analyzed by using terrain elevation. Since then, the research in the detection of terrain features has been evolving and improving.

2.1. Terrain Feature Identification

Early works on the detection and classification of terrain features were done by [28,29]. Map terrain features were created by using geometric criteria such as slope, elevation, and surface pattern or profile. In a project by Hammond [30], the United States was mapped and classified into 24 landform classes. Similarly, the detailed six-classes map of the Central European regions was proposed by Wood et al. [31]. A map with topographic regions of the world with a smaller scale was designed by Murphy et al. [32]. The advances of RS technologies and geographic information systems (GIS) have made the detection of terrain features for large geographic areas with high pixel resolution possible [33]. DEMs have allowed topography to be automatically analyzed by using terrain elevation.

The detection of linear terrain features is commonly done by pixel-based [20], stream network analysis, or object-based methods at a variety of different scales. To detect linear terrain features using a pixel-based method, Rana [20] used curvature to detect ridges and used DEM smoothing to cope with noise. Another approach to identify ridges is by using tools from the hydrology domain called stream network analysis [34,35,36,37]. From DEMs, stream network analysis calculates the direction of streams and simulates water accumulation to find watersheds. The disadvantages of these methods are that they can fail to catch the ‘bigger picture’ of terrain patterns and terrain features. An object-based terrain feature detection can efficiently partition DEM into image areas by combining pixels with related properties together to overcome the shortcomings of a pixel-based method [38,39,40]. The performance of current object-based feature detection methods has largely relied on that of segmentation and mathematical morphology [41,42,43]. Terrain features can be detected by using a single scale or a multi-scale approach. For an extensive overview of digital classifications at different scales, as well as suitable techniques, refer to [17,44,45]. Other existing linear terrain features detection methods include geomorphon, based on pattern recognition [23], and probabilistic, based on visual descriptors [22].

2.2. Shaded Relief

The hillshade or shaded relief is a technique based on light simulation applied for terrain visualization. In shaded relief, continuous color or grey-scale images can be created by simulating solar radiation on a DEM [46]. Shaded relief is concerned with building new attributes that refer to the three-dimensional form of a continuous surface and is applied in many applications. Example applications are presenting an image of terrain to enhance the realism of a terrain map and irradiance mapping to calculate the amount of solar energy falling directly to the continuous surface and shadow analysis. In shadow analysis, it is possible to identify the exact location of the continuous surface in the shadow at a specific time of day [47]. Other applications include extraction of lineament data from DEMs [48,49,50]. Using shaded relief to detect or map landslides was proposed by [51,52]. Na et al. [53] applied shaded relief and edge detection, which extracts only gully shoulder lines.

2.3. Edge Detection

The first goal of vision processing is to detect features, such as edges in images, that are important to determine the structure and properties of objects from the scene. Edges are significant local changes that occur on the border between two different regions. For this reason, edge detection is usually the first step in recovering information from an image [54]. An edge detection technique consists of three steps: filtering to reduce noise; enhancing to identify changes in the intensity between two different regions; detecting to select only lines with strong edge content. There are many edge detection techniques such as Roberts Operator, Sobel Operator, Prewitt Operator, and Canny Operator [54].

3. Methods

Our proposed method has five steps (Figure 2). The first step applies shaded relief (Equation (3)) on a digital terrain model (DTM) using several altitude and azimuth variables, followed by the application of an enhancement algorithm (reclassification of a reflectance map derived from the shaded relief) (Equation (4)). The second step applies selective filters (Equation (5)) for each reclassification results to get a line between shaded and non-shaded areas. The third step detects cliffs using different illumination altitudes. The fourth step removes detected features that do not persist under slight (± 44°) azimuth changes (Equation (6)). The final step is the classification (Equation (7)). The input for the method is a DTM of the continuous surface and the output is a raster dataset segmented into different classes, such as ridges, spurs, cliffs, and peaks. Shaded relief parameters are performed with a low 0° altitude of illumination source on the DTM, as described in Section 3.1.

3.1. Shaded Relief Computation

In our method, we adopt the shaded relief algorithm of [46]. The algorithm performs a few steps, and the first step is to calculate the slope p, q at each cell in two directions is computed:

$$p=\frac{\left[\left(z_9 + z_8 + z_7\right)-\left(z_3 + z_2 + z_1\right)\right]}{8d}$$

(1)

$$q=\frac{\left[\left(z_9 + z_6 + z_3\right)-\left(z_7 + z_4 + z_1\right)\right]}{8d}$$

(2)

where $d$ is distance between pixel centers and $z_i$ is the height at the location $i$ (Figure 3a). In other words, if we calculate a slope value from the elevation values presented in Figure 3a, the rate of change in the south-north direction for cell $z_5$can be calculated using Equation (1) and the rate of change in the east-west direction for cell $z_5$can be calculated using Equation (2).

