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Lunar surface roughness based on multiscale morphological method
Planetary and Space Science ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Lunar surface roughness based on multiscale morphological method Wei Cao a, Zhanchuan Cai a,b,n, Zesheng Tang a,b a b
Faculty of Information Technology, Macau University of Science and Technology, Macau Space Science Insitute, Macau University of Science and Technology, Macau
ar t ic l e i nf o
a b s t r a c t
Article history: Received 11 December 2013 Received in revised form 7 August 2014 Accepted 15 September 2014
Surface roughness is a useful tool to reflect numerous geological characteristics. Lunar Orbiter Laser Altimeter (LOLA) Gridded Data Records (GDRs) are used as the datum. In this paper, Lunar surface roughness maps are built based on morphological methods in image processing. As roughness measure, elevations of GDRs are considered as pixels of an image. Structuring element (SE) is employed as a scale-dependent measure of roughness maps. Global roughness maps with different resolutions are built to interpret the stability of our roughness measure. Global roughness with different-size SEs is mapped based on GDRs with the resolution of 64 pixels per degree to discuss the roughness variations in local regions determined by SEs. Regional roughness maps provide significant melt-related overviews of typical topography. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Lunar surface Morphological method Structuring element Multiscale roughness maps
1. Introduction Surface roughness is a useful measure of the texture of the surface. It plays an important role in terrain analysis, such as characteristics of landing site, distribution of various fragments and extraction of typical texture. The structure and ingredient of initial data, the roughness algorithm and the particular requirements of researchers affect the computation of surface roughness. Surface roughness has been proven to be important in lunar exploration. Rosenburg et al. (2011) first used Lunar Orbiter Laser Altimeter (LOLA) data to map global roughness of the Moon. A range of parameters (i.e. RMS slope, median differential slope and Hurst exponent) was used to characterize roughness textures. Kreslavsky et al. (2013) pointed out that the RMS slope was not stable enough to show roughness variations. Hurst exponent (Shepard et al., 2001; Orosei et al., 2003) is a fractal measure that is commonly used to indicate roughness characteristics of terrains. However, it is very difficult to prove that Hurst exponent is a stable statistical measure of roughness. Based on LALT onboard Kaguya (Araki et al., 2008, 2009), Kreslavsky (2010) produced maps of lunar topographic roughness to reveal the uniqueness of Orientale basin ejecta. The limit of these roughness maps is that the distances between measurements were too long. Kreslavsky et al. (2013) have presented topographic roughness maps derived from LOLA Reduced Data Records (RDRs) available from NASA Planetary Data System (PDS). The maps have shown scale dependence of roughness and
n
Corresponding author. E-mail address: [email protected] (Z. Cai).
high correlation with geological features. Roughness at each pixel had been defined as the interquartile range of along-profile curvature. This measure of roughness is tolerant to imperfections of the source data. However, it uses only topographic variations along individual LOLA profiles and ignores variations of topography between the orbital tracks; thus, this measure is highly anisotropic. We focus on the topographic roughness variations not only along tracks, but also between orbital tracks. For this reason, LOLA Gridded Data Records (GDRs) (Smith et al., 2010a,b), which is produced from the cumulative RDR data and LROC (Robinson et al., 2010) images, provides the multiple-resolution Digital Elevation Models (DEMs) to represent global lunar topography. More details of LOLA GDRs are given in Section 2. One of the advantage of gridded DEMs is that the elevation values can be considered as pixels of multi-value images (Dinesh, 2007; Ahmad-Fadzil et al., 2012) proposed an algorithm to compute surface roughness from DEMs. First, DEMs were rescaled as 2-D image (elevation values were mapped in the interval [0, 255]). The authors used the lifting scheme(Sweldens, 1996, 1997; Ahmad-Fadzil et al., 2011) to scan the rescaled DEMs row-by-row. The lifting scheme removed the “curvature regions” of rescaled DEMs. The generated surface was considered as the ideal smooth form of topography. Surface roughness was defined as the difference between original and generated smooth surfaces. Although this measure is anisotropy, it provides a view that the methods in image processing can be applied in DEMs roughness computation. Surface roughness is proved to be scale-dependent (Rosenburg et al., 2011; Ahmad-Fadzil et al., 2012; Kreslavsky et al., 2013). It means that topographic roughness variations are indicated in local spatial regions determined by defined scales. The morphological method in image processing
http://dx.doi.org/10.1016/j.pss.2014.09.009 0032-0633/& 2014 Elsevier Ltd. All rights reserved.
Please cite this article as: Cao, W., et al., Lunar surface roughness based on multiscale morphological method. Planetary and Space Science (2014), http://dx.doi.org/10.1016/j.pss.2014.09.009i
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(Gonzalez et al., 2013), which is often used to extract image component, can be used as a scale-dependent roughness measure of gridded DEMs. Morphological methods control the ranges of the local spatial regions by the size of a known shape called structuring element (SE). The sizes of SEs are then defined as the scales of roughness maps. Two types of ideal smooth surfaces are generated based on SEs with different sizes. The difference between the two surfaces is defined as surface roughness of topography. To evaluate the practicability of the roughness measure, we refer to the viewpoints of Kreslavsky et al. (2013) and give the experimental results in the latter sections. This paper is organized as follows. The description of the source data selection is provided in Section 2. In Section 3, the rationale of the statistical measure of roughness in our method is presented, especially the selection of SE. The global roughness maps and regional roughness maps are created in Sections 4 and 5 separately. In these two sections, the effectiveness of our roughness measure is also shown. The conclusions are listed in Section 6.
4 pixels per degree, 8 pixels per degree, 16 pixels per degree and 64 pixels per degree. Global maps based on higher-resolution GDRs are meaningless because the differences between high-resolution topographies (128 pixels per degree and 256 pixels per degree) and lowresolution topographies (4 pixels per degree, 8 pixels per degree, 16 pixels per degree and 64 pixels per degree) are not visible clearly. Regional roughness maps are built based on LOLA global GDRs with the resolution of 256 pixels per degree because it provides the highest-resolution representation of global topography. Our roughness measure is tested in global maps with different resolutions. Different scales (sizes of SEs) are applied to build global roughness maps based on LOLA GDRs with the resolution of 64 pixels per degree. The practicability of our roughness measure is discussed based on the experimental results and the requirements described in Kreslavsky et al. (2013). For regional roughness maps, the scaledependent features of typical surfaces and the correlation between roughness characteristics and geologic features are discussed.
