NASA Technical Reports Server (NTRS) 20140004932: LU60645GT and MA132843GT Catalogues of Lunar and Martian Impact Craters Developed Using a Crater Shape-based Interpolation Crater Detection Algorithm for Topography Data

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PlanetaryandSpaceScience60(2012)236–247
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Planetary and Space Science
journal homepage: www.elsevier.com/locate/pss
LU60645GT and MA132843GT catalogues of Lunar and Martian impact
craters developed using a Crater Shape-based interpolation crater
detection algorithm for topography data
Goran Salamunic´cara,b,n, Sven Loncˇaric´b, Erwan Mazaricoc,d
aAVL-ASTd.o.o.,Av.Dubrovnik10/II,10020Zagreb-NoviZagreb,Croatia
bFacultyofElectricalEngineeringandComputing,UniversityofZagreb,Unska3,10000Zagreb,Croatia
cNASAGoddardSpaceFlightCenter,PlanetaryGeodynamicsLaboratory,Greenbelt,MD20771,USA
dMassachusettsInstituteofTechnology,DepartmentofEarth,AtmosphericandPlanetarySciences,Cambridge,MA02139,USA
a r t i c l e i n f o a b s t r a c t
Articlehistory: ForMars,57,633cratersfromthemanuallyassembledcataloguesand72,668additionalcratersidentified
Received6July2011 using several crater detection algorithms (CDAs) have been merged into the MA130301GT catalogue.
Receivedinrevisedform Bycontrast,fortheMoonthemostcompletepreviouscataloguecontainsonly14,923craters.Tworecent
31August2011 missionsprovidedhigher-qualitydigitalelevationmaps(DEMs):SELENE(in1/161resolution)andLunar
Accepted2September2011 ReconnaissanceOrbiter(weusedupto1/5121).ThiswasthemainmotivationforworkonthenewCrater
Availableonline16September2011
Shape-basedinterpolationmodule,whichimprovespreviousCDAasfollows:(1)itdecreasesthenumberof
Keywords: false-detectionsfortherequirednumberoftruedetections;(2)itimprovesdetectioncapabilitiesforvery
Moon smallcraters;and(3)itprovidesmoreaccurateautomatedmeasurementsofcraters’properties.Theresults
Mars are:(1)LU60645GT,whichiscurrentlythemostcomplete(upto (cid:2)DZ8km)catalogueofLunarcraters;
Surface and(2)MA132843GTcatalogueofMartiancraterscompleteupto(cid:2)DZ2km,whichistheextensionofthe
Cratering
previousMA130301GTcatalogue.AspreviouslyachievedforMars,LU60645GTprovidesallpropertiesthat
Imageprocessing
wereprovidedbythepreviousLunarcatalogues,plus:(1)correlationbetweenmorphologicaldescriptors
fromusedcatalogues;(2)correlationbetweenmanuallyassignedattributesandautomatedmeasurements;
(3)averageerrorsandtheirstandarddeviationsformanuallyandautomaticallyassignedattributessuchas
positioncoordinates,diameter,depth/diameterratio,etc;and(4)areviewofpositionalaccuracyofused
datasets.Additionally,surfacedatingcouldpotentiallybeimprovedwiththeexhaustivenessofthisnew
catalogue.Theaccompanyingresultsare:(1)thepossibilityofcomparingalargenumberofLunarand
Martiancraters,ofe.g.depth/diameterratioand2Dprofiles;(2)utilisationofamethodforre-projectionof
datasetsandcatalogues,whichisveryusefulforcratersthatareveryclosetopoles;and(3)theextensionof
thepreviousframeworkforevaluationofCDAswithdatasetsandground-truthcataloguefortheMoon.
&2011ElsevierLtd.Allrightsreserved.
1. Introduction andLoncˇaric´,2010a),whereininsteadoftheCannyweusedShen–
Castanedgedetector;and(3)theCDAforopticalimages(Bandeira
Recently, all the craters from the major currently available et al., 2007) for four selected regions of interest. This resulted in
manually assembled catalogues have been merged into the MA130301GTcatalogue(Salamunic´caretal.,2011b),whichisatthe
MA57633GT catalogue with 57,633 known Martian impact-craters time of writing the most complete previously available public
(Salamunic´car and Loncˇaric´, 2008b). In addition, using our crater catalogue of Martian craters. By contrast, for the Moon the most
detectionalgorithm(CDA)and1/1281MOLAdata,57,592previously complete previous catalogue contains only 14,923 craters
uncatalogued craters have been identified resulting in the (Rodionovaetal.,1987).ThesizedifferencebetweenMarsandthe
MA115225GT catalogue (Salamunic´car and Loncˇaric´, 2010a). This Moononlypartiallyexplainsthedifference,becauseontheMoonthe
catalogue has been additionally extended using: (1) MA75919T average density of the largest craters is greater than on Mars
catalogue, which is the result of the CDA from Stepinski and according to size-frequency distribution of the largest craters, for
Urbach(2008);(2)theCDAfromourpreviouswork(Salamunic´car whichthesecataloguesaremostlycomplete(seebelow;Section3.2
– the distribution of craters from corresponding catalogues). Two
recent missions provided higher-quality digital elevation maps
nCorrespondingauthorat:AVL-ASTd.o.o.,Av.Dubrovnik10/II,10020 (DEMs):(1)SELENElaseraltimetry(LALT)datasetin1/161resolution
Zagreb-NoviZagreb,Croatia.Tel.:þ38598890725.
