Real-time landmine detection with ground-penetrating radar using discriminative and adaptive hidden Markov models

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EURASIPJournalonAppliedSignalProcessing2005:12,1867c 2005HindawiPublishingCorporationReal-TimeLandmineDetectionwithGround-PenetratingRadarUsingDiscriminativeandAdaptiveHiddenMarkovModelsHichemFriguiDepartmentofComputerEngineeringandComputerScience,UniversityofLouisville,Louisville,KY40292,USAEmail:h.frigui@louisville.eduK.C.HoDepartmentofElectricalandComputerEngineering,UniversityofMissouri-Columbia,Columbia,MO65211,USAEmail:hod@missouri.eduPaulGaderDepartmentofComputerandInformationScienceandEngineering,UniversityofFlorida,Gainesville,FL32611,USAEmail:pgader@cise.u.eduReceived25October2004;Revised3March2005;RecommendedforPublicationbyFulvioGiniWeproposeareal-timesoftwaresystemforlandminedetectionusingground-penetratingradarGPR).Thesystemincludesane cientandadaptivepreprocessingcomponent;ahiddenMarkovmodel-(HMM-)baseddetector;acorrectivetrainingcom-ponent;andanincrementalupdateofthebackgroundmodel.Thepreprocessingisbasedonfrequency-domainprocessingandperformsground-levelalignmentandbackgroundremoval.TheHMMdetectorisanimprovementofapreviouslyproposedsystem(baseline).Itincludesadditionalpre-andpostprocessingstepstoimprovethetimee ciencyandenablereal-timeapplica-tion.Thecorrectivetrainingcomponentisusedtoadjusttheinitialmodelparameterstominimizethenumberofmisclassicationsequences.Thiscomponentcouldbeusedo ine,oronlinethroughfeedbacktoadaptaninitialmodeltospecicsitesandenvi-ronments.Thebackgroundupdatecomponentadjuststheparametersofthebackgroundmodeltoadaptittoeachlaneduringtesting.Theproposedsoftwaresystemisappliedtodataacquiredfromthreeoutdoortestsitesatdi erentgeographiclocations,usingastate-of-the-artarrayGPRprototype.Therstcollectionwasusedastraining,andtheothertwocontaindatafrommorethan1200m2 ofsimulateddirtandgravelroads)fortesting.Ourresultsindicatethat,onaverage,thecorrectivetrainingcanimprovetheperformancebyabout10%foreachsite.Forindividuallanes,theperformancegaincanreach50%.Keywordsandphrases:landminedetection,hiddenMarkovmodels,correctivetraining,adaptivepreprocessing.1.INTRODUCTIONDetectionandremovaloflandminesisaseriousproblemaf-fectingciviliansandsoldiersworldwide.Itisestimatedthatmorethan100millionlandminesareburiedinmorethan80countriesaroundtheworld,andthat26000people,mostlycivilians,ayearareeitherkilledormaimedbyalandmine[ 1 2 ].Thedetectionproblemiscompoundedbythelargevarietyoflandminetypes,di eringsoilconditions,temper-atureandweatherconditions,andvaryingterrain,tonameafew.Detectionandremovaloflandminesisthereforeasignif-icantproblem,andhasattractedseveralresearchersinrecentyears.Onechallengeinlandminedetectionliesinplasticorlowmetalminesthatcannotoraredi culttodetectbytra-ditionalmetaldetectors.Varietiesofsensorshavebeenproposedorareunderin-vestigationforlandminedetection.Theresearchproblemforsensordataanalysisistodeterminehowwellsignaturesoflandminescanbecharacterizedanddistinguishedfromotherobjectsunderthegroundusingreturnsfromoneormoresensors.Ground-penetratingradarGPR)o ersthepromiseofdetectinglandmineswithlittleornometalcon-tent.Unfortunately,landminedetectionviaGPRhasbeenadi cultproblem[3 4 5 ].Althoughsystemscanachievehighdetectionrates,theyhavedonesoattheexpenseofhighfalse-alarmrates.Thekeychallengetominedetec-tiontechnologyliesinachievingahighrateofminedetec-tionwhilemaintaininglowleveloffalsealarms.Theper-formanceofaminedetectionsystemisthereforecommonlymeasuredbyareceiveroperatingcharacteristicsROC)curve

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1868EURASIPJournalonAppliedSignalProcessing thatjointlyspeciesrateofminedetectionandleveloffalsealarm.Automateddetectionalgorithmscangenerallybebro-kendownintofourphases:preprocessing,featureextrac-tion,condenceassignment,anddecision-making.Pre-processingalgorithmsperformtaskssuchasnormalizationofthedata,correctionsforvariationsinheightandspeed,removalofstationarye ectsduetothesystemresponse,andsoforth.MethodsthathavebeenusedtoperformthistaskincludewaveletsandKalmanlters[6 7 ],subspacemeth-odsandmatchingtopolynomials[8 ],andsubtractingopti-mallyshiftedandscaledreferencevectors[9 ].Featureextrac-tionalgorithmsreducethepreprocessedrawdatatoformalower-dimensional,salientsetofmeasuresthatrepresentthedata.Principalcomponent(PC)transformsareacom-montooltoachievethistask[10 11 ].Otherfeatureanaly-sisapproachesincludewavelets[6 ],imageprocessingmeth-odsofderivativefeatureextraction[12 ],curveanalysisusingHoughandRadontransforms[13 ],aswellasmodel-basedmethods[14 ].CondenceassignmentalgorithmscanusemethodssuchasBayesian[13 ],hiddenMarkovmodels[12 ], fuzzylogic[15 16 ],rulesandorderstatistics[17 ],neuralnetworks,ornearest-neighborclassiers[11 18 ],toassignacondencethatamineispresentatapoint.Decision-makingalgorithmsoftenpostprocessthedatatoremovespuriousre-sponsesanduseasetofcondencevaluesproducedbythecondenceassignmentalgorithmtomakeanalmine/no-minedecision.In[12 ],hiddenMarkovmodelingwasproposedforde-tectingbothmetalandnonmetalminetypesusingdatacollectedbyamoving-vehicle-mountedGPRsystem.This(baseline)systemusesbothcontinuousanddiscreteHMMs,andhasprovedthatHMMtechniquesarefeasibleandef-fectiveforlandminedetection.Incomparisonwithenergy-basedmethodsandfuzzygradient-baseddetector,theHMMtechniqueperformedsignicantlybetterthantheformer,andachievedcomparableperformancetothelatter[12 ].ThebaselinediscreteHMMwastrainedbyconventionalmethodsofvectorquantizationandtheBaum-Welchalgorithm.ForthebaselinecontinuousHMM,theparameterswereinitial-izedusingclusteringmethodsandlearnedusingtheBaum-Welchalgorithm.TheperformanceofthecontinuousHMMwasslightlybetterthanthediscreteHMM,andthefusionofthetworesultedinabetterperformancethanthoseoftheindividualdetectors.In[19 ],minimumclassicationerror(MCE)trainingwasproposedtoimprovetheperformanceofthediscretebaselineHMM.Aftertheinitialtraining,thisalgorithmusesasequentialgeneralizedprobabilisticdescentalgorithmthatminimizesanempiricallossfunctiontoestimatethemine/backgroundmodelparameters.Anevolutionaryalgo-rithm,basedonnessscoreofclassicationaccuracy,wasusedtogenerateandselectcodebooks.TheMCE-baseddiscreteHMMachievedasignicantperformanceimprove-mentoverthebaselinesystem.Inthispaper,weproposeandevaluateacompletereal-timesoftwaresystemforlandminedetectionusingGPR.ThedetectorisbasedoncontinuousHMM,andisanimprovedversionofthebaselinesystemproposedin[12 ].First,wepro-poseadi erentpreprocessingtechniquebasedonfrequency-domainprocessingtoperformground-levelalignmentandbackgroundremoval.Thispreprocessingapproachisdi er-entfromtheoneusedinthebaselinedetectorasthetwosystemsweredevelopedfordi erentGPRprototypes,andtheproposedsystemwasdesignedtooperateinareal-timemode.Second,pre-andpostprocessingstepsofthesequenceobservationswereaddedtoimprovethetimee ciencyofthedetectorandenablereal-timeapplication.Third,anim-provedmodeltrainingapproachisproposed.Theparam-etersofthebaselinesystemwerelearnedusingtheBaum-Welchalgorithm.Thisstandardapproachdoesnotguaran-teeminimizationoftheclassicationerrorrate,andcannotbeusedinanonlinemodetoadaptthemodelparameterstodi erentgeographicalsitesandenvironments.Theproposedsystemusesaheuristiccorrectivetrainingproceduretoad-justtheinitialparameterstominimizethenumberofmis-classicationsequences.Ourapproachisbasedontheopti-maldiscriminativetraining(ODTproposedbyMizutaandNakajima[20 ].Thistrainingcouldbeusedo ine,usingasignaturelibrary,toadjusttheparametersofagenericmodel.Itcouldalsobeusedinareal-worldoperationalmode,us-ingfeedbackonwhichmeasurementsareminesandfalsealarmsoncetheyaredug,toadapttheinitialmodeltospe-cicsitesandenvironments.Fourth,weproposeadynamicbackgroundmodelthatcontinuouslyadjustsitsparameterstoadaptittothedi erentlanesduringtesting.Theproposedsoftwaresystemisappliedtodataacquiredfromseveralout-doortestsites,usingastate-of-the-artarrayGPRprototype.Therestofthepaperisorganizedasfollows.InSection2, weproviderelatedbackgroundonHMM,anddi erenttrainingmethods.InSection3,wegiveanoverviewoftheGPRdata.InSection4,wedescribethedi erentcomponentsoftheproposedsystem.InSection5,theexperimentaldata,trainingprocedures,andresultsarediscussedandsumma-rized.ConcludingremarksaregiveninSection6. 2.BACKGROUND2.1.HiddenMarkovmodelsAnHMMisamodelofadoublystochasticprocessthatpro-ducesasequenceofrandomobservationvectorsatdiscretetimesaccordingtoanunderlyingMarkovchain.Ateachob-servationtime,theMarkovchainmaybeinoneofN s states{ s 1 ... s N } and,giventhatthechainisinacertainstate,thereareprobabilitiesofmovingtootherstates.Theseprob-abilitiesarecalledthetransitionprobabilities.AnHMMischaracterizedbythreesetsofprobabilitydensityfunctions,thetransitionprobabilitiesA ),thestateprobabilitydensityfunctionsB ),andtheinitialprobabilities ). LetT bethelengthoftheobservationsequencei.e.,numberoftimesteps),letO ={ O 1 ... O T } betheobserva-tionsequence,andletQ ={ q 1 ... q T } bethestatesequence.Thecompactnotation = A B 1

