remote sensing

Article Trace Evidence from Mars’ Past: Fingerprinting Transverse Aeolian Ridges

Louis Scuderi * , Timothy Nagle-McNaughton and Joshua Williams Department of Earth and Planetary Sciences, University of New Mexico, Albuquerque, NM 87131, USA; [email protected] (T.N.-M.); [email protected] (J.W.) * Correspondence: [email protected]



Received: 11 March 2019; Accepted: 2 May 2019; Published: 5 May 2019


Abstract: Linear dunes and human fingerprints share many characteristics. Both have ridges, valleys, and defects (minutiae) in the form of bifurcations and termination of ridgeline features. For dunes, determining how defects vary across linear and transverse dunefields is critical to understanding the physics of their formative processes and the physical forcing mechanisms that produce dunefields. Unfortunately, manual extraction of defect locations and higher order characteristics (type, orientation, and quality) from remotely sensed imagery is both time-consuming and inconsistent. This problem is further exacerbated when, in the case of imagery from sensors in orbit around Mars, we are unable to field check interpretations. In this research, we apply a novel technique for extracting defects from multiple imagery sources utilizing a robust and well-documented fingerprint minutiae detection and extraction software (MINDTCT: MINutiae DecTeCTion) developed by the National Institute of Standards and Technology (NIST). We apply our ‘fingerprinting’ approach to Transverse Aeolian Ridges (TARs), relict aeolian features commonly seen on the surface of Mars, whose depositional and formative processes are poorly understood. Our algorithmic approach demonstrates that automating the rapid extraction of defects from orbitally-derived high-resolution imagery of Mars is feasible and produces maps that allow the quantification and analysis of these features.

Keywords: Linear dunes; Transverse Aeolian Ridges (TARs); defects; minutiae; fingerprints; Mars

1. Introduction Even a cursory comparison of images of ripples, linear, and transverse dunes to human fingerprints reveals many similarities in the form and organization of features (Figure1). In general, dunes and fingerprints are composed primarily of fields of ridges with intervening valleys. In most cases, these features are parallel and somewhat regularly spaced with a width and characteristic wavelength that is potentially related to prevailing formative forces acting over a 3-dimensional surface [1–9]. Dunefields are found on planetary surfaces (Mars and Venus) [10–15] and their satellites [16–18] in environments that differ significantly from Earth. On Mars dunefields exhibit similar defect patterns over a range from centimeter-scale ripples to multi-kilometer-scale longitudinal dunes [9,19]. Many of these longitudinal Martian features are termed Transverse Aeolian Ridges (TARs) and are prevalent across much of the surface of Mars. Ridges, the primary features in both dunefield and fingerprint feature spaces, are typically the only uniquely identifiable and bonified features in a field of poorly defined objects (Figure2)[ 20]. Other objects within these feature spaces are defined with reference to ridges. Ridges can be defined by their length, orientation, and derived metrics (sinuosity, etc.), as well as the number, type, and spatial arrangement of secondary features. Since these features can be georeferenced, they can be used to define slip faces and other features with well-defined upper edges, and indirectly used to define valleys or interdune areas which are less distinct on all sides. Within the aeolian analysis environment these

Remote Sens. 2019, 11, 1060; doi:10.3390/rs11091060 www.mdpi.com/journal/remotesensing Remote Sens. 2019Remote, 11, Sens. 1060 2019, 11, x FOR PEER REVIEW 2 of2 of 24 25

used to define slip faces and other features with well‐defined upper edges, and indirectly used to secondary bonifieddefine valleys subfeatures, or interdune are termed areas which defects are with less splits distinct and on crest all sides. ends identifiedWithin the asaeolian Y-junctions analysis and terminationsenvironment respectively these secondary [3,5,6,21– 29bonified]. subfeatures, are termed defects with splits and crest ends From theidentified perspective as Y‐junctions of fingerprint and terminations analysis, respectively defects are [3,5,6,21–29]. termed minutiae, with subfeatures From the perspective of fingerprint analysis, defects are termed minutiae, with subfeatures termed bifurcations and ridge endings [30–35]. Minutiae are characterized by their type, position, and termed bifurcations and ridge endings [30–35]. Minutiae are characterized by their type, position, orientation, and are unique from fingerprint to fingerprint. Minutiae are classified as local features [36] and orientation, and are unique from fingerprint to fingerprint. Minutiae are classified as local occurring atfeatures unique [36] points occurring that areat unique invariant points with that respect are invariant to global with respect transformations to global transformations [37–39] and are [37– thus useful39] for and the are unique thus useful identification for the unique of individuals. identification They of individuals. differ from They global differ features from global which features are characterizedwhich by attributes are characterized that capture by attributes the global that spatial capture relationships the global spatial of a relationships fingerprint as of expresseda fingerprint by as ridge form (arch,expressed loop, by and ridge whorl), form (arch, orientation, loop, and and whorl), spacing orientation, [40]. and spacing [40].

a. b.

c. d.

e. f.

Figure 1. Dune crest and fingerprint ridgeline forms. a. Linear dunes Namib Desert 24.43 15.17, Figure 1. Dune crest and fingerprint ridgeline forms. (a) Linear dunes Namib Desert− −24.43 15.17, (b) b. TransverseTransverse Aeolian RidgesAeolian (TARS)Ridges (TARS) on Mars on (ImageMars (Image ESP_036397_1785) ESP_036397_1785)c. Linear (c) Linear dunes dunes on on Titan Titan (Cassini T8 flyby,(Cassini Oct. T8 flyby, 2005, Oct. 8◦ S,2005, 264 8°S,◦W, 264°W, ~ 300 ~300 m resolution). m resolution).d. (d)Perspective Perspective view view of of ripples ripples on larger on larger dune slope facet (1 cm resolution) from a digital handheld camera. Note crest bifurcations and

terminations. e. Ripples on dunes Nili Patera, Mars (High Resolution Imaging Science Experiment (HiRISE) image PIA18818). f. Raw ten-print image f0444_03 from the NIST fingerprint database [41] showing arch structure, ridge organization and bifurcations, and terminations (mm resolution). Remote Sens. 2019, 11, x FOR PEER REVIEW 3 of 25

dune slope facet (1 cm resolution) from a digital handheld camera. Note crest bifurcations and terminations. (e) Ripples on dunes Nili Patera, Mars (High Resolution Imaging Science Experiment (HiRISE) image PIA18818). (f) Raw ten‐print image f0444_03 from the NIST fingerprint database [41] Remote Sens. 2019, 11, 1060 3 of 24 showing arch structure, ridge organization and bifurcations, and terminations (mm resolution).

a. b.

c.

Figure 2.2. Dune types and wind direction relationships. (a.a) LinearLinear dunesdunes andand theirtheir generatinggenerating wind field.field. b.(b)Transverse Transverse dunes dunes and and their their generating generating wind wind field. field.c. Linear(c) Linear and and transverse transverse dune dune features features and theirand their attributes attributes [20]. [20]. 2. Materials and Methods 2. Materials and Methods 2.1. Background to the Problem 2.1. Background to the Problem 2.1.1. Dune Processes 2.1.1. Dune Processes Dune forms are the result of interactions between the local wind regime and topography, sand transport,Dune sand forms supply, are the and result other of localinteractions variables between including the vegetation local wind [ 2regime,5–7,42 –and44]. topography, Linear dunes sand are thetransport, most common sand supply, form ofand desert other dune local on variables Earth [45 including], occurring vegetation under climatic [2,5–7,42–44]. conditions Linear in hyperariddunes are desertsthe most to common subhumid form Sandy of desert Lands dune [28]. on These Earth dunes [45], occurring exhibit ridges under with climatic distinct conditions variability in inhyperarid spacing anddeserts organization, to subhumid potentially Sandy Lands reflective [28]. ofThese both dunes formative exhibit processes ridges with and the distinct evolution variability in the in dunefield spacing overand organization, time. potentially reflective of both formative processes and the evolution in the dunefield over Lineartime. dunes form parallel to the net sand transporting wind vector, while transverse dunes formLinear perpendicular dunes form to the parallel dominant to the wind net direction sand transporting [2,46] in regions wind withvector, restricted while transverse sediment supply dunes underform perpendicular a bidirectional to wind the dominant with relatively wind direction high wind [2,46] direction in regions variability with restricted [1,47,48 ].sediment Winds coming supply fromunder di aff bidirectionalerent directions wind and with striking relatively the dune high obliquely wind direction have been variability found to[1,47,48]. be responsible Winds coming for net transport,from different erosion directions or deposition and striking [2]. In contrast,the dune transverse obliquely duneshave been form found perpendicular to be responsible to the dominant for net windtransport, direction erosion in or areas deposition of high [2]. sand In contrast, abundance transverse with distinctly dunes form different perpendicular lee and windward to the dominant faces. Forwind both direction dune types, in areas the of interaction high sand betweenabundance a wind with fielddistinctly and a different mobile substrate lee and windward results in faces. erosional For andboth depositional dune types, processesthe interaction which between in turn a produce wind field dunefield and a mobile patterning substrate [1,46, 47results]. in erosional and depositionalIn recent processes years, there which have in beenturn produce important dunefield advances patterning in the knowledge [1,46,47]. of dune processes and dunefieldIn recent patterning years, through there have careful been field important and modeling advances studies in the of winds knowledge and sand of dune movement processes [1,49 –and51]. Telferdunefield et al. patterning [29] have suggested through careful that dunefield field and patterning modeling is studies an emergent of winds property and sand influenced movement by regional [1,49– and51]. /Telferor site-specific et al. [29] boundary have suggested conditions that dunefield [4–6]. However, patterning Kocurek is an etemergent al. [52] noted property that influenced the observed by varianceregional and/or in dunefield site‐specific defects boundary exceeds that conditions generated [4–6]. from However, numerical Kocurek modeling, et al. implying [52] noted that that dune the formationobserved variance and evolutionary in dunefield conditions defects are exceeds still poorly that generated understood from [52 –numerical54]. Werner modeling, and Kocurek implying [5,6] inferredthat dune that formation dune patterns and evolutionary should evolve conditions such that are dune still spacing poorly increases understood asymptotically [52–54]. Werner and defect and densityKocurek increases. [5,6] inferred that dune patterns should evolve such that dune spacing increases asymptoticallyLongitudinal and bedforms defect density typically increases. have long crests and large spacing that is inversely related to defect density [45]. If along-crest transport is sufficiently large, defects facing upstream, which are eroding, remain free standing, and defects facing downstream, where sediment is being deposited, typically attach to adjacent bedform crests in Y-junctions forming an upstream-branching network (Figure3)[ 6]. Upstream-facing defects move downstream due to erosion, and downstream-facing defects move upstream because of deposition at the junction of the Y. Remote Sens. 2019, 11, x FOR PEER REVIEW 4 of 25