(Arakietal.,2009);and(2)LunarReconnaissanceOrbiter(LRO)Lunar
E-mailaddresses:[email protected](G.Salamunic´car),
[email protected](S.Loncˇaric´),[email protected](E.Mazarico). orbiter laser altimeter (LOLA) dataset (Smith et al., 2010), wherein
0032-0633/$-seefrontmatter&2011ElsevierLtd.Allrightsreserved.
doi:10.1016/j.pss.2011.09.003
G.Salamuni´ccaretal./PlanetaryandSpaceScience60(2012)236–247 237
weusedresolutionsupto1/5121.Thiswasamotivationforourwork The following are made available online (http://informatika.
onaconsiderablymorecompletecatalogueofLunarcraters. tvz.hr/index.php?pred=17461):thesourcecode(Craters5_77.zip)
Research on CDAs is challenging for numerous reasons. On of the interpolation-based CDA presented in this paper; the
Mars,therearemanydifferentcratershapesdependingontheir Topolyzer application, which implements methods for the eva-
interiormorphologies(centralpeaks,peakrings,centralpits,and luation of CDAs and the registration to ground-truth (GT) catalo-
wall terraces) and ejecta structures (pedestal, pancake, rampart, gues;andthecataloguesLU60645GTandMA132843GT(aswellas
lobate, fluidized, radial or lunar-like, transitional or diverse) previousversions).Inaddition,thevariousdatasetsareavailableon
(Barlow et al., 2003). There is also a simple-complex transition request, in order to provide reproducibility of the methods pre-
from the smaller, mostly very circular bowl-shaped craters, to sentedinthispaperandinter-comparisonwithotherCDAs.
larger complex craters with central peaks, and to the largest
multi-ring impact basins (Melosh and Ivanov, 1999). In general, 2.1. ImprovementofcraterdetectionalgorithmusingnewCrater
CDAs are based on a large number of methods, including circle/ Shape-basedinterpolation
ellipsedetection(Cooper,2003;CooperandCowan,2004;Flores-
Me´ndez and Suarez-Cervantes, 2009; Krøgli and Dypvik, 2010), The CDA from this paper, which uses multi-resolution image
probabilityvolumecreatedbytemplatematching(Bandeiraetal., analysis and the Crater Shape-based interpolation algorithm
2007), machine-learning (Stepinski and Urbach, 2008), etc. describedinfollowingparagraphs,isshowninFig.1.Thealgorithm
An overview of 112 publications related to CDAs has been is an extension of our previous work (Salamunic´car and Loncˇaric´,
published in two recent papers (Salamunic´car and Loncˇaric´,
2008a;Salamunic´caretal.,2011b).Thelistisconstantlyincreas- load XML file with parameters
ing, as is e.g. the work regarding feature selection and boosting load DEM data
(Ding et al., 2010) and entropic quadtrees (Vetro and Simovici,
module 1
2010). However, the state of the art in image-analysis/object-
initialization of other modules
recognitionstilldoesnotofferanansweronhowtocreateaCDA
with planetary radius
thatisasrobustasthescientificcommunitywoulddesire.Hence,
it is not surprising that several research groups are working in
thisstillyoungfield,tryingtoachievethisgoal.SeveralCDAscan r = r1
process global datasets (Michael, 2003; Salamunic´car and
Loncˇaric´, 2010a; Stepinski and Urbach, 2008). The experience
withourCDAisasfollows:(1)itisnecessarytomanuallyprocess module 2
a large number of crater-candidates in order to considerably fuzzy edge detection
extendground-truth(GT)catalogue;(2)improvementsofdetec-
tion capabilities for very small craters increase the number of
detectedcratersfromanygivendataset;and(3)theinaccuracyin
module 3
measurementofcraters’propertiesincluding2Dprofilesincreases
fuzzy RH transform
withthedecreaseintheirsize.Thiswasamotivationforthework
search for maxima
onthenew CraterShape-basedinterpolation,whichconsiderably
improvesthepreviousCDAinaddressingtheseissues. module 4
The above led to the concurrent work on new catalogues and run-time interpolation of DEM
improvements of the previous CDA (Salamunic´car and Loncˇaric´, and parameter-space data
2010a). Resulting catalogues are: (1) MA132843GT for Mars; and module 5
(2)LU60645GTfortheMoon,createdusingLALT(Salamunic´carand
morphometry and parameter-
Loncˇaric´,2010b)andLOLA(Salamunic´caretal.,2011a)datasets.
space analysis
The rest of this paper is organised as follows. In Section 2, the
methodsanddatasetsofthispaperarepresentedindetail,aswellas module 6
usedandassembleddatasets.TheresultsarepresentedinSection3, probability modification
andtheconclusionisgiveninSection4.Readersmostlyinterested according to detected radius
intotheimprovedCDAfromthispapershouldbeprimarilyfocused
to Sections 2.1, 2.2, and 3.1, readers mostly interested into the r = r + 1 r = r2 / 2
resultingcataloguesshouldbeprimarilyfocusedtoSections2.3,2.4,
and3.2.,whileSection3.3demonstrateshownewcratercatalogues
canbeusedincombinationwiththeimprovedCDAwhichprovides YES r ≤r down-sample DEM
2
automated measurements, in order to outline differences between to half of its size
NO
MartianandLunarcraters.
YES
DEM-resolution > 4°
2. Methodsanddatasets
module 7 NO
Thedevelopedmethodsandthedatasetsusedaredescribedin slip-tuning of crater candidates
removal of multiple detections
thefollowingorder:
and low-probability detections
(cid:3)
improvement of crater detection algorithm using new Crater
Shape-basedinterpolation; save XML file
(cid:3)
utilisation of method for re-projection of datasets and with detected craters
catalogues;
(cid:3)
datasetsusedforcraterdetectionandevaluation;and
Fig.1. Schematicflowdiagramofoverallorganisationandprocessingstepsfor
(cid:3)
previouscataloguesofLunarcraters. ourCDA.