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Real-TimeLandmineDetectionwithGPRUsingDiscriminativeHMM1869 isgenerallyusedtoindicatethecompleteparametersetoftheHMMmodel.In1 ), A = [ a ij ]isthestatetransitionprobabilitymatrix,wherea ij = Prq t = j | q t 1 = i )fori j = 1, ... N s ; ={ i } ,where i = Prq 1 = s i aretheini-tialstateprobabilities;andB ={ b i O t ), i = 1, ... N } ,whereb i O t = PrO t | q t = i isthesetofobservationprobabilitydistributioninstatei AnHMMiscalledcontinuousiftheobservationprob-abilitydensityfunctionsarecontinuousanddiscreteiftheobservationprobabilitydensityfunctionsarediscrete.InthecaseofthediscreteHMM,theobservationvectorsarecommonlyvectorquantizedintoanitesetofsymbols,{ v 1 v 2 ... v M } ,calledthecodebook.Eachstateisrepre-sentedbyadiscreteprobabilitydensityfunctionandeachsymbolhasaprobabilityofoccurringgiventhatthesystemisinagivenstate.Inotherwords,B becomesasimplesetofedprobabilitiesforeachclass,thatis,b i O t = b i k = Prv k | q t = i ),wherev k isthesymbolofthenearestcodebookof O t .InthecontinuousHMM,b i O t saredenedbyamix-tureofsomeparametricprobabilitydensityfunctions.ThemostcommonparametricpdfusedincontinuousHMMisthemixtureGaussiandensity:b i O t = M i m = 1 c im b im O t i = 1, ... N ,(2whereM i isthenumberofcomponentsinstatei c im isthemixturecoe cientforthem thmixturecomponentinstatei ,andsatisestheconstraintsc im 0,and M i m = 1 c im = 1, for i = 1, ... N ,andb im O t )isaK -dimensionalmultivariateGaussiandensitywithmean im andcovariancematrixC im GiventheformofthehiddenMarkovmodeldenedin 1 ),Rabiner[21 ]denesthreekeyproblemsofinterestthatmustbesolvedforthemodeltobeusefulinreal-worldap-plications:i)theclassicationproblem,ii)theproblemofndinganoptimalstatesequence,and(iii)theproblemofestimatingthemodelparameters.Theclassicationprob-leminvolvescomputingtheprobabilityofanobservationse-quence{ O ={ O 1 ... O T }} givenamodel ,thatis,PrO | ). Bayesianmethodscanbeusedtoobtaintheprobabilityofthemodelgiventheobservation.Thisprobabilitycanbecom-putedwithO TN 2 computations.Inmostapplications,itoftenturnsoutthatcomputinganoptimalstatesequenceismoreusefulthanPr(O | ).Thereareseveralpossiblewaysofndinganoptimalstatesequenceassociatedwiththegivenobservationsequence,dependingonthedenitionoftheop-timalstatesequence,thatis,thereareseveralpossibleopti-malitycriteria.OnethatisparticularlyusefulistomaximizePrO Q | overallpossiblestatesequencesQ .TheViterbial-gorithm[22 ]isane cient,formaltechniqueforndingthismaximumstatesequenceandassociateprobability.Thethirdproblemisthetrainingproblem:Howdoesoneestimatetheparametersofthemodel?Theproblemisdi cultbecausethereareseverallevelsofestimationrequiredinanHMM.Firstofall,thestatesthemselvesmustbeestimated.Thenthemodelparameters = A B needtobeestimated.InthediscreteHMM,rstthecodebookisdetermined,usu-allyusingtheK-means[21 ],orothervectorquantizational-gorithms.ThentheparametersA B areestimateditera-tivelyusingtheBaum-Welchalgorithm[23 ].Inthecontin-uousHMM,andforthecaseofGaussianmixturedensityfunctions,themixturecomponentparameters, im C im c im arerstinitializedusuallybyclusteringthetrainingdata),andthenthecontinuousversionofBaum-WelchisusedtolearnA B ). 2.2.HMMtrainingforminimizingclassicationerrorThestandardapproachtoestimatetheHMMparametersistousetheexpectation-maximization(EM)algorithm[ 24 ],alsoknownastheforward-backwardorBaum-Welch(BWalgorithm[23 ]inthiscontext,tondthemaximum-likelihood(ML)estimator.Unfortunately,MLtrainingdoesnotguaranteeminimizationoftheclassicationerrorrate.Moreover,assumptionssuchasindependentobservationsorstatetransitionprobabilitiesbeingdependentonlyononepreviousstatemaynotbevalid,andmayresultinasub-optimalperformance.Toalleviatetheseproblems,severalal-ternativetrainingalgorithmshavebeenusedmainlyintheareaofspeechrecognition.Thesemethodscanberoughlydividedintothreecategories:maximummutualinformation(MMI)training,minimumclassicationerror(MCE)train-ing,andcorrectivetraining.InMMItraining,theHMMpa-rametersareestimatedbymaximizingthemutualinforma-tionbetweenanobservationsequenceandthecorrespond-ingsequenceofclasslabels.FortheimplementationofMMI,thereisnoe cientandrobustprocedurethatisguaranteedtoconvergetoanoptimalsolution.In[25 26 ],theobjec-tivefunctionisoptimizedusinggradientsearchtechniqueswithprojectiononconstraints.InMCEtraining,theHMMparametersareestimatedbyformulatingalossfunctionthatincorporatestheclassicationerrorrateoverasetoftrainingdata[27 28 ].Theempiricallossfunctionisminimizedusingageneralizedprobabilisticdescentalgorithm.UnlikeMMIandMCEtrainings,correctivetrainingismotivatedbyintuitionratherthantheoreticaloptimization.ItwasrstintroducedbyBahletal.[29 ]forthediscreteHMM.Asimilarapproach,calledoptimaldiscriminativetraining(ODTwasproposedbyMizutaandNakajima[20 ] forthecontinuousHMM.Inthisapproach,aninitialmodelisusedtoclassifythetrainingsamples,andtheparametersareadjustedwhenanerrorisobservedtoavoidrepeatingthemisclassication.3.GPRDATA3.1.GPRsensorTheGPRsensorsystemismountedunderneathavehicletoprovideathree-meterdetectionswath[30 ].Whenthevehi-clemoves,theGPRtransmitantennasendsoutpulsesthatpenetratetothegroundandthereceiveantennacapturesthereturnedsignalinordertofacilitatethedetectionofland-mine.