Longitudinal bedforms typically have long crests and large spacing that is inversely related to defect density [45]. If along‐crest transport is sufficiently large, defects facing upstream, which are eroding, remain free standing, and defects facing downstream, where sediment is being deposited, Remotetypically Sens. attach2019, 11 to, 1060 adjacent bedform crests in Y‐junctions forming an upstream‐branching network4 of 24 (Figure 3) [6]. Upstream‐facing defects move downstream due to erosion, and downstream‐facing defectsWhen move a mobile upstream defect because approaches of deposition a bedform at crestthe junction and attaches, of the it Y. forms a Y-junction (Figure3)[ 55]. ModelingWhen and a mobile field-based defect studies approaches [56,57] a show bedform that the crest downstream and attaches, fork it of forms the Y-junction a Y‐junction then (Figure detaches, 3) resulting[55]. Modeling in a free-standing and field‐based defect studies and a [56,57] new near show continuous that the downstream crest line. This fork result of the implies Y‐junction that dune then interactionsdetaches, resulting drive pattern in a free evolution‐standing at defect all scales and a [ 9new,28,58 near,59], continuous and defect crest organization line. This is result reflective implies of that evolution.dune interactions Therefore, drive data pattern on defect evolution locations at all and scales their organization,[9,28,58,59], and especially defect organization with respect tois direflectivefferent dune of that types evolution. and under Therefore, different data environmental on defect locations conditions, and may their profoundly organization, aid especially understanding with ofrespect dune to formation different processes. dune types and under different environmental conditions, may profoundly aid understanding of dune formation processes.

Figure 3. Figure 3. LinearLinear dune defect formation and migration. The The dominant dominant wind wind vector is represented here by the filled arrow, while the migration of the dune defects are represented as open arrows. Transport by the filled arrow, while the migration of the dune defects are represented as open arrows. Transport parallel to crest lines produces downwind migration of defects (terminations: black circles) and upwind parallel to crest lines produces downwind migration of defects (terminations: black circles) and migration of Y-junctions (bifurcations: white filled circle) [6]. upwind migration of Y‐junctions (bifurcations: white filled circle) [6]. 2.1.2. Transverse Aeolian Ridges on Mars 2.1.2. Transverse Aeolian Ridges on Mars Modern Mars is characterized by an aeolian dominated, hyperarid environment with a tenuous atmosphereModern (~6.36 Mars baris characterized on average). Theby an landscape aeolian dominated, has been extensively hyperarid modified environment by aeolian with a processes, tenuous includingatmosphere short (~6.36 term bar seasonal on average). winds thatThe entrain landscape and transporthas been dustextensively along with modified rare high by velocityaeolian winds,processes, possibly including linked short with term atmospheric seasonal densitywinds that changes entrain capable and transport of transporting dust along sand with grains rare [60 high–63]. Muchvelocity of winds, the surface possibly contains linked depressions with atmospheric and craters density where changes aeolian capable process of transporting have deposited sand grains linear aeolian[60–63]. featuresMuch of (Figure the surface4). contains depressions and craters where aeolian process have deposited linearMars aeolian contains features a wide (Figure diversity 4). of aeolian bedforms and Transverse Aeolian Ridges (TARs) are one of the most common [64,65]. TARs were first defined [66] to describe linear to curvilinear bedforms on Mars that formed as either large ripples or small transverse dunes. They were specifically named “ridges” by Bourke et al. [66] to preserve the possibility of both ripple or dune origins [67]. Alternatively they have been described as reversing dunes [68–72] or linked to similar periodic bedrock ridges [73]. Despite the name, TARs do not have to be composed of transverse dune forms alone. Symmetry in cross-section suggests that some TARs are in fact are linear rather than true transverse forms. TARs were first observed in images from the Viking orbiter [74,75] and Mars Orbiter Camera (MOC) [76,77]. They are concentrated in the mid to low latitudes [64], and can be found in most settings including the floors of the deepest impact basins to the highest volcanoes [77]. Similar features have been observed on Earth [69,78,79]. As Wilson [67] notes, TARs are widespread on Mars, but their formation mechanisms, age, composition, and controlling environmental factors, as well as their role in the global sediment cycle are poorly constrained. Spatial patterning of TAR fields, as expressed in the organization and relative occurrence of defects, is potentially a measure of underlying physical processes that formed TAR fields. Determining how defects may vary across features is critical to understanding TAR formation and evolution.

Remote Sens. 2019, 11, 1060 5 of 24 Remote Sens. 2019, 11, x FOR PEER REVIEW 5 of 25

a.

b.

FigureFigure 4. 4.Jezero Jezero Crater Crater Delta Delta (Mars (Mars 20202020 Landing site) site) (aa.) Color altimetry altimetry of of digital digital elevation elevation model. model. LatitudeLatitude 18.49 18.49°◦ Longitude Longitude 77.41 77.41°,◦, ScaleScale 1.001.00 mm/pixel./pixel. (DTEEC_002387_1985_003798_1985_U01) (DTEEC_002387_1985_003798_1985_U01) (b) b. TheThe large large unnamed unnamed crater crater on on the the southern southern portionportion of the delta delta that that contains contains a afield field of of TARs TARs that that will will potentiallypotentially be be visited visited and and interogated interogated during during thethe Mars 2020 rover rover mission. mission. This This TAR TAR field field is isanalyzed analyzed in Sectionsin Sections 3.1 3.1 and and 3.2 3.2.. Images Images provided provided byby NASANASA/JPL/University/JPL/University of of Arizona. Arizona. 2.1.3. The Extraction and Characterization Problem Mars contains a wide diversity of aeolian bedforms and Transverse Aeolian Ridges (TARs) are oneQuantification of the most ofcommon dunefield [64,65]. organization, TARs were both first in termsdefined of extraction[66] to describe of raw linear metrics to from curvilinear remotely sensedbedforms imagery on andMars characterization that formed as of either the spatial large arrangementripples or small of these transverse metrics, dunes. presents They significant were problemsspecifically in terms named of producing“ridges” by data Bourke that et can al. be [66] used to preserve to link form the possibility and underlying of both physical ripple or processes. dune Sinceorigins diff erent[67]. Alternatively observers may they define have been crests described and defects as reversing differently, dunes they [68–72] may manuallyor linked to place similar them inperiodic slightly bedrock different ridges locations [73]. Despite and/or the miss name, or misinterpret TARs do not bothhave to type be composed and position. of transverse The lack dune of an objective and systematic approach to quantify dunes limits our ability to analyze these environments and broadly characterize them [29]. Extraction and quantification of dune crests and the defects Remote Sens. 2019, 11, 1060 6 of 24 and Y-junctions of these crests is both time intensive, subjective, and often applied only for small areas of dunefields [9,20,24]. Geocoding their location is difficult, with both existing computer and human-based approaches outputting results that are not completely reproducible [20]. Day and Kocurek [9] estimated that visually measured defects estimated by multiple observers for a given dunefield varied by up to 20%. They also noted that measurement of defects and their interaction density is subjective, with image interpretation limiting an observer’s ability to discern small offsets (e.g., whether a Y-junction exists or “almost” exists), and with respect to images representing snapshots in time, capturing features that can migrate and change over short time intervals. As well, estimating direction of these defects is nearly impossible directly by humans, tending to be approximate at best and nonreproducible between different observers [9]. Extraction limitations severely impact analysis of dune defect location and type. If a consistent and repeatable automated defect extraction processes could be formulated, it would significantly augment our ability to map these features and to understand linear dunefield organization, evolution and dynamics. In this study the fingerprint minutiae extraction software (MINDTCT: MINutiae DeTeCTion) [31,32] was evaluated to determine whether dune defects could (1) be extracted from remotely sensed satellite imagery of aeolian features, (2) used to quantitatively characterize these features, (3) produce repeatable results, and (4) to determine whether this extraction can occur in an automated manner and be applicable over a wide range of scales, spatial extents and environments. We have chosen to examine this extraction using Transverse Aeolian Ridges (TARs) on Mars with the goal of extracting defects and using defect type and spatial organization to classify TAR type.

