ATHEER L. SALIH et al: CONSTRUCTION OF AN AGE MAP OF THE REGION AROUND THE YOUNG LUNAR …
Construction of an Age Map of the Region Around the Young Lunar Crater Hell Q
Atheer L. Salih1, Arne Grumpe1, Christian Wöhler1, Harald Hiesinger2 1Image Analysis Group, TU Dortmund, D-44227 Dortmund, Germany 2Institut für Planetologie, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany email: [email protected]
Abstract — The determination of the age of planetary surfaces basically depends on the areal density of detected craters. The analysis of the impact crater size frequency distribution (CSFD) is a classical approach that supports the age estimation process for planetary surfaces. Usually, manual crater counting and size evaluation is leading to an estimate of the CSFD, which is consequently considered as a time-consuming process especially for large surface areas provided with a high image resolution. The availability of global image mosaics at high resolution implies a need for automated crater detection algorithms. In this work, a template-based crater detection algorithm is applied to analyze image data under known illumination conditions. The results are used to produce the CSFD for a region around the young lunar crater Hell Q, where the threshold value of the applied automatic crater detection algorithm is calibrated based on a 16 km² region with known manual crater count data. As an advanced step, the accordingly configured crater detection algorithm is then applied to a much larger surface region of about 70 km² surrounding the selected calibration area, and a spatially resolved map of the surface age is calculated for overlapping rectangular areas, each covering 2 x 1.5 km2. The obtained age values range from 1-2 Ma for the immediate vicinity of Hell Q to about 60 Ma at about 10 km distance from Hell Q.
Keywords - Crater statistics; automatic crater detection; crater detection algorithm; absolute model age; age mapping; Hell Q
I. INTRODUCTION Except for Hell Q, the image exhibits only craters of small sizes, less than a few tens of meters in diameter [12]. An Estimation of the geologic age of planetary surfaces is of absolute model age (AMA) is obtained based on the resulting high interest in planetary research. The surface age automated crater counts. By examining the whole surface estimation relies basically on counting impact craters and area of the available high-resolution image a map of the measuring their diameters. The availability of large amounts surface age is created based on the automatically obtained of high-resolution planetary images that cover different solar crater counts. system objects provides the possibility to study them deeply and construct crater catalogues that contains large numbers of manually detected small craters [1] [2]. II. AUTOMATIC ALGORITHMS FOR CRATER DETECTION Apparently, impact craters are the results of previous impacts that happened in different intervals of time on In general, the field of crater detection is an interesting planetary surfaces [3]. Impact craters exist in large and important topic in planetary science, which traditionally abundances and are widespread on the Moon, Mars and relies on the manual inspection of orbital images [7]. In the Mercury due to lack of an atmosphere and conditions domain of remote sensing, automatic crater detection suitable for life [4]. The age of a planetary surface increases algorithms are an attractive approach for researchers that with increasing impact crater density, i.e. surfaces with a low reduce the time required to analyze large amounts of number of impact craters are usually younger than densely planetary image data and provide the locations and sizes of cratered surface parts. Estimations of the crater size- craters in images automatically [13] [14] [15]. frequency distribution (CSFD) are a basic tool for assessing Small craters are much more frequent than large craters, the ages of surface regions. The derivation of the absolute but these small craters are often not easily visible in global model age (AMA) of a surface requires obtaining the number image data sets. A variety of different CDAs have been of craters and their diameters [5] [6] [7] [8] [9] [10] [11]. constructed and developed by researchers who recognized In this context, manual counting and measuring of craters the importance of the impact craters distribution and its is a time-consuming process, while automatic crater strong effect on remote geologic studies of planetary surfaces detection may lead to increased false positive detections. A (e.g. [1]). An issue of special importance has been to increase comparison between automatic crater detection algorithms the level of detection performance for planetary images with and manual crater counts has been implemented before (e.g. reduced clarity of impact craters by creating new CDAs or [1]); the results of the automatic detection algorithm differed, by refining existing techniques [1]. Since more than a decade especially for craters of small size. ago, a multitude of new approaches for automatic crater In this paper, an automatic crater detection algorithm detection has been developed (see [14] for a detailed (CDA) is applied to a high-resolution image of the lunar overview). The developed CDAs are usually divided into crater Hell Q of about 4 km diameter and its ejecta blanket. two classes, where one group of algorithms detects craters in