2. Topography data
3. Rationale of morphological surface roughness (MSR) algorithm
We start with LOLA GDRs downloaded from the NASA Planetary Data System (PDS). To recover the topography between orbital tracks, the lacking data are filled based on LROC images and control points (Smith et al., 2010a, 2011). Global products of LOLA GDRs use the equi-rectangular map projection. In this paper, global topographic roughness is mapped based on global LOLA GDRs with resolution of
Mathematical morphology is often used to analyze binary images (Matheron, 1967, 1975; Serra, 1982, 1988). This theory can also be applied for the analysis of spatial structures because it concentrates on the form, shape, and size of structures (Dinesh, 2007). DEMs are 3-dimensional (3-D) representation of topography. It reflects the topographic variations by its elevations that are arranged by the
Fig. 1. The shape of SE in binary image: (a) line (length ¼ 7) with special angle of 01; (b) disk with R ¼ 4; (c) octagon with R ¼ 3; (d) square with size of 7. The origins of these structuring elements are at their centers.
Please cite this article as: Cao, W., et al., Lunar surface roughness based on multiscale morphological method. Planetary and Space Science (2014), http://dx.doi.org/10.1016/j.pss.2014.09.009i
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gridded spatial structures. In mathematical morphology, the extraction of spatial components has characteristic of parallel computing and is implemented easily (Hu et al., 2006). The essence of morphological operators is the simple mathematical operations. Its advantage is that the simple operators reduce the time of computation in huge source data. When applied in DEMs, mathematical morphology provides a wide range of methods and algorithms to solve scientific and practical problems (Soille and Ansoult, 1990; Dinesh, 2008).
Previous lunar roughness measures (Kreslavsky, 2010; Rosenburg et al., 2011; Kreslavsky et al., 2013) changed the sizes of baselines to reflect scale-dependent feature of roughness based on LOLA RDR data. Local roughness characteristics are shown in the regions determined by baselines. In this paper, SE is used as a scaledependent measure in LOLA GDRs. Fig. 1 shows some common shapes of SEs. Local roughness is computed in the regions controlled by SEs. The sizes of SEs are defined as the scales of roughness maps.
Fig. 2. (a) Erosion of measured profiles; (b) dilation of measured profiles. The selected SE is line segment with the size of 20.
Fig. 3. The same measure as that in Fig. 2. (a) Morphological opening of measured profiles; (b) morphological closing of measured profiles. It is obvious that the unexpected structures are recovered or reduced as much as possible. Concave and convex regions (covered by origin and generated profiles) are extracted easily.
Fig. 4. (a) The original topography of Clavius crater (58.621S, 14.731W) in global GDRs with the resolution of 256 per degree is shown. We build the regional roughness maps by using 118 m 118 m SEs with the shapes of (b) square; (c) octagon; (d) disk.
Please cite this article as: Cao, W., et al., Lunar surface roughness based on multiscale morphological method. Planetary and Space Science (2014), http://dx.doi.org/10.1016/j.pss.2014.09.009i
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The roughness characteristics are defined as scale-dependent slopes (Rosenburg et al., 2011) or curvature profiles (Kreslavsky et al., 2013) in LOLA initial data. Based on LOLA data, SE is applied to extract the concave and convex regions because the distribution of these regions indicates the surface roughness (Dinesh, 2007). When SEs slide over the spatial data, it implements the smooth processing of the spatial structure. The values in the origin of SEs are changed based on morphological operators (Soille, 2003) and the pixels in SEs. In mathematical terms, the erosion ε of spatial data f means that the origin pixel x of SEs is equal to the minimum value of the data in the regions defined by SE B: εB ðf Þ ðxÞ ¼ min f ðx þ bÞ ð1Þ bAB
where f ðx þ bÞ is the set of spatial data in the region. The dilation δ is the dual transformation of erosion. It is defined as a maximum filter: δB ðf Þ ðxÞ ¼ max f ðx þ bÞ ð2Þ bAB
To be used as an example, the eroded and dilated forms of a longitude profile at latitude 451 are shown in Fig. 2. The two operators give two different types of ideal smooth surfaces. In
Fig. 2a, the sharp and convex regions (the areas covered by blue and green lines) can be extracted while the concave regions are shown in Fig. 2b (the areas covered by blue and red lines). However, there are some additional structures because of the decrease (Fig. 2a) and increase (Fig. 2b) of elevations. The main effect of these unexpected structures is that they change the original structure of spatial data and the roughness (concave and convex) characteristics are not prominent so that these characteristics are very difficult to be extracted. To reduce or remove the effect of the unexpected structures, the other two operators in mathematical morphology are applied: Morphological Opening (MO) and Morphological Closing (MC). MO operator removes the redundant structures created by erosion. The function of dilation is added in the eroded surface so that unexpected structures are recovered (Fig. 3a). The MO function γ is defined as follows:
γ B ðf Þ ðxÞ ¼ δB εB ðf Þ
ð3Þ
MC solves the problem of dilation by implementing erosion in the dilated surface (Fig. 3b). MC ϕ is defined as
ϕB ðf Þ ðxÞ ¼ εB δB ðf Þ
ð4Þ
Fig. 5. Global roughness map with the resolution of 4 pixels per degree. Regional roughness characteristics are calculated in 11 11 disk-shape window. (a) The Northern Hemisphere and (b) the Southern Hemisphere are shown in orthographic projection. (c) Cylindrical equidistant projection of the latitudes from 701S to 701N. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
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As a result, MO and MC build two different types of roughness forms: MO operator extracts the convex regions while MC represent roughness characteristics by the concave distributions. A simple subtract algorithm is used to compute surface roughness RMSR at each pixel based on the results of MO and MC: RMSR ¼ ϕB ðf Þ γ B ðf Þ
ð5Þ
The shapes of SEs can be created as any shapes theoretically. For RDR data, it is effective to use baselines as the scale-dependent shapes because the roughness characteristics are indicated by the topographic profiles. However, LOLA GDRs represent the global topography with more complex structure in simple equirectangular map projection. In the Polar Regions, the gaps between two data points are narrower than that at the equator. It means that more roughness characteristics are shown in the Polar Regions when the same SE is used. In Fig. 4, the effects of SEs with different shapes are tested. The line segment is discarded because it is not a suitable measure in 3-D DEMs. Clavius crater (Fig. 4a) is one of the largest formations on the Moon and the floor of crater forms a convex plain by some craters impacts. The roughness maps in Fig. 4b–d indicate the
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convex roughness characteristics apparently. Obviously, it reveals that the roughness textures shown in Fig. 4c and d are more reasonable than that in Fig. 4b because of their circle-like shapes. Octagon shape is an approximation of disk shape (Soille, 2003) and it reserves the shape by limiting its radius as the multiple of 3. In this paper, SEs of disk shape are used to build roughness maps in simple cylindrical projection. To indicate the maps in Polar Regions, we use orthographic projection in global roughness maps. As described in Kreslavsky et al. (2013), 8 important properties are proposed to evaluate the statistical measure of roughness. In the latter sections, a “good” interpretation of MSR algorithm is given based on these properties.