2.2. Extracting Dune Defects from Remotely Sensed Imagery

2.2.1. Basic Approach The basic premise of this work is to produce a defect extraction approach that can be used to quantify and analyze dunefield organization, and to eventually answer the question: “Is there some fundamental organization of dunefields that reflects the physical forcing that produced the field?” As we noted above, no automated or semiautomated method to extract and analyze these defect features from remotely sensed imagery exists. We strive here to develop a methodology that is fast, simple to apply, easily repeatable, and that produces consistent results. The absence of quantitative metrics at the dunefield scale has been noted as a limitation in past studies [20,29]. An ideal approach would thus be an automated or semiautomated methodology to enable quantitative, systematic, objective, and large-scale morphometric analysis. Within aeolian science, this extraction has traditionally been done by manual interpretation of aerial and satellite imagery. However, as Telfer et al. [29] note, because of the time-consuming nature of this approach it has been limited to small dunefields [80] or derived from small subsamples of larger dunefields [81,82]. Most recently Telfer et al. [29] delineated linear dune crest trend lines over larger areas automatically from remotely sensed data using a combination of multispectral analysis using Landsat 8 imagery in concert with a LInear Dune Optimized edge detection algorithm (LIDO) based on Sobel operators, directional filtering, and topologically-constrained recursion. They also found that the high-resolution DEM data (~10 m) was useful in areas with simple patterning but was of marginal use generally since dune height was of the same order as the vertical precision of the dataset, precluding realistic extraction. Looking outside of aeolian science, we find a large range of approaches that may be applied to the extraction of dune defects. These include edge detection, segmentation, and thresholding [29], all of which are also used in extraction of minutiae (defects) from fingerprints and the identification of individuals. Computer based approaches relying on pattern recognition [83–86], edge detection [87–89], segmentation [90], and classification from remotely sensed data [91,92] have been used in part to address different portions of the problem of defect extraction. However, the extraction of these features in the aeolian environment is a very complex process and currently there is no simple solution in place. Each of the above approaches provides at least one part of an analysis package that would allow Remote Sens. 2019, 11, 1060 7 of 24 defect extraction, but not all parts are currently in place and no integrated system exists to utilize these myriad approaches in the aeolian sciences. The forensic science community has developed a robust and mature fingerprint software package that allows users to extract fingerprint minutiae and to further analyze these minutiae for fingerprint matching and identification [93–95]. The discipline standard is currently the well-documented MINDTCT (MINutiae DeTeCTion) fingerprint minutia detection and extraction software developed by the National Institute of Standards and Technology (NIST) [31,32]. It has the advantage over other approaches in that it is an open application written using the C sharp (C#) programming language and as such can run on many platforms and be called from other applications. The software is not subject to copyright protection, is in the public domain, and is available without license or cost. Therefore, the development and application of a modified version of MINDTCT may provide the aeolian science community with a robust tool for the extraction of dune defects. We discuss the MINDTCT approach and present its application over a range of imagery below. We specifically deal with the extraction of defects from Transverse Aeolian Ridges (TARs) on Mars, but note that the MINDTCT approach has also been successfully applied on terrestrial dunes and is potentially applicable to the automated extraction from imagery of any feature type that exhibits linear structures and defects.

2.2.2. The Underlying Algorithmic Approach of MINDTCT MINDTCT [31,32] is a set of algorithms used to detect minutiae and to assess the characteristics of each minutiae including location (x,y), type (termination of bifurcation), orientation, and quality. The starting point for MINDTCT is an input image with 256 gray levels (8 bit). Output files include image maps of ridge orientation, edge quality, local and regional metrics (surrounding field characteristics and statistics), and minutiae (Figure5). In the following we outline the basic process of generating these fields using MINDTCT and then turn to a discussion of how this processing flow can be altered to be applicable to theRemote problem Sens. 2019 of dune, 11, x FOR crest PEER and REVIEW dune defect extraction. 8 of 25

Figure 5. Flow chart forFigure the MINutiae 5. Flow chart DecTeCTion for the MINutiae (MINDTCT) DecTeCTion algorithm (MINDTCT [31,32]. ) algorithm [31–32].

Input Fingerprint FileInput Fingerprint File MINDTCT is designedMINDTCT to use the is standarddesigned 10-printto use the fingerprint standard 10 image‐print (Figurefingerprint1f) used image by (Figure the FBI 1f) used by the FBI with a resolution of 500with pixels a / resincholution or 19.69 of pixels 500 pixels/inch/mm. In humans or 19.69 this pixels/mm. average fingerprint In humans wavelength this average fingerprint is ~0.46 mm. We notewavelength that with this is input~0.46 mm. resolution, We note the that average with distance this input between resolution, fingerprint the average ridges distance between of ~0.46 mm equatesfingerprint to ~8 or 9 ridges pixels of in ~0.46 the inputmm equates image. to This ~8 or is 9 criticalpixels in both the forinput understanding image. This is critical both for many of the functionsunderstanding of MINDTCT described many of the below functions which utilize of MINDTCT 8 8 pixel described windows below (queen’s-case which utilize 8 x 8 pixel × nearest-neighbor pixelwindows operators) (queen’s for processing‐case nearest and‐neighbor extraction, pixel and potentially operators) for how processing MINDTCT, and extraction, and and the images input intopotentially MINDTCT, for how may MINDTCT, need to be and modified the images for use input in the int extractiono MINDTCT, of dune may defects.need to be modified for Applying MINDTCTuse in to the dune extraction images of requires dune defects. preprocessing of the raw image. As noted above, the scales of crests spacingApplying and dunefield MINDTCT sizes to vary dune by images orders requires of magnitude, preprocessing while fingerprintof the raw image. sizes As noted above, and ridge scales do notthe vary scales by of even crests an spacing order of and magnitude. dunefield Dune sizes vary imagery by orders must beof magnitude, resampled towhile the fingerprint sizes and ridge scales do not vary by even an order of magnitude. Dune imagery must be resampled to the MINDTCT tuned resolution of ~8 pixels between ridges. Further image manipulations may also be MINDTCT tuned resolution of ~8 pixels between ridges. Further image manipulations may also be required, including low‐pass filtering for smoothing, despeckling for noise removal, and thresholding for production of an image that ‘looks’ like a fingerprint. Image quality is important since high contrast is necessary to evaluate the quality of localized regions to detect directional flow of ridges, regions of low contrast, areas where ridge flow direction is indeterminate (low ridge flow), and regions where directional change is rapid (high curvature). Issues with these parameters, primarily in terms of localized contrast, produce unstable results and make minutiae detection difficult. To address these issues, contrast within an image is evaluated and if there is low contrast it is normally enhanced using a trimmed 10% sample [31,32]. There is also a low‐contrast setting that can be altered in the source code for further enhancement. The result is a process where both local information in the form of blocks of pixels and individual pixel values are used to derive minutiae information.

Image Map Production Direction Map: A derived directional ridge flow map is required for detection of terminations and bifurcations. Production of a direction map requires well‐formed and clearly visible ridges so that the algorithm can find areas of image with enough ridge structure for further analysis. This approach requires local detection which depends on answering the question “How much local information is required to characterize the image?” To evaluate this question the image is divided into 8x8 pixel blocks. The algorithm [96,97] uses a moving 24 x 24 window where the cells are convolved to produce an 8x8 output block centered in the 24 x 24 window. Each pixel in the center block is given the same value. Edges are padded with a mean expected intensity of 128. This block structure removes fine structure noise resulting in a smoothed image that minimizes discontinuities, while padding allows evaluation and defect extraction over the entire image field. Ridge Flow Direction: For each local 8x8 block the surrounding 24 x 24 window is rotated through 16 orientations. Each is separated by 11.25 degrees (16 x 11.25 = 180 degrees), with 0 representing due north (up) and 15 representing a flow direction of 168.75 degrees (Figure 6). This is

Remote Sens. 2019, 11, 1060 8 of 24 required, including low-pass filtering for smoothing, despeckling for noise removal, and thresholding for production of an image that ‘looks’ like a fingerprint. Image quality is important since high contrast is necessary to evaluate the quality of localized regions to detect directional flow of ridges, regions of low contrast, areas where ridge flow direction is indeterminate (low ridge flow), and regions where directional change is rapid (high curvature). Issues with these parameters, primarily in terms of localized contrast, produce unstable results and make minutiae detection difficult. To address these issues, contrast within an image is evaluated and if there is low contrast it is normally enhanced using a trimmed 10% sample [31,32]. There is also a low-contrast setting that can be altered in the source code for further enhancement. The result is a process where both local information in the form of blocks of pixels and individual pixel values are used to derive minutiae information.

Image Map Production Direction Map: A derived directional ridge flow map is required for detection of terminations and bifurcations. Production of a direction map requires well-formed and clearly visible ridges so that the algorithm can find areas of image with enough ridge structure for further analysis. This approach requires local detection which depends on answering the question “How much local information is required to characterize the image?” To evaluate this question the image is divided into 8 8 pixel × blocks. The algorithm [96,97] uses a moving 24 24 window where the cells are convolved to produce × an 8 8 output block centered in the 24 24 window. Each pixel in the center block is given the same × × value. Edges are padded with a mean expected intensity of 128. This block structure removes fine structure noise resulting in a smoothed image that minimizes discontinuities, while padding allows evaluation and defect extraction over the entire image field. Ridge Flow Direction: For each local 8 8 block the surrounding 24 24 window is rotated through × × 16Remote orientations. Sens. 2019, 11 Each, x FOR is PEER separated REVIEW by 11.25 degrees (16 11.25 = 180 degrees), with 0 representing9 of 25 × due north (up) and 15 representing a flow direction of 168.75 degrees (Figure6). This is the default forthe the default number for of the subdivisions number of insubdivisions a semicircle in buta semicircle can be changed but can andbe changed made finer and ormade coarser finer in or the coarser in the control structure of MINDTCT using NUM_DIRECTIONS parameter [32]. For each control structure of MINDTCT using NUM_DIRECTIONS parameter [32]. For each orientation pixels orientation pixels along each rotated row are summed producing a vector for the 24 row sums. The along each rotated row are summed producing a vector for the 24 row sums. The maximum sum is maximum sum is designated as the local ridge flow direction and is placed in the local 8x8 block designated as the local ridge flow direction and is placed in the local 8 8 block [31,32]. [31,32]. ×

Figure 6. Ridge Flow Direction Calculation. Top left: 24 24 grid oriented 0 . Top Right: Rotational Figure 6. Ridge Flow Direction Calculation. Top left: 24 × 24 grid oriented 0°.◦ Top Right: Rotational referencereference frame. frame.Lower: Lower:Range Range of of possiblepossible orientations separated separated by by 11.25° 11.25 ◦[31,32].[31,32 ].

