Automatic Identification and Mapping of Cone-Shaped Volcanoes Based on the Morphological Characteristics of Contour Lines

Abstract

Cone-shaped volcanoes have important research significance and application value due to their typical cone shape and unique structural features. The existing methods for recognizing volcanoes are mainly morphological feature matching and machine learning. In general, the former has low recognition accuracy, while the latter requires a large number of training samples. The contour lines of cone-shaped volcanoes are distributed in concentric circles. Furthermore, from the center outwards, the elevation of the contour lines increases first and then decreases. Based on the morphological characteristics of cone-shaped volcanoes and the Hough transform algorithm, the main algorithm includes (1) preliminary filtering of contour lines, (2) filtering circular contour lines based on random Hough transform, (3) grouping contour lines based on contour trees, (4) recognizing cone-shaped volcanoes based on concentric-circle contour lines, and (5) automatically mapping cone-shaped volcanoes. Case studies demonstrate the effectiveness of this method for detecting cone-shaped volcanoes in the Western Galapagos shield volcanoes and the Mariana Trench submarine volcano group. The proposed algorithm has low missed and false alarm rates, which is basically consistent with the manual recognition results. This method can effectively automatically recognize cone-shaped volcanoes and cone-shaped landscapes and is a powerful means to support deep-space and deep-sea exploration.

1. Introduction

Cone-shaped volcanoes have important research significance and application value in tourism and geographical environments due to their typical cone shape and unique structural features [1,2]. Furthermore, volcanic mapping is an important task of geomorphology [3]. However, the traditional method for volcanic surveying and mapping based on field exploration is inefficient and time-consuming [4]. With the development of remote sensing technology, it is possible to map volcanoes by visual interpretation of remote sensing images [5,6,7,8]. However, manual interpretation is time-consuming, costly, and subjective [9,10]. The manual interpretation is valid only for a small number of volcanoes. It is limited when the number of volcanoes is large, such as in the survey and mapping of underwater and planetary volcanoes [11].

Therefore, automatic algorithms for volcano recognition and delimitation have become a research focus, and the methods are mainly divided into two types: morphological feature matching and machine learning. The former mainly uses the morphological features of volcanoes in remote sensing images or digital elevation models (DEM) [12], including the morphometric characterization of volcanic edifices [9,10], visual morphometric characterization [13], and spectral and textural signatures [14]. Additionally, the algorithm is efficient. With remote sensing images of Venus, Wiles and Forshaw [11] used a template matching method to identify volcanoes. However, this method only considers the two-dimensional morphological features of volcanoes in remote sensing images; the recognition efficiency is low, and the accuracy is not high. In addition, when the volcanic cone is formed on very rough terrain, the automatic delineation of the boundary of the volcanic cone may be affected by the irregular terrain [10]. Cao et al. [15] proposed an automatic recognition method for cone-shaped volcanoes using a DEM matching template. Due to a large amount of data and a lack of apparent topological information in DEM, the algorithm has low applicability, and it is challenging to identify submarine volcanoes.

Machine learning can automatically improve the accuracy of identifying volcanoes through experience. This recognition method is mainly divided into supervised and unsupervised learning methods, including support vector machine [16], genetic [17], object-oriented [18], artificial neural network [19], and other algorithms [20,21]. Machine learning can deal with more complex cases, and with more training samples, the recognition accuracy is improved [22,23]. For example, Burl et al. [22] used machine learning to recognize the volcanoes on Venus using remote sensing images. The recognition was as good as a trained human observer. However, this method requires high quality and a large quantity of training set, and the workload to collect and sort samples is heavy.

The recognition methods based on morphological features fail to consider the three-dimensional morphology, spatial structure, and other features of volcanoes and are prone to misjudgment. Although the accuracy of machine learning algorithms will continuously improve with the increase of training samples, it requires a lot of time for model training, which has certain limitations in practical applications. In addition, the data sources for these two kinds of recognition methods are mostly based on quality remote sensing images or DEM. Although it is convenient to obtain, the data volume is large and has certain limitations when used for large-scale recognition.

