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Texture classification using spectral histograms

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IEEETRANSACTIONSONIMAGEPROCESSING,VOL.12,NO.6,JUNE2003661
TextureClassificationUsingSpectralHistograms
XiuwenLiu,SeniorMember,IEEE,andDeLiangWang,SeniorMember,IEEE
Abstract—Basedonalocalspatial/frequencyrepresentation,weemployaspectralhistogramasafeaturestatisticfortextureclas-sification.Thespectralhistogramconsistsofmarginaldistribu-tionsofresponsesofabankoffiltersandencodesimplicitlythelocalstructureofimagesthroughthefilteringstageandtheglobalappearancethroughthehistogramstage.Thedistancebetweentwospectralhistogramsismeasuredusing2-statistic.Thespec-tralhistogramwiththeassociateddistancemeasureexhibitssev-eralpropertiesthatarenecessaryfortextureclassification.Afilterselectionalgorithmisproposedtomaximizeclassificationperfor-manceofagivendataset.Ourclassificationexperimentsusingnat-uraltextureimagesrevealthatthespectralhistogramrepresenta-tionprovidesarobustfeaturestatisticfortexturesandgeneralizeswell.Comparisonsshowthatourmethodproducesamarkedim-provementinclassificationperformance.Finallywepointouttherelationshipsbetweenexistingtexturefeaturesandthespectralhis-togram,suggestingthatthelattermayprovideaunifiedtexturefeature.
IndexTerms—Filtering,spectralhistogram,textureanalysis,textureclassification.
I.INTRODUCTION
EXTUREclassificationisafundamentalproblemincom-putervisionwithawidevarietyofapplications[40].Twofundamentalissuesintextureclassificationarehowtocharac-terizetexturesusingderivedfeaturesandandhowtodefinearobustdistance/similaritymeasurebetweentextures,whichre-mainelusivedespiteconsiderableeffortsintheliterature[34].Becauseimagesofthesameunderlyingtexturecanvarysignif-icantly,texturalfeaturesmustbeinvariantto(largeimagevari-ationsandatthesametimesensitivetointrinsicspatialstruc-turesthatdefinetextures.Becausethereisnoobviousfeaturecommonforalltextureimages,texturefeaturesareoftenpro-posedbasedonassumptionsformathematicalconvenienceortask-specificheuristics(see[35],[40]forreviews.Forexample,geometricpropertiesbasedonthetextureelementsareoftenusedfortextureswithperiodicstructures[39].Earlyfeaturesincludingcooccurrencematrices[17]andMarkovrandomfieldmodels[7]havelimitedexpressivepowerbecausetheanalysisofspatialinteractionislimitedtoarelativelysmallneighbor-hood.Asaresult,theadequacyofthesefeaturesforcharacter-izingvarioustexturesisrarelychecked.
ManuscriptreceivedNovember29,2001;revisedJanuary23,2003.ThisworkwassupportedinpartbyNIMAgrant(NMA201-01-2010toX.Liu,anONRYoungInvestigatorAward(N00014-96-1-0676,anNSFgrant(IIS-0081058,andanAFOSRgrant(F49620-01-1-0027toD.L.Wang.Theas-sociateeditorcoordinatingthereviewofthismanuscriptandapprovingitforpublicationwasDr.JosianeB.Zerubia.
X.LiuiswiththeDepartmentofComputerScience,FloridaStateUniversity,Tallahassee,FL32306-4530USA(e-mail:liux@cs.fsu.edu.
D.L.WangiswiththeDepartmentofComputerandInformationScience,CenterforCognitiveScience,TheOhioStateUniversity,Columbus,OH43210USA(e-mail:dwang@cis.ohio-state.edu.
DigitalObjectIdentifier10.1109/TIP.2003.812327
T
Ontheotherhand,studiesonthehumanvisualsystemsug-gestthatittransformsaretinalimageintoalocalspatial/fre-quencyrepresentation[4],[10],whichcanbecomputationallysimulatedbyconvolvingtheinputimagewithabankoffil-terswithtunedfrequenciesandorientations.Themathematicalframeworkforthelocalspatial/frequencyrepresentationwaslaidoutbyGabor[13]andextendedbyDaughman[8].Re-cently,thistheoryhasalsobeenconfirmedbyderivingsim-ilarfeaturedetectorsfromnaturalimages[33].Theseadvanceshaveinspiredmuchresearchintextureclassificationbasedonfiltering(see[34]forareview.Inthisframework,atextureimageistransformedintofeaturevectorsbyfilteringtheinputimageusingabankoffilters,followedbysomenonlinearityandsmoothingsteps[34].Thenonlinearityisnecessaryfortex-tureclassification,since,otherwise,filterresponsescannotdis-criminatetextureswiththesamemeanintensity(see,e.g.,MalikandPerona[29];thesmoothingisnecessarysincethefilterre-sponsesarenothomogeneousevenwithinahomogeneoustex-tureregion.Whilethenonlinearityandsmoothingstepsarecrit-icalfortextureclassification,currentresearchfocusesinsteadonthefilteringstage,i.e.,derivingoptimalfiltersfortextureclassificationbasedoncertainoptimizationcriteria.Asaresult,whileboththetheoreticalandnumericalaspectsoffilterdesignfortextureclassificationarewellstudied[30],therecentcom-prehensivestudybyRandenandHusoy[34]showedthatthetextureclassificationperformanceisverylimitedforrealtex-tures.Thisstudyclearlyleadstotheneedforstudyingstatisticfeaturesbeyondthefilteringstagefortextureclassification.Recently,HeegerandBergen[18]proposedatexturesyn-thesisalgorithmthatcanmatchtextureappearance.Thealgo-rithmtransformsarandomnoiseimageintoonewithsimilarappearancetoagiventargetimagebymatchingindependentlythehistogramsofimagepyramidsconstructedfromtherandomandtargetimages.Thesuccessofsynthesizingnaturaltexturesbasedonhistogramshasmotivatedconsiderableresearch[43],[44].Zhuetal.[44]proposedatheoryforlearningprobabilitymodelsbymatchinghistogramsbasedonamaximumentropyprinciple.Zhuetal.[43]studiedefficientsamplingalgorithmsformatchinghistograms.Whilethesesynthesismethodspro-videfeaturestocharacterizeasingletexture,theeffectivenessofthesefeaturesfortextureclassificationisnotknownasagoodsynthesismodeldoesnotimplyagoodclassificationmodel(seeSectionIII.Also,whilethesesynthesismethodsareproposedtomodelhomogeneoustextures,naturaltexturesarerarelyho-mogeneousduetodeformationsandothervariations;thesevari-ationsrequirearobustdistancemeasurebetweentexturessothatthedistancebetweenimagesofthesametextureissmallandthatamongimagesfromdifferenttexturesislarge.Further-more,asthefeaturesdependonthechoiceoffilters,thereisnosystematicalgorithmtochoosefiltersfortextureclassification.Inaddition,textureclassificationisoftendonebasedonrela-
1057-7149/03$17.00©2003IEEE