This process produces 16 vectors, each of which is convolved with four waveforms with frequencies including a single period (12 pixels wide), two periods (six pixels wide), four periods (three pixels wide), and eight periods (1.5 pixels wide) (Figure 7). Discrete values for the sine and cosine function for each of the four functions are computed for each vector. The results are added together to produce a resonance coefficient that represents how well each vector fits the specific waveform. The dominant ridge flow direction recorded is the block orientation with the maximum waveform resonance. Further details are found in the source code documentation [31].

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the default for the number of subdivisions in a semicircle but can be changed and made finer or coarser in the control structure of MINDTCT using NUM_DIRECTIONS parameter [32]. For each orientation pixels along each rotated row are summed producing a vector for the 24 row sums. The maximum sum is designated as the local ridge flow direction and is placed in the local 8x8 block [31,32].

Remote Sens. 2019, 11, 1060 9 of 24 Figure 6. Ridge Flow Direction Calculation. Top left: 24 × 24 grid oriented 0°. Top Right: Rotational reference frame. Lower: Range of possible orientations separated by 11.25° [31,32]. This process produces 16 vectors, each of which is convolved with four waveforms with frequencies includingThis a single process period produces (12 pixels 16 vectors, wide), each two of periods which (sixis convolved pixels wide), with fourfour periodswaveforms (three with pixels wide),frequencies and eight including periods (1.5a single pixels period wide) (12 (Figure pixels 7wide),). Discrete two periods values (six for pixels the sine wide), and four cosine periods function for each(three of thepixels four wide), functions and eight are computedperiods (1.5 for pixels each wide) vector. (Figure The 7). results Discrete are addedvalues for together the sine to and produce a resonancecosine function coefficient for thateach representsof the four howfunctions well are each computed vector fits for theeach specific vector. waveform.The results are The added dominant together to produce a resonance coefficient that represents how well each vector fits the specific ridge flow direction recorded is the block orientation with the maximum waveform resonance. Further waveform. The dominant ridge flow direction recorded is the block orientation with the maximum details are found in the source code documentation [31]. waveform resonance. Further details are found in the source code documentation [31].

Figure 7. Waveform patterns over a 24-pixel field. Top to bottom: 1, 2, 4, and 8-cycle windows.

Contrast Enhancement Low contrast areas complicate ridge detection making extraction of minutiae difficult [93,94]. The contrast enhancement subroutine flags low contrast areas by comparing the block pixel intensity to the surrounding window intensity. The algorithm uses a 10% upper/lower trim of the pixel intensity distribution between 0 and 255 and then measures remaining values which represent the most significant portion of the distribution [32]. This has the effect of removing extreme outliers and enhancing contrast within the remaining values. If the dynamic range of the center 80% of the distribution of the block values is less than 10 the block is considered to be low contrast and is flagged as such and becomes part of the assessment of minutiae strength.

Low Flow Areas If 8 8 pixel blocks in the direction map have no dominant ridge flow they are labeled low flow. × No direction is assigned initially but may be carefully interpolated from surrounding blocks. Minutiae within these areas (blocks) have a lower quality assignment and as such tend to be suspect relative to minutiae found in areas with higher contrast and flow [31,32].

High Curvature While this is more of a problem with fingerprints, high curvature errors can occur when a dune makes a sharp turn in response to an obstacle. High curvature refers to a portion of a feature where the ridge exhibits a large change in direction over a short distance [31,32,93–97]. Two measures are calculated: vorticitythe cumulative change in ridge flow around all neighbors in a block—and curvature—the largest change between a blocks ridge flow and the ridge flow of its neighbors. Minutiae in blocks where there is high vorticity or curvature are given a reduced quality assessment. Remote Sens. 2019, 11, x FOR PEER REVIEW 10 of 25

Figure 7. Waveform patterns over a 24‐pixel field. Top to bottom: 1, 2, 4, and 8‐cycle windows.

Contrast Enhancement

Low contrast areas complicate ridge detection making extraction of minutiae difficult [93,94]. The contrast enhancement subroutine flags low contrast areas by comparing the block pixel intensity to the surrounding window intensity. The algorithm uses a 10% upper/lower trim of the pixel intensity distribution between 0 and 255 and then measures remaining values which represent the most significant portion of the distribution [32]. This has the effect of removing extreme outliers and enhancing contrast within the remaining values. If the dynamic range of the center 80% of the distribution of the block values is less than 10 the block is considered to be low contrast and is flagged as such and becomes part of the assessment of minutiae strength.

Low Flow Areas If 8 x 8 pixel blocks in the direction map have no dominant ridge flow they are labeled low flow. No direction is assigned initially but may be carefully interpolated from surrounding blocks. Minutiae within these areas (blocks) have a lower quality assignment and as such tend to be suspect relative to minutiae found in areas with higher contrast and flow [31,32].

High Curvature While this is more of a problem with fingerprints, high curvature errors can occur when a dune Remotemakes Sens. 2019 a sharp, 11, 1060 turn in response to an obstacle. High curvature refers to a portion of a feature where10 of 24 the ridge exhibits a large change in direction over a short distance [31,32,93–97]. Two measures are calculated: vorticitythe cumulative change in ridge flow around all neighbors in a block—and Qualitycurvature—the Map largest change between a blocks ridge flow and the ridge flow of its neighbors. Minutiae in blocks where there is high vorticity or curvature are given a reduced quality assessment. Each block is assigned a value from 0 to 5 based on the contribution of contrast, flow and curvature. Quality Map This value is later used along with measures of minutiae relaibility to evaluate and characterize the Each block is assigned a value from 0 to 5 based on the contribution of contrast, flow and qualitycurvature. of extracted This minutiaevalue is later [31, 32used]. along with measures of minutiae relaibility to evaluate and characterize the quality of extracted minutiae [31,32]. Binarize Image EachBinarize pixel Image is evaluated for the presence or absence of ridge flow. If there is no ridge flow for the current pixelEach blockpixel is then evaluated the pixel for the is presence set to black or absence (0). If of there ridge is flow. ridge If there flow is then no ridge the pixel flow for intensities the surroundingcurrent pixel the pixelblock are then analyzed the pixel with is set a to 7 black9 grid (0). aligned If there withis ridge the flow ridge then flow the direction pixel intensities (with rows × parallelsurrounding to the local the ridge pixel are flow analyzed direction) with (Figure a 7 x 9 8grid). Grayscale aligned with pixel the intensities ridge flow direction are accumulated (with rows along eachparallel row (C1 to to the C9) local and ridge compared flow direction) with the (Figure accumulated 8). Grayscale values pixel of intensities the center are row accumulated (C5). If C5*9 along is less than theeach sum row of(C1 all to rows C9) and then compared no ridge with is detected the accumulated and the values pixel is of set the to center black. row If C5*9(C5). If is C5*9 greater is less than or than the sum of all rows then no ridge is detected and the pixel is set to black. If C5*9 is greater than equal to the sum then a ridge is detected and the pixel is set to white. or equal to the sum then a ridge is detected and the pixel is set to white.

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Figure 8. Ridge flow detection approach. a. 7 9 grid is used to sum values. b. Rotated grid centered Figure 8. Ridge flow detection approach. (a) 7 ×× 9 grid is used to sum values. (b) Rotated grid centered onon the the pixel pixel to to which which the the sum sum will will acrue acrue [ [32].32]. Minutiae Detection Minutiae Detection The algorithm uses the feature detection templates shown in Figure9. These 10 feature types can The algorithm uses the feature detection templates shown in Figure 9. These 10 feature types can be decomposed into ridge terminations or bifurcations. The templates are used to detect features by be decomposed into ridge terminations or bifurcations. The templates are used to detect features by sweeping the image both horizontally (2 3 kernel) and vertically (3 2 kernel). The orientation of sweeping the image both horizontally (2× x 3 kernel) and vertically (3 x× 2 kernel). The orientation of extractedextracted minutiae minutiae can can be be in in any any one one of of 32 32 (0–31)(0–31) directions with with zero zero (0) (0) at at the the top top of of image. image. Direction Direction is quantizedis quantized in in 11.25 11.25 degree degree increments increments proceeding proceeding clockwiseclockwise from from the the zero zero reference reference direction. direction.

FigureFigure 9. 9.Feature Feature extraction extraction templates. templates Horizontal. Horizontal image image sweeps sweeps [31 [31,32].,32]. The The templates templates are are rotated rotated 90 ◦ for90° vertical for vertical image image sweeps. sweeps. Blue boxBlue (terminations) box (terminations) and and red boxred box (bifurcations) (bifurcations) represent represent the the most most basic extractionbasic extraction kernals. kernals.

Minutiae Quality High‐quality minutiae occur where the local neighborhood has both well‐defined ridges and valleys and when the values cover the entire gray scale [93,94,97]. So if the neighborhood has a mean of 127 (1/2 way between white 255 and black 0) and a standard deviation greater than 64 (wide range) individual minutiae extracted from this neighborhood are considered to be both high‐quality and reliable. The algorithm for assessing overall quality combines the quality map described in Table 1 with the specific gray scale values and ranges which define reliability as listed above.