4. Global roughness maps of lunar topography 4.1. Global roughness maps with different resolutions Global roughness maps are built with the resolutions of 4 pixels per degree (Fig. 5), 8 pixels per degree (Fig. 6) and 16 pixels per degree (Fig. 7). Because of the equirectangular projection (Lliffe
Fig. 6. Global roughness map with the resolution of 8 pixels per degree. Different from the results in Fig. 5, the subtle roughness variations are visible on the rims of craters or basins. The same measure as that is described in Fig. 5. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
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Fig. 7. Global roughness map with the resolution of 16 pixels per degree. Map projections are the same as in Fig. 5. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
and Lott, 2008), the topography in the regions from 721N to 901N (Figs. 5a, 6a and 7a) and from 721S to 901S (Figs. 5b, 6b and 7b) are distorting. The distortion is least obvious in roughness map with the resolution of 16 pixel per degree. Although roughness maps in Polar Regions are not “good” measure derived from global LOLA GDRs, it confirms that isotropic roughness measure can be applied in topography at well-defined scale and roughness variations are in all directions. In our roughness maps, the difference of global roughness maps from 701S to 701N (Figs. 5c, 6c and 7c) are subtle. Roughness at each pixel is calculated in 11 11 disk-shape window. Higher-resolution global map shows more local roughness variations because it involves more points in defined window. Crater distributions are seen clearly and the typical surfaces are characterized by the variations of elevations between the measured points and its neighbors determined by SE. The most prominent feature of multi-resolution (4 pixels per degree, 8 pixels per degree and 16 pixels per degree) roughness maps is the dichotomy between Maria ( 4 0:5 km) and rough highlands ( 4 1 km). The maria/highland boundary is associated with obvious roughness contrast in all roughness maps. The colour-coded maps in cylindrical equidistant projection (Fig. 5c,
6c and 7c) reveal significant roughness variations in the maria and some typical topography (i.e. Orientale basin). Prominent roughness characteristics in global maps are associated with lunar impact craters. The minor roughness variations shown on the crater floors, walls and some low regions relate to the distributions of impact materials. Outline units of impact craters and basins indicate strong roughness contrasts with other geological units on the Moon. The observation is that Orientale basin and Mare Crisium provide interesting examples of the roughness contrasts that coincide with the distributions of impact deposits. Most of crater-related features can be observed in Northpole and South-Aitken basin (Figs. 5b and c, 6b and c, 7b and c). However, global roughness maps ignore many details of typical surfaces. The local roughness variations are discussed in regional roughness maps. 4.2. Global roughness maps with different scales Subtle roughness variations are shown in different-resolution global roughness maps mentioned above. Different-size SEs are used to build roughness maps and the stability of MSR algorithm is discussed.
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Global multiscale roughness maps are created derived from LOLA GDRs with the resolution of 64 pixels per degree. Distorting topographies of Polar Regions in simple equirectangular projection
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are discarded. SEs with the sizes of 0.251 0.251, 0.51 0.51, 11 11 and 21 21 are chosen to create roughness maps (Fig. 8). Because the gap of the source data is 0.47 km at the equator, the sizes of
Fig. 8. Global roughness maps from 701S to 701N with (a) 7.5 km 7.5 km disk-shape SE; (b) 15 km 15 km disk-shape SE; (c) 30 km 30 km disk-shape SE; (d) 60 km 60 km disk-shape SE. Map projection is the same as Fig. 5c.
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SEs can be changed as 7.5 km 7.5 km, 15 km 15 km, 30 km 30 km, and 60 km 60 km. In small-scale (disk-shape SEs with the sizes of 7.5 km 7.5 km and 15 km 15 km) maps, regional roughness variations are subtle. Small craters are difficult to be observed. Mare Crisium, Mare Imbrium, Orientale basin and Oceanus procellarum show obvious roughness contrast in the outlines. Although roughness of typical surface should not be reflected only by its prominent features and other features of typical roughness characteristics are necessary, the prominent feature reflects the most intuitive observation in global maps. In other words, smallscale SEs are less objective roughness measures to provide the synoptic overviews of global topography because the local prominent feature of roughness is not visible. However, the observations of these roughness maps reflect that the roughness variations of typical surfaces are not obvious when observed within the scale 15 km. Global roughness maps provide better observation in large scales (disk-shape SEs with sizes of 30 km 30 km and 60 km 60 km). Red shades denote higher roughness. The characteristics of the prominent features of typical surfaces in large-scale roughness measure are more
visible clearly. The contrasts between large young craters and typical highlands are significantly higher than those of small-scale roughness. Most of the roughness characteristics are shown in the outlines of these typical areas. In a word, our roughness measure characterizes roughness stably at a defined scale. Roughness feature of a typical surface is characterized by the prominent features of local regions determined by SE. For this reason, it is important and interesting that a “good” global roughness map can be represented by a “well-defined” SE. For the example in this paper, 60 km 60 km SE is the most significant roughness measure to indicate most of roughness variations in LOLA GDRs with the resolution of 64 pixels per degree sampling. As observed in Fig. 8c, the boundary of maria ( o 0:5 km) and highlands ( 4 1 km) are easily distinguishable because of the strong roughness contracts. The multiring structure of Orientale basin is seen clearly. The continuous ejecta deposit indicates a long, radial shapes along with the secondary crater chains ½201S : 201N; 2001E : 2401E (the same observation as described in Rosenburg et al., 2011). In smaller scales (see Fig. 8a and b), roughness variations in highlands are less objective but they are
Fig. 9. Typical roughness maps of selected young craters, with the scale 1.18 km, local equirectangular projections. Red shades denote higher roughness. These maps were created in global LOLA GDRs with the resolution of 256 pixels per degree. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
Fig. 10. Typical roughness maps of selected young craters, with the scale 2.36 km, local equirectangular projections. Red shades denote higher roughness. These maps were created in global LOLA GDRs with the resolution of 256 pixels per degree. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
Please cite this article as: Cao, W., et al., Lunar surface roughness based on multiscale morphological method. Planetary and Space Science (2014), http://dx.doi.org/10.1016/j.pss.2014.09.009i
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Fig. 11. Roughness maps of Orientale basin (80–1101W, 5–351S) with the scale of (a) 1 km; (b) 2 km and (c) 4 km. Red shades denote higher roughness.
Please cite this article as: Cao, W., et al., Lunar surface roughness based on multiscale morphological method. Planetary and Space Science (2014), http://dx.doi.org/10.1016/j.pss.2014.09.009i
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always higher than those in maria on the nearside of the Moon. It is difficult to see the roughness contracts between maria and typical surfaces in highlands.
