A machine learning approach to crater detection from topographic data

Craters are distinctive features on the surfaces of most terrestrial planets. Craters reveal the relative ages of surface units and provide information on surface geology. Extracting craters is one of the fundamental tasks in planetary research. Although many automated crater detection algorithms have been developed to exact craters from image or topographic data, most of them are applicable only in particular regions, and only a few can be widely used, especially in complex surface settings. In this study, we present a machine learning approach to crater detection from topographic data. This approach includes two steps: detecting square regions which contain one crater with the use of a boosting algorithm and delineating the rims of the crater in each square region by local terrain analysis and circular Hough transform. A new variant of Haar-like features (scaled Haar-like features) is proposed and combined with traditional Haar-like features and local binary pattern features to enhance the performance of the classifier. Experimental results with the use of Mars topographic data demonstrate that the developed approach can significantly decrease the false positive detection rate while maintaining a relatively high true positive detection rate even in challenging sites.     

A new approach based on crater detection and matching for visual navigation in planetary landing

This paper provides an approach of crater detection and matching to visual navigation in planetary landing missions. The approach aims to detect craters on the planetary surface and match them to a landmark database during the descent phase of a planetary landing mission. Firstly an image region pairing method is proposed to detect the crater by using an image region feature detector. Then a WTA-rule is adopted to match the detected crater to the crater in database. To further reduce the false matching rate, an efficient method for reducing false matches using parameters of crater in 3-D database is proposed. Real images of planetary terrain and a semi-physical planetary landing simulation platform are utilized to test the performance of the approach, simulation results show the proposed approach is able to match the required number of craters to the database for pin-point planetary landing with a low rate of false detection and false matching, which will lead to an improved planetary landing precision.     

Exploring links between crater floor mineralogy and layered lunar crust

Floors of similar sized craters, representing material from similar depth horizons, have been studied to explore their suitability as mineralogy indicators at various depths within the lunar crust. Clementine UV–vis multispectral data was used to generate mineral abundance maps of crater floors and surroundings using a modified version of algorithm given by Pieters et al. (2001) [Pieters, C.M., Head, J.W., Gaddis, L., Jolliff, B. and Duke, M. Rock types of the south pole aitken basin and extent of basaltic volcanism, JGR (106) E11, 28001–28022, 2001.]. Substantial processing of the crater floor material due to variety of geological processes is evident in the generated maps, making straight forward interpretations difficult. However, systematic compositional trends in fresh craters on the floors of target craters seem to indicate the feasibility of such an effort.     

Single crater-aided inertial navigation for autonomous asteroid landing

In this paper, a novel crater-aided inertial navigation approach for autonomous asteroid landing mission is developed. It overcomes the major deficiencies of existing approaches in the literature, which mainly focuses on the case where craters are abundant in the camera field of view. As a result, traditional crater based methods require at least three craters to achieve crater matching, which limits their application in final landing phase where craters are scarce in the camera’s field of view. In contrast, the proposed algorithm enables single crater based crater matching based on a novel 2D-3D crater re-projection model. The re-projection model adopts inertial measurements as a reference, and re-projects the 3D crater model onto descent images to achieve the matching to its counterpart. An asteroid landing simulation toolbox is developed to validate the performance of the proposed approach. Through comparison with the state-of-the-art local image feature and crater based navigation algorithms, the proposed approach is validated to achieve a competitive performance in terms of feature matching and pose estimation accuracy with a much lighter computational cost.     

Integrated method for crater detection from topography and optical images and the new PH9224GT catalogue of Phobos impact craters

In a large majority of lunar and planetary surface images, impact craters are the most abundant geological features. Therefore, it is not surprising that crater detection algorithms (CDAs) are one of the most studied subjects of image processing and analysis in lunar and planetary science. In this work we are proposing an Integrated CDA, consisting of: (1) utilization of DEM (digital elevation map)-based CDA; (2) utilization of an optical-based CDA; (3) re-projection of used datasets and crater coordinates from normal to rotated view and back; (4) correction of the brightness and contrast of a used optical image; and (5) tile generation for the optical-based CDA and an assembling of results with an elimination of multiple detections, in combination with a pyramid approach down to the resolution of the available DEM image; and (6) a final integration of the results of DEM-based and optical-based CDAs, including a removal of duplicates. The proposed CDA is applied to one specific asteroid-like body, the small Martian moon Phobos. The experimental evaluation of the proposed CDA is done by a manual verification of crater-candidates and a search for uncatalogued craters. The evaluation has shown that the proposed CDA was used successfully for cataloging Phobos craters. The major result of this paper is the PH9224GT – currently the most complete global catalogue of the 9224 Phobos craters. The possible applications of the new catalogue are: (1) age estimations for any selected location; and (2) comparison/evaluation of the different chronology and production functions for Phobos. This confirms the practical applicability of the new Integrated CDA – an additional result of this paper, which can be used in order to considerably extend the current crater catalogues.     