238 G.Salamuni´ccaretal./PlanetaryandSpaceScience60(2012)236–247
2010a).Thealgorithmutilisesfuzzyedgedetectiontoextractcrater value is used inside the CDA for the computation of slopes and
featuresrequiredforthefuzzyRadon–Hough(RH)transformsearch diameter-rangeofcrateraccordingtoitssize.TheproposedCDAcan
for maxima in the parameter space. Following this step, DEM and usevariousedgedetectionmethodssuchasCanny(1986)andShen
parameter-space data are interpolated at run-time in order to be and Castan (1992). The experiments conducted in this work are
used for morphometry measurements (of depth/diameter ratio, basedontheCanny(1986)edgedetectionmethod,andhaveshown
circularity, topographic-cross-profile, rim, central peak, and radial considerablyimprovedcraterdetection.
rangewherethecraterispreserved)andparameterspaceanalysis The proposed DEM-based CDA is based on our previous CDA
(the circularity of votes is higher at craters’ centres than in the (Salamunic´car and Loncˇaric´, 2010a). It has been improved using a
centresoffalsedetections).Theinterpolationatrun-timeisusedto specially developed method for interpolation of DEM and para-
dynamically calculate interpolated values on demand, therefore meter-space data, which is suitable for detection of small craters.
reducing memory requirements. Next, the previously computed The most commonly-used interpolating functions are: nearest
probabilitythatadetectedfeatureisacraterismodifiedbasedon neighbour, bilinear, bicubic, quadratic splines, cubic B-splines,
itsassociateddiameter-range(notcomparedtotheresolutionofthe higher-order B-splines, Catmull–Rom cardinal splines, Gaussians,
imagecurrentlyusedinthemulti-resolutionsetup,butaccordingto andtruncatedsinc(Zitova´ andFlusser,2003).However,inthecase
classificationintooneofdiameter-ranges–seebelow;Section3.2– of their application to CDAs, we should consider that: (1) the
the distribution of craters from corresponding catalogues). These optimal implementation of interpolation should be computed in
steps arerepeatedfor allradiiand for alldataresolutions. Finally, runtimeonlyforrequiredDEMcoordinates,asopposedtoastatic
we perform slip-tuning of the crater-candidates, and removal of interpolation of the whole data set (this reduces computational
multiple detections. Because the previous version of CDA complexityandmemoryrequirements);(2)theinterpolationitself
(Salamunic´car and Loncˇaric´, 2010a) was used only for Mars, the should not introduce artifacts that will decrease the accuracy or
planetary-radius had been hard-coded. In the new version, it precision of the measurements obtained via CDA (e.g. compiled
becomes one parameter, so that the same CDA can be used for depth/diametervalues);and(3)forthesmallestdetectablecraters
Mars, the Moon, and potentially for other planetary bodies. This wehavesparsesampling,whereineachcraterisrepresentedwith
2000m depth Case: a) S027098B13104K01753T56623Y2007S from
1500m MA132843GT drawn using 1/128° MOLA data
1000m
500m
0m diameter
2000m depth Case: b)
1500m
1000m
500m
0m diameter
2000m depth Case: c)
1500m
1000m
500m
0m diameter
2000m depth Case: d)
1500m
1000m
500m
0m zoom-in diameter
2000m depth Case: e)
1500m
1000m
500m
0m diameter
... pixel -3 pixel -2 pixel -1 pixel 0 pixel 1 pixel 2 pixel 3 ...
The interpolation for distances smaller than 1 pixel, an example how to compute G is as follows:
C(1,y)
- ABis distance of 1 pixel;
- BCis elevation y at distance of 1 pixel;
- D is point for which the interpolation has to be computed; E(x, y·x) F(1,y·x)
- E is linear interpolation on AC;
- F is projection of E on BC; and G(x, y·x2)
- G is linear interpolation on AF.
A(0, 0) D(x, 0) B(1, 0)
Fig.2. IllustrationoftheCraterShape-basedinterpolationusedfortheCDAfromthispaper:(a)the2Dtopographicprofileofcrater;(b)therepresentationwithnearest-
neighbourinterpolationoftheelevation;(c)thesimplelinearinterpolation;(d)thesecond-orderinterpolationbasedontheadditionalinterpolation(seethebottom
frame),butonlyfordistancessmallerthan1pixel;and(e)thecomparisonswhichshowthat(d)isabetterapproximationoftheprofileshownin(a)thantheinitialcase
(b)andpreviouscase(c).
G.Salamuni´ccaretal./PlanetaryandSpaceScience60(2012)236–247 239
asmallnumberofpixels.Ontheotherhand,theimportanceofgood computationofcoefficientsofhigherdegreepolynomials).There-
interpolationliesin:(1)betterdetectioncapabilities,particularlyfor fore,weselectedapproach(d)forourCDA.
small craters; and (2) more accurate measurements of crater
properties.Basedontheseconsiderations,weproposethefollowing 2.2. Utilisationofmethodforre-projectionofdatasetsand
solution. catalogues
Crater Shape-based interpolation used for our CDA is illu-
strated in Fig. 2. Frame (a) shows the topographic profile of a Inpreviouswork(Salamunic´caretal.,2011b),weprovidedan
craterfromMA132843GT.Frame(b)showsapixelrepresentation orthographic projection view with the crater of interest in the
(knownalsoasthenearestneighbourfunction),whosepixelsize centre for better evaluation capabilities of northern-most and
with artificially degraded resolution illustrates the effect of the southern-most craters. This approach was sufficient for Mars
digitalizationofinputvalues.Italsoenablesustoseehowvarious where all the craters from MA130301GT (Salamunic´car et al.,
interpolation methods compare to the original full-resolution 2011b)arelocatedbetween871Nand871S.However,thisisnot
data.The resultof simple linearinterpolationisshowninframe the case for the Moon, where there are no polar-layer-deposits,
(c). It shows an improvement for most segments, except very and where craters exist at the most extreme polar latitudes. In
close to the crater centre. In such cases there is a decrease of additiontoorthographicprojections,weperformarotationofthe
accuracy (the curve shown in frame (c) has a first derivative entireDEMandopticalglobaldatasets,suchthatthegeographical
discontinuity at the crater centre, which is not the case for the North and South Poles are rotated on the equator of the new
curveshowninframe(a)).Inordertoovercomethisinterpolation coordinate system. The method works as follows: (1) a global
artifact, we modify the interpolation between the crater centre dataset is re-projected from the simple cylindrical projection to
and the nearest pixels, as shown in frame (d). The additional thesphere;(2)thesphereisrotatedbyaparameterizedamount
interpolationisshowninthebottomframeofFig.2.Itassumesa aroundthex,y,andzaxes;(3)theglobaldatasetisre-projected
paraboliccratershape,whichisthecaseforthemajorityofsmall back from the sphere to the simple cylindrical projection.