5. Regional roughness maps of lunar topography International Astronomical Union (IAU) Working Group for Planetary System Nomenclature (WGPSN) provides detailed information about all named typical surfaces having topographic and albedo features on the Moon. According to the coordinate information of latitudes and longitudes in four directions (Northernmost, Southernmost, Westernmost and Easternmost coordinate points), regional topography from LOLA GDRs is easily extracted. To show more details in roughness maps, GDRs with the resolution of 256 pixels per degree (118 m/pix at the equator) derived from NASA PDS are used as the source data. Because the datum is huge (total 46,080 92, 160 elevations), it is divided into 64 parts (each parts containing 5760 11,520 elevations) for extracting typical surfaces easily. Roughness characteristics of young craters in Figs. 9 and 10 are shown with the interval from 0 to 0.7 km. The central peaks and rims of craters reflect higher roughness feature (4 0:3 km) in smallscale (1 km) maps. Roughness variations are subtle so that the melt deposits in the interior of craters are not seen clearly. In larger-scale (2 km) maps, impact melts can be observed on the crater floor and rims typically. The melt forms pools on the crater floor, filling low regions (Plescia and Cintala, 2012). Most of impact melt pools are observed near the high-roughness areas (central peaks and outer rims). It is obvious that a few special roughness characteristics (from 0.2 to 0.3 km) are associated with the distribution of melt materials. Large melt pools appear on the surroundings of the central peaks of Tycho (95 Ma) (Krüger et al., 2013), and Jackson (150 Ma). However, the obvious melt-related variations of Copernicus (800 Ma) are just seen to the south of central peak (Dhingra et al., 2013). Based on the observation in Fig. 10, a strong wall failure appears on the northwest of Tycho crater. Jackson crater indicates a complete rim that has largest distribution of melt deposits. Orientale basin shows one of the most prominent roughness characteristics in all global roughness maps. Inner depression (as described in the location map provided by Whitten et al., 2011) shows the lowest roughness characteristics. A number of small melt ponds are observed on the basin interior (Martin and Spudis, 2014). The roughness values of these regions are subtle (o 0:05 km in Fig. 11a, o 0:2 km in Fig. 11b and o 0:5 km in Fig. 11c). Some higher roughness variations (4 0:15 km in Fig. 11a, 4 0:4 km in Fig. 11b and 4 1 km in Fig. 11c) shown on Inner Rook Ring (480 km) and Out Rook Ring (620 km) are associated with distributions of massif materials (Spudis et al., 2014). Other higher roughness features are reflected on the rims of craters.
6. Conclusions We create maps of lunar surface roughness based on morphological methods in image processing. Elevations of topography are considered as the pixels in 2-D image. The size of SE reflects the scale-dependent feature of our roughness measure. Closing and opening operators are used to extract roughness characteristics (concave regions and convex regions) from LOLA global GDRs (with the resolution of 4 pixels per degree, 8 pixels per degree, 16 pixels per degree, 64 pixels per degree and 256 pixels per degree). Surface roughness at each pixel is defined as the difference between the results of closing and opening processing. The dichotomy between maria and highlands shows strong roughness contrast in global roughness maps with different resolutions (4 pixels per degree, 8 pixels per degree and 16 pixels per degree). However, equirectangular map
projection of LOLA global GDRs has distortion in shapes of objects on the surfaces of Polar Regions. To show the scale-dependent feature of our roughness measure, different-size disk-shape SEs are applied to map global surface roughness from 701S to 701N in simple equirectangular projection. The observation is that 60 km 60 km SE provides the most significant roughness measure to reflect most of scale-dependent roughness features based on LOLA GDRs with the scale 64 pixels per degree sampling. Because of the highest resolution (256 pixels per degree) of LOLA global GDRs, typical craters and basins can be extracted to analyze their roughness features and discuss the correlations with geological units. Roughness characteristics of selected young craters and basins have significant associations with melt materials.
Acknowledgements We would like to thank the reviewer Dr. Maihail A. Kreslavsky and the other anonymous reviewer who provided very helpful and useful suggestions of paper. This work is supported by the Science and Technology Development Fund of Macau under Grant nos. 048/2012/A2, 084/2012/A3 and 091/2013/A3, National Basic Research Program of China (973 Program) under Grant nos. 2011CB302400, the Open Project Program of the State Key Lab of CAD&CG of Zhejiang University under Grant nos. A1310. References Ahmad-Fadzil, M.H., Dinesh, S., Viijanth-Sagayan, A., 2012. Computing surface roughness of individual cells of digital elevation models via multiscale analysis. Comput. Geosci. 43, 137–146. Ahmad-Fadzil, M.H., Dinesh, S., Vijanth-Sagayan, A., 2011. A method for computation of surface roughness of digital elevation model terrains via multiscale analysis. Comput. Geosci. 37, 177–192. Araki, H., Tazawa, S., Noda, H., Ishihara, Y., Goossens, S., Sasaki, S., Kawano, N., Kamiya, I., Otake, H., Oberst, J., Shum, C., 2009. Lunar global shape and polar topography derived from Kaguya lalt laser altimetry. Science 13, 897–900. Araki, H., Tazawa, S., Noda, H., Tsubokawa, T., Kawano, N., Sasaki, S., 2008. Observation of the lunar topography by the laser altimeter lalt on board Japanese lunar explorer selene. Adv. Space Res. 42, 317–322. Dhingra, D., Pieters, C.M., Head, J.W., Isaacson, P.J., 2013. Large mineralogically distinct impact melt feature at copernicus crater—evidence for retention of compositional heterogeneity. Geophys. Res. Lett. 104. Dinesh, S., 2007. Computation and characterization of surface roughness of catchments extracted from simulated digital elevation models. J. Appl. Sci. Res. 3, 1969–1978. Dinesh, S., 2008. Extraction of watersheds from digital elevation models using mathematical morphology. J. Appl. Sci. 8, 956–965. Gonzalez, R.C., Woods, R.E., Eddins, S.L., 2013. Digital Image Processing Using MATLAB, second ed. Publishing House of Electronics Industry, Beijing. Hu, Z., Gong, H., Li, X., Zhao, W., 2006. Advances in the application of mathematical morphology in spatial data processing and analysis. In: Norman Kerle, A.S. (Ed.), ISPRS Commission VII Symposium, Enschede, The Netherlands. Kreslavsky, M., 2010. New observational evidence of strong seismic effects of basinforming impacts on the moon. In: European Planetary Science Congress. Abstract # EPSC2010-357. http://meetings.copernicus.org/epsc2010/abstracts/ EPSC2010-357.pdf. Kreslavsky, M.A., Head, J.W., Neumann, G.A., Rosenburg, M.A., Aharonson, O., Smith, D.E., Zuber, M.T., 2013. Lunar topographic roughness maps from lunar orbiter laser altimeter (lola) data: scale dependence and correlation with geologic features and units. Icarus 266, 52–66. Krüger, T., van der Bogert, C.H., Hiesinger, H., 2013. New high-resolution melt distribution map and topographic analysis of tycho crater. In: 44th Lunar and Planetary Science Conference. Lliffe, J., Lott, R., 2008. Datums and Map Projections: For Remote Sensing, GIS and Surveying. Whittles Publishing, UK. Martin, D.J.P., Spudis, P.D., 2014. New geological map of the lunar orientale basin. In: 45th Lunar and Planetary Science Conference. Matheron, G., 1967. Éléments pour une théorie des milieux poreux. Masson et Cie, Paris. Matheron, G., 1975. Random Sets and Integral Geometry. Wiley, New York. Orosei, R., Bianchi, R., Coradini, A., Espinasse, S., Federico, C., Ferriccioni, A., Gavrishin, A.I., 2003. Self-affine behavior of martian topography at kilometer scale from mars orbiter laser altimeter data. J. Geophys. Res. 108. http://dx.doi. org/10.1029/2002JE001883. Plescia, I.B., Cintala, M.I., 2012. Impact melt in small lunar highland craters. J. Geophys. Res. 117, 23.
