Landforms are the result of geologic and geomorphologic processes that occur on the surface of the Earth and other planets (Bolongaro-Crevenna et al., 2005). Accurately collecting and processing information about landforms is necessary for landscape evaluation, hazard prediction, suitability and erosion studies, as well as various landscape and regional planning (Drăguţ and Blaschke, 2006). Consequently, mapping landforms on the surfaces of planets at broad spatial scales is becoming increasingly important; easily accessible digital elevation model (DEM) data has led to the development of a growing number of automated landform mapping techniques that utilize remote sensing (RS) and geographic information system (GIS) approaches (Butle and Walsh, 1998; Florinsky, 1998; Ehlers et al., 2002).

One pixel in a DEM encapsulates an elevation value vector as well as other extractable measures that relate to basic components of terrain, including slope, aspect, convexity, and relief amplitude. It is also expected to be the case that pixels constituting a particular landform will encapsulate similar terrain vectors; these vectors are considered to be similar if the Euclidean distance between them is small (Giles and Franklin, 1998; Miliaresis, 2001; Bue and Stepinski, 2006). Thus, landform classification can be achieved by applying a clustering algorithm across all attribute vectors to determine their exclusive similarity at a given site. Enabling these comparisons is the true value of a DEM and the essence of the classification method.

A range of manual methods was used in the past to classify macro-morphologic landforms from contour maps or stereo aerial photographs. However, as these approaches are relatively time-consuming and generate results that depend on subjective decisions made by the interpreter, they are less suitable for the efficient analysis of large datasets. Thus, a series of automated methods has been developed to identify individual terrain features; physical characteristics can be extracted from a DEM using a variety of methods including the combination of morphometric parameters like slope gradient, local convexity, and surface texture (Iwahashi and Pike, 2007), as well as fuzzy logic and unsupervised classification (Burrough et al., 2000; Adediran et al., 2004), supervised classification (Hengl and Rossiter, 2003; Prima et al., 2006), probabilistic clustering algorithms (Stepinski and Collier, 2004; Stepinski and Vilalta, 2005), multivariate descriptive statistics (Dehn et al., 2001), and double ternary diagram classification (Bolongaro-Crevenna et al., 2005). Although these methods have been applied to data from other planets, including Mars (Stepinski and Collier, 2004) and the Moon (Wang et al., 2015), they are too specific in the context of their respective fields of application to be successfully adapted for landscape classification over broad spatial scales. In addition, most of these applications are unable to adequately evaluate the characteristics of lunar landforms even though digital computers and GIS methods have removed many of the obstacles inherent to terrain classification based on surface geometry for areas of any size or suitable spatial resolution. We therefore present a method for the automatic classification of morphologic landforms that is based on a DEM within a GIS environment. We utilize ISO cluster unsupervised classification for landform mapping on the Moon based on a series of input raster bands that define six morphologic parameters. We use ISO clustering to automatically classify morphometric features into a series of classes, and assemble the morphometric parameters derived from a DEM to characterize landforms. We discuss the limitations inherent to the use of this automatic classification, and extend this DEM-based approach to map other Moon-like landforms.

The United States Geological Survey (USGS) lunar geologic mapping program divides the Moon into 30 quadrangles (Gaddis et al., 2006). To test our algorithm, we selected three test areas based on these data that include different landforms; thus, LQ-8 is a representative cratered highland area, LQ-11 is a mare region primarily covered with basaltic lava flows, while LQ-20 includes both mare plains and highlands. Each of our sites is almost 10⁵ km² in size (Figure 1); a DEM for each was constructed using the lunar orbiter laser altimeter (LOLA), an instrument mounted on the NASA lunar reconnaissance orbiter spacecraft. More than 6.5 billion LOLA measurements were converted into a DEM (Smith et al., 2010) using generic mapping tools software (Wessel and Smith 2001) at a resolution of 256 pixels per degree. In the Mercator projection, each of these pixels is 118 m in size at the equator; we used the USGS lunar geologic map that includes landform classification attributes as a reference to test our algorithm.