In the field of geomorphic recognition, a general trend is to use contour lines and multi-dimensional features to identify geomorphic features, which have the advantages of high efficiency and high accuracy [24,25,26,27,28,29]. The closed-contouring approach is one of the representative methods [24]. The method, using multi-dimensional features, considers not only the morphological features of landforms but also composite features such as spatial structure and statistical features, which can identify specific landforms with a lower probability of false detection. For example, Wang et al. [26] developed a method for automatically extracting lunar craters based on analyzing the relationships of contour lines and the accurate matching of crater morphological characteristics. Compared with the method based on remote sensing images and DEM, this method has better accuracy, stability, and real-time performance. Lunar craters are similar in shape to volcanic craters, and the automatic recognition of lunar craters has a high reference value for cone-shaped volcano recognition. Volcanoes are concentric structures of satellite images. The characteristics of volcanoes are well summarized by contour. Therefore, our proposed algorithm uses the spatial structure and statistical characteristics of the contour data to identify volcanoes.

The main contribution of this paper are as follows: Given the apparent characteristics of cone-shaped volcanoes in contour lines, this paper intends to propose an algorithm for automatically detecting and mapping cone-shaped volcanoes from contour lines. The Hough transform of vector data and the contour tree grouping make the algorithm fast and effective. Furthermore, the method has low missed and false alarm rates, which is consistent with the results of manual recognition.

This paper is organized as follows: Section 2 presents the methodology, Section 3 presents the experimental results, Section 4 discusses the stability and applicability of the method, and Section 5 gives the conclusions.

2. Methodology

The automatic identification of volcanoes mainly includes the following steps: (1) preliminary screening of contour lines, (2) recognition of circular contour lines based on the random Hough transform, (3) grouping of concentric contour lines using contour trees, (4) cone-shaped volcano identification based on concentric contour lines, and (5) automatic mapping of cone-shaped volcanoes. Figure 1 shows a flow diagram illustrating the method.

2.1. The Outline of Research Area and Applicability

In order to verify the validity of the algorithm, two study areas were selected to represent terrestrial and submarine volcanoes. Both are located in the Pacific Ring of Fire, a region around much of the rim of the Pacific Ocean where many volcanic eruptions and earthquakes occur. The first is Isabela Island (Figure 2 study area 1), part of the Republic of Ecuador. All volcanoes have distinct cones and craters. Therefore, it can represent the terrestrial volcanoes mentioned in Section 2.3.

Another study area is the Mariana Trench (Figure 2 study area 2), an oceanic trench located in the western Pacific Ocean, about 200 km east of the Mariana Islands. There are many submarine volcanoes in the Mariana Trench, which do not have apparent craters. It can represent the submarine volcanoes mentioned in Section 2.3.

2.2. Input Data

Standardizing input data is of great significance for effectively identifying cone-shaped volcanoes. In this paper, cone-shaped volcanoes are recognized according to the shape characteristics of contour lines, and the input data is the vector data of contour lines in shapefile (.shp) format.

When there is no available contour line data, the DEM data of the study area can be downloaded, and the contour layer can be generated from the DEM. If there are holes or missing data in the DEM, the data must be repaired first. The specific requirements for generating contour lines are as follows:

1.

The contour interval should not be too small, as that will increase the calculation workload. It highly depends on the type and size of the studied volcano. According to the experimental results, it is generally appropriate to set the range between 50 m and 300 m;

2.

The features of contour lines should include elevation attributes;

3.

The contour lines need to be processed by a smoothing operation. Contour lines are shown as broken line segments, which are stiff at corners and topographic changes. In order to make the contour line meet the visual requirements of being smooth and appropriate, it is necessary to smooth the contour line. Besides, the algorithm’s efficiency is mainly focused on the Hough transform. Compared with the original contour lines, smoothed contour lines can improve the efficiency of the Hough transform.