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W. Cao et al. / Planetary and Space Science ∎ (∎∎∎∎) ∎∎∎–∎∎∎ Robinson, M.S., Brylow, S.M., Tschimmel, M., Humm, D., Lawrence, S.J., Thomas, P.C., Denevi, B.W., Bowman-Cisneros, E., Zerr, J., Ravine, M.A., 2010. Lunar reconnaissance orbiter camera (lroc) instrument overview. Space Sci. Rev. 150, 81–124. Rosenburg, M.A., Aharonson, O., Head, J.W., Kreslavsky, M.A., Mazarico, E., Neumann, G.A., Smith, D.E., Torrence, M.H., Zuber, M.T., 2011. Global surface slopes and roughness of the moon from the lunar orbiter laser altimeter. J. Geophys. Res. 116. http://dx.doi.org/10.1029/2010JE003716. Serra, J., 1982. Image Analysis and Mathematical Morphology. Academic Press, ISBN 0-12-637240-3. Serra, J., 1988. Image Analysis and Mathematical Morphology Volume 2: Theoretical Advances. Academic Press, ISBN 0-12-637241-1. Shepard, M.K., Campbell, B.A., Bulmer, M.H., Farr, T.G., Gaddis, L.R., Plaut, J.J., 2001. The roughness of natural terrain: a planetary and remote sensing perspective. J. Geophys. Res. 106, 32777–32795. Smith, D.E., Zuber, M., Jackson, G.B., Cavanaugh, J.F., Neumann, G.A., Riris, H., Sun, X., Zeller, R.S., Coltharp, C., Connelly, J., Katz, R.B., Kleyner, I., Liiva, P., Matuszeski, A., Mazarico, E.M., McGarry, J.F., Novo-Gradac, A., Ott, M.N., Peter, C., Ramos-Izquierdo, L.A., Ramsey, L., Rowlands, D.D., Schmidt, S., Scott, V.S., Shaw, G.B., Smith, J.C., Swinski, J.P., Torrence, M.H., Unger, G., Yu, A.W., Zagwodzki, T.W., 2010a. The lunar orbiter laser altimeter investigation on the lunar reconnaissance orbier mission. Space Sci Rev. 150, 209–241. http://dx.doi.org/ 10.1007/s11214-009-9512-y. Smith, D.E., Zuber, M.T., Neumann, G.A., Lemoine, F.G., Mazarico, E., Torrence, M.H., McGarry, J.F., Rowlands, D.D., HeadIII, J.W., Duxbury, T.H., Aharonson, O., Lucey, P.G., Robinson, M.S., Barnouin, O.S., Cavanaugh, J.F., Sun, X., Liiva, P., Mao, D.,
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Planetary and Space Science journal homepage: www.elsevier.com/locate/pss
Lunar surface roughness based on multiscale morphological method Wei Cao a, Zhanchuan Cai a,b,n, Zesheng Tang a,b a b
Faculty of Information Technology, Macau University of Science and Technology, Macau Space Science Insitute, Macau University of Science and Technology, Macau
ar t ic l e i nf o
a b s t r a c t
Article history: Received 11 December 2013 Received in revised form 7 August 2014 Accepted 15 September 2014
Surface roughness is a useful tool to reflect numerous geological characteristics. Lunar Orbiter Laser Altimeter (LOLA) Gridded Data Records (GDRs) are used as the datum. In this paper, Lunar surface roughness maps are built based on morphological methods in image processing. As roughness measure, elevations of GDRs are considered as pixels of an image. Structuring element (SE) is employed as a scale-dependent measure of roughness maps. Global roughness maps with different resolutions are built to interpret the stability of our roughness measure. Global roughness with different-size SEs is mapped based on GDRs with the resolution of 64 pixels per degree to discuss the roughness variations in local regions determined by SEs. Regional roughness maps provide significant melt-related overviews of typical topography. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Lunar surface Morphological method Structuring element Multiscale roughness maps
1. Introduction Surface roughness is a useful measure of the texture of the surface. It plays an important role in terrain analysis, such as characteristics of landing site, distribution of various fragments and extraction of typical texture. The structure and ingredient of initial data, the roughness algorithm and the particular requirements of researchers affect the computation of surface roughness. Surface roughness has been proven to be important in lunar exploration. Rosenburg et al. (2011) first used Lunar Orbiter Laser Altimeter (LOLA) data to map global roughness of the Moon. A range of parameters (i.e. RMS slope, median differential slope and Hurst exponent) was used to characterize roughness textures. Kreslavsky et al. (2013) pointed out that the RMS slope was not stable enough to show roughness variations. Hurst exponent (Shepard et al., 2001; Orosei et al., 2003) is a fractal measure that is commonly used to indicate roughness characteristics of terrains. However, it is very difficult to prove that Hurst exponent is a stable statistical measure of roughness. Based on LALT onboard Kaguya (Araki et al., 2008, 2009), Kreslavsky (2010) produced maps of lunar topographic roughness to reveal the uniqueness of Orientale basin ejecta. The limit of these roughness maps is that the distances between measurements were too long. Kreslavsky et al. (2013) have presented topographic roughness maps derived from LOLA Reduced Data Records (RDRs) available from NASA Planetary Data System (PDS). The maps have shown scale dependence of roughness and
n
Corresponding author. E-mail address: [email protected] (Z. Cai).