(bowl-shaped) craters, and which is also appropriate for larger The same method can be used for crater locations, in both direc-
craters withcentral peaks or pits(concave vs. convex parabola). tions:(1)toconvertgeographicalcratercoordinatestocomplywith
Asshowninframe(e),thisapproximatesoriginal(full-resolution) there-projecteddatasets;and(2)toconverttherotatedcoordinates
values in all segments considerably better than previous cases backintotheoriginalform,tocomplywiththeinitialdatasets.
(b) and (c). At the same time, approach (d) is computationally
veryefficient,becausesimplelinearinterpolationsarecomputed 2.3. Datasetsusedforcraterdetectionandevaluation
inonlytwostages,thesecondofwhichisonlyexecutedwithina
one-pixel distance to the crater centre. Even within a one-pixel For Mars, we used datasets prepared in our previous work
distance to the crater centre, this is considerably faster than (Salamunic´car et al., 2011b). For the Moon, we used the 1/161
alternative, more complex interpolation approaches (e.g. the SELENELALT(Arakietal.,2009)andupto1/5121LROLOLA(Smith
depth
A-2) radial-resolution = 64, interpolation = no diameter
depth
A-3) radial-resolution = 176, interpolation = no diameter
depth 1km
A-4) radial-resolution = 176, interpolation = yes diameter
-5.1km -4km -3km -2km -1km 0km 1km 2km 3km 4km 5.1km
1/256° THM_DIR-FIXED & MDIM (122.93°E, 22.86°N) 1/256° THM_DIR-FIXED & MDIM (107.46°E, 29.59°N)
A-1) Crater-S027098B13104K01753T56623Y2007S B-1) Crater-S025657B13305C00918K22955T55434Y2007S
depth
B-2) radial-resolution = 64, interpolation = no diameter
depth
B-3) radial-resolution = 176, interpolation = no diameter
depth
1km
B-4) radial-resolution = 176, interpolation = yes diameter
-7.8km -6km -5km -4km -3km -2km -1km 0km 1km 2km 3km 4km 5km 6km 7.8km
Fig.3. Asshownforonesmaller(D¼5.1km)V-shapedcrater(A-1)andoneslightlylarger(D¼7.8km)bowl-shapedcraterwithanapproximatelyparabolicinteriorprofile
(B-1),theincreaseofthenumberofradial-resolutionscanscannotsolvethepixelization-side-effectproblem(A-3comparedtoA-2,B-3comparedtoB-2).Incontrast,the
CraterShape-basedinterpolationfromthispapersuccessfullysolvesthisproblem(A-4comparedtoA-3andA-2,B-4comparedtoB-3andB-2).Theresultingcrater3D
shapeand2Dtopographicprofiles(A-4andB-4)shownoartifactresultingfromthesub-optimaldata-processing.
240 G.Salamuni´ccaretal./PlanetaryandSpaceScience60(2012)236–247
et al., 2010) global DEMs, digitised at 1-m vertical resolution. catalogues–insightintodifferencesbetweenMartianandLunar
Unlikepreviouslaseraltimeters,whichmappedplanetarybodies, craters.
suchasMarsorbiterlaseraltimeter(MOLA),LOLAisafive-beam
laser altimeter with a firing rate of 28Hz, providing up to 140
measurements per second. The five-beam pattern was designed 3.1. ImprovedcraterdetectionalgorithmbasedonnewCrater
tocharacterizethelunarsurfaceatscalesrelevanttohumanand Shape-basedinterpolation
roboticexploration,andittranslatestoanunprecedentedalong-
trackmeasurementspacingof (cid:2)10m(comparedtoabout1.7km The Crater Shape-based interpolation used within the CDA
for SELENE). LOLA continues to operate, improving its coverage results in improved crater 3D-shapes and 2D topographic profiles,
(especially,reducingitsaveragelongitudinalgapbetweentracks). asshowninFig.3fortwofreshcraterswithlargedepth/diameter
TheglobalLunaropticalimagemosaicsusedduringtheregistra- ratios.ThecurveshowninFig.2frame(c)hasadiscontinuationof
tionofnewcratersintheGTcatalogueare:1/641LASGW(Lunar firstderivationatthecraterrimaswell(andnotonlyatthecrater
Airbrushed Shaded Relief Warped to ULCN2005); 1/2561 CLEM- centreaspreviouslydiscussed),aswellasthecurveshowninframe
BASE (Clementine Basemap Mosaic version 2); and 1/5121 LOM (d),whileforthecurveshowninframe(a)thisisnotthecase.From
(LunarOrbiterMosaic).InthecaseofLALTandLOLADEMdatasets thisperspective,anotherimportantobservationisthatthedisconti-
and LASGW optical dataset, post-processing tasks includes only nuity of the first derivative at the crater rim does not appear in
down-sampling and up-sampling to other resolutions, and ren- Fig.3.Thisissobecausethisproblemhasbeensolvedbyaveraging
dering of optical BMP files. For CLEMBASE, we performed an
interpolation fix (as done for Martian THEMIS-DIR) and bright- 1/128° LOLA
Image center: (94°W, 20°N)
ness/contrastcorrectionfixes(asdoneforMartianMOC).TheLOM
N
datasetwasoptimisedformemoryusagepurposes.
2.4. PreviouscataloguesofLunarcraters
TwoLunarcataloguesdevelopedbypreviousresearchersare:
(1) McDowell (2007) catalogue, which contains 8639 (named)
craters (hereafter LU8639N); and (2) Rodionova et al. (1987)
catalogue (hereafter LU14923R), which is the most complete
catalogue of Lunar craters prior to this work, containing 14,923
craters(1394identifiedbyname).AnadditionalLunarcatalogue
50 km
(Head et al., 2010; Kadish et al., 2011), which contains 5185 -3000m 3000m
craters (hereafter LU5185H) was developed very recently, and 1/128° LOM, shifts-XY = (-5, 1)
was not available when we had completed LU58357GT released
earlier in order to facilitate the use of LRO data to survey
and estimate impact melt volumes in small- to medium-sized
craters (Mazarico et al., 2011). LU5185H was thus included in
LU60645GT.