Then these values are converted to a reflectance value using an appropriate reflectance map (R) [46]:

$$\begin{array}{c}R\left(p,q\right)=\frac{1}{2} + \frac{\frac{1}{2}\left(\acute{p} + a\right)}{\sqrt{b^2 + {\left(\acute{p} + a\right)}^2} } \hfill \\ \acute{p}=\frac{\left(p_{0}p + q_{0}q\right)}{\sqrt{\left(p_0^2 + q_0^2\right)}}\hfill \end{array}$$

(3)

where $p_0= \frac{1}{\sqrt{2}}$ and $q_0= -\frac{1}{\sqrt{2}}$ for the light source is in standard cartographic position with 315° azimuth and 45° altitude of illumination source (Figure 3b). The parameters $a$ and $b$ allow control intensity of grey values for horizontal continuous surfaces for visualization purposes. Horn [46] recommended $a=0$ and $b=\frac{1}{\sqrt{2}}$.

The output is a reflectance map that ranges between 0 and 1 multiplied by 255. Since the goal of this work is to identify lines that serve as a boundary from the illumination, we focus on areas that were under the shade which have value equal to 0. For this reason, we reclassify the output of the reflectance map:

$$Reclassified output of shaded relie{f}_{ij}\left(x\right)=\left\{\begin{array}{c}0,forx=0\\ 1_{,}forx>0\end{array}\right\}$$

(4)

This step is similar to the enhancement step used in the edge detection method discussed above and in [54].

3.2. Selective Filtering

When shaded relief is performed on the continuous surface with a low altitude, the terrain features serve as a border between illuminated areas and shadowed areas. In the second step of the method, the shaded relief operation was repeated eight times, each time with a different azimuth orientation. These azimuth degrees are north (0°), northeast (45°), east (90°), southeast (135°), south (180°), southwest (225°), west (270°), and northwest (315°). To capture these borders, we implemented edge detection filters, which are designed to capture borderlines based on a specific azimuth degree. These are 3 × 3 filters that allow capturing borders (edges) from eight azimuthal directions [54]. For example, to detect terrain features from shaded relief with an azimuth of 45°, we used filter ${\mathrm{F}}_{45},$and with an azimuth of 90°, we used filter ${\mathrm{F}}_{90}$, and so on. The result of using a selective filter $F_{90}$ that captures border lines where a light source for the shaded relief coming from azimuth 90° is shown in Figure 4.

$$\begin{array}{c}{F}_{45}\left\{\begin{array}{ccc}0& 0& -1\\ 0& 0& 0\\ 1& 0& 0\end{array}\right\} F_{90}\left\{\begin{array}{ccc}0& 0& 0\\ 1& 0& -1\\ 0& 0& 0\end{array}\right\} F_{135}\left\{\begin{array}{ccc}1& 0& 0\\ 0& 0& 0\\ 0& 0& -1\end{array}\right\} F_{180}\left\{\begin{array}{ccc}0& 1& 0\\ 0& 0& 0\\ 0& -1& 0\end{array}\right\} \\ F_{225}\left\{\begin{array}{ccc}0& 0& 1\\ 0& 0& 0\\ -1& 0& 0\end{array}\right\} F_{270}\left\{\begin{array}{ccc}0& 0& 0\\ -1& 0& 1\\ 0& 0& 0\end{array}\right\} F_{315}\left\{\begin{array}{ccc}-1& 0& 0\\ 0& 0& 0\\ 0& 0& 1\end{array}\right\} F_{0/360} =\left\{\begin{array}{ccc}0& -1& 0\\ 0& 0& 0\\ 0& 1& 0\end{array}\right\}\end{array}$$

(5)

3.3. Removing Falsely Detected Spur Lines and and Thining with Non-Maximum Suppression

For flatter terrain or terrain that has a shape that resembles a cone or half-sphere, after the filtration, our proposed algorithm detected spur lines on fixed (every 45°) directions. (Figure 5a). To cope with this issue, two steps were implemented. In the first step, for each azimuth degree, an additional shaded relief by changing azimuth to ±44° is performed. This is the maximum allowable whole number because filters were designed to be compatible with specific shaded relief that is performed every 45°. If the value exceeds ±44°, these filters will not be able to capture border lines for specific shaded relief. We performed several experiments with different azimuth values and the results show that smaller values lead to a higher rate of false spur lines detection. Next, specific filtering for all three shaded relief outputs is performed. The output is a raster dataset with terrain features (TF) for each azimuth degree, TF1, TF45, TF89, and so on. By performing this operation, the true terrain features persist under slight azimuth changes and will get high weight (pixel value), whereas false spur lines do not persist under slight azimuth changes and will have a pixel value equal to 1 (Figure 5b). By deleting values that are equal to 1, we can remove false spur lines (Figure 5c). After removing false spur lines, to thin detected lines, we performed a non-maximum suppression algorithm that is commonly used in computer vision. Non-maximum suppression is a post-processing algorithm responsible for merging all detections that belong to the same object [55].