high correlation with geological features. Roughness at each pixel had been defined as the interquartile range of along-profile curvature. This measure of roughness is tolerant to imperfections of the source data. However, it uses only topographic variations along individual LOLA profiles and ignores variations of topography between the orbital tracks; thus, this measure is highly anisotropic. We focus on the topographic roughness variations not only along tracks, but also between orbital tracks. For this reason, LOLA Gridded Data Records (GDRs) (Smith et al., 2010a,b), which is produced from the cumulative RDR data and LROC (Robinson et al., 2010) images, provides the multiple-resolution Digital Elevation Models (DEMs) to represent global lunar topography. More details of LOLA GDRs are given in Section 2. One of the advantage of gridded DEMs is that the elevation values can be considered as pixels of multi-value images (Dinesh, 2007; Ahmad-Fadzil et al., 2012) proposed an algorithm to compute surface roughness from DEMs. First, DEMs were rescaled as 2-D image (elevation values were mapped in the interval [0, 255]). The authors used the lifting scheme(Sweldens, 1996, 1997; Ahmad-Fadzil et al., 2011) to scan the rescaled DEMs row-by-row. The lifting scheme removed the “curvature regions” of rescaled DEMs. The generated surface was considered as the ideal smooth form of topography. Surface roughness was defined as the difference between original and generated smooth surfaces. Although this measure is anisotropy, it provides a view that the methods in image processing can be applied in DEMs roughness computation. Surface roughness is proved to be scale-dependent (Rosenburg et al., 2011; Ahmad-Fadzil et al., 2012; Kreslavsky et al., 2013). It means that topographic roughness variations are indicated in local spatial regions determined by defined scales. The morphological method in image processing
http://dx.doi.org/10.1016/j.pss.2014.09.009 0032-0633/& 2014 Elsevier Ltd. All rights reserved.
Please cite this article as: Cao, W., et al., Lunar surface roughness based on multiscale morphological method. Planetary and Space Science (2014), http://dx.doi.org/10.1016/j.pss.2014.09.009i
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(Gonzalez et al., 2013), which is often used to extract image component, can be used as a scale-dependent roughness measure of gridded DEMs. Morphological methods control the ranges of the local spatial regions by the size of a known shape called structuring element (SE). The sizes of SEs are then defined as the scales of roughness maps. Two types of ideal smooth surfaces are generated based on SEs with different sizes. The difference between the two surfaces is defined as surface roughness of topography. To evaluate the practicability of the roughness measure, we refer to the viewpoints of Kreslavsky et al. (2013) and give the experimental results in the latter sections. This paper is organized as follows. The description of the source data selection is provided in Section 2. In Section 3, the rationale of the statistical measure of roughness in our method is presented, especially the selection of SE. The global roughness maps and regional roughness maps are created in Sections 4 and 5 separately. In these two sections, the effectiveness of our roughness measure is also shown. The conclusions are listed in Section 6.
4 pixels per degree, 8 pixels per degree, 16 pixels per degree and 64 pixels per degree. Global maps based on higher-resolution GDRs are meaningless because the differences between high-resolution topographies (128 pixels per degree and 256 pixels per degree) and lowresolution topographies (4 pixels per degree, 8 pixels per degree, 16 pixels per degree and 64 pixels per degree) are not visible clearly. Regional roughness maps are built based on LOLA global GDRs with the resolution of 256 pixels per degree because it provides the highest-resolution representation of global topography. Our roughness measure is tested in global maps with different resolutions. Different scales (sizes of SEs) are applied to build global roughness maps based on LOLA GDRs with the resolution of 64 pixels per degree. The practicability of our roughness measure is discussed based on the experimental results and the requirements described in Kreslavsky et al. (2013). For regional roughness maps, the scaledependent features of typical surfaces and the correlation between roughness characteristics and geologic features are discussed.
2. Topography data
3. Rationale of morphological surface roughness (MSR) algorithm
We start with LOLA GDRs downloaded from the NASA Planetary Data System (PDS). To recover the topography between orbital tracks, the lacking data are filled based on LROC images and control points (Smith et al., 2010a, 2011). Global products of LOLA GDRs use the equi-rectangular map projection. In this paper, global topographic roughness is mapped based on global LOLA GDRs with resolution of
Mathematical morphology is often used to analyze binary images (Matheron, 1967, 1975; Serra, 1982, 1988). This theory can also be applied for the analysis of spatial structures because it concentrates on the form, shape, and size of structures (Dinesh, 2007). DEMs are 3-dimensional (3-D) representation of topography. It reflects the topographic variations by its elevations that are arranged by the
Fig. 1. The shape of SE in binary image: (a) line (length ¼ 7) with special angle of 01; (b) disk with R ¼ 4; (c) octagon with R ¼ 3; (d) square with size of 7. The origins of these structuring elements are at their centers.
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gridded spatial structures. In mathematical morphology, the extraction of spatial components has characteristic of parallel computing and is implemented easily (Hu et al., 2006). The essence of morphological operators is the simple mathematical operations. Its advantage is that the simple operators reduce the time of computation in huge source data. When applied in DEMs, mathematical morphology provides a wide range of methods and algorithms to solve scientific and practical problems (Soille and Ansoult, 1990; Dinesh, 2008).
Previous lunar roughness measures (Kreslavsky, 2010; Rosenburg et al., 2011; Kreslavsky et al., 2013) changed the sizes of baselines to reflect scale-dependent feature of roughness based on LOLA RDR data. Local roughness characteristics are shown in the regions determined by baselines. In this paper, SE is used as a scaledependent measure in LOLA GDRs. Fig. 1 shows some common shapes of SEs. Local roughness is computed in the regions controlled by SEs. The sizes of SEs are defined as the scales of roughness maps.
Fig. 2. (a) Erosion of measured profiles; (b) dilation of measured profiles. The selected SE is line segment with the size of 20.
Fig. 3. The same measure as that in Fig. 2. (a) Morphological opening of measured profiles; (b) morphological closing of measured profiles. It is obvious that the unexpected structures are recovered or reduced as much as possible. Concave and convex regions (covered by origin and generated profiles) are extracted easily.
Fig. 4. (a) The original topography of Clavius crater (58.621S, 14.731W) in global GDRs with the resolution of 256 per degree is shown. We build the regional roughness maps by using 118 m 118 m SEs with the shapes of (b) square; (c) octagon; (d) disk.