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1870EURASIPJournalonAppliedSignalProcessing RxRxRxRxRxRxRxRxRxTxTxTxTxTxTxTxTxTxModule1Module23metersModule3 Figure1:Arrangementofthe9GPRradars.TheGPRsensorisatime-domain,transientsignalradarthatgivestargetsignalresponseinformationofadi erentnaturethanthatfrommoreconventionalcontinuous-waveradars.TheGPRhasapulsewidthof1. 258-nanosecondfullwidthathalfmaximum(FWHM).Itsoperatingfrequencyrangeisfrom320kHztoabout2GHz,anditssamplingrateis136. 6GHz.Theelectromagneticdesignoftheimpulsera-diatingantennasIRAsgivestheverybroadbandradiationpropertiesthatallowfortherequiredtransientresponse.Theimpulsegeneratoremployedinthetransmitterisdesignedtohaveaveryfastriseandaslowdecayinordertoenhancebothhigh-frequencyandlow-frequencycomponentsofthesignals.Thespectrumoftheradarsignalandfurtherde-tailsofthehardwareGPRsystemaredocumentedin[31 ]. Thereceiversamplingsystemtransformstheveryfastreal-timereturnsignalsfromburiedobjectsintomuchslowersampled-timedatasignalsthataredigitized,transmitted,andprocessed.Inparticular,ateachlocation,adatavectorof2048samplesisacquired,whichisthendown-sampledto512pointsforstorageandprocessing.TheGPRacquiresavectorsampleinevery7. 5cmspatialdistance.Eachvectorsampleisthenpassedontothesoftwarealgorithmsforthedetectionoflandmine. TheGPRsensorsystemhas3modules,andeachmod-ulecontainsthreetransmit-receiveradarpairs.Eachmod-ulecoversone-meterwideandthe3modulestogethercoverathree-meterswathseeFigure1).Eachtransmit-receiveradarpairconsistsofapulsegenerator,atransmitantenna,areceiveantenna,alow-noisepreamplier,andasamplingunit.Asignaltriggergeneratorandthedelayblockpro-videsforthetriggersforthecompletesensorsuiteofallnineradars.Theantennadesignisbasedonthatoftheimpulsera-diatingantennaasdevelopedbytheAirForceResearchLab-oratory,Albuquerque,NewMexico[32 33 34 ].Itconsistsofaparabolicconductingdishthatisilluminatedbytwopairsoftransmission-linefedarmsfromadrivepointatthefocalpointoftheparaboloid.Thetransmitandreceiveantennashaveadiameterof0. 3m.Figure1showsthearrangementofthe9transmit-receiveradarpairs.Inordertoincreasethespatialcoverageincaseaminetargetislocatedbetweentwoadjacentradarpairs,eachreceiverreceivesnotonlythesignalfromitscorrespondingtransmitterbutalsothesignalfromtheleftadjacenttrans-mitter.Thisisaccomplishedbyallowingeachreceiveran-tennatooperatewithtwosamplersineachreceiveroperatingsimultaneouslywithitsdirectandleftadjacentpulsers.Wereferthereaderto[31 ]forthedetailsofthisarrangement. Landminesignal1002003004005006007008009001000500 400 300 200 100 Depthindex (a) 1002003004005006007008009001000Landminesignal60 50 40 30 20 10 Depthindex (b) Figure2:GPRdatainasinglechannel:(a)databeforedownsam-plingindepth;(b)dataafterdownsamplingindepthbyafactorof8.Inreal-timeoperationalmode,thevehiclethatcarriestheGPRsystemadvancesataspeedof9km/h,andtheradarpro-videsathree-meterdetectionswath.Forinstance,toscanandprocess3 500squaremeters,ittakesabout0. 5km/ (9km/h)or3. 33minutes.3.2.DatarepresentationTheGPRdataisarrangedina3Darray,withthecross-track,down-track,anddepthcorrespondingtothethreedimen-sionsinthearray.Thetotalnumberofcross-trackchannelsis17andeachchannelcoversapproximately17centimeters.Thedown-tracksamplingrateis7. 5centimeters/sample.TheGPRprovides512depthdatapointsineachsamplelocation.Hence,fora3-meter-times-500-meterlane,theGRRdatahasasizeof17 6667 512.Inordertoreduceprocessingtime,eachdatasamplevectorisdownsampledfrom512to64bykeepingoneoutofeveryeightdatapoints.Figure2(a) givesasegmentoftheoriginalGPRdatainacertainchannelwith512pointsindepth,andFigure2(b)isthedownsam-pleddatabyafactorof8.Figure3showstypicalA-scanswithandwithoutdownsampling.Frequency-domainanalysisin-dicatesthatthedepthdatapointsareoversampled.More-over,extensivestudyhasshownthatdownsamplingindepthdimensionbyafactorof8doesnotintroducemuchdegra-dationintheperformanceofthedetector.Weshouldnoteherethatthey -axisinFigure2andthex -axisinFigure3arerelated,butnotequal,totherealdepth.Computingtheactualdepthvalueswouldrequiretheknowl-edgeofthefrequencybandwidthandthedielectricconstantofthesoil.Tofacilitatereal-timeoperationwithparallelprocessingcapability,theprocessingisperformedindependentlyfromchannel1tochannel17ateachdown-tracksamplelocation.Processingbeginswithpreprocessingofthedatatoremove

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Real-TimeLandmineDetectionwithGPRUsingDiscriminativeHMM1871 50100150200250300350400450500DepthindexAmplitude 5 0 5 (a) 50100150200250300350400450500DepthindexAmplitude 5 0 5 (b) 102030405060DepthindexAmplitude 5 0 5 (c) 102030405060DepthindexAmplitude 5 0 5 (d) Figure3:A-scansofGPRdatabeforeandafterdownsampling:a)A-scanofbackgroundsignalbeforedownsampling,b)A-scanoflandmineandbackgroundsignalbeforedownsampling,c)A-scanofbackgroundsignalafter8:1downsampling,and(d)A-scanoflandmineandbackgroundsignalafter8:1downsampling.systemresponse,groundbounce,andnoise.TheHMMal-gorithmisthenappliedtogenerateanalarmcondence.4.REAL-TIMELANDMINEDETECTIONUSINGHMM4.1.DatapreprocessingPreprocessingisanimportantsteptoenhancetheminesignaturesfordetection.Ingeneral,preprocessingincludesground-levelalignmentandsignalandnoisebackgroundremoval.Intheproposedsystem,weassumethatnoiseismuchsmallerthanthebackgroundsignal.Infact,theGPRhardwarecomponentperformswaveformaveragingtore-ducebackgroundnoisesothatitissmallenoughtobeig-nored.Theremainingbackgroundsignalsincludetheself-antennacouplingandgroundreection.Ourpreprocessingtechniqueisdesignedtosuppressthisbackgroundsignal.Ourpreprocessingfollowstheshift-and-scalemodelpro-posedbyBrunzell[9 ],wherethecurrentbackgroundvec-torsampleisassumedtobeashiftedandscaledversionofabackgroundreference.Backgroundremovalthenrequirestheestimationofbothshiftandscaleparameters,whicharechangingfromsampletosample.Theoriginalshift-and-scalemodelassumestheshiftisaninteger.Inpractice,thisassumptionmaynotbeaccurateastheshiftingcanbeintheorderofsubpixels,andinterpolationisneededtoperformsubpixelshifting.Unfortunately,interpolationincreasesthecomputationsignicantly,andprohibitsreal-timeprocess-ing.Inthispaper,weproposeane cientsubpixelshiftandscalepreprocessinginfrequencydomainsothatsubpixelshiftingcanberealizedinasimplemannertoreducecom-putation.Thesubpixelshiftandthescalefactorareobtainedusingthemaximum-likelihood(ML)approach.Experimen-tally,wehavefoundthatsubpixelshiftingreducesthenum-beroffalsealarmsbyatleastafactorof1. 5whencomparedtoBrunzellsintegershifting.Letx n denotetherawGPRdatameasuredatasamplelo-cation,wheren isthedown-tracklocationindex.Sincetheprocessingisperformedindependentlyineachcross-trackchannel,theindexforthechannelhasbeendroppedforno-tationsimplicity.Thevectorx n containsthedatapointsatdi erentdepthbins,thatis,x n = [ x n (1), x n (2), ... x n M )] T whereM = 64isthetotalnumberofdepthbinsinthedown-sampleddataasdescribedinSection3.2.Thevectorx n is modeledasx n = b n + s n + n ,(3where b n representsthebackgroundsignal,s n istheresponseproducedbyaminetargetoraclutterobject,and n isavec-torofbackgroundnoise.Notethatthesignals n willbezerointhesamplelocationthatdoesnothavemineorclutterob-ject.Thebackgroundreturnisrelativelystableinnormalen-vironmentandisconsideredtocomefromaglobalgenericbackgroundvectorb = [ b (1), b (2), ... b M )] T .Duetothesurfaceroughnessasthevehiclemoves, b n ismodeledasascaledandshiftedversionofb ,thatis, b n = a n b n ,(4wherea n isthescalingfactorclosetounity, n istheamountofshiftindepthwhichisnotnecessarilyaninteger,andb n = [ b (1+ n ), b (2+ n ), ... b M + n ] T .Theshiftbetweentwosuccessivesamplesistypicallyverysmall,thatis, | n n 1 n ,andlessthananintegerinmostcases.Thisshiftandscalebackgroundmodelhasbeenusedpre-viouslybyBrunzell[9 ]forbackgroundremoval,wheretheshiftisassumedtobeaninteger.Theproblemismorechal-lengingheresincetheshiftisnotnecessarilyaninteger.Thebackgroundreturnismuchstrongerthanthesignals n and dominatesthemeasurement.Theobjectivehereistoremovethebackgroundsignalcomponentsothattheminesignaturebecomesapparentfordetection.Thebackgroundremovalproblemcanbeconsideredasndingthepaira n n )givenx n and b ,sothatthebackgroundresponsecanbesubtractedout.Intheabsenceofthesignals n andassumingGaussian n ,themaximum-likelihoodsolutionisfoundbyminimiz-ing[9 ] J a n n = x n a n b n T W x n a n b n ,(5