Minutiae Output MINDTCT outputs several maps that define ridgelines and minutiae (Table 1). These maps contain grids of integers, where each cell in the grid represents an 8 x 8 pixel neighborhood in the image. These maps include the direction map, low contrast map, low flow map, high curve map, and quality map. The maps are represented by a grid of numbers, each corresponding to a 8 x 8 block in the fingerprint image. Here again we must note the importance of pixel‐based operations to the successful analysis of imagery. Extracted minutiae are contained in a formatted listing of attributes associated with each detected minutiae. This file is organized with one space delimited line per minutiae containing its x and y coordinate, direction angle, and the minutiae quality.

Table 1. MINDTCT Output.

Output Type Output Description 16 integer bidirectional units. A value of −1 in this map represents a Direction Map neighborhood where no valid ridge flow was determined. High‐ Cell values of 1 represent 8 x 8 pixel neighborhoods in the image that are Curvature Map located within a high‐curvature region, otherwise cell values are set to 0.

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Minutiae Quality High-quality minutiae occur where the local neighborhood has both well-defined ridges and valleys and when the values cover the entire gray scale [93,94,97]. So if the neighborhood has a mean of 127 (1/2 way between white 255 and black 0) and a standard deviation greater than 64 (wide range) individual minutiae extracted from this neighborhood are considered to be both high-quality and reliable. The algorithm for assessing overall quality combines the quality map described in Table1 with the specific gray scale values and ranges which define reliability as listed above.

Table 1. MINDTCT Output.

Output Type Output Description 16 integer bidirectional units. A value of 1 in this map represents a Direction Map − neighborhood where no valid ridge flow was determined. Cell values of 1 represent 8 8 pixel neighborhoods in the image that are High-Curvature Map × located within a high-curvature region, otherwise cell values are set to 0. Cell values of 1 represent 8 8 pixel neighborhoods in the image that are Low-Contrast Map × located within a low-contrast region, otherwise cell values are set to 0. Cell values of 1 represent 8 8 pixel neighborhoods in the image that are × Low-Flow Map located within a region where a dominant directional frequency could not be determined, otherwise cell values are set to 0. Five discrete levels of quality. Each value in the map representing an 8 8 × Quality Map pixel neighborhood in the fingerprint image. A cell value of 4 represents highest quality, while a cell value of 0 represents lowest possible quality. A text file with the minutiae number, x,y location, minutiae direction, Minutiae Detection Results quality and type (bifurcation (BIF) or ridge ending (RIG))

Minutiae Output MINDTCT outputs several maps that define ridgelines and minutiae (Table1). These maps contain grids of integers, where each cell in the grid represents an 8 8 pixel neighborhood in the × image. These maps include the direction map, low contrast map, low flow map, high curve map, and quality map. The maps are represented by a grid of numbers, each corresponding to a 8 8 block × in the fingerprint image. Here again we must note the importance of pixel-based operations to the successful analysis of imagery. Extracted minutiae are contained in a formatted listing of attributes associated with each detected minutiae. This file is organized with one space delimited line per minutiae containing its x and y coordinate, direction angle, and the minutiae quality.

3. Results As an example of the application of this approach, and an evaluation of its utility for remote sensing analysis and interpretation within the aeolian environment, we applied MINDTCT to a range of remotely sensed dunefield images derived from the Mars HiRISE data acquisition campaign [98], which produces 25 cm resolution images. However, we note that application of the MINDTCT algorithm is not limited to HiRISE and has been successfully applied to dune images from a wide range of Martian imagery sources including the MRO Context Camera (5.5 m resolution) and the Mars Orbiter Camera (MOC 1.5 to 12 m resolution). As well, we note that MINDTCT has been successfully applied over a range of terrestrial image types ranging from Landsat (14.8 m panchromatic and ~28 m multispectral resolutions) to hand held camera perspective images of centimeter-scale dune ripples. While our approach across all of these imagery types has focused on the extraction of dune defects (terminations and bifurcations), we note that our extraction process, in concert with other tools within the MINDTCT processing evironment and a Geographic Information System (GIS) spatial analysis environment may Remote Sens. 2019, 11, x FOR PEER REVIEW 12 of 25

Low‐Contrast Cell values of 1 represent 8 x 8 pixel neighborhoods in the image that are Map located within a low‐contrast region, otherwise cell values are set to 0. Cell values of 1 represent 8 x 8 pixel neighborhoods in the image that are Low‐Flow Map located within a region where a dominant directional frequency could not be determined, otherwise cell values are set to 0. Five discrete levels of quality. Each value in the map representing an 8 x 8 Quality Map pixel neighborhood in the fingerprint image. A cell value of 4 represents highest quality, while a cell value of 0 represents lowest possible quality. Minutiae A text file with the minutiae number, x,y location, minutiae direction, quality Detection and type (bifurcation (BIF) or ridge ending (RIG)) Results

3. Results As an example of the application of this approach, and an evaluation of its utility for remote sensing analysis and interpretation within the aeolian environment, we applied MINDTCT to a range of remotely sensed dunefield images derived from the Mars HiRISE data acquisition campaign [98], which produces 25 cm resolution images. However, we note that application of the MINDTCT algorithm is not limited to HiRISE and has been successfully applied to dune images from a wide range of Martian imagery sources including the MRO Context Camera (5.5 m resolution) and the Mars Orbiter Camera (MOC 1.5 to 12 m resolution). As well, we note that MINDTCT has been successfully applied over a range of terrestrial image types ranging from Landsat (14.8 m panchromatic and ~28 m multispectral resolutions) to hand held camera perspective images of centimeter‐scale dune ripples. While our approach across all of these imagery types has focused on Remote Sens. 2019, 11, 1060 12 of 24 the extraction of dune defects (terminations and bifurcations), we note that our extraction process, in concert with other tools within the MINDTCT processing evironment and a Geographic Information Systemalso be used(GIS) to spatial extract analysis dune crestlines, environment their local may direction, also be used and theto extract spatial organizationdune crestlines, of both their defects local direction,and crests. and the spatial organization of both defects and crests.

3.1. Application Application of of MINDTCT MINDTCT to to Remotely Remotely Sensed HiRISE Imagery of Martian TARs To evaluate MINDTCTMINDTCT inin itsits rawraw statestate we we first first applied applied MINDTCT MINDTCT to to a a high-resolution high‐resolution image image of of a asimple simple TAR TAR field field in in an an ~1 ~1 km km diameter diameter crater crater located located on on a a delta delta within within Jezero Jezero Crater Crater (Figures (Figure 44 andand 10a).10a). TARs crests average ~25–27 m m of of separation separation so so at at a pixel resolution of 25 cm/pixel cm/pixel the average pixel spacing is ~100–110 pixels. This is ~12–14 the resolution of the ten print fingerprint images pixel spacing is ~100–110 pixels. This is ~12–14x× the resolution of the ten print fingerprint images MINDTCT isis tuned tuned to. to. Figure Figure 10 b10b shows shows the resultsthe results of the of extraction the extraction process process with 136 with defects 136 extracted. defects extracted.Misplacement Misplacement of both bifurcations of both bifurcations (green) and (green) terminations and terminations (red) as well(red) as as missed well as defectsmissed ofdefects both oftypes, both especially types, especially along the along edge the of edge the TAR of the field, TAR are field, readily are apparent.readily apparent.

Remote Sens. 2019, 11, x FOR PEER REVIEW 13 of 25 a.

b.

Figure 10. ( a.a) UnnamedUnnamed cratercrater JezeroJezero delta.delta. High Resolution Imaging Science Experiment (HiRISE) Image ESP_037396_1985. ESP_037396_1985. Map Map projected projected scale scale 25 cm/pixel. 25 cm/pixel. North North is up. is Acquired up. Acquired 19 July 192014. July (Image 2014. (ImageNASA/JPL/University NASA/JPL/University of Arizona). of Arizona). (b) Defectsb. extractedDefects using extracted the full using resolution the full image resolution (3088 x image 2280 (3088 2280 pixels). Green circles and red squares are bifurcations and terminations respectively. pixels).× Green circles and red squares are bifurcations and terminations respectively. Defects missed byDefects the MINDTCT missed by algorithm the MINDTCT not shown. algorithm not shown. With the problems introduced by pixel resolution and edge issues in mind we used MINDTCT With the problems introduced by pixel resolution and edge issues in mind we used MINDTCT in concert with preprocessing of raw digital images to analyze TARs of different types at four in concert with preprocessing of raw digital images to analyze TARs of different types at four localities on the Meridini Plain Mars Exploration Rover (MER) Spirit landing site (Figure 11) (Image localities on the Meridini Plain Mars Exploration Rover (MER) Spirit landing site (Figure 11) (Image ESP_037709_1650 NASA/JPL/University of Arizona). We chose these four localities from over 300 TAR ESP_037709_1650 NASA/JPL/University of Arizona). We chose these four localities from over 300 occurrences to specifically evaluate the ability of MINDTCT to extract defects from different TAR types TAR occurrences to specifically evaluate the ability of MINDTCT to extract defects from different (defined below in Table2), image resolutions and complexity, as well TAR spacing and field complexity. TAR types (defined below in Table 2), image resolutions and complexity, as well TAR spacing and field complexity. Site F275‐276 on the southern flank of the Columbia Hills consists of a simple TAR field within a poorly defined crater (Figure 12). TARs at this locality are generally oriented N/S with crests spaced ~2.5 m apart. These TAR and image characteristics produce a ~10‐pixel TAR spacing at the raw image resolution (Figure 12a) which is close to the native MINDTCT tuning. There is some scanline noise in the image generally oriented N/S and while resolution is 0.25 cm/pixel, this portion of the raw image (Figure 11) exhibits some graininess and appears slightly degraded. Overall this image, both in appearance and crest spacing appears more like a raw 10‐print fingerprint image (Figure 1f) than other TAR fields that we analyzed. MINDTCT analysis (Figure 12b) resulted in the extraction of 123 defects with 71 terminations and 52 bifurcations (Termination to Bifurcation Ratio (T/B) ~1.37). With few exceptions, MINDTCT extracted all the interior defects correctly. Like the previous example MINDTCT missed some terminations at the edge of the TAR field but the percentage correctly detected improved to ~48% capturing 31 terminations at the edge of the field while missing ~33 terminations. Image enhancement using a combination of smoothing, despeckling and thresholding in ImageJ [99] (not shown) improved both the detection of local flow and contrast at the field edge, capturing ~60 to 75% of the field edge terminations depending on the combination of enhancements used.