2.3. Characteristics of Cone-Shaped Volcanoes

The characteristic analysis is the basis and premise of cone-shaped volcanoes identification. A cone-shaped volcano is a volcano with a cone-shaped crater mainly composed of basalt and andesite basalt. The crater of a volcano is a basin-like depression over a vent at the summit of the cone, which is large at the top and small at the bottom. It is often funnel-shaped or bowl-shaped and is the outlet for volcanic material. The craters are generally less than 200–300 m in depth and less than 1 km in diameter [30].

For the contour line layer, the cone-shaped volcano usually has the following morphological features (Figure 3):

1.

The contour lines of the cone-shaped volcano are usually a group of closed contour lines, approximately distributed in concentric circles;

2.

For terrestrial cone-shaped volcanoes, from the center outwards, the elevation of the contour lines first increases and then decreases because of the crater. For the submarine volcano, we can also call it a seamount. It is technically defined as an isolated rise in elevation of 1000 m or more from the surrounding seafloor, with a limited summit area, of the conical form [31]. A seamount does not have an obvious crater, and its elevation monotonically increases from the outside to the inside;

3.

The aspect ratio of the minimum bounding rectangle (MBR) is close to 1, usually within the interval [0.8, 1].

2.4. Preliminary Filtering of Contour Lines

Using the closed characteristics of cone-shaped volcano contour lines, the area threshold, and the aspect-ratio threshold of MBR (defined by the user), many irrelevant contour lines can be quickly removed by filtering contour lines, which can greatly improve the efficiency of the algorithm. The area threshold depends on the closed area of the minimum volcanic contour in the study area.

The specific steps for filtering contour lines are as follows: Firstly, the unclosed contour lines are eliminated. Secondly, according to the delineation area of the contour lines, contour lines larger than the area threshold are selected. Finally, according to the aspect ratio of the MBR, the contour lines that obviously do not meet the shape characteristics of cone-shaped volcanoes are deleted.

2.5. Circular Contour Line Recognition Based on Random Hough Transform

2.5.1. Random Hough Transform

The Hough transform (HT) is a common feature-detection algorithm in image recognition. It is widely used in recognizing straight lines, triangles, and circles [32]. The classical HT is widely used for its robustness and accuracy. However, the algorithm has the following disadvantages: high computational consumption, low detection accuracy, vulnerability to noise, and the possibility of missing objects [33].

At present, the improved HT mainly focuses on reducing memory consumption and improving timeliness, the random Hough transform (RHT) manages to considerably overcome these shortcomings. The algorithm can map any n points in the space to the Hough parameter space. Once the count of a point in the Hough parameter space reaches the threshold, the shape can be extracted. This algorithm reduces memory consumption because it does not need to prepare the Hough parameter space (generally, the linked list structure is used to store data) and can overcome the shortcomings of the classical HT by improving computation speed. Xu and Oja’s [34] experiments indicated that the computation efficiency of the RHT is 80 times that of the HT.

The basic idea of circle recognition using RHT [35] is as follows (Formula (1)): firstly, three non-collinear edge points($d_1$, $d_2$, $d_3$) are randomly selected in the image space. Then, they are transformed into a point in the parameter space by mapping ((x, y) to ($X_0$, $Y_0$, radius)),and the number of points in the parameter space is accumulated circularly. Finally, the number of accumulated points in the parameter space is compared; if it is more than the threshold, it is a true circle.

$$\left\{\begin{array}{c}({(x-X_0)}^2+{(y-Y_0)}^2=radiu{s}^2\hfill \\ d_1=(x_1,y_1)\hfill \\ d_2=(x_2,y_2)\hfill \\ d_3=(x_3,y_3).\hfill \end{array}\right.$$

(1)

2.5.2. Circular Contour Line Recognition Based on RHT

The contour lines of cone-shaped volcanoes are approximately a group of concentric circles, and the circles can be accurately identified by using the RTH. To verify the automated extraction algorithm of volcanoes, we developed software for the automatic recognition and mapping of cone-shaped volcanoes. The proposed methodology is the core module of the desktop program, which can be freely downloaded at https://github.com/Vencent6666/SGEDSystem.git (accessed on 17 December 2022). The algorithms were implemented using C# and Visual Studio 2017. The specific processing steps are as follows:

1.

