What Is a Polygonal Impact Crater? A Proposed Framework Toward Quantifying Crater Shapes

Impact craters are used for a wide array of investigations of planetary surfaces. A crater form that is somewhat rare, forming only ∼10% of impact craters, is the polygonal impact crater (or PIC). These craters have been visually, manually identified as having at least two rim segments that are best represented as straight lines. Such straight lines or edges are most often used to infer details about the subsurface crust where faults control the structure of the crater cavity as it formed. The PIC literature is scant, but almost exclusively these craters are identified manually, and the potentially straight edges are classified and measured manually. The reliance on human subjectivity in both the identification and measurement motivated us to design a more objective algorithm to fit the crater rim shape, measure any straight edges, and measure joint angles between straight edges. The developed code uses a Monte Carlo approach from a user-input number of edges to first find a reasonable shape from purely random possible shapes; it then uses an iterative Monte Carlo approach to improve the shape until a minimum difference between the shape and rim trace is found. It returns the result in a concise, parameterized form. This code is presented as a first step because, while we experimented with several different metrics, we could not find one that could consistently, objectively return an answer that stated which shape for a given crater was the best; this objective metric is an area for future improvement

Homography Estimation Based on Order-Preserving Constraint and Similarity Measurement

Copyright 2018 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.Homography is an important concept that has been extensively applied in many computer vision applications. However, accurate estimation of the homography is still a challenging problem. The classical approaches for robust estimation of the homography are all based on the iterative RANSAC framework. In this paper, we explore the problem from a new perspective by finding four point correspondences between two images given a set of point correspondences. The approach is achieved by means of an order-preserving constraint and a similarity measurement of the quadrilateral formed by the four points. The proposed method is computationally efficient as it requires much less iterations than the RANSAC algorithm. But this method is designed for small camera motions between consecutive frames in video sequences. Extensive evaluations on both synthetic data and real images have been performed to validate the effectiveness and accuracy of the proposed approach. In the synthetic experiments, we investigated and compared the accuracy of three types of methods and the influence of the proportion of outliers and the level of noise for homography estimation. We also analyzed the computational cost of the proposed method and compared our method with the state-of-the-art approaches in real image experiments. The experimental results show that the proposed method is more robust than the RANSAC algorithm

A Proposition for Geodetic Recording of Active Fault Zones

Establishing recent displacements along faults is an important and delicate task. Larger\ud faults are accompanied by broader fault zones that require a specific approach to geodetic\ud measurements of fault block displacements. The vector of fault block displacements, or\ud resultant, is a vector sum of differential displacements within the fault zone. For the purposes\ud of recording the displacements we propose the stabilization of a geodetic network of\ud points positioned in fault blocks outside the fault zone, whereby the displacements would\ud be manifested in the deformation of the network. The resultant displacement vector can\ud then be derived from the latter deformation, and from that, the dip and strike of the fault\ud zone as well as the extent of the displacement

Measuring shapes with desired convex polygons

In this paper we have developed a family of shape measures. All the measures from the family evaluate the degree to which a shape looks like a predefined convex polygon. A quite new approach in designing object shape based measures has been applied. In the most cases such measures were defined by exploiting some of shape properties. An illustrative example might be the shape circularity measure derived by exploiting the well-know result that the circle has the largest area among all the shapes with the same perimeter. In the approach applied here, no desired property is needed and no optimizing shape has to be found. We start from a desired/selected convex polygon, and develop the related shape measure. The measures obtained range over the interval (0,1] and pick the maximal possible value, equal to 1, if and only if the measured shape coincides with the selected convex polygon, used to develop the a particular measure. All the measures are invariant with respect to translations, rotations, and scaling transformations. The method used has an straightforward extension to a wider family of shape measures, dependent on a tuning parameter involved. Another extension leads to a family of the new shape convexity measures

Aging effects on the statistical and structural properties of the fornix of the brain

The brain consists of a complex network of axons, transmitting electrical impulses between interconnected neurons across distances that range from fractions of millimeters to meters. Myelinated axons, or nerve fibers, are axons that are wrapped by a myelin sheath, serving as an electrical insulation that increases the propagation speed of the signal along the nerve fiber while conserving the energy consumed and the space needed to maintain such propagation speed without myelin. Changes in the axon and surrounding myelin sheath during development and aging, or as a consequence of pathology, affect conduction and the proper functioning of the axon bundles. It is therefore important to be able to quantify the properties of these axons and their bundles and to discern which features best characterize the observed differences. We study the effects of aging on the myelinated axons in the fornix of the brain. The fornix is the principal subcortical output tract of the hippocampal formation, which plays a central role in memory. We obtain a collection of 328 high-quality electron micrographs from the fornix of 25 different rhesus monkey brains, ranging from young adults to the elderly, with both males and females. In this work, we develop a novel advanced recognition algorithm for automatically identifying myelinated axons and their surrounding myelin sheath. We extract multiple features of the nerve fibers and fully characterize their spatial structure. Using a feature selection algorithm, we discriminate between young and aged rhesus monkeys with a high level of accuracy and pinpoint the differences in the aging process at the ultrastructural level across the life span. We observe a decline in the density of myelinated axons as well as in the fraction of occupied axon area with age, while the average axon area shows no dependence on the age of the subjects. We show an increase in the myelin thickness of axons for the female subjects, while no dependence is observed for the male subjects. This sex dichotomy is also present in the g-ratio of the myelinated axons, i.e., the ratio of the axon diameter to the fiber diameter. The method detailed here could be adapted to enable recognition in other areas as well as for changes caused by brain pathologies or by developmental disorders. Furthermore, the data collected will ultimately be useable in better modeling conduction properties in myelinated axons and better understanding how the aging process affects them