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1872EURASIPJournalonAppliedSignalProcessing 51015202530IntensityRelativedown-trackscannumber60 50 40 30 20 10 (a) 51015202530IntensityRelativedown-trackscannumber60 50 40 30 20 10 (c) 51015202530IntensityRelativedown-trackscannumber60 50 40 30 20 10 (e) 51015202530IntensityRelativedown-trackscannumber60 50 40 30 20 10 (b) 51015202530IntensityRelativedown-trackscannumber60 50 40 30 20 10 (d) 51015202530IntensityRelativedown-trackscannumber60 50 40 30 20 10 (f) Figure4:Preprocessedsamples:a)datafromaplasticmineburiedat2 ,b)preprocessedresultofa),c)datafromaplasticmineburiedat3 ,d)preprocessedresultofd),e)datafromametalmineburiedat6 ,and(fpreprocessedresultofe).whereW istheweightingmatrixequaltoE [ n T n ] 1 .Opti-mizing5 )withrespectto a n yields a n = b n T Wx n b n T Wb n (6) Substituting6 into5 )givesJ n = x T n Wx n b n T Wx n 2 b n T Wb n (7) Because n isnotnecessarilyaninteger,theelementsofb n areformedbyinterpolation.Thatis,b i + n = M m = 1 b m )sinc i + n m i = 1,2,... M (8) wheresinc = sin( / ).Asaresult,7 isanonlinearfunctionwithrespectto n andnumericalsearchisneces-sarytothesolution n thatminimizes7 ).Equation8 requiresM 2 multiplicationstogenerateb n )foragiven n Assumingthesearchspaceof n has L values,thenatasinglesamplelocationndingtheoptimumsolutionof n requiresanorderofM 2 L operations,whichiscomputationallyveryintensive,andprohibitsreal-timeprocessing.Asanalterna-tive,weproposetouseafrequency-domain-basedapproachtoreducethecomputation.Thefrequency-domainrepresentationof8 )isB n = diag e 1 n e 2 n ... e M n B ,(9whereB n )andB arecolumnvectorscorrespondingtothediscreteFouriertransformsofb n )andb ,and m = 2 m 1) /M m = 1,2,... M .Furthermore,W infrequency

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Real-TimeLandmineDetectionwithGPRUsingDiscriminativeHMM1873 domainbecomestheinverseofadiagonalmatrixwhosem th diagonalelementisP m ),thepowerspectraldensityof n atfrequency m .Hence,byrepresenting7 inthefrequencydomainandapplyingtheParsevaltheorem[18 ],theobjec-tivefunctiontobemaximizedtoobtain n becomesJ n = M m = 1 1 P m X n m B n m 2 ,10)wheretheconstantsthatareindependentof n in7 )havebeenignored,andthesuperscript representscomplexconjugate.Notethat| B n m | 2 =| B m | 2 hasbeenusedsothatthedenominatorin7 isindependentof n ,andisthereforeignored.In10 ), X n m )andB n m )representthe m thelementofX n and B n ).Substituting9 into10 reducestoJ n = M m = 1 1 P m X n m B m e m n 2 (11) Notethatthevalueinsidethebracketisindependentof n andneedstobecomputedonce.Foratrialvalue n ,( 11 requiresonlyM +1complexmultiplications.Thecomputationcanfurtherbereducedbyusingthefactthat | n n 1 n .Atthepreviousspatialinstantn 1, weobtained n 1 .Atthecurrentinstantn ,wedeterminetherelativetranslation n = n n 1 bymaximizing J n = M m = 1 1 P m X n m X n 1 m e m n (12) Thesolutionof n isthenequalto n 1 + n .ThesearchspacenowreducesfromL of n to L of n ,whereL
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1874EURASIPJournalonAppliedSignalProcessing Figure5displaysahyperboliccurvesuperimposedonapre-processedmetalminesignaturetoillustratethefeaturesofatypicalminesignature.LetS x y z denotethepreprocessedthree-dimensionalGPRdataasillustratedinFigure6.Thedown-tracksecondderivativeisrstestimatedontherawdatausing D y x y z = S x y +2,z )+2 S x y +1,z 2 S x y 1, z S x y 2, z 3 D yy x y z = D y x y +2,z )+2 D y x y +1,z 2 D y x y 1, z D y x y 2, z 3 (15) Thederivativevaluesarethennormalizedalongthey direc-tionusingN x y z = D yy x y z x z x z ,16)where x z )and x z aretherunningmeanandstandarddeviationupdatedusingabu erofscansavailableduringsystemoperation.Thedown-trackdimensionistakenasthetimevariableintheHMMmodel.Thegoalistoproduceacondencethatamineispresentatvariouspositions,x y ),onthesurfacebeingtraversed.TointotheHMMcontext,asequenceofobservationvectorsmustbeproducedforeachpoint.Theseobservationvectorsencodethedegreetowhichedgesoccurinthediagonalandantidiagonaldirections.Theobservationvectoratapointx s y s consistsofasetof15featuresthatarecomputedonanormalizedarrayofGPRdataofsize32 8.Letx s and y s begivenandletA denotethearrayA = A y z = N x y z ),(17)wherex = x s y ={ y s 3, ... y s +4 } ,andz ={ 1,2,... ,32} ThearrayA isthenbrokenintopositiveandnegativepartsaccordingtotheformulasA + y z = A y z )ifA y z > 1, 0otherwise,A y z = A y z )ifA y z < 1, 0otherwise. (18) Next,foreachpointinthepositiveandnegativepartsofA thestrengthsofthediagonalandantidiagonaledgesareesti-matedandareusedtodenethe15-dimensionalobservationvectorassociatedwiththepointx s y s .Wereferthereaderto[12 ]foramoredetaileddescriptionoftheobservationvector.4.3.ImprovedcontinuousHMM-basedclassierforlandminedetectionTheproposedHMMclassierconsistsoftwoHMMmod-els,oneformineandoneforbackground.Theminemodel, z (depth) x (cross-track)o y (down-track) Figure6:AcollectionoffewGPRscans. m ,isdesignedtocapturethehyperbolicspatialdistributionofthefeatures. m has3stateswhichcorrespondtotheris-ingedge,at,anddecreasingedge.Eachstateisrepresentedby3Gaussiancomponents.Theminemodelisillustratedin Figure7.Thebackgroundmodelisneededtocapturethebackgroundcharacteristicsandtorejectfalsealarms.Eachofthe17channelsistreatedindependentlyfromtheoth-ers,andhasitsownbackgroundmodel, b c .Inadditiontoallowingeachchanneltohaveamodelthatreectsitsowndata,thisdecouplingallowsthechannelstobeprocessedinparallel,andthusfacilitatingreal-timeoperation.All b c (for c = 1, ... ,17)have3statesand3Gaussiancomponentsperstate.ThemodelarchitectureisillustratedinFigure8. EachHMMproducesaprobabilitybybacktrackingthroughmodelstatesusingtheViterbialgorithm[22 ].Theprobabilityvalueproducedby m b c canbethoughtofasanestimateoftheprobabilityoftheobservationsequencegiventhatthereisamine(background)present.TheproposedHMMclassierisbasedonapreviousworkbyGaderetal.[12 ].Inthefollowing,weonlyoutlinethemodicationswemadetothebaselinesystemtoimproveitsperformanceande ciency.