Bayesian network-based extraction of lunar impact craters from optical images and DEM data

Impact craters are among the most noticeable geomorphological features on the planetary surface and yield significant information about terrain evolution and the history of the solar system. Thus, the recognition of impact craters is an important branch of modern planetary studies. Aiming at addressing problems associated with the insufficient and inaccurate detection of lunar impact craters, a decision fusion method within the Bayesian network (BN) framework is developed in this paper to handle multi-source information from both optical images and associated digital elevation model (DEM) data. First, we implement the edge-based method for efficiently searching crater candidates which are the image patches that can potentially contain impact craters. Secondly, the multi-source representations of an impact crater derived from both optical images and DEM data are proposed and constructed to quantitatively describe the two-dimensional (2D) and three-dimensional (3D) morphology, consisting of Histogram of Oriented Gradient (HOG), Histogram of Multi-scale Slope (HMS) and Histogram of Multi-scale Aspect (HMA). Finally, a BN-based framework integrates the multi-source representations of impact craters, which can provide reductant and complementary information, for distinguishing craters from non-craters. To evaluate the effectiveness and robustness of the proposed method, experiments were conducted on three lunar scenes using both orthoimages from the Lunar Reconnaissance Orbiter (LRO) and DEM data acquired by the Lunar Orbiter Laser Altimeter (LOLA). Experimental results demonstrate that integrating optical images with DEM data significantly decreases the number of false positives compared with using optical images alone, with F₁-score of 84.8% on average. Moreover, compared with other existing fusion methods, our proposed method was quite advantageous especially for the detection of small-scale craters with diameters less than 1000 m.     

Crater detection via genetic search methods to reduce image features

Recent approaches to crater detection have been inspired by face detection’s use of gray-scale texture features. Using gray-scale texture features for supervised machine learning crater detection algorithms provides better classification of craters in planetary images than previous methods. When using Haar features it is typical to generate thousands of numerical values from each candidate crater image. This magnitude of image features to extract and consider can spell disaster when the application is an entire planetary surface. One solution is to reduce the number of features extracted and considered in order to increase accuracy as well as speed. Feature subset selection provides the operational classifiers with a concise and denoised set of features by reducing irrelevant and redundant features. Feature subset selection is known to be NP-hard. To provide an efficient suboptimal solution, four genetic algorithms are proposed to use greedy selection, weighted random selection, and simulated annealing to distinguish discriminate features from indiscriminate features. Inspired by analysis regarding the relationship between subset size and accuracy, a squeezing algorithm is presented to shrink the genetic algorithm’s chromosome cardinality during the genetic iterations. A significant increase in the classification performance of a Bayesian classifier in crater detection using image texture features is observed.     

Hydrocode modelling of hypervelocity impacts on ice

Experimental data are now widely available for the size of craters resulting from hypervelocity impacts of millimetre scale projectiles onto water ice targets. At such size scales the bowl shaped crater formed in ductile materials, or in larger scale impacts, is here surrounded by a large spallation zone due to the brittle nature of the ice. Modelling of these impacts therefore has to take account of this spallation. Here we used the iSALE2 hydrocode to simulate such impacts and compared the results to experimental data. We found that it was possible to reproduce the experimental data over a range of speeds (1–7 km s⁻¹) for aluminium and copper projectiles. Initially, to reproduce the large spallation regions around the craters it was assumed that above a certain degree of damage, material was removed by spallation. However this simple one-parameter model failed to model the crater depth adequately. Accordingly, to obtain the best agreement of the simulations with the experimental data, a two-step ice strength was introduced, whereby above a critical amount of damage (0.95), the yield strength reduced from 1 MPa (intact) to 70 kPa (damaged). As a result, experimental data for crater depth and diameter and the results of the simulations agree to within 6% for diameter and 5% for depth over the impact energy range used in the experiments (1–240 J).     