Take any contour line $l{o}_i$ from the contour line set L, get all the points of $l{o}_i$, and put them into the point set P = $p_j$ | j = 0, 1, ⋯, m−1, where m is the point number of contour line $l{o}_i$;

2.

Randomly select three points from P, marked as $p_1$, $p_2$, and $p_3$, respectively. The three degrees of freedom ($X_0$, $Y_0$, radius) of the RHT are calculated according to Formula (2):

$$\left\{\begin{array}{c}{X}_0=(b\ast f-d\ast e)/(b\ast c-a\ast d)\hfill \\ Y_0=(c\ast e-a\ast f)/(b\ast c-a\ast d)\hfill \\ radius=\sqrt{{(p_1.x-X_0)}^2+{(p_1.y-Y_0)}^2}\hfill \end{array}\right.,$$

(2)

where a = $p_1$.x − $p_2$.x, b = $p_1$.y − $p_2$.y, c = $p_1$.x − $p_3$.x, d = $p_1$.y − $p_3$.x, and e and f are calculated according to Formulas (3) and (4), respectively:

$$e=({(p_1.x)}^2-{(p_2.x)}^2-{(p_2.y)}^2+{(p_1.y)}^2)/2,$$

(3)

$$f=({(p_1.x)}^2-{(p_3.x)}^2-{(p_3.y)}^2+{(p_1.y)}^2)/2,$$

(4)

3.

Organize related parameters into a tuple hc (Formula (5)). If there is no element in a tuple set HC, store it in a tuple set HC = {$h{c}_k$ | k ∈ N} and go to Step 7:

$$hc=\{X_0,Y_0,radius,Poi,cnt\},$$

(5)

where $X_0$, $Y_0$ is the center point coordinate of the circle, radius is the radius of the circle, Poi = $p_1$, $p_2$, $p_3$ is the set of points on the current circle, and cnt is the count of the parameter group hc in the HC;

4.

Traverse the set HC. If an element $h{c}_k$ matches condition 1, then $h{c}_k$.cnt = $h{c}_k$.cnt + 1, and $p_1$, $p_2$, $p_3$ are assigned to $h{c}_k$.Poi. Otherwise, save hc into set HC and go to Step 7.

Condition 1: (hc.$X_0$ ∈ ($h{c}_k$.$X_0$ − $T{h}_3$, $h{c}_k$.$X_0$ + $T{h}_3$)) & & (hc.$Y_0$ ∈ ( $h{c}_k$.$Y_0$ − $T{h}_3$, $h{c}_k$.$Y_0$ + $T{h}_3$)) & & (hc.radius∈ ($h{c}_k$.radius − $T{h}_4$, $h{c}_k$.radius + $T{h}_4$)). where $T{h}_3$ and $T{h}_4$ are the preset threshold values of the circle center and radius. The symbol hck.() represents the corresponding members in $h{c}_k$;

5.

If $h{c}_k$.cnt > $T{h}_5$ (Hough transform threshold), go to Step 6; otherwise, go to Step 7;

6.

If the number of points of $h{c}_k$.Poi > $T{h}_6$ (the minimum number of true circle points) ($T{h}_6$ ∈ [3,3*$T{h}_5$]), the contour line is stored in the circular contour line set L1; $h{c}_k$.$X_0$, $h{c}_k$.$Y_0$ and $h{c}_k$.radius are stored in the circular parameter set $parm$ as the parameter set of the contour line, and the algorithm ends. Otherwise, $h{c}_k$.cnt = 0;

7.