3. Resultsanddiscussion
In order to evaluate the performance of the proposed CDA,
accordingtotheframeworkforevaluationofCDAs(Salamunic´car
et al., 2011b), the resulting new catalogues MA132843GT and
LU60645GT are used in addition to the previously assembled
catalogue MA57633GT (Salamunic´car and Loncˇaric´, 2008b).
Fig. 4. Part of the 1/1281 LOLA dataset and output of our Crater Shape-based
Theresultsanddiscussionaregiveninthefollowingorder: interpolationCDAwithin(blue)andoutside(red,notshowninthebottomframe)
theselectedregion(top);crater-candidateswiththeassignedprobabilitylargerthan
(cid:3) improved crater detection algorithm based on new Crater theusedthresholdwhichdefinesthosemanuallyevaluated,true(blue)andfalse
(red, labelledwith white arrow-pointers) detections, according to the automated
Shape-basedinterpolation;
(cid:3) verificationusingLU60645GT(bottom).(Forinterpretationofthereferencestocolor
assembled new catalogues MA132843GT and LU60645GT of
inthisfigurelegend,thereaderisreferredtothewebversionofthisarticle).
MartianandLunarcraters;and
(cid:3)
differences between Martian and Lunar craters in depth/
diameterratioand2Dprofiles. Table1
Definitionsandgraphs(TP¼TruePositives;FP¼FalsePositives;FN¼FalseNega-
tives;GT¼GroundTruth;TDR¼TrueDetectionRate;FDR¼FalseDetectionRate;
Section 3.1 additionally includes: (1) interpolation-based ROC¼ReceiverOperatingCharacteristics;F-ROC¼Free-responseROC;ROC’¼the
improvements in 3D-shapes of craters and 2D-topography-pro- closestapproximationthatcanbeachievedforROC;Q¼Qualitypercentage)used
files;and(2)evaluationofachievedperformanceofinterpolation- forevaluationofCDAs(Salamunic´caretal.,2011b).
based crater detection algorithm. Section 3.2 additionally
Useddefinitions Usedgraphs
includes: (1) verification of assigned coordinates and diameters
(horizontalrange/verticalrange)
tocratersfrompolar-regions;(2)typicalnewlycataloguedcraters
from MA132843GT and LU60645GT catalogues; (3) statistics of GT¼TPþFN F-ROC[TP/FP]
LU60645GT and MA132843GT catalogues; and (4) advances in TDR¼TP/(TPþFN)¼TP/GT ROC’[TDR/FDR]
FDR¼FP/(TPþFP) Q[Q/FDR]
integration of diverse morphological descriptors from previous
Q¼TP/(TPþFPþFN)¼TP/(GTþFP)
catalogues.Section3.3describesonepossibleapplicationofcrater
G.Salamuni´ccaretal./PlanetaryandSpaceScience60(2012)236–247 241
a large number of profiles (we average 176 profiles at different (Salamunic´car et al., 2011b), using F-ROC (Salamunic´car and
azimuths/angles of the same crater, partially because our CDA Loncˇaric´,2008a)andROC’(Salamunic´caretal.,2011b).TheROC’
searches for craters in radius range between 2 and 28 pixels and evaluationsfor Mars show thatthe proposedCDA is better than
insuchcasethelengthofriminpixelsis28(cid:4)2p¼(cid:2)176). all other available CDAs, according to the area under the ROC’
The difference compared to the CDA from previous work curve criterion (AUROC’ is 50.1% for the CDA by Stepinski and
(Salamunic´carandLoncˇaric´,2010a),whichutilisedonlytheMartian Urbach (2008), 54.0% for the CDA by Salamunic´car and Loncˇaric´
DEM (MOLA) is that in this work the Lunar DEMs have been used (2010a), and 57.4% for the proposed interpolation-based CDA).
(LALT, LOLA) as well. The proposed interpolation-based CDA can The ROC’ evaluations based on lunar datasets (shown in Fig. 5
successfullydetectLunarcratersasshowninFig.4:(1)mostofthe bottom)showthattheproposedinterpolation-basedCDAisalso
cratersaresuccessfullydetected;(2)thenumberoffalse-detectionsis better for Lunar datasets than the CDA from the previous work
low; and (3) coordinates and diameters are precisely defined (Salamunic´car and Loncˇaric´, 2010a), while other CDAs have not
for a large majority of the craters. As shown, for this region beenusedbeforeforglobalprocessingofLunarDEM.
(x1¼‘‘(cid:5)96.578132’’ y1¼‘‘20.195315’’ x2¼‘‘(cid:5)90.929678’’ y2¼ In order to compare the relative improvements of overall
‘‘16.921865’’; x1 and x2 are longitudes, y1 and y2 are latitudes of achieved performance between our previous CDA (Salamunic´car
the corners, in theeast/planetocentric coordinate system) thereare and Loncˇaric´, 2010a) and the CDA from this paper (wherein the
17truedetectionsand6falsedetections.Allfalsedetectionshavea only difference is in the usage of Crater Shape-based interpola-
diameter smaller than 3.317km and for larger craters thereare no tion) with the improvements between the CDA from Stepinski
false detections within this region. For parameterization of the and Urbach (2008) and our previous CDA (Salamunic´car and
interpolation-based CDA proposed with this paper, we used the Loncˇaric´,2010a),thefollowingmethodwasused.Letussuppose
planetary radius value for Mars of 3390km, and for the Moon thatCDA-A,CDA-B,andCDA-CachievedperformanceA,BandC,
1737.4km. wherein:(1)eachvalueisinthenormalisedrangebetween0and
The evaluation was performed using the framework for eva- 100%; (2) larger value means better performance; and (3) AoB
luation of CDAs (for definition see Table 1) from previous work andBoC.Inthiscase,forCDA-Bpossibleimprovementis(1(cid:5)A)
τ1 F-ROC evaluations based on 1/128° MOLA, old 100% ROC' evaluations based on 1/128° MOLA, new
τ)1 registration method (fm < 0.5) and MA57633GT. registration method (fm < 3) and MA132843GT.