DOI 10.5013/IJSSST.a.17.33.59 59.1 ISSN: 1473-804x online, 1473-8031 print ATHEER L. SALIH et al: CONSTRUCTION OF AN AGE MAP OF THE REGION AROUND THE YOUNG LUNAR …
images while another group relies on digital elevation to allow for the detection of craters across a broad range of models (DEMs) for crater detection [14] [16]. diameters. As a matching criterion, the normalized cross- Many existing CDAs are limited to the detection and correlation coefficient between the templates on the one hand counting of craters without retrieving more detailed and the analyzed image part on the other hand is used. information [17] [18]. The developing step after such CDAs A fusion process for the crater candidates is applied after is the automatic classification and extraction of further the template matching stage that will choose only the most contextual information in addition to the crater detection significant detection result in the presence of multiple itself [19]. The CDA implemented in [19] divides the craters detections at the same position and/or with slight diameter into groups with different floor shapes. It was used to differences. distinguish between different crater degradation states and for the detection of simple lunar craters of small diameter [19]. Furthermore, crater detection should have a high priority for additional mapping due to the important role of the CSFD as a remote sensing tool for surface age estimation [20]. Some image-based CDAs rely on techniques that process the test image to detect characteristics similar to the circular or elliptical shapes of crater rims, followed by a matching process between the resulting candidates and the manually detected craters [1]. Machine learning approaches applied in other CDAs are trained on image data labeled before by a human expert, followed by applying the resulting system to new image data [21]. In this paper, the CDA described in [22] is applied to the Lunar Reconnaissance Orbiter Narrow Angle Camera (LRO NAC) image M126961088LE (http://wms.lroc.asu.edu/lroc/ view_lroc/LRO-L-LROC-2-EDR-V1.0/M126961088LE) showing the small crater Hell Q and its surroundings. This CDA is a template matching based system which is able to Figure 1. The three basic crater shapes derived from LOLA track data. detect craters of less than about 10 pixels diameter in lunar images without the need for DEM data. The image-based algorithm will be applied to a part of the image, which will be divided into three equally sized areas for the purpose of evaluation and calibration of the optimal detection threshold. Consequently, the statistical analysis of the automatically estimated CSFD is the main element for the AMA estimation. Furthermore, a spatially resolved AMA map of Hell Q and the neighboring surface will be constructed.
III. IMAGE-BASED CRATERS DETECTION ALGORITHM
The template-based detection algorithm introduced in [22] is applied to the image data for analysis. The algorithm relies on six generated 3D crater models, which were generated depending on the analysis of track data of the Lunar Orbiter Laser Altimeter (LOLA) instrument [23] covering 23 small craters of about 8 km diameter located near lunar crater Plato [22]. These craters were related to three basic shapes: the simple bowl shape, flat-floored shape and central-mounded complex shape. Three representative profiles of these three shapes are shown in Fig. 1. These profiles were split in half, and by rotating the half-profiles a set of six 3D crater temples Figure 2. The six 3D crater models. Models 1 and 2 represent the small were created (Fig. 2), which were in turn used to synthesize central mounded shape, flat-floored craters correspond to models 3 and 4, and models 5 and 6 represent simple bowl-shaped craters. six artificially illuminated image templates using the Hapke model [24] [25] given the known illumination conditions Figure 3. under which the image was acquired. These six templates were rescaled to a size range of 5-200 image pixels in order