$$\begin{array}{c}TF45\_True=(TF1+TF45+TF89)\hfill \\ TF45\_True{ }_{ij}\left(x\right)=\left\{\begin{array}{c}0, for x=1 \\ 1{ }_{ij, } for x>1 \end{array}\right\}\hfill \end{array}$$

(6)

3.4. Cliff Detection

The detection of the cliffs requires manipulation of the altitude value of the shaded relief algorithm. If we apply shaded relief using two altitude values such as 0° and 45°, it resembles the position of the sun during the sunrise and during the day. Hence, the cliffs are lines that appear in 0° altitude of an illumination source and disappear in 45° altitude of the illumination source (Figure 6). Similarly, with previous steps to detect cliffs, we perform shaded relief sixteen times with eight different azimuth orientations and two altitude values. Since shaded relief with an altitude value of 0° is already performed in previous steps, we only need to perform shaded relief with an altitude value of 45° and with eight different azimuth orientations. Then, by using raster calculation, we selected pixels that appear in 0° altitude of an illumination source and disappear in 45° altitude of the illumination source. Note that we implement with 45° altitude of the illumination source only to detect cliffs, and for the rest, we use 0° altitude.

3.5. Terrain Feature Differentiation

After performing filtering and removing falsely detected spur lines, we receive terrain features from different azimuth orientations. By manipulating these features, we can derive specific terrain features such as ridges, spurs, and peaks. In the real-world, if we have a mountain peak, the peak is visible from any azimuth orientation. When we add all values from 8 different azimuth directions, we get a raster with maximum values equal to 8 and minimum values equal to 0. For this reason, the terrain features that can be detected from all 8 directions are peaks, and their values equals 8. The ridges are lines that are visible from any directions except where ridges are pointed. For example, in the real-world, if we have a ridge that is pointing from south to north, and if we are looking at this ridge directly from the north, we would not be able to see that ridge. In such cases, the values of ridges are smaller than 8 but larger than 5. Finally, the values that are larger than 1 can be counted as a spur.

$$\begin{array}{c}\mathrm{Total}=\left(\right(\mathrm{TF}45\_\mathrm{True}+\mathrm{TF}90\_\mathrm{True}+\dots +\mathrm{TF}360\_\mathrm{True})-\mathrm{cliff})\hfill \\ {\mathrm{Total}}_{ij}\left(x\right)=\left\{\begin{array}{cc}peak& for x = 8\\ ridge& for (x<8 and>5 \\ spur& for (x<5 and>1 \\ noise& for x\le 1 \end{array}\right\}\hfill \end{array}$$

(7)

4. Experimental Setup

For synthetic datasets (see Supplementary Materials), terrain features (peaks, spurs, and ridges) are known and we, therefore, compared method results to those ‘manually’ detected known features. For real-world datasets (see Supplementary Materials), since there was no dataset of linear terrain features as a benchmark, in order to evaluate the performance of our proposed terrain feature detection method, we compared our results with other terrain features detection methods: geomorphon [23], curvature-based [56], and probabilistic [22]. We used a DTM as an input to all methods, obtained points for the peaks and lines for the spurs and ridges, and evaluated the results, which are in pixels and not in lines or polygons.

Geomorphon is a method that uses the principle of pattern recognition to classify landforms from DEMs [23]. Geomorphon detects common local morphological elements such as flats, peaks, ridges, shoulders, spurs, slopes, hollows, footslopes, valleys, and pits, using the concept of local ternary patterns (LTPs) [57]. LTPs are a nonparametric, computationally effective local texture descriptor of the image [58]. To extract these LTPs, instead of using a fixed size neighborhood, geomorphon uses a neighborhood with size and shape suitable for the local topography. Hence, it can identify landforms at various spatial scales and is computationally efficient [23]. From the nine local morphological elements that geomorphon detects, we focus on peaks, ridges, and spurs. In the curvature-based method, terrain features are extracted from surface curvatures, which are in raster form, by using a certain threshold, a multiplication of the curvature’s standard deviation, with no classification of a feature type. This algorithm includes a combination of the first derivatives of an elevation called slope, and second derivatives, called curvature. Curvature is one of the basic terrain parameters and is commonly used in terrestrial terrain analysis [56]. It defines the orientation of a slope and quantifies morphologies, where a positive value is convex, and a negative value is concave. Hence, a ridge cell will have positive curvature values while channels will have a negative value [20]. In the probabilistic method, terrain features are extracted from the raster-type aspect and slope data, by using a certain aspect and slope threshold, again with no classification of a feature type. This method uses spatio-contextual information to identify terrain changes. More specifically, linear terrain features are detected by deriving spatio-contextual information and by using multiple neighborhood analysis in combination with a probability model [22].

Our proposed method uses the shaded relief data generated by the Geospatial Data Abstraction Library [24]. We used the geomorphon and curvature functions in the Geographic Resources Analysis Support System software tool in our work [59]. For the probabilistic method, aspect and slope were generated by the Geospatial Data Abstraction Library [24].