3 ( 50000
63 80%
7
5 3
o 40000
e from 0 t 30000 321 ction rate 60% 12
g e
n ran L1 e- gMenAd7:5 919T catalogue e det 40% 1 - MLeAg7e5n9d1:9 T catalogue
ons i 20000 2 - owlodr kC aonpntimy bizaesde fdo rC lDarAg efrro amn dp rmevidiodules- tru 2 - oplrde vCioaunsn yw obraks eodp tCimDizAe dfr ofomr
cti sized craters smaller craters
ete 10000 3 - new Canny based CDA, difference 20% 3 - new Canny based CDA, difference
d according to (2) is included according to (2) is included
ue- interpolation based improvement interpolation based improvement
tr
0 0
0 10000 20000 30000 40000 50000 τ 1 0 20% 40% 60% 80% 100%
false-detections in range from 0 to 57633 (τ1) false detection rate
100% 100%
ROC' evaluations based on 1/16° LALT, new ROC' evaluations based on 1/128° (2, 3a) and
registration method (fm < 3) and LU60645GT. 1/64° (3b) LOLA, new registration method (fm < 3)
and LU60645GT.
80% 80%
3a
n rate 60% on rate 60% 2 3b Legend:
true detectio 40% 3 2 - old CaLnengye bnads:ed CDA true detecti 40% 3a - new C2a nCws- nmooDylradA kbl l Caeofrsrpao ectnmidrmna ypCitz erbDeerasvdAs i o,fe oudrs
2 from previous work optimized for difference according to (2) is
20% smaller craters 20% included interpolation based
improvement
3 - new Canny based CDA, difference
3b - new Canny based CDA like (3a),
according to (2) is included interpolation
but used with 1/64° LOLA data
based improvement
0 0
0 20% 40% 60% 80% 100% 0 20% 40% 60% 80% 100%
false detection rate false detection rate
Fig.5. AccordingtotheF-ROCevaluationsforMars(top–left)CDA#2issuperiortoCDA#1(StepinskiandUrbach,2008),whileCDA#3providesbetterresultsthanthe
othertwo.AccordingtotheROC’evaluationsforMars(top–right)CDA#3issuperiortoCDA#2,butCDA#1showsbetterresultsforfalsedetectionratesbetween5%and
30%.AccordingtotheROC’evaluationsfortheMoon(bottom–leftandbottom–right),CDA#3issuperiortoCDA#2likeinthecaseforMars.For1/1281LOLAdataobtained
resultsarebetterthanfor1/161LALTor1/641LOLAdata.
242 G.Salamuni´ccaretal./PlanetaryandSpaceScience60(2012)236–247
and achieved improvement is (B(cid:5)A), while for CDA-C possible detected by either CDA because of dataset limitations, an addi-
improvement is (1(cid:5)B) while achieved improvement is (C(cid:5)B). tional GT catalogue was created from which 19,886 craters not
Usingthis,theratiobetweenachievedandpossibleimprovement detectablebyeitherCDAhavebeenremoved.Theoverallresults
is R ¼(B(cid:5)A)/(1(cid:5)A) for CDA-B and R ¼(C(cid:5)B)/(1(cid:5)B) for CDA-C. are shown in Fig. 6, wherein we also averaged the results from
B C
At the end, these two values are compared, having I ¼R (cid:6)100/ individualcomputationsinordertohaveasrealisticaspossiblea
B B
(R þR ) and I ¼R (cid:6)100/(R þR ). For AUROC’ values from the comparisonofachievableperformancesbetweendifferentCDAs.
B C C C B C
previous paragraph, computed values are 50.6% and 49.4%.
Similarly, we can compute for AUFROC1t, in which case we are 3.2. AssemblednewcataloguesMA132843GTandLU60645GTof
notinterestedinareasunderF-ROCforahorizontalrangelarger MartianandLunarcraters
t t
than 1 ( is the number of craters in GT catalogue) because in
suchacase thenumberof false detectionsis alwayslargerthan The results of the method for re-projection of datasets and
thenumberofcorrectdetections.Inordertotakeintoaccountthe cataloguesareshowninFig.7.Usingthismethod,thecoordinates
fact that some craters from MA132843GT catalogue cannot be and diameters of 22 Lunar craters were corrected. After that,
AUFROC1τ AUROC' Average
MA132843GT
48.5% 51.5% 50.6% 49.4% 49.6% 50.4%
MA132843GT
reduced to
112957 craters 32.9% 67.1% 51.5% 48.5% 42.2% 57.8%
Average
40.7% 59.3% 51.1% 48.9% 45.9% 54.1%
Fig. 6. Comparison of the relative improvements of overall achieved performance between: (1) the CDA from Stepinski and Urbach (2008) and our previous CDA
(Salamunic´carandLoncˇaric´,2010a)–leftparts(blue);and(2)ourpreviousCDA(Salamunic´carandLoncˇaric´,2010a)andtheCDAfromthispaperwhereintheonly
difference,whichinfluencesperformanceisintheusageofCraterShape-basedinterpolation–rightparts(green).(Forinterpretationofthereferencestocolorinthisfigure
legend,thereaderisreferredtothewebversionofthisarticle).
A-1) 1/1° MOLA NP B-1) 1/1° LOLA NP
SP SP
A-2) 1/1° MOLA - ROTATED B-2) 1/1° LOLA - ROTATED
NP SP NP SP
-8463m 13853m
C-1) 1/64° LOLA - ROTATED C-2) 1/64° LOLA - ROTATED
NP SP
50 km
Fig.7. Standard(A-1andB-1)androtated(A-2andB-2)viewfor1/11MOLA(A-1andA-2)and1/11LOLA(B-1andB-2)data.Therotatedviewwasusedtocheckthe
accuracyofassignedcoordinatesanddiametersofcraters,asshownfor1/641LOLA(C-1andC-2)North-Pole(C-1)andSouth-Pole(C-2).