The classification algorithm used in this study includes DEM preprocessing, morphologic parameterization, ISO cluster unsupervised classification, and final landform map (Figure 2). Module implementation was designed to take advantage of publically available software packages in ArcGIS.

The values of topographic attributes averaged over pixels within each landform class for the three test areas are shown in Tables 1, 2, and 3. Average values where then used to construct a dendrogram of landform classes (Figure 3) that summarizes their degree of similarity. In these diagrams, classes that are more similar to one another are more closely connected; thus, Figure 3a shows that, of all possible pairs, class 2 and class 3 are most similar to one another, and also indicates that all 20 classes can be divided naturally into four larger groups which correspond to major landform types, A = (1, 2, 3, 4, 5, 6, 7, 8), B = (9, 10, 11, 12, 13), C = (14, 15, 16), and D = (17, 18, 19, 20). A thematic map constructed on the basis of this landform classification is shown in Figure 4. The different colors on this map denote pixel class membership; a physical interpretation was applied by reviewing the statistical and topographic attributes of pixels comprising each class and by studying their spatial relationships. The legends to Figures 4-6 summarize our interpretations; our results divide the 20 landform classes into five larger groups, encompassing mares, craters, lowlands, areas of highrelief, and highlands. This manual division, which also takes spatial relationships into account, closely corresponds with the algorithmic grouping shown in Figure 3 based only on the Euclidean distances between average attribute vectors.

The results of this study show significant agreement between the results of automated classification and the reference map for the three test areas. Results reveal slightly higher OA and K values in area LQ-11 because just a few simple shaped craters with clear rims and a large area of mare plain are present in this region and are easily recognized. In contrast, OA and K values for area LQ-20 are the lowest because of the relatively complex landform types in this region. Values for UA and PA in the case of crater and mare morphologies are also relatively higher than for other landforms, while UA values for lowlands are also relatively high. The main explanation for these results is that this procedure assumes that craters have steep slopes, while mare plains occur at low elevation, and that lowland and highrelief regions are transitional areas with few distinctive geomorphometric characteristics. However, some old craters that have been heavily eroded can actually be as flat as the surrounding lava plains, while highreliefs that have been partly submerged by subsequent lava flows are also problematic as they cause exposed highrelief units to become less topographically distinct. Similarly, lava flows that have moved down steep highland slopes to form blankets pose a different problem because they form plains but will be classified incorrectly as lowlands (Table 4).

Although visual inspection of the topographies shown on the thematic landform map (Figure 6) reveals that our classification is in close agreement overall with expectations, our automatic classification approach has nevertheless misclassified pixels in some regions because of the effects of aggradation (i.e., effusion and deposition) and degradation (i.e., erosion and deformation). Most of these misclassifications, however, occur on low, flat floors inside craters and on lowlands as the similarity measures we calculated between attribute vectors do not correspond to actual landform similarities. For example, infilling will have occurred within basins just up to the level of the lowest pour point around their edges; thus, a crater with undisturbed walls will have been filled to the rim and thus its internal pixels will be classified correctly, while one with a broken wall will be only partially filled and its internal pixels will be misclassified. Results suggest that the degree of misclassification will depend on the severity of the break; ghosted craters that lack clear boundaries will not be filled at all and so these pixels will be severely misclassified compared to other landscape types. To further discuss this issue, we selected three craters for closer examination, labeled A (3.96°E, 11.4°S), B (2.62°E, 11.9°S), and C (24.79°E, 28.33°S). Local views of these craters are shown in Figures 7a and 7b; the two panels of this figure illustrate the topography of these features via topographic contours superimposed onto thematic landform maps (Figure 7).