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The roughness characteristics are defined as scale-dependent slopes (Rosenburg et al., 2011) or curvature profiles (Kreslavsky et al., 2013) in LOLA initial data. Based on LOLA data, SE is applied to extract the concave and convex regions because the distribution of these regions indicates the surface roughness (Dinesh, 2007). When SEs slide over the spatial data, it implements the smooth processing of the spatial structure. The values in the origin of SEs are changed based on morphological operators (Soille, 2003) and the pixels in SEs. In mathematical terms, the erosion ε of spatial data f means that the origin pixel x of SEs is equal to the minimum value of the data in the regions defined by SE B: εB ðf Þ ðxÞ ¼ min f ðx þ bÞ ð1Þ bAB
where f ðx þ bÞ is the set of spatial data in the region. The dilation δ is the dual transformation of erosion. It is defined as a maximum filter: δB ðf Þ ðxÞ ¼ max f ðx þ bÞ ð2Þ bAB
To be used as an example, the eroded and dilated forms of a longitude profile at latitude 451 are shown in Fig. 2. The two operators give two different types of ideal smooth surfaces. In
Fig. 2a, the sharp and convex regions (the areas covered by blue and green lines) can be extracted while the concave regions are shown in Fig. 2b (the areas covered by blue and red lines). However, there are some additional structures because of the decrease (Fig. 2a) and increase (Fig. 2b) of elevations. The main effect of these unexpected structures is that they change the original structure of spatial data and the roughness (concave and convex) characteristics are not prominent so that these characteristics are very difficult to be extracted. To reduce or remove the effect of the unexpected structures, the other two operators in mathematical morphology are applied: Morphological Opening (MO) and Morphological Closing (MC). MO operator removes the redundant structures created by erosion. The function of dilation is added in the eroded surface so that unexpected structures are recovered (Fig. 3a). The MO function γ is defined as follows:
γ B ðf Þ ðxÞ ¼ δB εB ðf Þ
ð3Þ
MC solves the problem of dilation by implementing erosion in the dilated surface (Fig. 3b). MC ϕ is defined as
ϕB ðf Þ ðxÞ ¼ εB δB ðf Þ
ð4Þ
Fig. 5. Global roughness map with the resolution of 4 pixels per degree. Regional roughness characteristics are calculated in 11 11 disk-shape window. (a) The Northern Hemisphere and (b) the Southern Hemisphere are shown in orthographic projection. (c) Cylindrical equidistant projection of the latitudes from 701S to 701N. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
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As a result, MO and MC build two different types of roughness forms: MO operator extracts the convex regions while MC represent roughness characteristics by the concave distributions. A simple subtract algorithm is used to compute surface roughness RMSR at each pixel based on the results of MO and MC: RMSR ¼ ϕB ðf Þ γ B ðf Þ
ð5Þ
The shapes of SEs can be created as any shapes theoretically. For RDR data, it is effective to use baselines as the scale-dependent shapes because the roughness characteristics are indicated by the topographic profiles. However, LOLA GDRs represent the global topography with more complex structure in simple equirectangular map projection. In the Polar Regions, the gaps between two data points are narrower than that at the equator. It means that more roughness characteristics are shown in the Polar Regions when the same SE is used. In Fig. 4, the effects of SEs with different shapes are tested. The line segment is discarded because it is not a suitable measure in 3-D DEMs. Clavius crater (Fig. 4a) is one of the largest formations on the Moon and the floor of crater forms a convex plain by some craters impacts. The roughness maps in Fig. 4b–d indicate the
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convex roughness characteristics apparently. Obviously, it reveals that the roughness textures shown in Fig. 4c and d are more reasonable than that in Fig. 4b because of their circle-like shapes. Octagon shape is an approximation of disk shape (Soille, 2003) and it reserves the shape by limiting its radius as the multiple of 3. In this paper, SEs of disk shape are used to build roughness maps in simple cylindrical projection. To indicate the maps in Polar Regions, we use orthographic projection in global roughness maps. As described in Kreslavsky et al. (2013), 8 important properties are proposed to evaluate the statistical measure of roughness. In the latter sections, a “good” interpretation of MSR algorithm is given based on these properties.
4. Global roughness maps of lunar topography 4.1. Global roughness maps with different resolutions Global roughness maps are built with the resolutions of 4 pixels per degree (Fig. 5), 8 pixels per degree (Fig. 6) and 16 pixels per degree (Fig. 7). Because of the equirectangular projection (Lliffe
Fig. 6. Global roughness map with the resolution of 8 pixels per degree. Different from the results in Fig. 5, the subtle roughness variations are visible on the rims of craters or basins. The same measure as that is described in Fig. 5. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
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Fig. 7. Global roughness map with the resolution of 16 pixels per degree. Map projections are the same as in Fig. 5. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
and Lott, 2008), the topography in the regions from 721N to 901N (Figs. 5a, 6a and 7a) and from 721S to 901S (Figs. 5b, 6b and 7b) are distorting. The distortion is least obvious in roughness map with the resolution of 16 pixel per degree. Although roughness maps in Polar Regions are not “good” measure derived from global LOLA GDRs, it confirms that isotropic roughness measure can be applied in topography at well-defined scale and roughness variations are in all directions. In our roughness maps, the difference of global roughness maps from 701S to 701N (Figs. 5c, 6c and 7c) are subtle. Roughness at each pixel is calculated in 11 11 disk-shape window. Higher-resolution global map shows more local roughness variations because it involves more points in defined window. Crater distributions are seen clearly and the typical surfaces are characterized by the variations of elevations between the measured points and its neighbors determined by SE. The most prominent feature of multi-resolution (4 pixels per degree, 8 pixels per degree and 16 pixels per degree) roughness maps is the dichotomy between Maria ( 4 0:5 km) and rough highlands ( 4 1 km). The maria/highland boundary is associated with obvious roughness contrast in all roughness maps. The colour-coded maps in cylindrical equidistant projection (Fig. 5c,
6c and 7c) reveal significant roughness variations in the maria and some typical topography (i.e. Orientale basin). Prominent roughness characteristics in global maps are associated with lunar impact craters. The minor roughness variations shown on the crater floors, walls and some low regions relate to the distributions of impact materials. Outline units of impact craters and basins indicate strong roughness contrasts with other geological units on the Moon. The observation is that Orientale basin and Mare Crisium provide interesting examples of the roughness contrasts that coincide with the distributions of impact deposits. Most of crater-related features can be observed in Northpole and South-Aitken basin (Figs. 5b and c, 6b and c, 7b and c). However, global roughness maps ignore many details of typical surfaces. The local roughness variations are discussed in regional roughness maps. 4.2. Global roughness maps with different scales Subtle roughness variations are shown in different-resolution global roughness maps mentioned above. Different-size SEs are used to build roughness maps and the stability of MSR algorithm is discussed.
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Global multiscale roughness maps are created derived from LOLA GDRs with the resolution of 64 pixels per degree. Distorting topographies of Polar Regions in simple equirectangular projection
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are discarded. SEs with the sizes of 0.251 0.251, 0.51 0.51, 11 11 and 21 21 are chosen to create roughness maps (Fig. 8). Because the gap of the source data is 0.47 km at the equator, the sizes of
Fig. 8. Global roughness maps from 701S to 701N with (a) 7.5 km 7.5 km disk-shape SE; (b) 15 km 15 km disk-shape SE; (c) 30 km 30 km disk-shape SE; (d) 60 km 60 km disk-shape SE. Map projection is the same as Fig. 5c.