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Real-TimeLandmineDetectionwithGPRUsingDiscriminativeHMM1875 Minestate1Minestate3Minestate2StatesMinestate1Minestate2Minestate3x 1 x 2 x 3 x 14 x 15 Figure7:IllustrationoftheHMMminemodel.4.3.1.ObservationsequencepreprocessingMostmineshavesignaturesofdi erentsizes,andtheirdis-tributioncannotbecapturede cientlybxednumberofobservations.Toaddressthisproblem,thebaselinesys-temusesaminemodelwith5states.Therstandlaststatesarebackgroundstates.Duringtesting,eachsequenceisal-lowedtostartineitherthebackgroundstateortherstminestate.Moreover,twooptimalstatesequencesarecom-puted:oneassumingthemodelassignsthelastobservationtothethirdminestate,andtheotherassumingthelastob-servationisassignedtothebackgroundstate.Thestatese-quencewiththehighestprobabilityistakenasthemodelout-put. Theproposedsoftwaresystemusesobservationse-quencesofvariablelength.Thisapproachismoree cientasonly3statesareneededfortheminemodel,andonlyoneop-timalstatesequenceisneeded.Initially,eachsequencecan-didatehasaednumberofobservations,T max .Beforefeed-ingthesequencetotheHMMclassier,weignorealllead-ingandtrailingobservationswithweakfeaturevectors.Inotherwords,weexcludeobservationO t fromthesequenceif O t min .ThisprocessresultsinasequenceoflengthT whereT
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1876EURASIPJournalonAppliedSignalProcessing GradientfeatureextractionHMM mine model HMM backgroundmodel+ Figure8:IllustrationoftheHMM-basedmodelarchitecture. ReadmineandbackgroundsignaturelibrariesEstimateinitialminemodelparametersusingBWprocedureEstimateinitialbackgroundmodelparametersusingBWprocedureRepeatForeachsignatureobservationsequenceO Letc denotethechannelfromwhichsignatureisextractedUseViterbiproceduretocomputeP O | m )& P O | b c IfP O | m > = P O | b c classifyO asmineElseClassifyO asbackgroundIf signatureismisclassiedLetr denotethecorrectmodelLetw denotetheincorrectmodelForeachobservationO t ofthesequenceO i = stateassignedtoO t bymodelr k = mostprobablecomponentofstatei ofmodelr k = argmaxm = 1, ... M i b r m O t r ki (new) = r ki (old+ x t r ki (old) j = stateassignedtoO t bymodelw l = mostprobablecomponentofstatej ofmodelw l = argmaxm = 1, ... M j b w m O t w lj (new) = w lj (old) x t w lj (old) (20) Endforloop Endifloop Endforloop ReestimateminemodelparametersusingBWprocedureReestimatebackgroundmodelsparametersusingBWprocedureUntil(convergenceormaximumno.ofpassesreached) Algorithm1:Correctivetrainingformine/backgroundHMMmodels.observed,theparametersof m and b c areadjustedtoreducethelikelihoodofrepeatingthiserror.Inparticular,theGaus-sianmeansofthemostprobablecomponentofthestatesintheViterbipathsareadjustedusinganLVQ-type[35 ]learn-ingrule.Theabovestepsarerepeateduntilallthetrain-ingdataisclassiedcorrectly,orthemaximumnumberofpassesisreached.TheproposedcorrectivetrainingalgorithmisoutlinedinAlgorithm1. Inthistrainingalgorithm,20 )isanLVQ-type[35 ] learningrule.ThemeanvectorsoftheGaussiancomponentsaremovedclosertotheobservationsofthecorrectlyclassi-sequences,andfurtherfromtheobservationsofthemis-classiedsequences.In(20 ),theconstant isthelearningrate,andhassimilarbehaviorasinstandardLVQalgorithms.If istoosmall,thenseveralpasseswouldbeneededforthealgorithmtoconverge.Ontheotherhand,if istoolarge,thetrainingalgorithmmaynotconvergeaslargecorrectionsmadebysomesequencesmaybereversedbyothersequences.Inthispaper,wereporttheresultsusing = 1 0e-3fortheminemodel,and = 1 0e-4forthebackgroundmodel.Thereasonforusingasmallerrateforthebackgroundisthatthismodelis,ingeneral,lessconsistentthantheminemodel,andthemagnitudeoftheerrorsecondpartof20 isusuallylargerthanthatcausedbytheminemodel.

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Real-TimeLandmineDetectionwithGPRUsingDiscriminativeHMM1877 Let b c bethebackgroundmodelofchannelc estimatedusingtrainingdata, c ij = meanofcomponenti ofstatej of b c C c ij = covariancematrixofcomponenti ofstatej of b c n ij = numberoftrainingobservationsthatcontributedtotheestimationof c ij and C c ij LetN ij = K n ij ; S ij = N ij c ij ; SSqij = N ij [ C c ij + c ij c ij T ]denotethesu cientstatisticsofGaussiancomponenti ofstatej ForeachtestedobservationsequenceO withConfO < Min ConfForeachobservationO t of O j = stateassignedtoO t i = mostprobablecomponentofstatej : i = argmaxm = 1, ... M j b mi O t S ij = S ij + x t SSqij = SSqij + x t x T t N ij = N ij +1 EndEnd c ij = Sumij /N ij ; C c ij = SumSqij /N ij c ij c ij T ;fori = 1, ... N and j = 1, ... M i Algorithm2:Incrementalupdateofthebackgroundmodels.Asinmostlearningalgorithms,thenumberoftrain-ingiterationsfortheproposedcorrectivetrainingalgorithmisimportant.Generally,thisnumberwoulddependonthelearningrate, ,thedielectricconstantofthesoilfromwhichthetrainingsignatureswereextracted,theconsistencyofthetrainingsignatures,andthelevelofvariationsbetweenthesignaturesusedfortheinitialtrainingandthesignaturesusedforthesubsequentcorrectivetraining.Ifthenumberofcorrectivetrainingiterationsisnotsu cient,theparame-tersofthemodelswouldnotadaptsu cientlytothegivensite.Ontheotherhand,iftoomanycorrectiveiterationsareapplied,themodelsmaygetovered.Thestandardap-proachestoaddressthisissueistoeitherstopthetrainingwhentheperformancedoesnotimprovesignicantly,oruseacrossvalidationdatasetandstopthetrainingwhentheper-formanceonthevalidationsetnotusedfortraining)startstodecrease.Currently,oursystemusestheformerapproachasourlabeledtrainingdataisnotlargeenoughtobesplitintotrainingandcrossvalidationsets.Experimentally,wehavefoundthatonly5to10iterationsareneededwhenthecorrectivetrainingalgorithmisappliedo inetothetrainingsignatures.Applyingthealgorithmformoreiterationsdoesnotimprovetheperformanceofthedetectoranyfurther.Thecorrectivetrainingproceduredescribedaboveop-eratesonasignaturelibrary,andisfortheo inemode.Itcanbeeasilymodiedtooperateinareal-timemodeandadapttheHMMstodi erentsitesandenvironmentsusingfeedbackonwhichmeasurementsareminesandfalsealarmsoncetheyaredug.Inthiscase,insteadofreadingthesigna-tures,thealgorithmstartsbyreadingthelanegroundtruth.Then,thelanedataisprogressivelyreadandprocessedastheGPRmountedvehiclemoveroverthelane.Asintheo ine mode,theparametersareadjustedwheneveramisclassica-tionoccurs.Toperformmorethanoneiterationofcorrectivetraining,onecouldeitherdriveoverthelanemultipletimes,orsimplystorethedataandreprocessitfewmoretimeswhentheendofthelaneisreached.Inthisreal-timemode,themodelparametersareadoptedtonewdatathatwasnotincludedintheinitialtrain-ingphase.Thus,itisexpectedthatmoreiterationswouldbeneeded.Experimentally,wehavefoundthat,forallthecali-brationlanes,10to20correctivetrainingiterationsaresuf-cient.Applyingthealgorithmformoreiterationsdoesnotimprovetheperformanceanyfurther.4.5.AdaptivebackgroundmodelTheminemodeliswelldenedandneedstobedesignedtocapturethehyperbolicminesignatures.Thebackgroundmodel,ontheotherhand,isnotwelldened.Itisneededtomodelthebackgroundcharacteristicssoastoreducethenumberoffalsealarms,however,itisalmostimpossibletospecifythecharacteristicsofthismodel.Thisisbecausethebackgroundmodelisa ectedbyseveralfactorssuchasdif-feringsoilconditions,temperatureandweatherconditions,andvaryingterrain.Infact,thebackgroundcanchangebe-tweenthestartandtheendofthesametestlaneasthehard-waresettingsandweatherconditionscanchange.Sinceitisnotpossibletocollecttrainingdatathatcoversalldi erentsettings,oursystemsusesanadaptivebackgroundmodel.Ouradaptiveapproachinvolvestwomainsteps.4.5.1.AdaptivedatanormalizationTomaintainthesamedynamicrange,anduseconstantthresholds,weadaptivelynormalizethepreprocesseddatasothatitsvaluesarenormallydistributedwithzeromeanandunitvariance.Thedatastatisticsaredynamicallyupdatedus-ingabu erofthemostrecentobservations.Observationse-quencesareaddedtothebu eronlyiftheirlikelihoodofbe-longingtothebackgroundmodelishigh.Wethebu er sizeto50observations,andasthebu ergetsfull,newobser-vationswouldreplacetheoldones.4.5.2.IncrementalupdateofthebackgroundmodelsAninitialbackgroundmodel, b c ,isestimatedforeachchan-nel, c ,byapplyingthecorrectivetrainingprocedureonthetrainingsignatures.Whiletesting,observationsequenceswithhighP O | b c andlowP O | m areusedtoadjusttheparametersofthebackgroundmodelofchannelc .Inpartic-ular,weuseAlgorithm2.