Images show that walls have mostly been damaged by erosion or by the superposition of other craters. The local view in Figure 7a shows that the walls of Crater A are broken in the 8 o’clock direction by Crater B. The pour point level is relatively high in this case, which means that most of the pixels on the crater floor are located beneath it and so are assigned to class 3 and class 4. However, some pixels on the rim of Crater B that are also on the flat floor of Crater A are also located below the pour point level and so are assigned to class 5 and class 6 rather than class 15 and class 16. Similarly, for the same reason, the pixels located on the walls of these craters will also be assigned to class 11 and class 12 rather than to class 15 and class 16. The small craters that comprise the deep basin within the flat floor of Crater A will also be assigned to class 1 because of their low elevation and maximal fill.

The local view of Crater C (Figure 7b) shows that this feature is also heavily eroded and has shallow walls that are broken in both 1 o’clock and 7 o’clock directions. The pour point level in this case is also very low, resulting in minimal fill; thus, most pixels in the interior of this crater will be assigned to highrelief class 17 and class 18 because they are located at high elevation. Results show that just a handful of deeper points will be classified as lowland and shallow crater floor within Crater D (25.12°E, 28.61°S) and Crater E (25.49°E, 29.15°S).

This study outlines an ISO cluster unsupervised classification approach for lunar landforms that is based on the hypothesis that each topographic entity on the Moon will be geomorphometrically distinct from the surrounding background. We test this approach using data for three representative lunar areas, LQ-8, LQ-11, and LQ-20. Numerous existing automated extraction approaches aim to identify and extract discrete landforms, including impact craters, valley networks, and other elements, by emphasizing their particular surface shapes; fewer, generically applicable, methodologies are available that evaluate the geometry of continuous surfaces (e.g., the whole lunar surface) and that are founded on statistical characterization. In this study, we have shown that our methodology is applicable by utilizing techniques drawn from the fields of data mining and artificial intelligence and applying them to planetary geomorphology. Thus, automated recognition of landforms can be achieved using our method at the local level of constituent pixels; each pixel in a continuous topography represented by a DEM is automatically classified by our ISO cluster unsupervised classification into one of 20 undefined landform types using the terrain parameters, elevation, filled elevation, slope, filled slope, relief amplitude, and filled relief amplitude. We chose an ISO cluster approach to generate initial groupings because of speed; ISO cluster processing of each DEM took approximately five minutes on a 2.50 GHz Core i3 machine for each test area.

Our results show that while elevation appears to be critical in recognizing highlands, filled elevation is of greater utility in distinguishing craters and mare plains. Subsequent to separating obvious landforms from other topographic features, our procedure then automatically adjusts the sensitivity of its criteria to accommodate subtler surface forms such as lowland and highrelief using filled slope and relief amplitude. In order to ensure statistically robust class definitions, thresholds for subdividing images are arbitrarily set as the mean values of frequency distributions and the signatures of input parameters. We quantitatively evaluated our approach using a series of confusion matrices and achieved overall accuracies as high as 83.34% and K values as high as 0.77. Our method represents a step forward because it is a reproducible and directly transferable approach to map lunar landforms; this technique can be performed easily using a GIS mapping platform, effortlessly edited, and incorporated into a general mapping procedure along with other landforms.

Automated classification generally results in less focused, more general purpose, thematic maps that incorporate broadly defined semantic meanings for landform classes. This reflects the unsupervised nature of the classifier; no landforms are defined beforehand and their meanings are established afterwards. Thus, the only available control over the emphasis placed on a landform is through choice of topographic attributes. In contrast, artificial landform classifications apply narrowly defined semantic definitions before mapping; thus, unsupervised landform classification facilitates automated searches for unexpected landscape features, while use of an automated classifier enables the quantitative determination of topographic similarities between different sites. Furthermore, the use of automated classification at the pixel level can delineate landscape features that exhibit detailed geomorphologic characteristics; lunar impact craters, for example, can be conveniently counted and described on the basis of constituent elements such as the crater rim, crater wall, ejecta, and central peak. We also tested the behavior of our classification system in this study, running it many times over the same dataset and generating identical results in each case. Results show that our classification system can accurately generate reproducible outputs, although further research will be required to establish optimal algorithm parameter values in a planetary context given the availability of high quality datasets, as well as to generate more complete terrestrial and planetary landform maps.