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SEs can be changed as 7.5 km 7.5 km, 15 km 15 km, 30 km 30 km, and 60 km 60 km. In small-scale (disk-shape SEs with the sizes of 7.5 km 7.5 km and 15 km 15 km) maps, regional roughness variations are subtle. Small craters are difficult to be observed. Mare Crisium, Mare Imbrium, Orientale basin and Oceanus procellarum show obvious roughness contrast in the outlines. Although roughness of typical surface should not be reflected only by its prominent features and other features of typical roughness characteristics are necessary, the prominent feature reflects the most intuitive observation in global maps. In other words, smallscale SEs are less objective roughness measures to provide the synoptic overviews of global topography because the local prominent feature of roughness is not visible. However, the observations of these roughness maps reflect that the roughness variations of typical surfaces are not obvious when observed within the scale 15 km. Global roughness maps provide better observation in large scales (disk-shape SEs with sizes of 30 km 30 km and 60 km 60 km). Red shades denote higher roughness. The characteristics of the prominent features of typical surfaces in large-scale roughness measure are more
visible clearly. The contrasts between large young craters and typical highlands are significantly higher than those of small-scale roughness. Most of the roughness characteristics are shown in the outlines of these typical areas. In a word, our roughness measure characterizes roughness stably at a defined scale. Roughness feature of a typical surface is characterized by the prominent features of local regions determined by SE. For this reason, it is important and interesting that a “good” global roughness map can be represented by a “well-defined” SE. For the example in this paper, 60 km 60 km SE is the most significant roughness measure to indicate most of roughness variations in LOLA GDRs with the resolution of 64 pixels per degree sampling. As observed in Fig. 8c, the boundary of maria ( o 0:5 km) and highlands ( 4 1 km) are easily distinguishable because of the strong roughness contracts. The multiring structure of Orientale basin is seen clearly. The continuous ejecta deposit indicates a long, radial shapes along with the secondary crater chains ½201S : 201N; 2001E : 2401E (the same observation as described in Rosenburg et al., 2011). In smaller scales (see Fig. 8a and b), roughness variations in highlands are less objective but they are
Fig. 9. Typical roughness maps of selected young craters, with the scale 1.18 km, local equirectangular projections. Red shades denote higher roughness. These maps were created in global LOLA GDRs with the resolution of 256 pixels per degree. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
Fig. 10. Typical roughness maps of selected young craters, with the scale 2.36 km, local equirectangular projections. Red shades denote higher roughness. These maps were created in global LOLA GDRs with the resolution of 256 pixels per degree. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
Please cite this article as: Cao, W., et al., Lunar surface roughness based on multiscale morphological method. Planetary and Space Science (2014), http://dx.doi.org/10.1016/j.pss.2014.09.009i
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Fig. 11. Roughness maps of Orientale basin (80–1101W, 5–351S) with the scale of (a) 1 km; (b) 2 km and (c) 4 km. Red shades denote higher roughness.
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always higher than those in maria on the nearside of the Moon. It is difficult to see the roughness contracts between maria and typical surfaces in highlands.
5. Regional roughness maps of lunar topography International Astronomical Union (IAU) Working Group for Planetary System Nomenclature (WGPSN) provides detailed information about all named typical surfaces having topographic and albedo features on the Moon. According to the coordinate information of latitudes and longitudes in four directions (Northernmost, Southernmost, Westernmost and Easternmost coordinate points), regional topography from LOLA GDRs is easily extracted. To show more details in roughness maps, GDRs with the resolution of 256 pixels per degree (118 m/pix at the equator) derived from NASA PDS are used as the source data. Because the datum is huge (total 46,080 92, 160 elevations), it is divided into 64 parts (each parts containing 5760 11,520 elevations) for extracting typical surfaces easily. Roughness characteristics of young craters in Figs. 9 and 10 are shown with the interval from 0 to 0.7 km. The central peaks and rims of craters reflect higher roughness feature (4 0:3 km) in smallscale (1 km) maps. Roughness variations are subtle so that the melt deposits in the interior of craters are not seen clearly. In larger-scale (2 km) maps, impact melts can be observed on the crater floor and rims typically. The melt forms pools on the crater floor, filling low regions (Plescia and Cintala, 2012). Most of impact melt pools are observed near the high-roughness areas (central peaks and outer rims). It is obvious that a few special roughness characteristics (from 0.2 to 0.3 km) are associated with the distribution of melt materials. Large melt pools appear on the surroundings of the central peaks of Tycho (95 Ma) (Krüger et al., 2013), and Jackson (150 Ma). However, the obvious melt-related variations of Copernicus (800 Ma) are just seen to the south of central peak (Dhingra et al., 2013). Based on the observation in Fig. 10, a strong wall failure appears on the northwest of Tycho crater. Jackson crater indicates a complete rim that has largest distribution of melt deposits. Orientale basin shows one of the most prominent roughness characteristics in all global roughness maps. Inner depression (as described in the location map provided by Whitten et al., 2011) shows the lowest roughness characteristics. A number of small melt ponds are observed on the basin interior (Martin and Spudis, 2014). The roughness values of these regions are subtle (o 0:05 km in Fig. 11a, o 0:2 km in Fig. 11b and o 0:5 km in Fig. 11c). Some higher roughness variations (4 0:15 km in Fig. 11a, 4 0:4 km in Fig. 11b and 4 1 km in Fig. 11c) shown on Inner Rook Ring (480 km) and Out Rook Ring (620 km) are associated with distributions of massif materials (Spudis et al., 2014). Other higher roughness features are reflected on the rims of craters.
6. Conclusions We create maps of lunar surface roughness based on morphological methods in image processing. Elevations of topography are considered as the pixels in 2-D image. The size of SE reflects the scale-dependent feature of our roughness measure. Closing and opening operators are used to extract roughness characteristics (concave regions and convex regions) from LOLA global GDRs (with the resolution of 4 pixels per degree, 8 pixels per degree, 16 pixels per degree, 64 pixels per degree and 256 pixels per degree). Surface roughness at each pixel is defined as the difference between the results of closing and opening processing. The dichotomy between maria and highlands shows strong roughness contrast in global roughness maps with different resolutions (4 pixels per degree, 8 pixels per degree and 16 pixels per degree). However, equirectangular map
projection of LOLA global GDRs has distortion in shapes of objects on the surfaces of Polar Regions. To show the scale-dependent feature of our roughness measure, different-size disk-shape SEs are applied to map global surface roughness from 701S to 701N in simple equirectangular projection. The observation is that 60 km 60 km SE provides the most significant roughness measure to reflect most of scale-dependent roughness features based on LOLA GDRs with the scale 64 pixels per degree sampling. Because of the highest resolution (256 pixels per degree) of LOLA global GDRs, typical craters and basins can be extracted to analyze their roughness features and discuss the correlations with geological units. Roughness characteristics of selected young craters and basins have significant associations with melt materials.
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Please cite this article as: Cao, W., et al., Lunar surface roughness based on multiscale morphological method. Planetary and Space Science (2014), http://dx.doi.org/10.1016/j.pss.2014.09.009i