Our assumption, consistent with common practice, is that manually detected features, from both the synthetic and real-world datasets, are the most accurate baseline datasets. For this, we manually detected terrain features and followed a protocol for creating shaded relief maps with illumination at 45° altitude and varying azimuths every 45° starting at 0°. The shaded relief and varying orientations aided in identifying terrain features. However, with manual detection, feature types were not identified (ridge, peak, cliff, or spur).

4.1. Dataset

We used both synthetic and real-world data to evaluate our method. Synthetic data with common shapes such as cone, square pyramid, half-sphere, and two terrains with known linear and curvilinear terrain features were used. Each of these terrains has seven and eight hills (ridges), respectively, with a different level of sharpness. These datasets were generated using software called World Machine Basic [60]. Since terrain features were synthetically generated, we know the number, length, and location of the generated terrain features. For real-world data, we used two locations: the first is Crater Lake in Klamath County, Oregon (latitude 42°95′N and longitude 122°10′W), a radial topographic system, and the second is a trending linear topographic system from the southern half of the Lackawanna synclinorium to the southeast of the city of Wilkes-Barre in Luzerne County, Pennsylvania (latitude 41° 10′ 25.56”N and longitude −75° 54′ 1.8”W).

4.2. Evaluation Metrics

To evaluate our proposed terrain features detection method, we overlaid the detected terrain features with those detected by the curvature-based and geomorphon methods and manually detected ridges. We also manually collected ridges, as a baseline, and analyzed its results with the results of the four methods through a confusion matrix. In the confusion matrix, four common validation metrics—accuracy, precision, recall, and Cohen’s Kappa coefficient—were considered:

$$Accuracy= \frac{TP + TN}{TP + TN + FP + FN}$$

(8)

$$Precision= \frac{TP}{TP + FP}$$

(9)

$$Recall= \frac{TP}{TP + FN}$$

(10)

$$Cohen’s Kappa coefficient= \frac{P_c- P_{exp}}{1- P_{exp}}$$

(11)

where

$$\begin{array}{c}{P}_c=Accuracy\hfill \\ P_{exp}= \frac{(\left(TP + FN\right)\ast \left(TP + FP\right) + \left(FP + TN\right)\ast \left(FN + TN\right)}{sqrt\left(TP + TN + FN + FP\right)}\hfill \end{array}$$

TP stands for true positive; FP stands for false positive; FN stands for false negative; TN stands for true negative. The values for all four metrics range from 0 to 1, where 0 represents worst and 1 represents best. Depending on the percentage of terrain features areas in the whole area, accuracy can be biased. Precision is a ratio of correctly detected terrain features areas to all detected terrain features. Recall is a ratio of correctly detected terrain feature areas to all existing terrain feature areas. Cohen’s Kappa coefficient [61,62] is a measure of agreement between the detection method and reality or a measure of how the result is significantly better than random [63].

5. Results

5.1. Synthetic Dataset

Table 1. Cohen’s Kappa coefficient, accuracy, precision, recall for synthetic dataset method results as compared to known terrain features.

Dataset	Method	Cohen’s Kappa	Accuracy	Precision	Recall
Cone	Proposed	0.133	0.999	0.071	1
	Geomorphon	0.0003	0.978	0.0001	1
	Curvature	0.011	0.9993	0.005	1
	Probabilistic	0.0097	0.9992	0.004	1
Half sphere	Proposed	0.333	0.999	0.2	1
	Geomorphon	0.0003	0.979	0.0001	1
	Curvature	−0.0007	0.993	0	0
	Probabilistic	−0.0007	0.999	0	0
Square Pyramid	Proposed	1	1	1	1
	Geomorphon	0.589	0.997	0.979	0.422
	Curvature	1	1	1	1
	Probabilistic	0.497	0.993	0.334	0.994
Lines	Proposed	0.653	0.992	0.488	1
	Geomorphon	0.137	0.931	0.081	0.863
	Curvature	0.691	0.995	0.671	0.7165
	Probabilistic	−0.0072	0.985	0	0
Lines Curved	Proposed	0.735	0.994	0.594	0.972
	Geomorphon	0.133	0.898	0.079	0.99
	Curvature	0.274	0.982	0.216	0.404
	Probabilistic	0.225	0.981	0.18252	0.326

shows the evaluation metrics of the results for synthetic datasets produced by our proposed method and those produced by the curvature-based, probabilistic, and geomorphon methods, as compared to the known terrain features that were manually detected.

Table 2. Pairwise comparison of the different methods results for synthetic datasets.