Repeat Step 2 to Step 6 until the number of elements in HC > $k_{max}$. Where $k_{max}$ ≈ (10∼100) × $m^3$ /($n_{min}^3$ ) [36] and $n_{min}$ is the minimum number of points of a true circle. In this paper, to simplify things, $n_{min}$ = 0.8 × m, meaning the true circle has 80% of its contour line points.

2.6. Concentric Circle Contour Line Grouping Based on Contour Trees

A contour tree is a data structure used to represent the spatial topological relationship of contour lines. The topological relationship mainly includes the inclusion relation and adjacency relation [37,38,39]. The construction process of a contour tree is the process of grouping contour lines. The construction of a contour tree can quickly find a group of concentric contour lines and get the topological relationship of contour lines. In this paper, the contour tree can easily compare elevations and count the number of cone-shaped volcanoes. It is the basis for the identification of volcanic cones.

This paper develops a method to group concentric circle contour lines based on the contour tree. The specific steps are as follows (Figure 4):

1.

From largest to smallest, successively store each contour line in the set L1 in the set S = $s_j$|j = 0, 1, 2, ⋯, v−1, where v is the number of circular contour lines in the set L1;

2.

Traverse the set L1 and obtain each circular contour line’s center point p ($par{m}_i$.$X_0$, $par{m}_i$.$X_0$). If there is a circular contour line within the MBR of $l{1}_{smax}$ (initially, it is the circular contour line with the largest area in S), assign it to the temporary circular contour line group $c_{temp}$. Update $l{1}_{smax}$ and continue to traverse;

3.

If the number of circular contour lines in $c_{temp}$ is greater than 1, the contour lines in $c_{temp}$ are sorted in descending order according to the delineation area and stored as a subset in set C. Remove the delineation area corresponding to elements in $c_{temp}$ from S;

4.

Repeat Steps 2 and 3 until S is empty, and get the grouping result (as shown in Figure 5).

2.7. Cone-Shaped Volcano Recognition Based on Concentric Contour Lines

Cone-shaped volcanoes can be identified based on whether the elevation of the contour lines follows the rules of “increase first and then decrease” or “gradually increase”. The degree of membership evaluated on the interval (0,1) was used to characterize the degree to which x belongs to A (x is the identified crater and A is the actual crater) [40]. If a volcano follows the rule of “increase first and then decrease”, it can be marked as a high degree of membership. Some submarine volcanoes, with no apparent craters, follow the “gradually increase” rule, which can be marked as a low degree of membership.

2.8. Cone-Shaped Volcano Mapping

According to the position information and attributes of the volcano, a cone volcano can be automatically mapped, which has important application value for tourism, engineering site selection, and natural resource exploration. The mapping of cone volcanoes mainly involves determining the geographical scope of volcanoes and calculating the related attributes.

First, the geographical scope of each cone-shaped volcano can be approximately regarded as a circular area centered on the crater. Therefore, the circle contour line with the largest area in each group can be regarded as the geographical scope of the cone-shaped volcano (Figure 6).

Second, according to the geographical range of cone-shaped volcanoes, we can further calculate the perimeter, height, radius, overall area, profile shape, the slope of the edifice, and other attributes of each cone-shaped volcano [9]. The meanings and calculation methods of the related attributes are shown in the following

Table 1. Properties of cone volcanoes.

Name	Meaning	Computing Method
Perimeter	The perimeter of a volcano’s outline	The perimeter of the largest contour line in each group is approximated to the perimeter of the cone-shaped volcano
Height	Maximum and minimum elevation difference of a volcano	The height difference between the maximum area and the maximum elevation contour line in each group is approximated as the cone volcanic height difference (Figure 7)
Radius	The near circle radius of the volcanic profile	The radius of the Hoff circle of the largest contour line in each group is approximately the radius of a conical volcano
Maximum Area	The area of the volcanic profile	The area of the largest contour line in each group is the largest area outside the cone-shaped volcano
Profile Shape	The height–width ratios	The height/basal width ratio (H/WB) is an estimate of the overall steepness of the edifice [9] (Figure 7)

.