G.Salamuni´ccaretal./PlanetaryandSpaceScience60(2012)236–247 243
wecheckedthe50northern-mostand50southern-mostcraters, and the associated probability threshold (cid:2)0.3907 (hereafter t)
inordertoconfirmthatadditionalcorrectionsarenotrequiredfor and removed all crater-candidates with associated probabilities
LU60645GT. A similar check was performed for MA132843GT, smaller than t. The recomputed t for MA132843GT is the same
whereincorrectionshavenotbeenrequired. number. The value of t computed for Mars has been used for
To extend the GT catalogues, we used the framework for Lunar catalogues as well because it was obtained using GT
evaluation of CDAs from previous work (Salamunic´car et al., catalogue, which was much more complete than that available
2011b), where all crater-candidates proposed by our CDA are for the Moon at that time. When we assembled LU60645GT we
manuallyevaluatedforrejection,orcorrectionofcoordinatesand recomputed the Lunar value of t. It is remarkably similar to
diameterandinclusionintotheGTcatalogues.Themainphasesof thepreviouslycomputedforMars(differenceisonlyoftheorder
thenewworkonGTcataloguesforMarsandtheMoonareshown 10–5). This is explainable by completeness of LU60645GT in
in Fig. 8. We rejected some of the crater-candidates before comparison with MA132843GT and the robustness of the inter-
manual evaluation, using the framework for evaluation of CDAs polation-based CDA proposed by this paper, regarding detection
frompreviouswork(Salamunic´caretal.,2011b).Inthefirststep ofcratersontwodifferentplanetarybodies(MoonandMars).
(Mars – 1/1281 MOLA), we found the maximum of Q (Quality As shown in Fig. 9 (top), typical new entries in Martian GT
percentage)curve(fordefinitionseeTable1)usingMA130301GT catalogue are mostly small craters, and some larger much
degraded craters. These are the craters that the new interpola-
tion-basedCDAfromthispapersuccessfullydetected,whichwas
not the case for our previous CDA (Salamunic´car and Loncˇaric´,
MA130301GT
2010a). As shown in Fig. 9 (bottom), there are many more new
catalogue
entriesinLunarGTcataloguethanintheMartianone.Thereason
is that preceding Lunar catalogues were considerably less com-
MA132843GT #2542 / #53101 from
pletethantheprecedingMA130301GTMartiancatalogue.
new catalogue Canny CDA and 1/128° MOLA
Thedistributionofcratersfromcorrespondingcataloguesand
classificationintooneofdiameter-rangesisgiveninFig.10.The
LU8639N catalogue LU14923R catalogue
completeness is estimated using the Craterstats (Michael, 2010)
from McDowell from Rodionova et al.
programme.Theflatteningoflinesatsmalldiametersisrelatedto
the input dataset resolution. The CDA detected numerous small
catalogue with craters(Do8km)intheLOLAdataset,whichcouldnotbeverified
18229 craters
due to inadequate high-resolution imagery coverage, and there-
fore has not been included into LU60645GT. In addition, we
catalogue with #8987 / #16892 from
expect a correlation between poorer imagery coverage and
27216 craters Canny CDA and 1/16° LALT
reduced density of small craters (Do8km) (e.g. fewer smaller
detected craters validated on the farside or higher-latitudes,
LU58357GT #31141 / #61741 from
whereimagerycoveragewasworse).
new catalogue Canny CDA and 1/128° LOLA
Thecatalogueintegrationisusefulforresearchersinterestedin
cratersonMarsandtheMoon.ThenewcatalogueLU60645GTisa
catalogue with LU5185Hcatalogue
superset of the previous Lunar catalogues, as shown in Fig. 11.
58581 craters from Head et al.
With our approach, LU60645GT contains everything that was
included in these catalogues, plus: (1) the correlation between
catalogue with #171/ #299 from
various morphological descriptors from the catalogues used;
58752 craters Canny CDA, 1/256° LOLA and
(2) the correlation between manually assigned attributes and
region(0°E~10°E&20°S~30°S)
automated depth/diameter measurements from LU60645GT by
our CDA; (3) average errors and their standard deviations for
catalogue with #268 / #407 from
59020 craters Canny CDA, 1/256° LOLA and manuallyandautomaticallyassignedattributes,suchasposition
region(10°W~0°W&20°N~30°N) coordinates, diameter, depth/diameter ratio, etc; and (4) posi-
tional accuracy of features in the used datasets, wherein our
catalogue with #364 / #448 from catalogue contains 60,645 cross-references between each of
59384 craters Canny CDA, 1/256° LOLA and the used datasets. Additionally, surface dating could potentially
region(30°W~20°W&0°S~10°S) be improved with the exhaustiveness of this new catalogue.
The same kind of contribution was also made in the case of the
catalogue with #380 / #542 from newMartiancatalogueMA132843GT,asdescribedintomoredetail
59764 craters Canny CDA, 1/256° LOLA and inthepreviousworkforMA130301GT(Salamunic´caretal.,2011b).
region(20°E~30°E&0°N~10°N)
3.3. DifferencesbetweenMartianandLunarcratersindepth/
catalogue with #415 / #1691 from
diameterratioand2Dprofiles
60179 craters Canny CDA and 1/256° LOLA
wherein D≥ 8km
TheCraterShape-basedinterpolationCDAfromthispapercanbe
used in combination with the new LU60645GT and MA132843GT
LU60645GT #466 / #690 from
new catalogue Canny CDA and 1/256° LOLA cataloguesofLunarandMartianimpactcratersinordertoprovide
wherein 8km > D≥ 4km automated morphometry measurements of depth/diameter ratio,
topographic-cross-profiles, etc. (Salamunic´car and Loncˇaric´, 2009,
Legend: #n/ #m means m candidates 2010a). Now that catalogue LU60645GT exists, in addition to
andn previously uncatalogued craters MA132843GT(extensionofthepreviouslyavailableMA130301GT),
it is possible to compare morphometry measurements of Martian
andLunarimpactcraters.AsshowninFig.12(top),thetransition
Fig.8. MainphasesofthenewworkonGTcataloguesforMars(top)andthe
Moon(bottom)inwhichthenewworkisbasedontheinterpolation-basedCDA. ofthedepth/diameterratiooftheyoungestcratersonMarsoccurs
244 G.Salamuni´ccaretal./PlanetaryandSpaceScience60(2012)236–247
1/256° THM_DIR – FIXED
Image center: (69.2°E, 9.3°S)
N
50 km
1/128° LOM
Image center: (94°W, 20°N)
N
50km
Fig.9. PreviousMA130301GTcatalogue(green)andadditions(yellow,labelledwithwhitearrow-pointers)ofthenewMA132843GTcatalogueofMartiancraters(top).