Dataset		Method 1	Method 2	Cohen’s Kappa	Accuracy	Precision	Recall
Cone	Peak	Proposed	Geomorphon	1	1	1	1
	Spur	Proposed	Geomorphon	0.001	0.978	0.0008	0.625
	Ridge	Proposed	Geomorphon	0.26	0.999	0.157	0.75
	Peak Spur Ridge	Proposed	Curvature	0.144	0.999	0.077	1
		Proposed	Probabilistic	0.128	0.999	0.068	1
Half sphere	Peak	Proposed	Geomorphon	0.333	0.999	0.2	1
	Spur	Proposed	Geomorphon	0	0	0	0
	Ridge	Proposed	Geomorphon	0.1249	0.999	0.071	0.5
	Peak, Spur, Ridge	Proposed	Curvature	−0.00003	0.993	0	0
		Proposed	Probabilistic	−0.00003	0.999	0	0
Square Pyramid	Peak	Proposed	Geomorphon	1	1	1	1
	Spur	Proposed	Geomorphon	−0.00002	0.999	0	0
	Ridge	Proposed	Geomorphon	0.587	0.998	0.989	0.418
	Peak, Spur, Ridge	Proposed	Curvature	0.997	0.999	1	0.995
		Proposed	Probabilistic	0.497	0.993	0.334	0.994
Lines	Peak	Proposed	Geomorphon	0	0	0	0
	Spur	Proposed	Geomorphon	0.002	0.939	0.001	0.285
	Ridge	Proposed	Geomorphon	0.927	0.998	0.925	0.931
	Peak, Spur, Ridge	Proposed	Curvature	0.654	0.992	0.96	0.5
		Proposed	Probabilistic	0.643	0.992	0.918	0.499
Lines Curved	Peak	Proposed	Geomorphon	0.62	0.999	0.456	0.971
	Spur	Proposed	Geomorphon	−0.006	0.904	0.0014	0.026
	Ridge	Proposed	Geomorphon	0.59	0.989	0.441	0.912
	Peak, Spur, Ridge	Proposed	Curvature	0.369	0.981	0.355	0.405
		Proposed	Probabilistic	0.488	0.985	0.475	0.519

shows pairwise evaluation metrics between the proposed and three other comparable methods. For the geomorphon method, we compared the detection of peaks, spurs, and ridges separately. Since in the curvature and probabilistic method, peaks, spurs and ridges are identified as one object, we combined our detected ridges, spurs, and peaks to compare with the curvature method.

For the synthetic data, we already know the number, length, and locations of the terrain features. DTM derived shapes such as a cone or half-sphere have only one peak that can be detected as one point shown in Figure 7 and Figure 8.

For the conical shape (Figure 7), all four methods were able to detect the known peak, though with varying levels of success, resulting in a recall value of 1 (Table 1). The area representing a detected peak from the curvature and probabilistic methods is much larger. Cohen’s Kappa coefficients are 0.011 and 0.009, respectively (Table 1), which indicate slight or no agreement. Geomorphon correctly detected the location of the peak. However, it falsely detected ridges and spurs from the dataset. Since the area of falsely detected ridges and spurs is large, Cohen’s Kappa coefficient is 0.0003 (Table 1), which indicates slight or no agreement. In comparison with the above three methods, the area representing a detected peak from the proposed method is smaller, with Cohen’s Kappa coefficient at 0.133, which is larger than the other methods and indicates slight agreement [64]. Evaluation metrics between methods and the known terrain features (Table 1) show that the proposed method has the highest Cohen’s Kappa coefficient, accuracy, precision, and recall for a conical topographic feature.

For a pairwise comparison, the maximum values for the evaluation metrics occur between the proposed and geomorphon methods where Cohen’s Kappa coefficient is 1, which means both methods precisely identified the location of the peak. However, many of the accuracy and recall values for other method comparisons are almost as high, if not equal (Table 2).

For the evaluation metrics between the methods and the known terrain features from a half sphere, our proposed method had the highest values for Cohen’s Kappa coefficient at 0.333 (Table 1), which indicates moderate agreement. The proposed and geomorphon methods were able to detect the peak with recall value of 1 (Table 1), while the curvature-based and probabilistic methods detected the line around the half sphere and around the peak, respectively, as a terrain feature that does not represent a peak, ridge, or spur (Figure 8). Cohen’s Kappa coefficient is −0.00003 (Table 1) for both methods, which indicates no agreement [64]. Similarly, the geomorphon method falsely detected spurs that do not exist in the dataset, with Cohen’s Kappa coefficient at 0.0003 (Table 1), which indicates slight or no agreement. For a pairwise comparison, the proposed and geomorphon methods shared the greatest evaluation metric values, specifically for peak feature types (Table 2).

A square pyramid topographic dataset should have two lines (ridges) that divide the whole area into four equal spaces, and a peak in the middle of the DTM. All four methods were able to detect the ridges and peak accurately (Figure 9), resulting in a recall value of 1 for all methods. When the method results are compared to the manually detected known features, the proposed and curvature methods result in a value of 1 for all four metrics, which indicates perfect agreement [64], while the geomorphon has a particularly low Cohen’s Kappa coefficient (0.589) and recall (0.422), and the probabilistic method has a low Cohen’s Kappa coefficient (0.497) and precision (0.334) (Table 1). For a pairwise comparison, the proposed and geomorphon methods once again shared the greatest evaluation metric values, specifically for peak feature types (Table 2) where Cohen’s Kappa coefficient is 1 (Table 2). Comparison with the curvature-based method also resulted in similarly high values, while comparison with the probabilistic method resulted in some of the lowest evaluation metric values, where Cohen’s Kappa coefficient is 0.497 (Table 2).

