Classification of Hyperspectral Remote Sensing

October 29, 2014  |  By  | 


MELGANIANDBRUZZONE:CLASSIFICATIONOFHYPERSPECTRALREMOTESENSINGIMAGESWITHSVMs1779 classi  edbyusingtheavailabletrainingsamples.Then,theclas- si  edsamples,togetherwiththetrainingones,areexploitedit- erativelytoupdatetheclassstatisticsand,accordingly,there- sultsoftheclassi  cationuptoconvergence[4],[5].Theprocess ofintegrationbetweenthesetwotypologiesofsamples(i.e., thetrainingandthesemilabeledsamples)iscarriedoutbythe expectation – maximization(EM)algorithm,whichrepresentsa generalandpowerfulsolutiontotheproblemofMLestimation ofstatisticsinthepresenceofincompletedata[6],[7].Themain advantageofthisapproachisthatit  tsthetrueclassdistribu- tionsbetter,sincealargerportionoftheimage(availablewithno extracost)contributestotheestimationprocess.Themainprob- lemsrelatedtothissecondapproacharetwo:1)itisdemanding fromthecomputationalpointofviewand2)itrequiresthatthe initialclassmodelestimatedfromthetrainingsamplesshould matchwellenoughtheunlabeledsamplesinordertoavoiddi- vergenceoftheestimationprocessand,accordingly,toimprove theaccuracyofthemodelparameterestimation. Inordertoovercometheproblemofthecurseofdimension- ality,thethirdapproachproposestoreducethedimensionality ofthefeaturespacebymeansoffeatureselectionorextraction techniques.Feature-selectiontechniquesperformareductionof spectralchannelsbyselectingarepresentativesubsetoforiginal features.Thiscanbedonefollowing:1)aselectioncriterionand 2)asearchstrategy.Theformeraimsatassessingthediscrim- inationcapabilitiesofagivensubsetoffeaturesaccordingto statisticaldistancemeasuresamongclasses(e.g.,Bhattacharyya distance,Jeffries – Matusitadistance,andthetransformeddiver- gencemeasure[8],[9]).Thelatterplaysacrucialroleinhyper- dimensionalspaces,sinceitde  nestheoptimizationapproach necessarytoidentifythebest(oragood)subsetoffeaturesac- cordingtotheusedselectioncriterion.Sincetheidenti  cationof theoptimalsolutioniscomputationallyunfeasible,techniques thatleadtosuboptimalsolutionsarenormallyused.Among thesearchstrategiesproposedintheliterature,itisworthmen- tioningthebasicsequentialforwardselection(SFS)[10],the moreeffectivesequentialforward  oatingselection[11],and thesteepestascent(SA)techniques[12].Thefeature-extraction approachaddressestheproblemoffeaturereductionbytrans- formingtheoriginalfeaturespaceintoaspaceofalowerdi- mensionality,whichcontainsmostoftheoriginalinformation. Inthiscontext,thedecisionboundaryfeatureextraction(DBFE) method[13]hasprovedtobeaveryeffectivemethod,capable ofprovidingaminimumnumberoftransformedfeaturesthat achievegoodclassi  cationaccuracy.However,thisfeature-ex- tractiontechniquesuffersfromhighcomputationalcomplexity, whichmakesitoftenunpractical.Thisproblemcanbeover- comebycouplingwiththeprojectionpursuit(PP)algorithm [14],whichplaystheroleofapreprocessortotheDBFEby applyingapreliminarylimitedreductionofthefeaturespace with(hopefully)analmostnegligibleinformationloss.Anal- ternativefeature-extractionmethod,whoseclass-speci  cnature makesitparticularlyattractive,wasproposedbyKumar etal. [15].Itisbasedonacombinationofsubsetsof(highlycorre- lated)adjacentbandsintofewerfeaturesbymeansoftop-down andbottom-upalgorithms.Ingeneral,itisevidentthatevenif feature-reductiontechniquestakecareoflimitingthelossofin- formation,thislossisoftenunavoidableandmayhaveanega- tiveimpactonclassi  cationaccuracy. Finally,theapproachinheritedfromspectroscopicmethods inanalyticalchemistrytodealwithhyperspectraldataisworth mentioning.Theideabehindthisapproachisthatoflooking attheresponsefromeachpixelinthehyperspectralimageas a one -dimensionalspectralsignal(signature).Eachinformation classismodeledbysomedescriptorsoftheshapeofitsspectra [16],[17].Themeritofthisapproachisthatitsigni  cantlysim- pli  estheformulationofthehyperspectraldataclassi  cation problem.However,additionalworkisrequiredto  ndoutappro- priateshapedescriptorscapableofcapturingthespectralshape variabilityrelatedtoeachinformationclassaccurately. Othermethodsalsoexistthatarenotincludedinthegroup ofthefourmainapproachesdiscussedabove.Inparticular,itis interestingtomentionthemethodbasedonthecombinationof differentclassi  ers[18]andthatbasedoncluster-spacerepre- sentation[19]. Recently,particularattentionhasbeendedicatedtosupport vectormachines(SVMs)fortheclassi  cationofmultispectral remotesensingimages[20] – [22].SVMshaveoftenbeenfound toprovidehigherclassi  cationaccuraciesthanotherwidely usedpatternrecognitiontechniques,suchasthemaximum likelihoodandthemultilayerperceptronneuralnetworkclassi-  ers.Furthermore,SVMsappeartobeespeciallyadvantageous inthepresenceofheterogeneousclassesforwhichonlyfew trainingsamplesareavailable.Inthecontextofhyperspectral imageclassi  cation,somepioneeringexperimentalinvestiga- tionspreliminarilypointedouttheeffectivenessofSVMsto analyzehyperspectraldatadirectlyinthehyperdimensional featurespace,withouttheneedofanyfeature-reductionpro- cedure[23] – [26].Inparticular,in[24],theauthorsfound thatasigni  cantimprovementofclassi  cationaccuracycan beobtainedbySVMswithrespecttotheresultsachieved bythebasicminimal-distance-to-meansclassi  erandthose reportedin[3].Inordertoshowitsrelativelylowsensitivity tothenumberoftrainingsamples,theaccuracyoftheSVM classi  erwasestimatedonthebasisofdifferentproportions betweenthenumberoftrainingandtestsamples.Aswillbe explainedinthefollowingsection,thismainlydependsonthe factthatSVMsimplementaclassi  cationstrategythatexploits amargin-based “ geometrical ” criterionratherthanapurely “ statistical ” criterion.Inotherwords,SVMsdonotrequire anestimationofthestatisticaldistributionsofclassestocarry outtheclassi  cationtask,buttheyde  netheclassi  cation modelbyexploitingtheconceptofmarginmaximization.The growinginterestinSVMs[27] – [30]iscon  rmedbytheirsuc- cessfulimplementationinnumerousotherpatternrecognition applicationssuchasbiomedicalimaging[31],imagecompres- sion[32],andthree-dimensionalobjectrecognition[33].Such aninterestisjusti  edbythreemaingeneralreasons:1)their intrinsiceffectivenesswithrespecttotraditionalclassi  ers, whichresultsinhighclassi  cationaccuraciesandverygood generalizationcapabilities;2)thelimitedeffortrequiredfor architecturedesign(i.e.,theyinvolvefewcontrolparameters); and3)thepossibilityofsolvingthelearningproblemaccording tolinearlyconstrainedquadraticprogramming(QP)methods (whichhavebeenstudiedintenselyinthescienti  cliterature). However,amajordrawbackofSVMsisthat,fromatheoretical pointofview,theywereoriginallydevelopedtosolvebinary

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