Remote Sens. 2019, 11, 1060 13 of 24 Remote Sens. 2019, 11, x FOR PEER REVIEW 14 of 25

Figure 11. MeridiniMeridini Plain Plain MER Spirit landing and exploration site. Four Four TAR TAR test sites indicated.

Site F275-276 on the southern flank of the Columbia Hills consists of a simple TAR field within a poorly defined crater (Figure 12). TARs at this locality are generally oriented N/S with crests spaced ~2.5 m apart. These TAR and image characteristics produce a ~10-pixel TAR spacing at the raw image resolution (Figure 12a) which is close to the native MINDTCT tuning. There is some scanline noise in the image generally oriented N/S and while resolution is 0.25 cm/pixel, this portion of the raw image (Figure 11) exhibits some graininess and appears slightly degraded. Overall this image, both in appearance and crest spacing appears more like a raw 10-print fingerprint image (Figure1f) than other TAR fields that we analyzed. MINDTCT analysis (Figure 12b) resulted in the extraction of 123 defects with 71 terminations and 52 bifurcations (Termination to Bifurcation Ratio (T/B) ~1.37). With few exceptions, MINDTCT extracted all the interior defects correctly. Like the previous example MINDTCT missed some terminations at the edge of the TAR field but the percentage correctly detected improved to ~48% capturing 31 terminations at the edge of the field while missing ~33 terminations. Image enhancement using a combination of smoothing, despeckling and thresholding in ImageJ [99] (not shown) improved both the detection of a. local flow and contrast at the field edge, capturing b. ~60 to 75% of the field edge terminations depending on the combination of enhancements used. Figure 12. Site F275‐276 (175.615°, −14.633°, Projection GCS_Mars). (a) Full resolution image (25cm/pixel). TAR spacing in image pixels approximates MINDTCT input fingerprint ridge spacing. (b) Defect extraction. Color key same as Figure 10. Radiating lines represent defect orientation.

Site L09‐10 (Figure 13a) is a TAR field within a double crater with a low dividing ridge. TAR spacing is ~2.75 m which is equal to ~13 pixels at the raw image resolution. Unlike the relatively

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Remote Sens. 2019, 11, 1060 14 of 24 Figure 11. Meridini Plain MER Spirit landing and exploration site. Four TAR test sites indicated.

a. b.

FigureFigure 12. Site12. Site F275-276 F275‐ (175.615276 (175.615°,, 14.633 −14.633°,, Projection Projection GCS_Mars). GCS_Mars).a. Full(a) Full resolution resolution image image ◦ − ◦ (25 cm(25cm/pixel)./pixel). TAR TAR spacing spacing in image in image pixels pixels approximates approximates MINDTCT MINDTCT input input fingerprint fingerprint ridge ridge spacing. spacing. b. Defect(b) Defect extraction. extraction. Color Color key same key same as Figure as Figure 10. Radiating 10. Radiating lines representlines represent defect defect orientation. orientation.

Table 2. TAR classification system [100,101]. Site L09‐10 (Figure 13a) is a TAR field within a double crater with a low dividing ridge. TAR spacing is ~2.75 m which is Crestequal Pattern to ~13 pixels Topographic at the raw Control image resolution. Unlike the relatively Remote Sens. 2019, 11, x FOR PEER REVIEW 15 of 25 Simple Confined Forked Controlled simple TAR structure exhibited at SiteSinuous F275‐276, this Influencedfield is more complex with indications of an interference pattern between the two subfields, branching structures, and short connecting low ridges Barchan-like Independent perpendicular to the primary TARNetworked orientation. Analysis of the field with MINDTCT resulted in the extraction of 245 defects with 141 terminations and 104 bifurcations (Figure 13b). The T/B ratio of ~1.35 suggests a tendency towards a forkedSite pattern. L09-10 A (Figure variation 13 a)in isthe a TARdefect field direction within horizontally a double crater across with the a image low dividing and an ridge.abrupt TAR90‐ degreespacing change is ~2.75 in mthe which upper is right equal of to the ~13 image pixels potentially at the raw complicate image resolution. defect extraction. Unlike the Unlike relatively the priorsimple extraction TAR structure issues with exhibited algorithmic at Site F275-276,edge effects, this it field appears is more that complexMINDTCT with correctly indications extracted of an mostinterference terminations pattern at betweenthe edge the of the two field. subfields, This is branching likely due structures, to the higher and shortcontrast connecting between low the ridges field andperpendicular the edge of tothe the double primary crater. TAR orientation.

a. b.

FigureFigure 13. 13. SiteSite L09 L09-10‐10 (175.613, (175.613, −14.51414.514 decimal decimal degrees, degrees, −260101.2515260,101.2515 m, m, −860177.3776860,177.3776 m, m, Projection Projection − − − GCS_Mars).GCS_Mars). (aa.) RawRaw image. image. (b.b) Enhanced MINDTCT processed image.image. Color key same as Figure 1010..

SiteAnalysis L188 (Figure of the field 14a) with illustrates MINDTCT a far resultedmore complex in the extraction TAR field of with 245 sinuous defects with features, 141 terminations significant directionaland 104 bifurcations variability (Figure and crest 13b). spacing, The T /andB ratio a networked of ~1.35 suggests structure. a tendency Dune spacing towards varies a forked from pattern. 2.0 to 3.0A variationm equating in theto a defect pixel directionspacing of horizontally eight to 12 acrosspixels. the The image western and edge an abrupt of the 90-degree field has changeexcellent in contrast while other portions of the edge of the field are characterized by low contrast and poorly defined crests. MINDTCT extracted 351 defects, with an almost equal quantity of terminations (180) and bifurcations (171) (T/B ~1.05) (Figure 14b). In areas where the underlying TAR structure resembles a fingerprint (Figure 14b; lower left and upper right) MINDTCT performs well. However, in the portions of the field that are sinuous (lower right) or networked (upper center) MINDTCT performs poorly. This is potentially indicative of patterns that differ significantly from the regular spacing, roughly parallel ridges and noncrossing structure that characterizes standard MINDTCT 10‐print input.

a.

Remote Sens. 2019, 11, x FOR PEER REVIEW 15 of 25 simple TAR structure exhibited at Site F275‐276, this field is more complex with indications of an interference pattern between the two subfields, branching structures, and short connecting low ridges perpendicular to the primary TAR orientation. Analysis of the field with MINDTCT resulted in the extraction of 245 defects with 141 terminations and 104 bifurcations (Figure 13b). The T/B ratio of ~1.35 suggests a tendency towards a forked pattern. A variation in the defect direction horizontally across the image and an abrupt 90‐ degree change in the upper right of the image potentially complicate defect extraction. Unlike the prior extraction issues with algorithmic edge effects, it appears that MINDTCT correctly extracted most terminations at the edge of the field. This is likely due to the higher contrast between the field and the edge of the double crater.

Remote Sens. 2019, 11, 1060 15 of 24

a. b. the upper right of the image potentially complicate defect extraction. Unlike the prior extraction issuesFigure with 13. algorithmic Site L09‐10 edge (175.613, effects, −14.514 it appears decimal that degrees, MINDTCT −260101.2515 correctly m, extracted −860177.3776 most m, terminations Projection at the edgeGCS_Mars). of the field.(a) Raw This image. is likely (b) Enhanced due to theMINDTCT higher processed contrast betweenimage. Color the key field same and as the Figure edge 10. of the double crater. Site L188 (Figure 14a)14a) illustrates a far more complex TAR field field with sinuous features, significant significant directional variability variability and and crest crest spacing, spacing, and and a a networked networked structure. structure. Dune Dune spacing spacing varies varies from from 2.0 2.0 to 3.0to 3.0 m mequating equating to toa pixel a pixel spacing spacing of of eight eight to to 12 12 pixels. pixels. The The western western edge edge of of the the field field has excellent contrast while other portions of the edge of the field field are characterized by low contrast and poorly defineddefined crests. MINDTCT extracted 351 defects, with an almost equal quantity of terminations (180) and bifurcations (171) (T/B (T/B ~1.05) (Figure 14b).14b). In In areas areas where where the the underlying TAR TAR structure resembles a fingerprintfingerprint (Figure(Figure 14 14b;b; lower lower left left and and upper upper right) right) MINDTCT MINDTCT performs performs well. However, well. However, in the portions in the portionsof the field of the that field are sinuousthat are sinuous (lower right) (lower or right) networked or networked (upper center)(upper MINDTCTcenter) MINDTCT performs performs poorly. Thispoorly. is potentiallyThis is potentially indicative indicative of patterns of patterns that diff erthat significantly differ significantly from the from regular the spacing,regular spacing, roughly parallelroughly ridgesparallel and ridges noncrossing and noncrossing structure thatstructure characterizes that characterizes standard MINDTCT standard 10-printMINDTCT input. 10‐print input.

