Applying the mathematical theory of stochastic processes to lunar and planetary science: the ancient oceans on Mars case

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 represents different aspects of some physical processes we can analyze using mathematics. Each model of a stochastic process according to the MTSP can provide one or more interpretations in the MST domain. The importance of MTSP is that each such interpretation can provide large amount of new information. While large body of work on the impact crater statistics according to MST has already been done, it is yet to be investigated as to how we can model a stochastic process according to MTSP; for example, bombardment of the planetary surface or something else in a Lunar and Planetary Science (LPS) domain. In order to show possible achievements, the possible existence of a Martian ocean was chosen as a query that could be addressed through computations using presumptions according to MTSP, including probability of existence as well as lateral and vertical extent and duration of time. While the presumptions for this particular case will also be addressed in certain degree, this will be done primarily to show complexities of some physical process that can be modeled, rather than to prove correctness of the concrete values computed here. While this in itself can be the objective in some future work toward the formal proof of the probability, extent, and timing of oceans on Mars, the basic idea here is to show the basic principles of MTSP, and its potential for addressing LPS-related phenomena. Here, I attempt to show how this approach can: (1) provide large amounts of previously unknown information about physical processes on the surface of the planet, (2) lead to a better understanding of the processes that have shaped the surface of the planet, and/or (3) help constrain the amount of resurfacing. Coupled with other current methodologies, MTSP can result in a better understanding of the history of Mars, as well as other lunar and planetary bodies.     

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.     

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.     

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.     

Laboratory investigations of the survivability of bacteria in hypervelocity impacts.

It is now well established that material naturally moves around the Solar System, even from planetary surface to planetary surface. Accordingly, the idea that life is distributed throughout space and did not necessarily originate on the Earth but migrated here from elsewhere (Panspermia) is increasingly deemed worthy of consideration. If life arrived at the Earth from space, its relative speed will typically be of order many km s-1, and the resulting collision with the Earth and its atmosphere will be in the hypervelocity regime. A mechanism for the bacteria to survive such an impact is required. Therefore a programme of hypervelocity impacts in the laboratory at (4.5 +/- 0.6) km s-1 was carried out using bacteria (Rhodococcus) laden projectiles. After impacts on a variety of target materials (rock, glass and metal) attempts were made to culture Rhodococcus from the surface of the resulting craters and also from the target material ejected during crater formation. Control shots with clean projectiles yielded no evidence for Rhodococcus growth from any crater surface or ejecta. When projectiles doped with Rhodococcus were used no impact crater surface yielded colonies of Rhodococcus. However, for four shots of bacteria into rock (two on chalk and two on granite) the ejecta was afterwards found to give colonies of Rhodococcus. This was not true for shots onto glass. In addition, shots into aerogel (density 96 kg m-3) were also carried out (two with clean projectiles and two with projectiles with Rhodococcus). This crudely simulated aero-capture in a planetary atmosphere. No evidence for Rhodococcus growth was found from the projectiles captured in the aerogel from any of the four shots.     

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。      

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。     

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.     

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,...     

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.     

Large-scale impact cratering on the terrestrial planets

Impact cratering as a geologic process on the terrestrial planets is addressed. The crater densities on the Earth and Moon form the basis for a standard flux-time curve, which can be used to date unsampled planetary surfaces and constrain the temporal history of endogenic geologic processes. The attached uncertainties and the shape of the flux curve (a rapid exponential decay for the period 4.6 – 4.0 by, followed by the establishment of a constant fluid by 3.5 – 3.0 by which continues more or less to the present) are such that only very old (3.8 by) and very young ( 1.0 by) surfaces can be dated with some confidence. Dating of intermediate-aged surfaces is more imprecise; a problem which is most significant for the geologic history of Mars.

The cratering mechanics of simple craters are fairly well understood. A transient cavity of roughly parabolic cross-section results from the combined excavation and displacement of the target rocks by the cratering flow-field, which can be approximated by the Z-model derived from shallow-buried explosive events. The walls of the transient crater are unstable and slump inwards, resulting in a final bowl-shaped crater partially filled by breccia. The formation process of larger, shallow complex structures is less well understood. Recent models favor the complete collapse of the initial cavity, with the dynamic uplift of the excavated cavity floor. Regardless of the driving force for uplift, yield strength of the target rocks must be drastically reduced during cavity modification by an, as yet, imprecisely known process.

The formation of large impact basins had a profound effect on planetary evolution. They define the basic tectonic and stratigraphic framework of the Moon and their secondary effects lasted for 10⁸ y. The evidence is less compelling from other planets, but a general feature appears to be the concentration of later endogenic activity in and around basins. On Earth, it is possible that basin-formation contributed to the establishment of the dichotomy between proto-continental and proto-oceanic crusts. The effects of impact continue into recent geologic history and may be linked to major biological changes on Earth, such as at the Cretaceous-Tertiary boundary.     

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.     

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.     

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.     

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).     

Characterizing bedrock lithologies using Small Crater Rims and Ejecta Probing (SCREP)

This paper describes the rationale, methodology, and importance of focusing on the rim and proximal ejecta of small (<5 km in diameter), immature impact craters to explore an underlying crustal lithology. Small Crater Rim and Ejecta Probing (SCREP) describes a methodology and application program that extracts bedrock spectral and compositional information from a remote sensing image. Extracted data can yield the pristine lithologies of a planetary crust that would otherwise be obscured by the products of space weathering processes. SCREP was developed with lunar data, specifically Clementine multispectral image mosaics, therefore the technique is discussed in this context. However, its application to other airless solar system bodies is apparent. Knowledge of the pristine bedrock compositions of a planetary crust provides insight into geological surface processes, which can be used to refine models of planetary interiors and their evolution.     

The lunar dust pendulum

An analytic model for the motion of a positively charged lunar dust grain in the presence of a shadowed crater at a negative potential in vacuum is presented. It is shown that the dust grain executes oscillatory trajectories, and an expression is derived for the period of oscillation. Simulations used to verify the analytic expression also show that because the trajectories are unstable, dust grains are either ejected from the crater’s vicinity or deposited into the crater forming “dust ponds.” The model also applies to other airless bodies in the solar system, such as asteroids, and predicts that under certain conditions, particularly near lunar sunset, oscillating dust “canopies” or “swarms” will form over negatively charged craters.     

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.     

基于多因子综合评估的月球探测软着陆区域及最佳巡航路线分析

选择合适的软着陆区域及规划合理的巡航路线是月球探测的基础工作。以位于月球背面南极—艾肯（South Pole-Aitken,SPA）盆地内的冯·卡门（Von Kármán）撞击坑作为研究区域,综合使用多因子分析评估了月球探测的着陆区域和巡航路线。评价体系主要包括能表征着陆安全性的撞击坑的密度、撞击坑的影响区域、整个区域的平整情况、部分区域的平整情况等因子和体现科学探索意义的区域垂直结构、岩石属性和（FeO+TiO₂）含量等因子,其中科学探索的评估分析是在安全可行性的基础上进行的。结果表明：在多因子叠加分析的基础上可选择出A、B及C 3个着陆区,并通过科学研究因子分析出路线2及路线3为合适的巡航路线。本研究为月球探测器着陆和巡航路线的规划提供了科学依据,为后续的月球探测工作提供了技术支持。