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1878EURASIPJournalonAppliedSignalProcessing Table1:Summaryofthethreedatacollectionsusedintheexperiments. CollectionLocationContent (1)SignaturesSite12945mineobservationsequences.5737falsealarm/backgroundobservationsequences. (2)LanedataSite2Lane4100m 3m14mines21passesLane6100m 3m10mines24passesLane8100m 3m19mines20passesLane9100m 3m18mines18passes (3)LanedataSite3Lane51200m 3m21mines6passesLane52200m 3m16mines6passesLane56200m 3m21mines6passes 5.EXPERIMENTS5.1.ExperimentaldataGPRdatacollectedfromthreedi erentsitesintheUnitedStateswasusedinourexperiments.Wewillrefertotheseascollection1,collection2,andcollection3,respectively.Col-lection1containsminesandfalsealarms/backgroundsigna-turesextractedfromdatacollectedatsite1.Thesesignatureswereselectedusingacombinationofgroundtruthandvi-sualexamination,andconsistof2945minesand5737falsealarms/backgroundobservationsequences.Amoredetaileddescriptionofthissignaturelibraryandtheextractionpro-cesscanbefoundin[12 ].ThiscollectionisusedtolearntheinitialmineandbackgroundHMMmodelparametersusingthebasicBaum-Welchalgorithm.Collections2and3containGPRlanedatacollectedfromsites2and3,respectively.Someoftheselaneswereusedforcorrectivetraining,andtheremainingfortesting.Test-ingandadaptingthemodelparametersonlanesisthemostrepresentativeofreal-worldoperationalmode.Site2has4laneslabeledlane4,6,8,and9.Site3has3laneslabeledlane51,52,and56.Eachlaneis3mwide,anditslengthvariesfrom50to200m.Thegroundtruth,thatis,loca-tionofthemines,ofthesecalibrationlanesisavailable,andweuseitonlyduringthecorrectivetrainingorintheeval-uationofthealgorithm,andnotintheHMMtestingal-gorithmitself.Multipledataleswerecollectedfromeachlane.Eachle,referredtoasonepass,correspondstorun-ningavehicle-mountedGPRsystemoverthelane.Ato-talof83passeswerecollectedfromsite2,andonlyoneofthesepasses(fromlane4)wasusedforcorrectivetrainingtoadapttheHMMstothissite.Collection3includes18passes,andoneofthepasses(fromlane51)wasusedfortraining.Table1summarizesthedatacollectionsusedinourexperi-ments. Weshouldnoteherethatalthoughthelanesusedinourexperimentsdonothaveexplicitlyemplacedclutter,theyweresetuptorepresentrealon-roadconditionsthatavehicle-mountedminedetectionsystemwillencounter.Thus,theydoincludeclutterobjectssuchasvoid,rocks,andprobablysomemetalpieces.5.2.BasicHMMtrainingThesignaturelibraryi.e.,collection1wasusedtotrainthebasicHMMmodels.Usingthiscollection,BWalgorithmwasusedtoestimatetheHMMparameters = m b ),where m isestimatedfromtheminesignaturesand b isestimatedfromthefalsealarms/backgroundsignatures.Wewillrefertotheseasthebaselinemodels,orsimply base 5.3.CorrectiveHMMtrainingusingthesignaturelibraryUsing base asinitialmodelparameters,weappliedthecor-rectivetrainingproceduretothesignaturelibraryandad-justedtheparameterstoreducethenumberofmisclassiedsignatures.Atotalof10iterationswereneededforthepa-rameterstostabilize.Wewillrefertothesemodelsas Sig. 5.4.CorrectiveHMMtrainingusinglanedataTherationaloftheproposedtrainingapproachistoadaptthemodelparameterstodi erentgeographicalsitesthathavedi erentcharacteristicsduetovariationsinsoiltypeandotherconditions.Thus,wehaveselectedonepassfromcol-lection2anduseditalongwithitsgroundtruth)toadaptthebaselineHMMstothissite.Thetrainingpasswasselectedfromlane8asthislanecontainsmoremineswithmoreva-riety.Inallexperimentsreportedinthispaper,atotalof20correctivetrainingiterationswereperformed,andinterme-diatemodelparametersweresavedaftereachiteration.Wewillrefertothesemodelsas S2-L8 k i.e.,modelsadaptedtosite2usinglane8afterk iterations).Similarly,wehaveadaptedthebaselineHMMstosite3byapplyingthecorrectivetrainingusingonepassfromthiscollection(fromlane51).Forthissite,weobtainedtheinter-mediatemodels S3-L51 k ). 5.5.ExperimentalresultsInthissection,wepresent,analyze,andcomparetheresultsobtainedusingthecorrectivetrainingprocedurewiththoseobtainedusingthebaselinemodel.Ourresultscouldnotbecomparedwiththebasicsystemintroducedin[12 ],asthesesystemsusedi erentGPRprototypes,andthus,havepre-processedthedatadi erently.However,weshouldpointout

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Real-TimeLandmineDetectionwithGPRUsingDiscriminativeHMM1879 thatthetwosystemsareverysimilar.Themajordi erencesaretheadditionalpre-andpostprocessingstepsoutlinedinSection4.3.Thesestepsdonota ectthedetectionresultssignicantly.Theyareaddedmainlytoreducetheexecutiontime,andthus,enablereal-timeimplementationandtesting.Thisisbecause1)thesequencesarenolongerrequiredtohaveaconstantlengthof15(maximumlength);2)only3not5statesareneededfortheminemodel;and3)severalsequencesarerejectedwithouttestingthemwiththeback-groundmodelsusingtheViterbialgorithm.Theperformanceofthedi erentmodelparameterswasscoredintermsofprobabilityofdetectionPD)versusfalsealarmrateFAR).Condencevalueswerethresholdedatdi erentlevelstoproducereceiveroperatingcharacteristics(ROCcurves.Foragiventhreshold,amineisdetectedifthereisanalarmwithin0. 25metersfromtheedgeoftheminewithcondencevalueabovethethreshold.Givenathreshold,thePDforalaneorasetoflanesisdenedtobethenumberofminesdetecteddividedbythetotalnumberofmines.TheFARisdenedasthenumberoffalsealarmspersquaremeter.Figure9ashowstheoverallROCsforallofthe83passesofcollection2.TheROCsaredisplayedforthecondencevaluesgeneratedusingthebaselinemodel, base (nocorrec-tivetraining),the Sigmodelcorrectivetrainingusingsig-naturelibrary),andthe S2-L8 k )models(k iterationsofcor-rectivetrainingusingonepassfromcollection2).Ascanbeseen,whencomparedtothe base ROC,the Sigand S2-L8 k ROCsareshiftedleft(i.e.,lowerFARforthesamePD)andshiftedup(higherPDforthesameFAR).Thus,onecanconcludethatcorrectivetrainingimprovestheoverallde-tectionrate.Toquantifytheimprovementinthedetectionrate,wecomputetheareaundertheROCinthe[0,0. 02]FARrange.1 Fortherestofthispaper,wewillusethetermperformancetorefertothisarea.Aperfectdetector(detectsallthemineswithnofalsealarms)wouldhaveanareaof0. 02. Figure9b displaysthevaluesoftheseareasfortheROCsofthedi er-entmodels.Ascanbeseen,theareajumpsfrom0. 013(forthebaselineparameters)to0. 0134forthe Sigparameters,andto0. 014 S2-L8 (20),achievinganoverallperformancegainofabout10%.Ascanbeseen,theperformancecurvestartstoattenafter15iterations.Performingthecorrectivetrainingformorethan20iterationsdoesnotimprovetheperformanceanyfurther.Figure9displaystheresultsaveragedover83passes.Theperformance(measuredbytheareaundertheROC)fortheindividualpassesvariessignicantly.Forinstance,forsomepasses,theperformanceremainsconstant.Thesepassesareusuallyeitherclean,withallmineseasilyde-tectable,orverynoisywithseveralweakminesignatures.Thus,theperformanceiseitherclosetooptimal,andcan-notbeimprovedanyfurther,orpoorandcannotbeim-proved,asmanyoftheminescouldnotbedetectedusing 1 Theperformancecriterionforthevehicle-mountedminedetectionsys-temtechnologywassetto0. 02/m 2 FARat90%PD,andisdescribedin[36 ]. 00 0050. 010. 0150. 020. 0250. 03 FAR/ m 2 0 5 0 55 0 6 0 65 0 7 0 75 0 8 0 85 0 9 0 95 1 PD base sig S2 L8 (1iter.) S2 L8 (3iter.) S2 L8 (5iter.) S2 L8 (10iter. (a) BaseSig135101520No.ofcorrectivetrainingiterations0 0125 0 013 0 0135 0 014 0 0145 AreaunderROC (b) Figure9:AverageperformanceoftheHMMdetectorwithdi er-entmodelparametersonthe83passesofcollection2.a)ROCswithandwithoutcorrectivetraining.b)Improvementintheper-formance(areaunderROCinthe[0,0.02]FARrange)versusnum-berofcorrectivetrainingiterations.thecurrentpreprocessingandfeaturerepresentationtech-niques. Formostpasses,theperformanceimproves.Figures10 and 11 displaytheresultsfortwodi erentpassesoverlanes4and6,respectively,wheretheperformanceimprovesbyabout50%.ForFigure10,theimprovementoccursaftertheinitialcorrectivetrainingwiththesignaturelibrary,andmoretrainingwiththelanedatadoesnota ecttheresults.Ontheotherhand,forFigure11,nosignicantimprove-mentwasobtainedafterthecorrectivetrainingwiththesig-naturelibrary.Thelargestperformancegainwasobtainedusing S2-L8 (10).