Thecataloguewith18,229cratersassembledbyhumanlabelers(green)andadditions(yellow,labelledwithwhitearrow-pointers)ofthenewLU60645GTcatalogueof
Lunarcraters(bottom).(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle).
Martiancatalogues: Lunarcatalogues:
Conclusion: Conclusion:
MA132843GT is LU60645GT is
more complete than forD≥ 2km more complete than forD≥8km
other Martian MA132843GT the other Lunar LU60645GT
catalogues at all is mostly complete catalogues at all is mostly complete
diameter ranges. diameter ranges.
a1
Legend: (a1) 18 229 craters a3
5 MA130301GT MA132843GT LU18229 LU60645GT previously found; (a2) 8 987
rs 000 1e+ cdforaauttane;dr as wn fdoit uh(an L3d)O w 3Li3At h4 d2La9At aLc.r Taters
e 0
at 1
Cr 00
of 10 a2
mber 100
u
N 0
1
1
1 2 4 8 16 32 64 128
Diameter Ranges [km]
MA130301GT 29700 14818 19888 14026 13848 10382 8225 6448 4895 3512 2308 1304 603 227 117
MA132843GT 31630 15129 20073 14059 13876 10394 8238 6464 4901 3518 2309 1305 603 227 117
LU18229 78 23 122 456 972 1316 3165 4026 3194 1936 1311 816 459 229 126
LU60645GT 9755 8758 5005 5439 3994 5332 6282 5908 4069 2471 1606 1006 568 283 169
Fig.10. AnassessmentofcompletenessofthecataloguesandthedistributionofcratersfromLU60645GTregardingthecontributions.
G.Salamuni´ccaretal./PlanetaryandSpaceScience60(2012)236–247 245
Fig.11. TheresultingLU60645GTcataloguecontainsLU8639N,LU14923R,andLU5185H,whereinitispossibletocomparethepropertiesofnumerouscratersbetween
catalogues.
atD¼5.8km,whileontheMoonitoccursatD¼18.4km.According newLU60645GTcatalogueprovideseverythingthatwasprovided
to its diameter, we can classify each crater into one of the seven by the previous Lunar catalogues, plus numerous new possibili-
following ranges: (1) 1kmrDo2km; (2) 2kmrDo4km; ties as enumerated in Section 3.2. The accompanying results of
(3)4kmrDo8km;(4)8kmrDo16km;(5)16kmrDo32km; thispaperare:(1)thepossibilityofcomparingLunarandMartian
(6) 32kmrDo64km; and (7) 64kmrD. As shown in Fig. 12 cratersregardingdepth/diameterratio,2Dprofiles,etc.,whereina
(centre),itispossibletocompareaveragetopography-cross-profiles considerably larger number of craters than available from the
ofLunarandMartiancraters.Theyfollowthetrendoftheyoungest previousworkleadstogloballymorerepresentative,statistically
craters,whereinforLunarcratersdepth/diameterratioandheightof moresignificant,morepreciseresults;(2)utilisationofamethod
crater rim is approximately two times larger than for Martian for the re-projection of datasets and catalogues, which is very
craters.Foreachaveragetopographic-cross-profile,usingd/Dratio, usefulfortheevaluationandregistrationofcratersthatarevery
allcratersfromaselectedrangeareinadditionclassifiedaccording close to poles; and (4) the extension of the previous framework
to whether they have higher or lower d/D ratio. The whole forevaluationofCDAs(Salamunic´caretal.,2011b)withdatasets
procedure is recursively repeated 3 times. The result is that the andGTcataloguefortheMoon,whichcanbeusedinparallelwith
craters within each diameter range are additionally classified into thosepreviouslypreparedforMars.
8 sub-groups according to their d/D value. As shown in Fig. 12 The new Crater Shape-based interpolation module improves
(bottom), the above trend is consistent for all ranges from the ourpreviousCDAasfollows:(1)itdecreasesthenumberoffalse-
freshesttothemostheavilydegraded/erodedcraters. detections for the required number of true detections, which
leads to a smaller number of crater-candidates that need to be
evaluatedmanuallyandatthesametimetolargerextensionsof
4. Conclusions GT catalogues with previously uncatalogued craters; (2) it
improvesdetectioncapabilitiesforverysmallcraters,whichleads
The main results of this paper are: (1) the new catalogue todetectionofconsiderablymorecratersfromthesamedataset;
LU60645GT of Lunar craters (complete up to(cid:2)DZ8km), and(3)itprovidesmoreaccurateautomatedmeasurementsof2D
which contains a considerably larger number of craters and profilesandothercraterpropertiessuchasdepth-diameterratio
associatedattributesthananyothercurrentlyavailablecatalogue and more precise comparison of Lunar and Martian impact
ofLunarcraters;(2)thenewcatalogueMA132843GTofMartian craters. In fact, the measure of relative difference in overall
craters(anexpansionofthepreviousMA130301GT),whichisthe achievedperformancebetweentheCDAsfromourpreviouswork
most complete(upto(cid:2)DZ2km)publiclyavailable catalogue of andthispaperis54.1%(whereintheonlydifferenceisinthenew
Martian craters; (3) considerable improvement of previous CDA Crater Shape-based interpolation module – different from the
(Salamunic´car and Loncˇaric´, 2010a) using new Crater Shape- linearoneexclusivelyfordistancessmallerthanonepixel),which
based interpolation method from this paper, wherein the ismorethanthedifferenceinperformanceof45.9%betweenthe
improvedCDAwassuccessfullyusedduringworkonLU60645GT CDA from Stepinski and Urbach (2008) and our previous CDA
and MA132843GT. As previously achieved for Mars with our (wheretheCDAsarecompletelydifferent).Apossibleexplanation
previous catalogue MA130301GT (Salamunic´car et al., 2011b) – based on the presumption that CDA usually looks (in the first
and catalogue MA132843GT from this paper, for the Moon the approximation) for circles/ellipses wherein all planetary bodies