3. Case Studies

3.1. Case 1: Isabela Island Volcano Group

3.1.1. Study Area and Data

The Isabela Island volcano group (Galápagos Islands) is located in the Pacific Ocean 1000 km west of the South American continent. It was formed by repeated volcanism. There are tall volcanoes on the island; the highest is Wolf Volcano (1707 m), and the second highest, Azul mountain, is an extinct volcano (1689 m). Most of the islands have a typical cone shape, which is often associated with volcanic activity. The largest island, Isabela, is made up of six volcanoes. Due to limited DEM data, the experimental area is located from longitude of 90°19${}^{\prime }$11${}^{″}$ W to 91°41${}^{\prime }$4${}^{″}$ W, latitude of 0°12${}^{\prime }$11${}^{″}$ N to 0°55${}^{\prime }$46${}^{″}$ S. There are five conical craters in the island volcano group (Figure 8a).

The experimental data from this study area is from 12.5 m resolution ALOS DEM (Figure 8a). It can be downloaded for free from https://search.asf.alaska.edu/#/ (accessed on 17 December 2022 ). The contour lines of the experimental area were extracted by ArcMap 10.6 (Figure 8b) and smoothed by Polynomial Approximation with Exponential Kernel (PAEK) algorithm [41], with a contour interval of 50 m. The geographic coordinate system of the data was WGS1984, and the projection was Transverse_Mercator.

3.1.2. Evaluation of Experimental Results

To verify the effectiveness of this method, we overlaid the recognition results on the contour line data of the experimental area and compared it with the results of expert visual interpretation.

In this experiment, the high degree of membership and low degree of membership was set to 0.9 and 0.8, respectively. The closer the degree of membership is to 1, the higher the possibility that identified crater belongs to the actual crater. The closer it is to 0, the lower the possibility that identified crater belongs to the actual crater.

In this paper, the standard missed alarm rate (MAR) and the false alarm rate (FAR) was used to quantitatively evaluate the effectiveness of the identification results [42].

$$MAR=nMAD/nED\times 100\%,$$

(6)

$$FAR=nFAD/nAD\times 100\%,$$

(7)

where nMAD is the number of cone-shaped volcanoes missed by our proposed algorithm, nED is the number of cone-shaped volcanoes identified by experts, nFAD is the number of cone-shaped volcanoes mistakenly detected by our proposed algorithm, and nAD is the number of cone-shaped volcanoes detected by our proposed algorithm.

The recognition results of this case are shown in Figure 9a, which are compared with the results of expert interpretation (Figure 9b). The experts identified volcanoes using some extra data, such as the picture of the research area, geological survey report, and experience. The result can almost be regarded as actual. The method of this paper correctly identified five volcanoes. The MAR and FAR in this case, are both 0%. The experiment results are shown in Figure 10.

3.2. Case 2: Submarine Volcanoes in the Mariana Trench

3.2.1. Study Area and Data

This study area, between the coordinates 142°50${}^{\prime }$19${}^{″}$ E, 19°5${}^{\prime }$40${}^{″}$ N and 145°42${}^{\prime }$22${}^{″}$ E, 22°38${}^{\prime }$44${}^{″}$ N, is located in the northeastern Mariana Trench, where the plate subduction is very active. Many submarine volcanoes rise from a seafloor of 1000–4000 m in depth [43]. Most of the volcanoes have no typical crater, and the elevation of the contour lines increases monotonically. According to NOAA Pacific Marine Environmental Laboratory(PMEL) Earth-Ocean Interaction Program exploration results (https://oceanexplorer.noaa.gov/explorations/03fire/welcome.html, accessed on 17 December 2022), there are 10 conical volcanoes in the test area (Figure 11).