Hybrid method for crater detection based on topography reconstruction from optical images and the new LU78287GT catalogue of Lunar impact craters

Impact craters are ubiquitous and well-studied structures of high geological relevance on the surfaces of the Earth’s Moon, the terrestrial planets, the asteroids and the satellites of the outer planets. Therefore, it is not surprising that crater detection algorithms (CDAs) are one of the most studied subjects of image processing and analysis in lunar and planetary science. In this paper we are proposing a Hybrid CDA: a modified DEM (digital elevation map) reconstruction method used as a step in an existing CDA based on Hough transform. The new Hybrid CDA consists of: (1) reconstruction of topography from optical images using a shape from shading approach; (2) utilization of the DEM-based CDA; (3) correction of brightness and contrast of optical images used in order to be more suitable for evaluation of detections. An additional result of this work is a new method for evaluation of topography reconstruction algorithms, using a DEM-based CDA and an earlier approach for evaluation of CDAs. The new Hybrid CDA was tested using two Chandrayaan-1 Moon Mineralogy Mapper (M³) images and two excerpts of the Lunar Reconnaissance Orbiter (LRO) Wide Angle Camera (WAC) global optical image mosaic. As a result, the number of craters inside these four regions increased considerably from 1754 (as available in the previous LU60645GT catalogue) to 19 396 craters (as available in the resulting new LU78287GT catalogue). This confirmed the practical applicability of the new Hybrid CDA, which can be used in order to considerably extend current crater catalogues.     

基于深度学习的大型陨石坑识别方法研究

陨石坑是天体表面最为显著的地形特征,传统陨石坑识别方法主要是对小型陨石坑正负样本的二分类问题研究,且效率和精度均不高。以星体宏观视角下的大型陨石坑作为研究对象,结合图像处理和神经网络等方面的知识,创建了来自不同数据源的陨石坑样本数据库,研究了数据源对网络模型泛化能力的影响,提出了一种效率更高的陨石坑多分类识别方法。在非极大值抑制（NMS）算法基础上,提出了一种精度更高的陨石坑检测算法。经过参数优化和实验验证,构建的基于深度学习的多尺度多分类陨石坑自动识别网络框架取得了较高的准确率,在同源验证集上识别率可达0.985,在异源验证集上识别率可达0.863,并且有效改善了目标检测时检测框冗余及误检测的问题。      

Detection of sub-kilometer craters in high resolution planetary images using shape and texture features

Counting craters is a paramount tool of planetary analysis because it provides relative dating of planetary surfaces. Dating surfaces with high spatial resolution requires counting a very large number of small, sub-kilometer size craters. Exhaustive manual surveys of such craters over extensive regions are impractical, sparking interest in designing crater detection algorithms (CDAs). As a part of our effort to design a CDA, which is robust and practical for planetary research analysis, we propose a crater detection approach that utilizes both shape and texture features to identify efficiently sub-kilometer craters in high resolution panchromatic images. First, a mathematical morphology-based shape analysis is used to identify regions in an image that may contain craters; only those regions - crater candidates - are the subject of further processing. Second, image texture features in combination with the boosting ensemble supervised learning algorithm are used to accurately classify previously identified candidates into craters and non-craters. The design of the proposed CDA is described and its performance is evaluated using a high resolution image of Mars for which sub-kilometer craters have been manually identified. The overall detection rate of the proposed CDA is 81%, the branching factor is 0.14, and the overall quality factor is 72%. This performance is a significant improvement over the previous CDA based exclusively on the shape features. The combination of performance level and computational efficiency offered by this CDA makes it attractive for practical application.     