Remote Sens. 2019, 11, x FOR PEER REVIEW 16 of 25 a.

b. Figure 14. Site L188. (175.64, 14.727 decimal degrees, 258,319.587 m, 872,801.8553 m, Projection Figure 14. Site L188. (175.64, −−14.727 decimal degrees, −−258,319.587 m, −−872,801.8553 m, Projection GCS_Mars). a. Raw image. b. MINDTCT processed image. Color key same as Figure 10. GCS_Mars). (a) Raw image. (b) MINDTCT processed image. Color key same as Figure 10. As a final test of MINDTCT we selected a TAR field at Site L02 (Figure 15a) that exhibited a complexAs a combination final test of ofMINDTCT ridge types we and selected spacings. a TAR The field spacing at Site of much L02 (Figure of the TAR 15a) field that rangesexhibited from a 2complex to 3 m. combination The exception of ridge is the types central and portion spacings. of the The field spacing which of much has both of the a di TARfferent field structure ranges from and well-defined2 to 3 m. The ridges exception with anis the ~10 central m spacing. portion These of largerthe field features which exhibit has both a branching a different structure structure as welland aswell smaller‐defined narrow ridges crests with radiatingan ~10 m spacing. at rightangles These to larger the main features crest exhibit lines. a branching structure as well as smaller narrow crests radiating at rightangles to the main crest lines. The results (Figure 15b), as expected from the prior examples, display a high degree of variability depending of the spacing, structure and TAR type. A large number of defects (1314) were extracted with type and quality varying significantly. The termination/bifurcation ratio (T/B) for the entire image is ~0.98 (651/663), however it is clear from Figures 15c–f that this ratio varies considerably. Portions of the field with a combination of sinuous and crossing ridges (Figure 15c) are dominated by terminations with a T/B of ~1.4, while other parts of the field exhibit a hatched pattern (Figure 15d) with far more terminations than bifurcations (T/B ~1.7). Portions of the field with primarily linear ridges (Figure 15e) are characterized by T/B ratios ranging from ~0.5 to 0.7. Defects on the widely spaced ridges of central portion of the image (Figure 15f) were poorly captured, however the closely spaced ridges that branch off of them were partially captured. Our results suggest that further refinement of the MINDTCT algorithm, with specific tuning for imagery of aeolian features, may be required for before it can be applied to TAR fields with variable complexity and scale. However, and even with this constraint, it is clear that MINDTCT output, through quantification of the T/B ratio across different portions of complex fields, may be useful in determining their underlying spatial pattern. This spatial patterning, as expressed in the organization, relative occurrence, and T/B ratio [29,67], is potentially a measure of underlying physical processes that formed them. Quantification of TAR field metrics therefore can aid our understanding TAR formation and evolution.

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a. b.

c. d.

e. f.

FigureFigure 15. Site 15. L02.Site L02. (175.561, (175.561,14.53 −14.53 decimal decimal degrees, degrees, −263,485.6683m,263,485.6683m, −860,874.5724m,860,874.5724m, Projection Projection − − − GCS_Mars).GCS_Mars).a. Raw (a) Raw image. image. 25 cm25 /cm/pixel.pixel. b. (bDefect) Defect extraction. extraction. c.(c)Zoom Zoom ofof fieldfield with a a combination combination of sinuousof sinuous and crossing and crossing ridges. ridges.d. Zoom (d) Zoom of field of field with with primarily primarily crossing crossing pattern. pattern.e .(e Zoom) Zoom of of field field with primarilywith linearprimarily ridges. linearf. ridges.Zoom ( off) centralZoom of region central with region widely with spacedwidely spaced ridges andridges crossing and crossing structure. Colorstructure. key same Color as Figure key same 10. as Figure 10.

The3.2. Extraction results (Figure Enhancement 15b), as By expected Tuning MINDTCT from the prior examples, display a high degree of variability dependingClearly, of the the spacing, application structure of MINDTCT and TAR to type.aeolian A features large number is just a first of defects step towards (1314) more were robust extracted with typefeature and extraction quality varying methodologies. significantly. Many Thedefects termination are located/bifurcation inaccurately ratio or not (T/B) detected for the at entire all. In image is ~0.98Figures (651/ 10b663), and however 14b the total it is clearlack of from extraction Figure in 15 portionsc–f that of this the ratioimage varies where considerably. TAR crests are Portionswidely of the fieldspaced with indicates a combination that the of algorithmic sinuous and approach crossing of ridges MINDTCT (Figure does 15c) not are work dominated on high by resolution terminations images with a large number of pixels between crests. with a T/B of ~1.4, while other parts of the field exhibit a hatched pattern (Figure 15d) with far more terminations than bifurcations (T/B ~1.7). Portions of the field with primarily linear ridges (Figure 15e) are characterized by T/B ratios ranging from ~0.5 to 0.7. Defects on the widely spaced ridges of central Remote Sens. 2019, 11, 1060 17 of 24 portion of the image (Figure 15f) were poorly captured, however the closely spaced ridges that branch off of them were partially captured. Our results suggest that further refinement of the MINDTCT algorithm, with specific tuning for imagery of aeolian features, may be required for before it can be applied to TAR fields with variable complexity and scale. However, and even with this constraint, it is clear that MINDTCT output, through quantification of the T/B ratio across different portions of complex fields, may be useful in determining their underlying spatial pattern. This spatial patterning, as expressed in the organization, relative occurrence, and T/B ratio [29,67], is potentially a measure of underlying physical processes that formed them. Quantification of TAR field metrics therefore can aid our understanding TAR formation and evolution.

3.2. Extraction Enhancement By Tuning MINDTCT Clearly, the application of MINDTCT to aeolian features is just a first step towards more robust feature extraction methodologies. Many defects are located inaccurately or not detected at all. In Figures 10b and 14b the total lack of extraction in portions of the image where TAR crests are widely spaced indicates that the algorithmic approach of MINDTCT does not work on high resolution images with a large number of pixels between crests. Remote Sens. 2019, 11, x FOR PEER REVIEW 18 of 25 To improve the application of the MINDTCT algorithm, and assuming, as noted above, that the underlyingTo improve programming the application is tuned of specificallythe MINDTCT to normalalgorithm, 10-print and assuming, fingerprint as noted inputs, above, we resampled that the theunderlying Figure 10 programmingTAR image such is tuned that specifically the average to pixel normal spacing 10‐print between fingerprint TAR inputs, crests matchedwe resampled that of fingerprintthe Figure ridges 10 TAR (eight image pixels). such Namelythat the weaverage resampled pixel spacing the data between in ImageJ TAR [99 crests] (Image- matched> Transform- that of > Bin-)fingerprint using a ridges 10 resample (eight pixels). and a Namely mean operator. we resampled The results the data (Figure in ImageJ 16) show[99] (Image a realistic‐> Transform extraction‐ × of> terminations Bin‐) using a (25)10x resample and bifurcations and a mean (18). operator. This extraction The results is (Figure best in 16) the show center a realistic of the extraction field but is inconsistentof terminations at the (25) upper and and bifurcations lower edges (18). of This the field,extraction failing is tobest capture in the 42center terminations of the field at thebut edgeis ofinconsistent the field and at 8the bifurcations. upper and lower Manually edges adding of the field, these failing missing to capture 42 terminations 42 terminations and 8 at bifurcations the edge producesof the field a termination and 8 bifurcations./bifurcation Manually ratio (T /addingB) of 2.62 these which missing conforms 42 terminations to the simple and to 8 forkedbifurcations class of Balmeproduces et al. a [100 termination/bifurcation,101]. MINDICT found ratio fewer (T/B) defects of 2.62 which in the conforms resampled to image, the simple but to their forked locations class of and distributionsBalme et al. are [100,101]. far more MINDICT even and found accurate, fewer even defects though in the the resampled software image, did not but identify their locations a majority and of fielddistributions edge terminations. are far more even and accurate, even though the software did not identify a majority of field edge terminations.

FigureFigure 16. 16.MINDTCT MINDTCT extractionextraction fromfrom aa resampledresampled image (binned (binned by by 10 10 pixels). pixels). Green Green boxes boxes (terminations)(terminations) and and red red circles circles (bifurcations) (bifurcations) with with direction direction indicated indicated by vectors by vectors from from their their center center points. points. This result is not dissimilar to incomplete extraction of fingerprint minutiae at the edge of a 10-printThis image. result Figure is not 17 dissimilar illustrates to anincomplete extraction extraction from a 10-print of fingerprint (f0275_02.png). minutiae at Here the mostedge of defects a 10‐ in theprint center image. of the Figure image 17 are illustrates correctly an extracted. extraction Because from a 10 the‐print algorithmic (f0275_02.png). approach Here of MINDTCTmost defects views in thethe edge center of each of the fingerprint image are ridgecorrectly relative extracted. to an adjacentBecause the unpopulated algorithmic field approach as neighborhoods of MINDTCT where views no validthe ridgeedge of flow each exists fingerprint and with ridge low relative contrast to an and adjacent low flow unpopulated as defined field in as Table neighborhoods1, defects are where rarely no valid ridge flow exists and with low contrast and low flow as defined in Table 1, defects are rarely defined in low contrast areas. The few defects found at these locations are usually considered to be of poor quality and normally are not used in fingerprint matching algorithms [38,102–106].

Remote Sens. 2019, 11, x FOR PEER REVIEW 18 of 25

To improve the application of the MINDTCT algorithm, and assuming, as noted above, that the underlying programming is tuned specifically to normal 10‐print fingerprint inputs, we resampled the Figure 10 TAR image such that the average pixel spacing between TAR crests matched that of fingerprint ridges (eight pixels). Namely we resampled the data in ImageJ [99] (Image‐> Transform‐ > Bin‐) using a 10x resample and a mean operator. The results (Figure 16) show a realistic extraction of terminations (25) and bifurcations (18). This extraction is best in the center of the field but is inconsistent at the upper and lower edges of the field, failing to capture 42 terminations at the edge of the field and 8 bifurcations. Manually adding these missing 42 terminations and 8 bifurcations produces a termination/bifurcation ratio (T/B) of 2.62 which conforms to the simple to forked class of Balme et al. [100,101]. MINDICT found fewer defects in the resampled image, but their locations and distributions are far more even and accurate, even though the software did not identify a majority of field edge terminations.

