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AStatisticalApproachtoTextureClassi cationfromSingleImagesManikVarmaandAndrewZissermanRoboticsResearchGroupDept.ofEngineeringScienceUniversityofOxfordOxford,OX13PJ,UK(manik,az)@robots.ox.ac.ukAbstract.Weinvestigatetextureclassi cationfromsingleimagesobtainedunderunknownviewpointandillumination.Astatisticalapproachisdevelopedwheretexturesaremodelledbythejointprobabilitydistributionof lterresponses.Thisdistributionisrepresentedbythefrequencyhistogramof lterresponseclustercentres(textons).Recognitionproceedsfromsingle,uncalibratedimagesandthenoveltyhereisthatrotationallyinvariant ltersareusedandthe lterresponsespaceislowdimensional.Classi cationperformanceiscomparedwiththe lterbanksandmethodsofLeungandMalik[IJCV2001],Schmid[CVPR2001]andCulaandDana[IJCV2004]anditisdemonstratedthatsuperiorperformanceisachievedhere.Classi cationresultsarepresentedforall61materialsintheColumbia-Utrechttexturedatabase.Wealsodiscussthee ectsofvariousparametersonourclassi cationalgorithm{suchasthechoiceof lterbankandrotationalinvariance,thesizeofthetextondic-tionaryaswellasthenumberoftrainingimagesused.Finally,wepresentamethodofreliablymeasuringrelativeorientationco-occurrencestatisticsinarotationallyinvariantmanner,anddiscusswhetherincorporatingsuchinformationcanenhancetheclassi er'sperformance.Keywords:materialclassi cation,3Dtextures,textons, lterbanks,rotationin-variance1.IntroductionInthispaper,weinvestigatetheproblemofclassifyingmaterialsfromtheirimagedappearance,withoutimposinganyconstraintson,orre-quiringanyaprioriknowledgeof,theviewingorilluminationcon-ditionsunderwhichtheseimageswereobtained.Classifyingtexturesfromsingleimagesundersuchgeneralconditionsisaverydemandingtask.Atextureimageisprimarilyafunctionofthefollowingvariables:thetexturesurface,itsalbedo,theillumination,thecameraanditsviewingposition.Evenifweweretokeepthe rsttwoparameters xed,i.e.photographexactlythesamepatchoftextureeverytime,minorchangesintheotherparameterscanleadtodramaticchangesinc2004KluwerAcademicPublishers.PrintedintheNetherlands.2VarmaandZissermanFigure1.Thechangeinimagedappearanceofthesametexture(PlasterB,texture#30fromtheColumbia-Utrechtdatabase)withvariationinimagingconditions.Toprow:constantviewingangleandvaryingillumination.Bottomrow:constantilluminationandvaryingviewingangle.Thereisaconsiderabledi erenceintheappearanceacrossimages.theresultantimage(see gure1).Thiscausesalargevariabilityintheimagedappearanceofatextureanddealingwithitsuccessfullyisoneofthemaintasksofanyclassi cationalgorithm.Anotherfactorwhichcomesintoplayisthat,quiteoften,twotextureswhenphotographedunderverydi erentimagingconditionscanappeartobequitesimilar,asisillustratedby gure2.Itisacombinationofboththesefactorswhichmakesthetextureclassi cationproblemsohard.Astatisticallearningapproachtotheproblemisdevelopedandin-vestigatedinthispaper.Texturesaremodelledbythejointdistributionof lterresponses.Thisdistributionisrepresentedbytexton(clustercentre)frequencies,andtextonsandtexturemodelsarelearntfromtrainingimages.Classi cationofanovelimageproceedsbymappingtheimagetoatextondistributionandcomparingthisdistributiontothelearntmodels.Assuch,thisprocedureisquitestandard(LeungandMalik,2001),buttheoriginalitycomesinattwopoints: rst,textonFigure2.Smallinterclassvariationsbetweentexturescanmaketheproblemharderstill.Inthetoprow,the rstandthefourthimageareofthesametexturewhilealltheotherimages,eventhoughtheylooksimilar,belongtodi erentclasses.Similarly,inthebottomrow,theimagesappearsimilarandyettherearethreedi erenttextureclassespresent.AStatisticalApproachtoTextureClassi cationfromSingleImages3clusteringisinaverylowdimensionalspaceandisalsorotationallyinvariant.Thesecondinnovationistoclassifytexturesfromsingleimageswhilerepresentingeachtextureclassbyasmallsetofmodels.OurapproachismostcloselyrelatedtothoseofLeungandMa-lik(LeungandMalik,2001),Schmid(Schmid,2001)andCulaandDana(CulaandDana,2004).LeungandMalik'smethodisnotro-tationallyinvariantandrequiresasinputasetofregisteredimagesacquiredundera(implicitly)knownsetofimagingconditions.Schmid'sapproachisrotationallyinvariantbuttheinvarianceisachievedinadif-ferentmannertoours,andtextonclusteringisinahigherdimensionalspace.CulaandDanaclassifyfromsingleimages,butthemethodisnotrotationallyinvariantandtheiralgorithmformodelselectiondi ersfromtheonedevelopedinthispaper.Thesepointsarediscussedinmoredetailsubsequently.Thepaperisorganisedasfollows:insection2,thebasicclassi ca-tionalgorithmisdevelopedwithinarotationallyinvariantframework.Theclustering,learningandclassi cationstepsofthealgorithmaredescribed,andtheperformanceoffour ltersetsiscompared.ThesetsincludethoseusedbySchmid(Schmid,2001),LeungandMalik(LeungandMalik,2001),andtworotationallyinvariantsetsbasedonmaximal lterresponses.Insection3,methodsaredevelopedwhichminimisethenumberofmodelsusedtocharacterisethevarioustextureclasses.Section4thendealswithvariousmodi cationsandgeneralisationsofthebasicalgorithm.Inparticular,thee ectofthechoiceoftextondictionaryandtrainingimagesupontheclassi erisinvestiga