The experimental data of this case were derived from the DEM generated by the bathymetric data, which was downloaded from the International Hydrographic Organization’s Data Centre (https://www.ncei.noaa.gov/maps/autogrid/, accessed on 17 December 2022). The data was obtained by sonar detection, but there are holes in the generated DEM. The undefined cells were filled with the ETOPO1 global relief model. The DEM data before and after background filling is shown in Figure 12a,b. The experimental data of this study area is 250 m resolution DEM, and the interval of the extracted contour lines is 250 m (Figure 11). The geographic coordinate system of the data is WGS1984, and the projection is World Mercator.

3.2.2. Evaluation of Experimental Results

The recognition results of this case are shown in Figure 13a. Compared with the results of expert interpretation (Figure 13b), the method of this paper correctly identified eight volcanoes, misidentified two volcanoes, and missed two volcanoes. The MAR and FAR in this case were 20%. The experiment result are shown in Figure 14.

Some reasons might have caused the high MAR and FAR. Some submarine volcanoes do not have a typical conical shape, and some rise from a seafloor, becoming an island. Those reasons affect the algorithm’s ability to identify volcanoes correctly. However, there are estimated to be 40,000 to 55,000 seamounts in the global oceans [44]. Most of them have not been named or explored. Some unnamed submarine volcanoes were identified, most of which are not marked on maps.

4. Discussion

4.1. Stability of the Method

The algorithm uses RHT to identify circular contour lines with certain randomness. The results will be slightly different even if the parameters are the same.

In this paper’s automatic identification of cone-shaped volcanoes, the main factors affecting the identification result are area threshold, MBR aspect ratio threshold, Hough transform threshold, true circle minimum number, contour interval, the threshold of the center, and radius. Among them, the parameters affecting the algorithm’s efficiency are the area threshold and the MBR aspect-ratio threshold. Users set the value according to the application requirements to improve the algorithm’s efficiency. The parameters that affect the accuracy of the results are the center threshold $T{h}_3$ and radius threshold $T{h}_4$. $T{h}_3$ and $T{h}_4$ are the thresholds of the center and radius; that is, the center and radius are regarded as the same value within a specific error range and can be set by themselves according to the contour line shape. Generally, it can be set as 1% of the map unit. For example, if the map unit is 1 km, the tolerance is set to 10 m.

The parameters that affect the accuracy of recognition results are (1) Hough transforms threshold $T{h}_5$, (2) the minimum number of true circles $T{h}_6$, and (3) contour interval. The following sections discuss these parameters, which greatly influence the accuracy of recognition results.

4.1.1. Contour Interval

Under the condition that all parameters remain unchanged, only the interval between contour lines is changed, and the different recognition results are shown in Figure 15.

The experimental results show that the larger the contour interval, the fewer the number of identified cone-shaped volcanoes, the higher the miss detection rate, and the lower the false detection rate. On the contrary, contour lines that are too dense also have a certain impact on recognition efficiency. The best interval will depend on the type of volcano, its size range, and the type of DEM. According to the experimental results, it is relatively appropriate to set the contour interval between 50 m and 300 m.

4.1.2. Threshold of the Hough Transform

The following comparative experiments were carried out using the experimental data from Case 2. The area threshold, the length-width ratio threshold of MBR, the center threshold, the radius threshold, and the minimum number of true circles were always equal to 0.001, 1.2, 0.2, 0.2, and 7, respectively. The threshold values of the Hough transform were set to 4, 7, 10, 13, 16, 19, and 22, respectively. The experimental results are shown in Figure 16a.

The experimental results show that the larger the threshold value of the Hough transform, the closer the shape of the extracted cone-shaped volcano is to a circle. Changing the threshold has little effect on the number of identified volcanoes. When the threshold value of the Hough transform reaches a specific value, MAR and FAR tend to be stable.