662tivelysmallimagewindowsandtheeffectofthewindowsizeonhistogram-basedrepresentationsneedstobestudied.
Motivatedbytheresearchontexturesynthesis,weproposealocalspectralhistogram,consistingofmarginaldistributionsofresponsesfromabankoffiltersforanimagewindow,asafeaturestatisticfortextureclassification.Wedefineadistancebetweentwoimagewindowsasthe
andabankoffilters
throughlinearconvolution.2Thatis,
,
whereacircularboundaryconditionisused.For
(1
where
IEEETRANSACTIONSONIMAGEPROCESSING,VOL.12,NO.6,JUNE2003
(3
where
beanimagedefinedonafinitelattice,
,thepropositionholds.Assumethat,animagedefinedonthefinitelattice
mustbea
permutationof
,the
maximumresponseofthefilterisbounded
isapermutationof
mustbeequivalentto

LIUANDWANG:TEXTURECLASSIFICATIONUSINGSPECTRALHISTOGRAMS663
Fig.1.AtypicalimagethatsatisfiesH

664examplesshowninFig.2weregeneratedusingaGibbssampler[14],[43].InFig.2(a,thespectralhistogramcapturestheperceptualappearanceofbothregions.Giventhatthecircularboundaryisused,thesynthesizedimagematchescloselytheobservedimage.Fig.2(bshowsasynthetictextureimage,wherethespectralhistogramcapturesthetextureelementanditsdensity.Fig.2(cand(dshowthatthespectralhistogramsoftwostochastictexturescapturetheirperceptualappearancewell.
C.ImplementationIssues
Becauseaspectralhistogramisdefinedwithrespecttoabankoffilters,thefirstimplementationissueiswhatfiltersshouldbeusedsothatvarioustexturescanbemodeledeffectively.Hereweusefourdifferenttypesoffilterssuggestedfromthestudiesofvisualperceptionandtheempiricalstudiesofindependentcomponentsofnaturalimages[2],[33],[44].1Theintensityfilter,whichisthe
,
(4
where
determinesthescaleofthefilterand
isascale.Thecosineandsinecomponentsof
thesefiltersarereferredtoas
IEEETRANSACTIONSONIMAGEPROCESSING,VOL.12,NO.6,JUNE2003
isakernelfunction(Gaussiankernelisusedinthis
paper,and
tex-turetypes,werepresenteachtype
and
,wedefineclassificationgain
as
isthetotalnumberofclassesinthedatabase,andthus
istheexpectedcorrectclassificationratebasedonarandomdecision.measurestheeffectivenessoffiltersin
.Hereweuse

LIUANDWANG:TEXTURECLASSIFICATIONUSINGSPECTRALHISTOGRAMSFig.3.Filterselectionalgorithm.Here,Bisthesubsetofthefiltersthathasnotbeenchosen,Sisthesubsetthathasbeenchosen,and

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