Understanding the brain through its spatial structure

The spatial location of cells in neural tissue can be easily extracted from many imaging modalities, but the information contained in spatial relationships between cells is seldom utilized. This is because of a lack of recognition of the importance of spatial relationships to some aspects of brain function, and the reflection in spatial statistics of other types of information. The mathematical tools necessary to describe spatial relationships are also unknown to many neuroscientists, and biologists in general. We analyze two cases, and show that spatial relationships can be used to understand the role of a particular type of cell, the astrocyte, in Alzheimer's disease, and that the geometry of axons in the brain's white matter sheds light on the process of establishing connectivity between areas of the brain. Astrocytes provide nutrients for neuronal metabolism, and regulate the chemical environment of the brain, activities that require manipulation of spatial distributions (of neurotransmitters, for example). We first show, through the use of a correlation function, that inter-astrocyte forces determine the size of independent regulatory domains in the cortex. By examining the spatial distribution of astrocytes in a mouse model of Alzheimer's Disease, we determine that astrocytes are not actively transported to fight the disease, as was previously thought. The paths axons take through the white matter determine which parts of the brain are connected, and how quickly signals are transmitted. The rules that determine these paths (i.e. shortest distance) are currently unknown. By measurement of axon orientation distributions using three-point correlation functions and the statistics of axon turning and branching, we reveal that axons are restricted to growth in three directions, like a taxicab traversing city blocks, albeit in three-dimensions. We show how geometric restrictions at the small scale are related to large-scale trajectories. Finally we discuss the implications of this finding for experimental and theoretical connectomics

Statistical Analysis of Simple Martian Impact Crater Morphometry

Mars, a planet with a tenuous atmosphere and starved of surface water, is a prime location for studying impact craters. Earth’s thick atmosphere stops small craters from forming, and erosion destroys the craters that do. The size range of Martian craters is much greater and craters last much longer than terrestrial craters. The variety of Martian terrain makes it possible to study effects of geology on crater morphology and crater modification, making Mars a much more interesting study location than the Moon. In this project, we investigate the effects of crater size and target geology on crater shape for small (D \u3c 5km), simple impact craters. For example, we see morphometry differences between Vastitas Borealis, sedimentary rocks and volcanics. In addition, we investigate changes in morphology between fresh and modified craters. To study craters on a global scale, we adapted computer programs to generate digital elevation models using stereo images from the HiRISE camera on the Mars Reconnaissance Orbiter and developed new software and algorithms to extract crater rim traces and crater shape statistics automatically. We show that moderate crater age has no apparent effect on rim roundness, and that crater flank elevation profiles in the Northern lowlands have lower power-law decay exponents (αF≤−4) than the global distribution (αF≤−6). We identify a possible crater shape transition at D≈300m to increased rim sharpness. Our results show geologic dependence on crater formation, and can be used to test models of crater formation and modification in the future

Advances in planetary geology

Topics discussed include: (1) Martian global tectonics; (2) the origin and evolution of a circular and an irregular lunar mare; (3) stratigraphy of Oceanus Procellarum basalts: sources and styles of emplacement; (4) the tectonic evolution of the Oceanus Procellarum Basin; (5) charting the Southern Seas: the evolution of the Lunar Mare Australe; (6) the stratigraphy of Mare Imbrium; and (7) Storms and rains: a comparison of the Lunar Mare Imbrium and Oceanus Procellarum

Investigations into the Tectonics of Uranian and Saturnian Icy Satellites

This dissertation reports a range of analyses of tectonic structures on various icy satellites and the implications of these analyses for each satellite’s geologic history. On Miranda, I tested the hypothesis that faults of the Arden Corona boundary and the 340º [degree] Chasma are listric in geometry. A listric fault geometry implies the presence of a subsurface detachment, which likely marked Miranda’s brittle-ductile transition (BDT) at the time of faulting. Results support the hypothesis for the Arden Corona boundary, although not for the 340˚ [degree] Chasma. Using the Arden Corona fault system geometry, the BDT depth, thermal gradient, and heat flux were estimated. Those estimates are consistent with a previously hypothesized heating event associated with an ancient tidal resonance of Miranda with Umbriel and/or Ariel. On the Saturnian satellites Tethys, Rhea, and Dione, I analyzed normal fault slope geometries to test the hypothesis that faults on icy bodies reflect dip values derived from laboratory deformation experiments in cryogenic H2O [water] ice. The results show that faults within Ithaca Chasma on Tethys, Avaiki Chasmata on Rhea, and one scarp within Dione’s Wispy Terrain exhibits scarp slopes that are shallower than these values. Analyses of these fault systems indicate that viscous relaxation is the most viable explanation for these shallow slopes. I modeled the potential role of viscous relaxation in creating these shallow fault slopes. The modeling results support the formation of these faults with steep dips, consistent with deformation experiments, followed by their relaxation due to lithospheric heating events. Finally, I tested for the presence of subtle and/or non-visible fractures within Dione’s Non-Wispy Terrain. A set of statistical analyses of crater rim azimuth data was used to test for polygonal impact craters (PICs) at randomly distributed study locations. The results indicate that PICs are widespread throughout the Non-Wispy Terrain, supporting the hypothesis that fractures are widespread throughout this terrain, despite the lack of visible fractures. These results demonstrate that analysis of crater geometries is a useful tool for identifying and mapping fractures with dimensions below the resolution of available images