The DTM derived from terrain with seven straight ridges of equal length (Figure 10) exhibits variation from sharp ridges to curved ridges. When comparing the different methods to the known features (Table 1), the curvature-based method had the highest Cohen’s Kappa coefficient (0.691), accuracy (0.995), and precision (0.671), while the highest recall (1) was from the proposed method. Overall, each method had a high (>0.9) accuracy, and Cohen’s Kappa coefficient (0.653) for the proposed method was similar to that from the curvature-based method results (0.671). In a pairwise comparison with the proposed method (Table 2), ridge features from geomorphon exhibited the highest Cohen’s Kappa coefficient (0.927), accuracy (0.998), and recall (0.931). Precision was highest for a pairwise comparison of the proposed and curvature-based methods which is 0.96 (Table 2).

The DTM derived from terrain with eight curvilinear ridges (Figure 11) also exhibits variation from sharp ridges to curved ridges. When comparing the different methods to the known features (Table 1), the proposed method outperformed the other methods for all metrics, with a high Cohen’s Kappa coefficient (0.735), accuracy (0.994), and precision (0.972), except for recall, for which the geomorphon method had the highest value (0.99). However, the recall for the proposed (0.972) and geomorphon (0.99) methods were both high. In a pairwise comparison, the proposed and geomorphon methods result in the highest metrics for peak and ridges, where Cohen’s Kappa coefficients were 0.62 and 0.59, respectively. However, Cohen’s Kappa coefficient of the geomorphon method for detecting spur lines is negative, which means that lines representing spurs extracted from both methods do not intersect.

5.2. Real-World Dataset

For real-world data, we selected two regions exhibiting different patterns of terrain features. The first is a linear topographic system south of Wilkes-Barre, Pennsylvania that is part of the valley and ridge province, while the second is a radial topographic system for Crater Lake, Oregon (Figure 12). For these two regions, there is no known baseline, so ridges, peaks, and spurs were selected manually for subregions, by two data collectors, to be used as a baseline.

Table 3. Cohen’s Kappa coefficient, accuracy, precision, recall for real-world dataset method results as compared with manually detected feature.

Dataset	Method	Cohen’s Kappa	Accuracy	Precision	Recall
Wilkes-Barre	Proposed	0.056	0.940	0.063	0.125
	Geomorphon	0.007	0.811	0.026	0.209
	Curvature	0.061	0.951	0.073	0.1
	Probabilistic	0.058	0.944	0.066	0.117
Crater Lake	Proposed	0.115	0.961	0.109	0.172
	Geomorphon	0.123	0.905	0.088	0.481
	Curvature	0.116	0.968	0.126	0.138
	Probabilistic	0.113	0.927	0.86	0.333

shows the accuracy, precision, recall, and Cohen’s Kappa coefficient (evaluation metrics) of the results for the real-world datasets produced by the proposed and three other methods, as compared to manually detected terrain features.

Table 4. Pairwise comparison of the different methods results for real-world datasets.

Dataset		Method 1	Method 2	Cohen’s Kappa	Accuracy	Precision	Recall
Wilkes-Barre	Peak	Proposed	Geomorphon	0.207	0.995	0.119	0.83
	Spur	Proposed	Geomorphon	0.103	0.866	0.122	0.257
	Ridge	Proposed	Geomorphon	0.387	0.96	0.284	0.695
	Peak Spur Ridge	Proposed	Curvature	0.181	0.921	0.375	0.15
		Proposed	Probabilistic	0.109	0.952	0.189	0.101
Crater Lake	Peak	Proposed	Geomorphon	0.313	0.999	0.195	0.794
	Spur	Proposed	Geomorphon	0.132	0.933	0.094	0.404
	Ridge	Proposed	Geomorphon	0.549	0.988	0.438	0.753
	Peak, Spur, Ridge	Proposed	Curvature	0.184	0.969	0.279	0.154
		Proposed	Probabilistic	0.172	0.946	0.158	0.265

shows pairwise evaluation metrics between the proposed and three other comparable methods. As was the case for the synthetic datasets, we compared the detection of peak, spurs, and ridges separately where possible. Since in the curvature and probabilistic methods, peak, spur and ridge are identified as one object, we combined our detected ridge, spur, and peak to compare with these methods.