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1880EURASIPJournalonAppliedSignalProcessing 00 0050. 010. 0150. 020. 0250. 03 FAR/ m 2 0 5 0 55 0 6 0 65 0 7 0 75 0 8 0 85 0 9 0 95 1 PD base sig S2 L8 (1iter.) S2 L8 (3iter.) S2 L8 (5iter.) S2 L8 (10iter. (a) BaseSig135101520No.ofcorrectivetrainingiterations0 01 0 011 0 012 0 013 0 014 0 015 0 016 0 017 0 018 0 019 0 02 AreaunderROC (b) Figure10:PerformanceoftheHMMdetectorononepassfromlane4.(a)ROCswithandwithoutcorrectivetraining.b)Improve-mentintheperformance(areaunderROCinthe[0,0. 02]FARrange)versusnumberofcorrectivetrainingiterations.Wehavealsogroupedthepassesbylanes,andgener-atedoneROCforeachlane.Theperformanceofthedi er-entlanesisshowninFigure12(a).Ascanbeseen,theper-formancevariessignicantly.Lane4hasanalmostperfectperformance,whilelane9hastheworstperformance.Thistypeofperformanceisexpectedsincelane4containsmainlymetalmines,whilelane9containsmainlysmallplastic-casedmines.Lanes6and8containamixtureofbothtypesofmines.Forallthelanes,theimprovementduetothecor-rectivetrainingisnotobviousinFigure12(a).Thisisduetotherelativelylargevariationintheverticalaxis.Toout-linethee ectofthecorrectivetraining,inFigure12(b),wedisplaytheareasobtainedwiththecorrectivetrainingmod00 0050. 010. 0150. 020. 0250. 03 FAR/ m 2 0 5 0 55 0 6 0 65 0 7 0 75 0 8 0 85 0 9 0 95 1 PD base sig S2 L8 (1iter.) S2 L8 (3iter.) S2 L8 (5iter.) S2 L8 (10iter. (a) BaseSig135101520No.ofcorrectivetrainingiterations0 0125 0 013 0 0135 0 014 0 0145 0 015 0 0155 0 016 0 0165 0 017 AreaunderROC (b) Figure11:PerformanceoftheHMMdetectorononepassfromlane6.(a)ROCswithandwithoutcorrectivetraining.b)Improve-mentintheperformance(areaunderROCinthe[0,0. 02]FARrange)versusnumberofcorrectivetrainingiterations.elsnormalizedwithrespecttotheareaofthecorrespond-ingbaselinesystem.Ascanbeseen,theimprovementvariesfrom4%to27%.Thebestimprovementisobtainedforlane9,whichwasthemostdi cultlane.Thisillustratestheabilityoftheproposedcorrectivetrainingtoadaptthemodelsparametersandimprovethedetectionofdi cult mines. Datacollection2hasatotalof83passesthatwerecol-lectedoverthreedi erentdates.Therst20passeswerecol-lectedonApril8and9,thenext27passeswerecollectedonJune11and12,andthelast36passeswerecollectedonJune27and28.Oneachdate,datawascollectedfromall4lanes.WehavegeneratedoneROCforeachdateusingthedi erent

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Real-TimeLandmineDetectionwithGPRUsingDiscriminativeHMM1881 BaseSig135101520No.ofcorrectivetrainingiterations0 004 0 006 0 008 0 01 0 012 0 014 0 016 0 018 0 02 AreaunderROCLane4Lane6Lane8Lane9 (a) BaseSig135101520No.ofcorrectivetrainingiterations1 1 05 1 1 1 15 1 2 1 25 1 3 1 35 NormalizedareaunderROCLane4Lane6Lane8Lane9 (b) Figure12:AverageperformanceoftheHMMdetectoroncollec-tion2groupedbylanes.(a)AreaunderROCsinthe[0,0. 02]FARrangeversusnumberofcorrectivetrainingiterations.b)Normal-izedareasunderROCinthe[0,0. 02]FARrangewithrespecttotheareaofthebaselinesystem.HMMs. Figure13(a)displaystheperformanceoneachdate.Ascanbeseen,eventhoughthesamelaneswereused,theperformanceonthedi erentdatesvaries.Thisisduemainlytothedi erentweatherandsoilconditions,andpossiblydif-ferentradarsettings,onthedi erentdates.Figure13(b)dis-playsthenormalizedareastoemphasizetheimprovementsduetothecorrectivetraining.Theimprovementvariesfrom4%to12. 5%.Itisinterestingtonoticethat,inthiscase,thebestimprovementAprildata)doesnotcorrespondtothedatethathadtheworstperformanceJune27and28data).ThiscanbeexplainedbythefactthatthepassusedforthecorrectivetrainingwascollectedinAprilalso.Thus,thesereBaseSig135101520No.ofcorrectivetrainingiterations0 012 0 0125 0 013 0 0135 0 014 0 0145 0 015 AreaunderROCJune11&12April8&9June27&28 (a) BaseSig135101520No.ofcorrectivetrainingiterations1 1 05 1 1 1 15 NormalizedareaunderROCApril8&9June27&28June11&12 (b) Figure13:AverageperformanceoftheHMMdetectoroncollec-tion2groupedbydates.(a)AreaunderROCsinthe[0,0. 02]FARrangeversusnumberofcorrectivetrainingiterations.b)Normal-izedareasunderROCinthe[0,0. 02]FARrangewithrespecttotheareaofthebaselinesystem.sultsshowthatthecorrectivetrainingcouldbeusedtoadaptthemodelparameterstothedi erentsoilandenvironmentconditions.Theaboveexperimentswererepeatedusingcollection3andtheHMMsobtainedbyperformingcorrectivetrainingusingonepassfromlane51ofthiscollection( S3-L51 k ), k = 1, ... ,20).Theresultsandconclusionswerecompa-rabletothoseobtainedforcollection2.Figure14(a)showstheoverallROCsforallofthe18passesofcollection2.TheROCsaredisplayedforthecondencevaluesgeneratedusingthebaselinemodel, base ,and S3-L51 (10)models.Nosigni-cantimprovementcanbenoticedusingmodelslearnedwith

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1882EURASIPJournalonAppliedSignalProcessing 0246810121416182010 2 FAR/ m 2 0 5 0 55 0 6 0 65 0 7 0 75 0 8 0 85 0 9 0 95 0 1 PD base S3L51(10iter. (a) BaseSig13510No.ofcorrectivetrainingiterations0 015 0 0155 0 016 0 0165 0 017 0 0175 AreaunderROC (b) Figure14:AverageperformanceoftheHMMdetectorwithdi er-entmodelparametersonthe18passesofcollection3.(aROCswithandwithoutcorrectivetraining.b)Improvementintheper-formance(areaunderROCinthe[0,0. 02]FARrange)versusnum-berofcorrectivetrainingiterations.morethan10iterationsofcorrectivetraining.Figure14(b) showstheareaundertheROCinthe[0,0. 02]FARrange.Ascanbeseen,after5iterations,theoverallperformanceim-provesbyabout8%.Figure15displaystheperformancegroupedbylanes.Asincollection2,sincethelaneshavedi erentmixturesofminetypes,theirperformancevaries.Lane51benetedmostfromthecorrectivetraining.Thisisduetothefactthatthislanehadtheworstinitialperformance,sothereismoreroomforimprovement.Also,thepassthatwasusedforcorrectivetrainingwasextractedfromthislane.Thus,thetrainedmod-elswereadaptedtothislane.Itisinterestingtonoticethattheperformanceonlane51using Sigisslightlyworsethantheperformanceusing base .Thismaybeduetothefactthatthedatafromthislanehasdi erentcharacteristicsthanthe BaseSig13510No.ofcorrectivetrainingiterations0 014 0 0155 0 015 0 0155 0 016 0 0165 0 017 0 0175 0 018 0 0185 AreaunderROCLane51Lane52Lane56 (a) BaseSig13510No.ofcorrectivetrainingiterations0 98 1 1 02 1 04 1 06 1 08 1 1 1 12 1 14 NormalizedareaunderROCLane51Lane52Lane56 (b) Figure15:AverageperformanceoftheHMMdetectoroncollec-tion3groupedbylanes.(a)AreaunderROCsinthe[0,0. 02]FARrangeversusnumberofcorrectivetrainingiterations.b)Normal-izedareasunderROCinthe[0,0. 02]FARrangewithrespecttotheareaofthebaselinesystem.signaturelibrary.Thus,amodelthatminimizesthemisclas-sicationofthesignaturesmaynotbesuitedforasitewithdi erentcharacteristics.6.CONCLUSIONSAreal-timesoftwaresystemforlandminedetectionus-ingground-penetratingradarisproposedandevaluated.