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IV. THE REGION OF INTEREST: HELL Q While in the study in [12] the software Craterstats2 (http://www.geo.fu-berlin.de/en/geol/fachrichtungen/planet/ The roughly 4 km sized crater Hell Q is located at software/index.html) is used, in our study we use our own 33.0° S and 4.4° W in the eastern part of the large walled Matlab implementation of the CSFD-based AMA estimation plain Deslandres [12], roughly 300 km northwest of the well- method described in [6] [7] [8] [9] [10] in order to be able to known large crater Tycho. In [12], the Hell Q region is apply the AMA estimation to a large number of small regarded for an AMA estimation based on very small craters overlapping sub-areas of the test region. The AMA value with diameters between 5 m and 41 m, where potential obtained based on our implementation, regarding the same secondary craters are excluded by detecting non-uniform set of 678 craters as in [12], corresponds to 1.500.069 Ma, spatial distributions using a statistical test. According to [12], 0.076 which is close to the value of 1.37±0.052 Ma obtained in the ejecta blanket of Hell Q exhibits a lower density of small [12]. The small difference is probably due to undocumented impact craters than an impact melt pond of Tycho. features in the software Craterstats2 [10]. Consequently, the age of Hell Q is lower than the age of The template matching based CDA applied in this study Tycho [26]. strongly depends on a detection threshold that controls the In the study in [26], which regards among others the CDA sensitivity and efficiency. This threshold value is craters Hell Q and Tycho, an age of 110-110 Ma is estimated adjusted such that the automatically determined AMA for the crater Tycho and a value below this range for Hell Q. corresponds as closely as possible to the value obtained by The young age of Hell Q is inferred from the fact that this manual crater counting. For validation purposes, the crater is superposed on one of the rays formed by ejecta 16.3 km2 reference region is divided into three adjacent areas material of Tycho [26]. In [27] the structure of a small of equal size, and the minimum absolute difference between impact melt deposit on the floor of Hell Q is described. In the CDA-based and the manually determined AMA has been the morphological and spectral study in [28] about the calculated for each of the three sub-areas. The detection central peak region of Tycho, this crater is considered as a threshold obtained for each area is then applied to the other young impact crater of an approximate age of 110 Ma. In the two areas. Table 1 summarizes the resulting number of works in [29] and [30] age values of Tycho of 100 Ma and craters in each sub-area detected by the CDA and by manual 96 Ma, respectively, are given. Similarly, an age of about counting respectively. Table 2 presents the AMA values 100 Ma is estimated for Tycho in [31]. A slightly higher age 24 derived from the CDA-based algorithm, which range from of 13820 Ma has been determined for Tycho in [32]. 1.25 Ma to 2.39 Ma. The arithmetic mean of the three The image data used in this study is LRO NAC image obtained threshold values, corresponding to 0.677, can be M126961088LE. It has a resolution of about 0.49 m/pixel. considered as the “optimal” threshold. Applying this The solar angle of incidence amounts to 43.47° threshold value to the total 16.3 km² reference area results in (http://wms.lroc.asu.edu/lroc/view_lroc/LRO-L-LROC-2- an AMA of 1.650.023 Ma. EDR-V1.0/M126961088LE). The AMA estimation process 0.024 relies on the resulting CSFD which represents the number of craters per diameter interval per area. As a reference for crater detection, we chose an area of 16.3 km2 size from the surface near Hell Q, which is the same as the region analyzed in [12]. All craters in the test region with diameters between 3 m and 41 m were counted manually in [12], where very small craters with diameters between 3 m and 7 m were neglected in the crater counts for the AMA estimation due to the occurrence of the rollover point in the CSFD. Furthermore, craters with diameters between 13 m and 21 m is neglected in [12] due to the non-randomness of the craters in this diameter range which indicates their origin as secondary craters. As a result, a set of 678 craters is considered suitable in [12] for estimating the AMA.
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TABLE I. RESULTS OF THE THRESHOLD ADAPTATION: NUMBER OF CRATERS.
Trained on Tested on Area 1 Area 2 Area 3 Manual Count Optimal Threshold 0.668 0.677 0.686 - Area 1 92 craters 79 craters 72 craters 247 Area 2 127 craters 108 craters 95 craters 228 Area 3 97craters 84craters 74 craters 203
TABLE II. RESULTS OF THE THRESHOLD ADAPTATION: ESTIMATED AMAS.