For Wilkes-Barre (Figure 13 and Figure 14), a comparison of method results to manually detected topographic features provides similar evaluation metric value ranges for the curvature, probabilistic, and proposed methods, while the geomorphon has the lowest values for all four metrics (Table 3). The curvature-method resulted in the highest values of Cohen’s Kappa coefficient (0.061), accuracy (0.951), and precision (0.073), while the geomorphon method had the highest recall (0.209) value. In a pairwise comparison, once again the geomorphon and proposed method resulted in the highest Cohen’s Kappa coefficient (0.207, 0.387), accuracy (0.995, 0.96), and recall (0.83, 0.695), but only for peaks and ridges, not spurs (Table 4) where Cohen’s Kappa coefficient is equal to 0.103 which indicates slight or no agreement. The highest precision value (0.375) was between the proposed and curvature-based methods.

For the topographic dataset of Crater Lake (Figure 15 and Figure 16), there was far more variability in the results. When comparing method results to manually detected features, the geomorphon had the highest Cohen’s Kappa coefficient (0.123), and recall (0.481) (Table 3). The proposed, probabilistic, and curvature-based methods resulted in identical evaluation metric values where Cohen’s Kappa coefficient is equal to 0.115, 0.113, and 0.116, respectively. In a pairwise comparison, the proposed and geomorphon methods resulted in the highest metric values for peak and ridge features where Cohen’s Kappa coefficient is equal to 0.313 for peak and 0.549 for ridge features (Table 4).

6. Discussion

When interpreting the results, we begin with a qualitative evaluation. In general, the detection of terrain features based on geomorphometry and DEM analysis is a challenging process. The main drawbacks of pixel-based approaches are that they cannot detect global features and can falsely identify spurs on the flanks of peaks/ridges, an example being the result of the curvature method. We visually compared the results of the four methods with the manually detected baseline and made the following observations (see

Table 5. Comparison of four terrain features detection methods.

Method	Proposed	Geomorphon	Curvature	Probabilistic
Can detect specific terrain features such as ridge, spur, slope	Yes	Yes	No	No
Software tool	No	Yes	Yes	No
Requires threshold value	No	No	Yes	No
Disadvantages	Cannot detect as many terrain features as geomorphon	For some terrains detected false positive spurs at specific directions, and cannot detect vertical cliffs	Requires threshold value and failed to detect peak on objects such as half sphere	Fails to detect on smooth terrain

). The success of all the utilized methods depends on the type of terrain, as there is variability in the level of success of each method for different synthetic and real-world datasets. Looking at all real-world figures (Figure 13, Figure 14, Figure 15 and Figure 16), such seems to be the case, particularly for the geomorphon method, which tends to fail when looking at a dataset with multiple topographic expressions (from smooth to highly variable). In order to further test false positive spurs that were generated by the geomorphon method, we rotated our image by 10° to west and east directions. The detected spurs from the geomorphon method did not change its direction even after rotation (Figure 17). The probabilistic method is based on thresholds imposed on aspect and slope and is more suited to detect lines on rugged terrain. For smoother terrain, this method showed poor results. On the half-sphere synthetic dataset (Figure 8), this method could not detect a peak, but instead generated two sets of parallel lines that represented a square-perimeter around the actual peak. The curvature-based method tended to accurately detect only a small portion of the features, though at times—such as in the case of the square pyramid—it was particularly successful. Our proposed method visually seemed to be consistently successful in detecting terrain features that matched those manually detected. From a qualitative or visual standpoint, our proposed method overall outperformed all three other methods. For example, our proposed method was able to identify a peak in the synthetic datasets (Figure 7, Figure 8 and Figure 9) and crater lines in the real-word dataset.

For a more quantitative interpretation of the results, we primarily considered evaluation metrics sourced by comparing method results to manually detected lines, assuming this baseline has the highest accuracy/precision. Looking at synthetic dataset results (Table 1), our proposed method more often resulted in the highest evaluation metric values, suggesting it outperforms or is at the very least competitive against, other comparable methods. In one instance, for a synthetic square pyramid (Figure 9), the proposed and curvature methods both precisely identified four ridges. The geomorphon approach identified ridges in every other pixel and the probabilistic method identified what should have been a 1-pixel width linear feature as having a 3-pixel width. On more complex synthetically generated ridge systems (Figure 10 and Figure 11), the proposed, probabilistic, and geomorphon methods were able to identify all known features. On the other hand, the curvature-based method failed to detect more rounded topographic ridges, likely a result of a limiting threshold value, which in this case is a multiple of the curvature’s standard deviation. For the curvature-based method, more rounded ridges/peaks resulted in a wider line or larger circle representing the detected features. In the half-sphere example (Figure 8), the curvature-based method completely failed to detect the peak. That is why Cohen’s Kappa coefficient is so close to 0 (Table 1). It should be noted that we used the multiplication of the curvature’s standard deviation as a threshold to automatically detect linear terrain features. The threshold value is sensitive to the smoothing filters because smoothing decreases noise in the DTM that affect the derivative values of the DTM [20]. For complex real-world data, an optimal threshold value is usually determined through a manual process where the value is iteratively selected and compared either visually or by checking against a known dataset; this process was used in [22,56,65], and showed that an optimal threshold value is achieved by two times the curvature’s standard deviation.

