18 - SMACC.pdf - ENVI Tutorials - Crispini

ENVITutorial:Using

SMACCtoExtract

Endmembers

Using SMACC to Extract Endmembers

Files Used in this Tutorial

Introduction to the SMACC Endmember Extraction Method

Open and Display the Input Data

Examine the Data and Start SMACC

Select the Input File

Specify the SMACC Parameters

Analyze the Extracted Endmembers and Their Abundance Images

ENVITutorial:UsingSMACCtoExtractEndmembers

UsingSMACCtoExtractEndmembers

ThistutorialisdesignedtointroduceyoutoENVI’sSMACCendmemberextractiontool.Inthistutorial,

youwillextractendmembersfromanimageofanairfieldinSanDiego,California.

FilesUsedinthisTutorial

ENVIResourceDVD: Data\aviris

File Description

sandiego_reflectance.img (.hdr) HyperspectraldataofanairfieldinSanDiego

sandiego_mask.dat (.hdr) Maskforremovingsaturatedpixelsfromtheairfielddata

Thehyperspectralimage( sandiego_reflectance.img )isofanavalairstationinSanDiego,

California,collectedbytheAirborneVisible/InfraredImagingSpectrometer(AVIRIS)sensor.The

imagewasatmosphericallycorrectedusingENVI’sFLAASHmodule,resultinginareflectanceimage.

ENVITutorial:UsingSMACCtoExtractEndmembers

IntroductiontotheSMACCEndmemberExtraction

Method

TheSequentialMaximumAngleConvexCone(SMACC)spectraltoolfindsspectralendmembersand

theirabundancesthroughoutanimage.Thistoolisdesignedforusewithpreviouslycalibrated

hyperspectraldata.IncomparisontoENVI’sSpectralHourglassWizard,SMACCprovidesafasterand

moreautomatedmethodforfindingspectralendmembers,butitismoreapproximateandyieldsless

precision.

Endmembersarespectrathatarechosentorepresentpuresurfacematerialsinaspectralimage.

Endmembersthatrepresentradianceorreflectancespectramustsatisfyapositivityconstraint

(containingnovalueslessthanzero).Otherphysically-basedconstraintsmaybeimposed,suchasa

sum-to-unityconstraint(thepixelsareweightedmixturesoftheendmembers)orasum-to-unityorless

constraint(thepixelsareweightedmixturesoftheendmembersplusblack).Ifthehyperspectraldataare

calibratedtoeitherradianceorthermalIRemissivity,youshoulduseasum-to-unityunmixingconstraint.

Ifthedataarecalibratedtoreflectance,youshoulduseeitherapositivityonlyorsum-to-unityorless

constraint.SMACCallowsyoutoselectofanyoftheseconstraints.

SMACCusesaconvexconemodel(alsoknownasResidualMinimization)withtheseconstraintsto

identifyimageendmemberspectra.Extremepointsareusedtodetermineaconvexcone,whichdefines

thefirstendmember.Aconstrainedobliqueprojectionisthenappliedtotheexistingconetoderivethe

nextendmember.Theconeisincreasedtoincludethenewendmember.Theprocessisrepeateduntila

projectionderivesanendmemberthatalreadyexistswithintheconvexcone(toaspecifiedtolerance)or

untilthespecifiednumberofendmembersarefound.

Inotherwords,SMACCfirstfindsthebrightestpixelintheimage,thenitfindsthepixelmostdifferent

fromthebrightest.Then,itfindsthepixelmostdifferentfromthefirsttwo.Theprocessisrepeateduntil

SMACCfindsapixelalreadyaccountedforinthegroupofthepreviouslyfoundpixels,oruntilitfindsa

specifiednumberofendmembers.ThespectraofpixelsthatSMACCfindsbecometheendmembersof

theresultingspectrallibrary.

Unlikeconvexmethodsthatrelyonasimplexanalysis,thenumberofendmembersisnotrestrictedby

thenumberofspectralchannels.AlthoughendmembersderivedfromSMACCareunique,aone-to-one

correspondencedoesnotexistbetweenthenumberofmaterialsinanimageandthenumberof

endmembers.SMACCderivesendmembersfrompixelsinanimage.Eachpixelmaycontainonlyone

materialoritmaycontainahighpercentageofasinglematerialwithuniquecombinationsofother

materials.Eachmaterialidentifiedinanimageisdescribedbyasubsetspanningitsspectralvariability.

SMACCprovidesanendmemberbasisthatdefineseachofthesematerialsubsets.SMACCalso

providesabundanceimagestodeterminethefractionsofthetotalspectrallyintegratedradianceor

reflectanceofapixelcontributedbyeachresultingendmember.

Mathematically,SMACCusesthefollowingconvexconeexpansionforeachpixelspectrum

(endmember),definedas:

where:

ENVITutorial:UsingSMACCtoExtractEndmembers

i isthepixelindex

j and k aretheendmemberindicesfrom1totheexpansionlength, N

R isamatrixthatcontainstheendmemberspectraascolumns

c isthespectralchannelindex

A isamatrixthatcontainsthefractionalcontribution(abundance)ofeachendmember j ineach

endmember k foreachpixel.

The2Dmatrixrepresentationofaspectralimageisfactoredintoaconvex2Dbasis(aspanofavector

space)timesamatrixofpositivecoefficients.Intheimagematrix(R),therowelementsrepresent

individualpixels,andeachcolumnrepresentsthespectrumofthatpixel.ThecoefficientsinAarethe

fractionalcontributionsorabundancesofthebasismembersoftheoriginalmatrix.Thebasisformsann-

Dconvexconewithinitssubset.Theconvexconeofthedataisthesetofallpositivelinear

combinationsofthedatavectors,whiletheconvexhullisthesetofallweightedaveragesofthedata.

Thefactormatricesarethendeterminedsequentially.Ateachstep,anewconvexconeisformedby

addingtheselectedvectorfromtheoriginalmatrixthatliesfurthestfromtheconedefinedbytheexisting

basis.

SeethefollowingreferenceformoreinformationonSMACC:

Gruninger,J,A.J.RatkowskiandM.L.Hoke.“TheSequentialMaximumAngleConvexCone

(SMACC)EndmemberModel”.ProceedingsSPIE,AlgorithmsforMultispectralandHyper-spectraland

UltraspectralImagery,Vol.5425-1,OrlandoFL,April,2004.

ENVITutorial:UsingSMACCtoExtractEndmembers

OpenandDisplaytheInputData

1. FromtheENVImainmenubar,select File>OpenImageFile .Afileselectiondialogappears.

2. Navigateto Data\aviris andselect sandiego_reflectance.img .Click Open .A

colorcompositeisautomaticallyloadedintoadisplaygroup.

18 - SMACC.pdf

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