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Real-TimeLandmineDetectionwithGPRUsingDiscriminativeHMM1883 Thesystemincludesthreemaincomponents:preprocessing;HMM-baseddetector;andcorrectivetraining.Theprepro-cessingcomponent,whichisneededtoenhancetheminesignatures,requirestheestimationofsubpixelshiftandscalefromonevectorsampletothenext.Toreducethecompu-tationalrequirementsandfacilitatereal-timeimplementa-tion,weproposedane cientfrequency-domain-basedpro-cessing.TheHMMdetectorisanimprovementofaprevi-ouslyproposedsystembaseline).Itincludesadditionalpre-andpostprocessingstepsoftheobservationsequencestoim-provethetimee ciencyandenablereal-timeapplication.Italsotreatsthesensorschannelsindependently,andusesonebackgroundmodelperchannel.Thisallowsparallelprocess-ingofthedi erentchannelsandbetteradaptation.Thecor-rectivetrainingcomponentisusedtoadjusttheinitialmodelparameterstominimizethenumberofmisclassicationse-quences.Twocorrectivetrainingscenarioswereused.Therstoneiso ine,andisappliedtoasignaturelibrarytoad-justtheparametersofagenericmodel.Thesecondscenariomimicsareal-worldoperationalmodewhere,feedbackonwhichmeasurementsareminesandfalsealarmsoncetheyaredug,wouldbeusedtoadapttheinitialmodelstospecicsitesandenvironments.Theproposedsystemwastestedinreal-timesettings.Ex-tensiveexperimentsindicatethatthecorrectivetrainingcanimprovetheoverallperformancebyabout10%,andthatforsomeindividuallanes,theperformancegaincanreachupto50%.Moreover,thebestgaininperformanceisusuallyob-tainedforthedi cultlanesthathadlowminedetectionandhighfalse-alarmratesusingthebaselineparameters.Inthecurrentsystem,onepass(fromonelane)wasusedtoadaptthemodelparameterstoallthedatacollectedfromonesite.Inthefuturework,wewillexperimentwithadapt-ingtheparameterstoindividuallanesusingasmallcalibra-tionsegmentfromeachlane.Anotherdirectionforfutureresearchinvolvesbuildingandlearningdi erentmodelsforthedi erentminetypese.g.,plasticversusmetal).Thismayrequireextractingmultiplefeaturesets,andusingdi erentsubsetstocharacterizethedi erentmodels.Finally,weshouldnotethatouradaptivesystemcanlearntodiscriminatebetweenminesandclutterobjectsaslongastheyhavedi erentsignatures.However,someclutterobjectsmayhaveGPRsignaturesverysimilartominesignatures.Forinstance,a5cmthickmetaldiskwitha30cmdiame-ter,orametalcanmaybeincorrectlyclassiedasmines.Inthiscase,di erentfeaturesandclassiers,orevendi erentsensors,maybeneeded.ACKNOWLEDGMENTSTheworkreportedonherewassupportedinpartbytheUS-Army-Research-O ce-fundedMultidisciplinaryRe-searchonMineDetectionandNeutralizationSystems,Contractno.DAAG55-97-1-0014,andbytheUSArmyGrantnos.DAAB15-01-D-0004andDAAB15-02-D-0003.WethankDr.JamesHarveyandMr.PeteHowardfortheirsupportofthisresearch.Wealsothankthereviewersfortheirconstructivecomments.REFERENCES [1]Landmines,MineActionNewsfromtheUnitedNations,vol.3.2,4thQuarter,1998.[2]HiddenKillers:TheGlobalLandmineCrisis,UnitedStatesDepartmentofStateReport,Publicationno.10575,Septem-ber1998.[3]T.R.Witten,resentstateoftheartinground-penetratingradarsforminedetection,inDetectionandRemediationTechnologiesforMinesandMinelikeTargetsIII,vol.3392ofProceedingsofSPIE,pp.576,Orlando,Fla,USA,April1998. 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1884EURASIPJournalonAppliedSignalProcessing [15]H.Frigui,K.Satyanarayana,andP.D.Gader,Detectionoflandminesusingfuzzyandpossibilisticmembershipfunc-tions,inProc.12thIEEEInternationalConferenceonFuzzySystemsFUZZ,vol.2,pp.834,SaintLouis,Mo,USA,May2003.[16]P.D.Gader,B.N.Nelson,H.Frigui,G.Vaillette,andJ.M.Keller,Fuzzylogicdetectionoflandmineswithgroundpen-etratingradar,SignalProcessing,vol.80,no.6,pp.1069,2000. 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[30]J.R.R.Pressley,D.Pabst,G.D.Sower,L.Nee,B.Green,andP.Howard,Groundstando minedetectionsystem(GSTAMIDS)engineering,manufacturing,anddevelopment(EMD)Block0,inDetectionandRemediationTechnologiesforMinesandMinelikeTargetsVI,vol.4394ofProceedingsofSPIE ,pp.1190,Orlando,Fla,USA,April2001.[31]G.D.Sower,J.Eberly,andE.Christy,GSTAMIDSground-penetratingradar:hardwaredescription,inDetectionandRemediationTechnologiesforMinesandMinelikeTargetsVI, vol.4394ofProceedingsofSPIE,pp.651,Orlando,Fla,USA,April2001.[32]E.G.FarrandC.E.Baum,repulseassociatedwiththeTEMfeedofanimpulseradiatingantenna,SensorandSimulationNote37,AirForceResearchLaboratory,March1992.[33]E.G.Farr,Optimizingthefeedimpedanceofimpulseradiat-ingantennasPartI:ReectorIRAs,SensorandSimulationNote354,AirForceResearchLaboratory,January1993.[34]E.G.FarrandC.J.Buchenauer,ExperimentalvalidationofIRAmodels,SensorandSimulationNote364,AirForceRe-searchLaboratory,January1994.[35]T.Kohonen,mprovedversionsoflearningvectorquantiza-tion,inProc.InternationalJointConferenceonNeuralNet-worksIJCNN,vol.1,pp.545,SanDiego,Calif,USA,June1990.[36]J.R.R.Pressley,D.Pabst,G.D.Sower,L.Nee,B.Green,andP.Howard,Groundstando minedetectionsystem(GSTAMIDS)engineering,manufacturinganddevelopment(EMD)block0,inDetectionandRemediationTechnologiesforMinesandMinelikeTargetsVI,vol.4394ofProceedingsofSPIE ,pp.1190,Orlando,Fla,USA,April2001. HichemFriguiisanAssistantProfessorandtheDirectoroftheMultimediaResearchLab,theUniversityofLouisville,Kentucky.HereceivedhisPh.D.degreeincomputerengineeringandcomputersciencefromtheUniversityofMissouri,Columbia,in1997.From1998to2004,hewasanAssistantPro-fessorattheUniversityofMemphis.Hehasbeenactiveintheresearcheldsofpatternrecognition,datamining,imageprocessing,andcontent-basedimageretrieval.Hehaspublishedover60jour-nalandrefereedconferencearticles,andhasreceivedtheNationalScienceFoundationCareerAwardforoutstandingyoungscientists.Dr.Friguihasbeenactiveinlandminedetectionalgorithmresearchsince1998.Hewasamemberoffewteamsthatdeveloped,imple-mented,andeld-testedseveralreal-timealgorithmsforminede-tectionusinggroundpenetratingradar.Dr.FriguiisaMemberoftheIEEE,IEEEComputerSociety,andACM.Heiscurrentlyserv-ingasanAssociateEditoroftheIEEETransactionsonFuzzySys-tems,andtheInternationalJournalofFuzzySystems. K.C.HowasborninHongKong.Here-ceivedtheB.S.degreewithrst-classhon-oursinelectronicsandthePh.D.degreeinelectronicengineeringfromtheChineseUniversityofHongKong,HongKong,in1988and1991,respectively.HewasaRe-searchAssociateintheRoyalMilitaryCol-legeofCanadafrom1991to1994.HejoinedtheBell-NorthernResearch,Mon-treal,Canada,in1995,asamemberofthescienticsta .HewasafacultymemberattheUniversityofSaskatchewan,Saskatoon,Canada,fromSeptember1996toAu-gust1997.SinceSeptember1997,hehasbeenwiththeUniversityofMissouri,Columbia,whereheiscurrentlyanAssociateProfessorintheElectricalandComputerEngineeringDepartment.Hisresearchinterestsareinstatisticalandadaptivesignalprocessing,sub-surfaceobjectdetection,sourcelocalizations,wavelettransform,andwirelesscommunications.Dr.Hoiscurrentlyservingasan

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Real-TimeLandmineDetectionwithGPRUsingDiscriminativeHMM1885 AssociateEditoroftheIEEETransactionsonSignalProcessing,andtheIEEESignalProcessingLetters.HeisalsotheEditoroftheITU StandardRecommendationG.168:DigitalNetworkEchoCancellers. HehasthreeUSpatents,threeCanadianpatents,andthreeEuro-peanpatentsintheareaofmobilecommunications. PaulGaderreceivedhisPh.D.degreeinmathematicsin1986fromtheUniversityofFlorida.HehasworkedasaSeniorRe-searchScientistatHoneywesSystemsandResearchCenter,asaResearchEngineerandManagerattheEnvironmentalResearchIn-stituteofMichigan,andasafacultymem-berattheUniversityofWisconsin,theUni-versityofMissouri,andtheUniversityofFlorida,whereheiscurrentlyaProfessorofcomputerandinformationscienceandengineering.Heledteamsinvolvedinreal-time,handwrittenaddressrecognitionsystemsfortheUSpostalservicedevelopingalgorithmsforhandwrittendigitrecognitionandsegmentation,numericeldrecognition,wordrecognition,andlinesegmentation.Hehasledteamsthatdevisedandtestedseveralreal-timealgorithmsintheeldforminedetec-tion.HeservedasaTechnicalDirectoroftheUniversityofMissouriMURIonHumanitarianDeminingfortwoyears.Heiscurrentlyinvolvedinlandminedetectionprojectsinvestigatinghandheldandground-baseddetectionsystems,acousticdetection,EO/IRdetec-tionofminesandtrip-wires,hyperspectraldetection,andmulti-sensorfusion.Dr.GaderisaSeniorMemberoftheIEEEandhasover165technicalpublicationsintheareasofimageandsignalpro-cessing,appliedmathematics,andpatternrecognition,includingover50refereedjournalarticles.