Trained on Tested on Area 1 Area 2 Area 3 Manual Count Optimal Threshold 0.668 0.677 0.686 - 2.39 Ma 1.68 Ma 1.25 Ma 2.42 Ma Area 1 +0.064 -0.066 Ma +0.092 -0.100Ma +0.194 -0.194Ma +0.157 -0.174Ma 1.97 Ma 1.60 Ma 1.32 Ma 1.58 Ma Area 2 +0.144 -0.177Ma +0.236 -0.236Ma +0.205 -0.205Ma +0.102 -0.113Ma 1.68 Ma 1.53 Ma 1.40 Ma 1.38 Ma Area 3 +0.086 -0.095Ma +0.101 -0.109Ma +0.103 -0.110Ma +0.111 -0.145Ma
V. AGE MAP OF THE HELL Q REGION blue color in the age map of Fig. 3 presumably corresponds to the ejecta blanket of Hell Q. The automatic construction of a surface age map is a new The more or less gradual increase of the surface age with interesting task. To create such map, the template-based increasing distance from Hell Q may be due to a gradual CDA has been applied to an orthorectified 1 m/pixel version thinning of the ejecta blanket of Hell Q with increasing of LRO NAC image M126961088LE with a wide sliding distance from the crater. In the thinner parts of the ejecta window of 2000 × 1500 pixels (2 × 1.5 km2) moving over the blanket, craters on the older underlying surface “shine whole image at a step width of 10 pixels (10 m). Given the through” the ejecta and thus indicate a higher surface age. very small size of the craters and their limited number in our The observation that the AMA of the outer parts of the ejecta case study, the template-based CDA is able to identify a blanket of Hell Q is younger than 100 Ma, the approximate large fraction of the manually determined craters (a more age of the crater Tycho, can be attributed to the superposition detailed performance analysis of the CDA is currently in of Hell Q on one of the ejecta rays of Tycho as noted in [26]. progress). Only a small fraction is missed due to neighboring The study area is considered as being partially affected by or overlapping craters. In addition, there might occur a slight secondary crater contamination [12]. Some of the detected positional offset between template-based CDA and manually craters are distributed as clusters that might influence the detected crater positions, but that does not affect the AMA inferred AMAs [12] (see e.g. [33] for a general description of estimation process as it only relies on the craters density per the effect of secondary craters on CSFD-derived ages of area and their diameters values. planetary surfaces). In [12], each diameter interval of the The CSFDs were computed for the overlapping histogram representing the CSFD is analyzed with respect to rectangular sub-areas of LRO NAC image M126961088LE the uniform distribution of the respective craters, where a using the “optimal” threshold value of 0.677. Using our diameter interval with non-uniform crater distribution is Matlab implementation of the CSFD-based technique detected using statistical F and G tests and is excluded from according to [7] [8] [9] [10], the sub-area specific AMA the CSFD [12]. Since this approach might remove uniformly values were computed and translated into an age map distributed craters together with the clustered craters from the (Fig. 3). The AMA values of the map range from between 0.1 and 15 Ma in the center of the region to about 55-70 Ma same diameter interval, leading to a removal of too many in the southern, northwestern and southeastern parts of the craters from the CSFD, a useful feature of future versions of region. our system will be a refined statistical analysis of the spatial The CDA-derived AMA map indicates that the crater crater distribution to separate clustered craters from Hell Q and its immediate surroundings are younger than the uniformly distributed craters without the need for removing surface to the north and south, due to the very young age of all craters of one or several diameter intervals. Hell Q. The AMA values are gradually increasing from the crater towards the north and more abruptly at about 4 km distance south of the crater (Fig. 3). The region depicted in
DOI 10.5013/IJSSST.a.17.33.59 59.4 ISSN: 1473-804x online, 1473-8031 print ATHEER L. SALIH et al: CONSTRUCTION OF AN AGE MAP OF THE REGION AROUND THE YOUNG LUNAR …
VI. SUMMARY AND CONCLUSION
N An image-based template matching CDA has been applied to the high-resolution LRO NAC image M126961088LE showing the region around the small lunar crater Hell Q. The applied CDA has yielded a reliable CSFD based on the detected craters and their estimated diameters, and the AMA of the surface has been derived. A calibration process based on reference manual crater counts for a sub- region of the total image was applied to obtain an appropriate detection threshold value. The resulting average AMA of the crater floor is consistent with the reference age obtained by manual crater counting in [12]. A construction of a spatially resolved map of the AMA has been obtained by applying the template-based CDA to overlapping sub-regions of the study area. The age map shows that the crater Hell Q is only 1-2 Ma old and thus clearly much younger than the neighboring surface. The estimated AMA increases continuously with increasing distance from Hell Q, which may be due to a gradual decrease in thickness of its ejecta blanket. The described automatic age map construction technique allows for a comparison between surface parts or geological units in terms of their AMAs. It can be easily applied to any other surface areas once manual crater count data are available as a reference for a small sub-region. As a step of future work, it might be useful to increase the detection rate for more uncommon crater types by providing the CDA with a larger number of templates representing a larger variety of crater shapes, especially degraded craters. Another future approach is to distinguish between primary and secondary craters according to their shape or spatial distribution and then to analyze the effect of the secondary craters on the AMA estimation.
ACKNOWLEDGMENTS We would like to thank Kurt Fisher for providing us with the ortho-rectified 1 m/pixel version of LRO NAC image M126961088LE and the full manual crater count, localization and diameter data set as described in [12].
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