Figure 16. MINDTCT extraction from a resampled image (binned by 10 pixels). Green boxes (terminations) and red circles (bifurcations) with direction indicated by vectors from their center points.

This result is not dissimilar to incomplete extraction of fingerprint minutiae at the edge of a 10‐ print image. Figure 17 illustrates an extraction from a 10‐print (f0275_02.png). Here most defects in the center of the image are correctly extracted. Because the algorithmic approach of MINDTCT views Remote Sens. 2019, 11, 1060 18 of 24 the edge of each fingerprint ridge relative to an adjacent unpopulated field as neighborhoods where no valid ridge flow exists and with low contrast and low flow as defined in Table 1, defects are rarely defineddefined inin lowlow contrastcontrast areas. areas. The The few few defects defects found found at at these these locations locations are are usually usually considered considered to to be be of poorof poor quality quality and and normally normally are are not not used used in fingerprintin fingerprint matching matching algorithms algorithms [38 [38,102–106].,102–106].

Figure 17. Fingerprint minutiae extraction. Image f0275_02.png from the NIST fingerprint database [41]. Note the lack of termination extraction at the edges of the fingerprint like that seen in the TAR extraction in Figure 16.

4. Discussion The application of fingerprint minutiae extraction software to remotely sensed dunefield imagery provides several advantages to the dune defect extraction process over existing methods: ease of use, well-developed and researched processing environment [32], availability of the software at minimal or no cost [32,99], and the ability for the software to run within many processing environments. Nevertheless, the extraction of minutiae from fingerprints [33,102] as well as defects from satellite derived dune field images remains a difficult task [20,29]. A future application of our methodology could be to use extracted defects to more objectively classify TAR morphologies. Past efforts have been made to categorize TARs [100,101,107]. These categorization systems broadly address two features of the TARs—(1) relative spatial context and (2) crest patterns (Table2)—both of which are important in understanding the formative and evolutionary processes that produce TARs. However, at present, classifying TARs by either of these schemes remains a time-intensive and subjective manual endeavor. Building a database of TARs and their spatial arrangement would potentially allow for the correlation of defect properties in TARs (e.g., termination/bifurcation occurrence ratio, defect orientation and location) with their corresponding ridge crest pattern. These connections would provide a more objective method for categorizing TARs by ridge crest pattern (Table3). A generalized example is provided in Figure 18.

Table 3. Expected TAR defect properties.

Balme et al. [101] Expected Defect Properties Crest Pattern Termination Termination Bifurcation Bifurcation Termination: Categories Frequency Orientation Frequency Orientation Bifurcation Ratio Simple Many Unidirectional None N/A Very high Forked Many Unidirectional Few Unidirectional High Sinuous Many Unidirectional Few Unidirectional Intermediate Barchan-like Few Bidirectional Many Bidirectional Low Networked Few None Many Bidirectional Very low Remote Sens. 2019, 11, 1060 19 of 24 Remote Sens. 2019, 11, x FOR PEER REVIEW 20 of 25

(a) (b) (c)

Figure 18. TAR representational schemes. (a) (Traced) Generalized TAR crests following the categorization scheme of [101]. (A) Simple, (B) forked, (C) sinuous, (D) barchan-like, and (E) networked. Figure 18. TAR representational schemes. a. (Traced) Generalized TAR crests following the (b) (Annotated) Generalized TAR crests with annotated defects. Terminations (red circles) and categorization scheme of [101]. (A) Simple, (B) forked, (C) sinuous, (D) barchan‐like, and (E) bifurcations (green circles) are marked. More than 400 defects were located in these five small examples. networked. b. (Annotated) Generalized TAR crests with annotated defects. Terminations (red circles) (c) (Defects) Extracted defects from each TAR morphology. Even without direction information, each and bifurcations (green circles) are marked. More than 400 defects were located in these five small morphology’s defects are distinctly different, with the exception of forked vs. sinuous TARs. examples. c. (Defects) Extracted defects from each TAR morphology. Even without direction 5. Conclusionsinformation, and each Suggestions morphology’s for defects Future are Research distinctly different, with the exception of forked vs. sinuous TARs. Establishing a link between crest defects, which are well documented and understood in terrestrial environments,5. Conclusions andand TARSuggestions morphologies, for Future which Research are distinct, but poorly understood, could provide a new and robust perspective into the formative history of TARs. However, further refinement and automationEstablishing of a the link ‘fingerprinting’ between crest extraction defects, techniquewhich are from well satellite documented imagery and is requiredunderstood before in rigorousterrestrial large-scale environments, studies and of TAR this type morphologies, can be conducted. which are distinct, but poorly understood, could provideAs wea new have and shown, robust the diperspectivefficulty increases into the when formative high resolution history imageryof TARs. does However, not conform further to therefinement ‘tuned’ 10-printand automation resolution of used the by‘fingerprinting’ MINDTCT. These extraction issues aretechnique exacerbated from whensatellite the imagery dune field is isrequired complex before with rigorous a mix of large features‐scale that studies do not of conform this type to can the be characteristics conducted. of a fingerprint, namely perpendicularAs we have ridges, shown, and the crossing difficulty structures. increases However,when high even resolution with theseimagery constraints, does not MINDTCTconform to appliedthe ‘tuned’ to ‘properly 10‐print formatted’resolution used remotely by MINDTCT. sensed dune These/TAR issues imagery are was exacerbated shown to when extract the aeolian dune dune field fieldis complex defects with quickly a mix and of accurately. features that do not conform to the characteristics of a fingerprint, namely perpendicular‘Properly formatted’ridges, and in crossing our approach structures. in essence However, implies even that with the original these constraints, dune/TAR image MINDTCT must beapplied reformmatted to ‘properly to lookformatted’ more likeremotely a fingerprint. sensed dune/TAR This includes imagery (1) redefiningwas shown an to imageextract of aeolian dune crests,dune field which defects are typically quickly sharp and accurately. edged and often indicated by rapid brightness change (sunlit/shadow transitions),‘Properly through formatted’ filtering in our and approach thresholding, in essence such implies that they that resemble the original the 10-print dune/TAR dark image ridge /mustlight valleybe reformmatted format of fingerprint to look more images; like a (2) fingerprint. altering the This dune includes image resolution (1) redefining through an image resampling of dune such crests, that itwhich matches are thetypically native resolutionsharp edged of the and 10-print often indicated image (~8–10 by pixelrapid spacing brightness between change ridges); (sunlit/shadow (3) altering imagetransitions), quality through and removing filtering noiseand thresholding, through despeckling such that whenthey resemble necessary the to 10 remove‐print dark fine ridge/light detail that valley format of fingerprint images; (2) altering the dune image resolution through resampling such ‘confuses’ the MINDTCT algorithm; (4) dealing with edge effects where the MINDTCT algorithm that it matches the native resolution of the 10‐print image (~8–10 pixel spacing between ridges); (3) fails to capture defects in low-contrast, low-directionality, and low-flow portions of the image; and altering image quality and removing noise through despeckling when necessary to remove fine detail (5) dealing with defects in critical zones of the dune field (such as singular points) that are deleted that ‘confuses’ the MINDTCT algorithm; (4) dealing with edge effects where the MINDTCT algorithm by MINDTCT even though they may be correctly detected in the initial subroutines [32,103,104] or fails to capture defects in low‐contrast, low‐directionality, and low‐flow portions of the image; and spurious defects outside of the dune field area [104]. In addition to these issues, the quality of the (5) dealing with defects in critical zones of the dune field (such as singular points) that are deleted by defects should also be assessed to determine how estimated defect positions and angles differ from MINDTCT even though they may be correctly detected in the initial subroutines [32,103,104] or the real defect characteristics [29,108]. Erroneous detections, including identifying both missing and spurious defects outside of the dune field area [104]. In addition to these issues, the quality of the spurious defects may be dealt with using post-processing techniques [32,109–111]. defects should also be assessed to determine how estimated defect positions and angles differ from the real defect characteristics [29,108]. Erroneous detections, including identifying both missing and spurious defects may be dealt with using post‐processing techniques [32,109–111].

Remote Sens. 2019, 11, 1060 20 of 24

Our work suggests that additional ‘tuning’ of the MINDTCT source code, such that it can better be applied to remotely sensed imagery for dune defect extraction, is possible. While we used remotely sensed imagery of Transverse Aeolian Ridges (TARs) on Mars to illustrate our approach, the algorithmic formulation of MINDTCT may also be appropriate for extraction of defects from imagery for a wide range of aeolian features from fine-scale ripples to fields of longitudinal and transverse dunes. We further note that this technique could also, through discipline specific modifications, be applied to remotely sensed images of features exhibiting defects ranging from crevasses in ice sheets [112–114] to bedform ripples in streams [115,116].

Author Contributions: Conceptualization, L.S.; Methodology, L.S., T.N.-M., & J.W.; Formal Analysis, L.S., T.N.-M., & J.W.; Writing—Original Draft Preparation, L.S.; Writing—Review & Editing, L.S., T.N.-M., & J.W. Funding: This research received no external funding. Acknowledgments: Administrative and technical support provided by the University of New Mexico, Department of Earth and Planetary Sciences. Computing resources provided by the Center for Rapid Environmental Assessment and Terrain Evaluation CREATE) and the Center for Advanced Research Computing (CARC) at the University of New Mexico. Travel funds for presenting an early version of this research provided by the University of New Mexico’s Earth and Planetary Sciences Caswell/Silver Foundation. The authors would also like to thank two anonymous reviewers who provided insightful comments that improved the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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