For the real-world datasets (Figure 13, Figure 14, Figure 15 and Figure 16), the curvature-based method resulted in the highest Cohen’s Kappa coefficient, accuracy, and precision (Table 3); however, the proposed and probabilistic methods both had values in a narrow range from the curvature-based results. This suggests that the curvature-based, probabilistic, and proposed methods all perform similarly and that the geomorphon results include far too many poorly detected (incomplete), and false-positive terrain features. While synthetic data allows for known terrain features, real-world data has many unknowns that were overcome assuming superior accuracy and precision from manual detection. If we accept that manually detected topographic features have the highest accuracy and precision, then the curvature-based approach is likely the best method for detecting terrain features, though the proposed and probabilistic approaches are close seconds. From Figure 7, Figure 9, Figure 11 and Figure 15, we can observe that for some shapes the curvature-based and probabilistic approaches generate thicker lines in comparison with the proposed approach or geomorphon. Since we used the manually collected lines, which are thin lines, to evaluate the results of the lines detected by the four methods, those methods whose outputs are thick lines overlap better with the results of the manually collected lines. This might be a reason why the curvature-based and probabilistic approaches have a slightly higher Cohen’s Kappa coefficient. However, if we do not make this assumption, then the results of the synthetic data are more appropriate for determining the best performing method, which in this case would be the proposed method. Additionally, we must consider the downside to requiring threshold values, which are required for the curvature method, but not for the proposed method. Considering factors presented in Table 5, as well as our qualitative evaluation, the proposed method is a robust approach to detecting terrain features (ridges, spurs, cliffs, and peaks) that does not extract false-positive terrains, and can effectively differentiate terrain features, that is competitive, if not better, than existing methods.

The proposed method detects ridges and peaks as well as those detected by the geomorphon method. The main difference between the two methods is that the proposed method can detect spurs with higher accuracy than the geomorphon method can (Figure 17). The high accuracy of detecting spurs with the proposed method is possible by removing the detected features that do not persist under slight azimuth change. We experimented with several azimuth values (Figure 18 and Figure 19). From the experiment, we discovered that if we do not implement slight azimuth change, we get spur lines that are identical to the spur lines detected by the geomorphon method (Figure 7 and Figure 16).

To test the computational complexity of the proposed method we generated synthetically 100 $\ast$ 100, 1000 $\ast$ 1000, and 10000 $\ast$ 10000-pixel DTMs. We conducted our experiments using a workstation with 3.2-GHz Intel Core i5 PC with 16 GB of RAM. The curvature-based method includes the time of running the curvature tool, acquiring standard deviation, and reclassification based on the threshold value. The geomorphon method includes the time of only running the geomorphon tool. The algorithm for the probabilistic method was re-implemented from the article [22]; this method is complex and includes time of running aspect and slope tools [24] and time of running Python code that selects slope and aspect values on neighboring pixels. The algorithm for the proposed method includes the time of running the shaded relief tool, reclassification, and selective filters for detecting ridges, spurs, peaks, and cliffs.

Table 6. Time performance of each method in seconds.

Method	100 × 100 pixels	1000 × 1000 pixels	10000 × 10000 pixels
Curvature	1.21 s	1.34 s	15.76 s
Geomorphon	2.24 s	4.67 s	248.07 s
Probabilistic	12.047 s	1519.23 s	39,936.44 s
Proposed	0.123 s	3.906 s	396.518 s

shows that the proposed method performs faster than the other methods for a small (100 $\ast$ 100) number of pixels. For a moderate number of pixels (1000 × 1000), the curvature method is fastest followed by the proposed and geomorphon methods. The proposed method is one of the slowest for large numbers of pixels (10000 × 10000), except for the probabilistic method.

7. Conclusions

The detection of terrain features has many applicable uses and plays a key role in our learning of land surface architecture, identification of geologic structures, and geomorphological processes that change the surface over time. Precise detection of terrain features from widely available and accurate terrain information is a challenging process and has a high degree of uncertainty. To solve this problem, the majority of research is focused on numerically identifying or classifying terrain features using DEMs and their derivatives. Then, usually, the accuracy of identified terrain features is manually evaluated using shaded relief. Humans perceive and interpret information about terrain features using perceptual cues (elements of image interpretation) such as light angle, shadows, patterns, and texture. A shaded relief distinctly shows these cues, and it can be used as a visual representation of topography. By using perceptual cues such as light angle, shadows, patterns, and texture on shaded relief, researchers can manually examine and identify terrain features. Our proposed method automatically detects terrain features using shaded relief by controlling altitude and azimuth of the illumination source and by applying spatial filters and does not require thresholding values. The qualitative and quantitative evaluation of our proposed method results, as well as the results of the three most common detection methods, show that it has similar performance in some cases and better performance compared with current ridge detection methods. Considering that the proposed method consists of several tasks, future work is to analyze the potentiality to vectorize or parallelize each task and then create an efficient geospatial tool.