Application of hydrocode modelling to the study of hypervelocity impact crater morphology

In order to obtain a better understanding and model of the natural and artificial particulate environment from measurements of impact damage features on returned spacecraft materials, it is necessary to be able to determine how the size and shape of an impact feature are related to the parameters of the impacting particle. The AUTODYN-3D hydrocode has been used to study the effects of projectile density, velocity and impact angle on the depth, diameter and ellipticity of the impact craters. The results are used to determine the distributions of crater depth to crater diameter ratios and of crater ellipticities to be expected on an aluminium surface exposed to an isotropic distribution of incident particles of given densities and velocities. Comparison of these calculated distributions with those observed for craters on aluminium clamps on various faces of the Long Duration Exposure Facility shows that particles with a wide range of densities, including significant proportions both greater and smaller than that of aluminium, were responsible for these craters.     

月球阿波罗盆地区域月壳结构及光谱特征

位于月球南极–艾肯(South Pole-Aitken Basin,SPA)盆地内的前酒海纪阿波罗盆地跨越了SPA盆地的瞬时穴和盆缘。SPA盆地是已确认的月球上最大最古老的撞击盆地,因此阿波罗盆地对于认识月球的内部结构和成分、区域地质作用和演化历史具有不可替代的作用。阿波罗盆地区域月壳具有很强的不对称性,靠近SPA盆缘处厚而靠近SPA盆地中心处薄,其峰环内部拥有最薄的月壳厚度。阿波罗盆地区域具有不同的光谱吸收特征。在阿波罗盆地外,靠近SPA盆缘具有更多Mg辉石吸收特征的短波吸收,而靠近SPA中心区域具有更多高Ca辉石吸收特征的长波吸收。盆地内部不同地质单元的光谱吸收特征也有差异,月海为高Ca辉石的吸收特征,峰环为Mg辉石的短波长吸收。阿波罗盆地具有最薄的月壳厚度、高程差达8 km的地层剖面、位于月球背面SPA盆地内的月海、发育充分的中央峰环,其独特性使它成为最有价值的采样点。     

月球撞击坑辐射纹的形成和消失机制及可能的年代学应用

辐射纹是年轻撞击坑周缘呈辐射状分布的明亮细条纹,是月表最显著的地貌特征之一,也是月球科学领域热点研究之一.根据目前对于月球撞击坑辐射纹的形成和类型的认识,分析辐射纹消失相关的空间风化、撞击导致的物质混合等地质过程;比较不同形成年龄撞击坑辐射纹的光学成熟度(OMAT)剖面,发现溅射物逐渐成熟过程中OMAT剖面的演变过程,...     

一种基于多尺度边缘提取的陨石坑检测算法

针对星体表面的陨石坑可用于探测器的自主导航、障碍识别等任务,提出一种基于多尺度边缘提取的陨石坑检测算法。该算法首先利用高斯金字塔得到不同尺度的陨石坑图像;其次,针对不同尺度的陨石坑图像,利用EDPF边缘提取算法对陨石坑进行边缘提取,并连接关键边缘像素点为直线段来近似表示图像边缘;然后将具有相同偏转方向的边缘直线段连接成圆弧,并将有相似半径和中心的圆弧拟合成候选圆和椭圆;最后对候选圆、椭圆进行验证。该算法的优点在于,能够准确地检测出陨石坑,有较高的检测率,且对存在较多陨石坑的图像有较好的检测结果。     

The first new application of the Mathematical Theory of Stochastic Processes to lunar and planetary science: Topography-Profile Diagrams of Mars

The Mathematical Statistics Theory (MST) and the Mathematical Theory of Stochastic Processes (MTSP) are different branches of the more general Mathematical Probability Theory (MPT) that can be used to investigate physical processes through mathematics. Each model of a stochastic process, according to MTSP, can provide one or more interpretations in the MST domain. A large body of work on impact crater statistics according to MST exists, showing cumulative crater frequency (N km⁻²) as a function of age (years) for some particular crater diameter. However, this is only one possible representation in the MST domain of the bombardment of the planetary surface modeled as a stochastic process according to MTSP. The idea that other representations are possible in the MST domain of the same stochastic process from MTSP has been recently presented. The importance of the approach is that each such mathematical-based interpretation can provide a large amount of new information. Coupled with MOLA data, Topography-Profile Diagrams (TPD) are one of the many examples that can provide a large amount of new information regarding the history of Mars. TPD consists of: (1) Topography-Profile Curve (TPC), which is a representation of the planet’s topography, (2) Density-of-Craters Curve (DCC), which represents density of craters, (3) Filtered-DCC (FDCC), which represents DCC filtered by a low-pass filter, included with the purpose of reducing the noise, and (4) Level-of-Substance-Over-Time Curve (LSOTC), which represents interpretation of the influence on the distribution of craters shown by FDCC. TPC uniquely corresponds to the computation of TPD, whereas DCC depends on algorithms for computing the elevation of each crater according to the topography, center coordinates, and radius of impact crater, and FDCC relies on the architecture of the custom designed low-pass filter for filtering DCC. However, all variations of DCC and FDCC, which includes the various impact crater data sets, showed a correlation among the density of craters and elevation over 70–80% of the planet surface. Additionally, if we assume that the ocean primarily caused the noted correlation, LSOTC offers a mathematical approach for estimating topographic change of the ocean’s extent over time. Accordingly, TPD is the first new practical application of MTSP to lunar and planetary sciences, showing correlation of topography to a physical process.     