4.1.3. Minimum Number of True Circle Points

The following comparative experiments were carried out using the experimental data from Case 2. The area threshold, the length-width ratio threshold of MBR, the center threshold, the radius threshold, and the Hough transform threshold were always equal to 0.001, 1.2, 0.2, 0.2, and 7, respectively. The threshold values of the minimum number of true circle points were set to 4, 7, 10, 13, 16, 19, and 21, respectively. The experimental results are shown in Figure 16b.

The experimental results show that when the minimum number of true circles is relatively large, it will identify fewer volcano cones and lead to a higher MAR and lower FAR. According to the experimental results, it is relatively appropriate to set the minimum number of true circles between 3 and 7.

4.2. Applicability of the Method

The results show that the proposed method can identify the typical conical volcano, which is basically consistent with the expert identification results. However, for cone-shaped volcanoes that have been eroded by external forces for a long time and do not have complete craters, such as eroded dormant volcanoes, extinct volcanoes, and collapsed ancient calderas, the recognition effect will be affected. Moreover, for a small cone-shaped volcano with slight fluctuation, the contour interval greatly influences the recognition effect. Especially in the submarine volcano identification, the method is limited by the data quality of the seabed DEM.

Although the algorithm proposed in this paper is designed for conical volcanoes, it cannot directly identify non-conical volcanoes (such as shield volcanoes). However, the morphological characteristics of contour lines based on this paper can also be applied to identifying non-conical volcanoes. For example, the main distinguishing features of shield volcanoes are that the contour lines are closed and circular, and the contour elevations gradually increase from the outside to the inside, etc. The proposed method can also identify shield volcanoes by adjusting the relevant identification rules and parameter thresholds.

The recognition algorithm of this paper can be used to identify cone-shaped landforms, such as craters, sinkholes, stone peaks, stone forests, etc. Furthermore, the method has a reference value for recognizing the geomorphic types with apparent morphological features, such as dunes, domes, etc. Further work can be extended by adding new cone-volcano characteristics, such as height difference, slope, and aspect.

4.3. Comparison between the Proposed Algorithm and the Raster Image Algorithms

The circular Hough transform method using raster images has a good recognition effect on craters and a good recognition effect on discontinuous edges [20]. However, the difficulty is that the computational and memory requirements of the Hough transform grow exponentially as the number of parameters increases.

Compared with raster image/DEM, the algorithm proposed in this paper uses contour data to identify volcanoes. This method mainly has the following features: firstly, contour data contain not only the morphological characters but also composite features such as spatial structure and statistical features; secondly, compared with remote sensing images, the data value of contour is less, performs more efficiently, and is suitable for large-scale recognition, which can avoid the omission of volcanoes at the boundary during DEM segmentation recognition; finally, the RTH method does not need to prepare Hough parameter space and has low memory consumption.

5. Conclusions

Given the problems of low efficiency, difficulty in large-scale identification, and low availability of existing methods, an automatic identification and mapping method of conical volcanoes based on HT was proposed. The advantages of this algorithm are as follows: first, considering the three-dimensional shape characteristics of conical volcanoes and avoiding the impact of data segmentation on volcanic integrity, this method has high accuracy; secondly, using contour line data, which is smaller than traditional remote sensing images and DEM, the algorithm has higher execution efficiency and can be used for volcano identification on a larger scale. Experiments on the Isabella volcano group and the Mariana Trench submarine volcano group demonstrate that the proposed algorithm has a low missed alarm rate and low false alarm rate, which is basically consistent with the results of expert recognition.

The method of this paper has practical value for the automatic recognition of cone-shaped volcanoes. It can also be applied to the automatic recognition of cone-shaped landforms, such as craters, sinkholes, stone peaks, and stone forests. The method presented in this paper is a powerful means to support deep-space and deep-sea exploration and has great significance for the volcanic exploration of the seabed and other planets.