Experimental study of impact-cratering damage on brittle cylindrical column model as a fundamental component of space architecture

The cylindrical column of brittle material processed from soil and rock is a fundamental component of architectures on the surface of solid bodies in the solar system. One of the most hazardous events for the structure is damaging by hypervelocity impacts by meteoroids and debris. In such a background, cylindrical columns made of plaster of Paris and glass-bead-sintered ceramic were impacted by spherical projectiles of nylon, glass, and steel at velocity of about 1–4.5 km/s. Measured crater radii, depth, and excavated mass expressed by a function of the cylinder radius are similar irrespective of the target material, if those parameters are normalized by appropriate parameters of the crater produced on the flat-surface target. The empirical scaling relations of the normalized crater radii and depth are provided. Using them, crater dimensions and excavated mass of crater on cylindrical surface of any radius can be predicted from the existing knowledge of those for flat surface. Recommendation for the minimum diameter of a cylinder so as to resist against a given impact is provided.     

Open framework for objective evaluation of crater detection algorithms with first test-field subsystem based on MOLA data

Crater Detection Algorithms (CDAs) applications range from estimation of lunar/planetary surface age to autonomous landing on planets and asteroids and advanced statistical analyses. A large amount of work on CDAs has already been published. However, problems arise when evaluation results of some new CDA have to be compared with already published evaluation results. The problem is that different authors use different test-fields, different Ground-Truth (GT) catalogues, and even different methodologies for evaluation of their CDAs. Re-implementation of already published CDAs or its evaluation environment is a time-consuming and unpractical solution to this problem. In addition, implementation details are often insufficiently described in publications. As a result, there is a need in research community to develop a framework for objective evaluation of CDAs. A scientific question is how CDAs should be evaluated so that the results are easily and reliably comparable. In attempt to solve this issue we first analyzed previously published work on CDAs. In this paper, we propose a framework for solution of the problem of objective CDA evaluation. The framework includes: (1) a definition of the measure for differences between craters; (2) test-field topography based on the 1/64° MOLA data; (3) the GT catalogue wherein each of 17,582 craters is aligned with MOLA data and confirmed with catalogues by N.G. Barlow et al. and J.F. Rodionova et al.; (4) selection of methodology for training and testing; and (5) a Free-response Receiver Operating Characteristics (F-ROC) curves as a way to measure CDA performance. The handling of possible improvements of the framework in the future is additionally addressed as a part of discussion of results. Possible extensions with additional test-field subsystems based on visual images, data sets for other planets, evaluation methodologies for CDAs developed for different purposes than cataloguing of craters, are proposed as well. The goal of the proposed framework is to contribute to the research community by establishing guidelines for objective evaluation of CDAs.     

小行星形貌测绘与表征技术

小行星表面形貌测绘是深空小行星探测的首要任务。提出了一种适应探测器抵近观测的立体视觉在线测绘小行星形貌的方法,即先由立体相机获得所摄重叠区的三维地形,再用前后立体模型的连接点将各个独立模型连成一个完整地形信息,经整体最小二乘平差,确定小行星的形貌模型及特征;同时提出了一种基于等值线分析的撞击坑特征提取方法,即通过提取、分析地形等值线识别出地形中撞击坑特征。实验结果显示,本文所构建的原型系统能够快速重建出探测区域的三维地形,并识别出地形中撞击坑特征,证明了所提方法具有实用性。