A statistical approach to texture classification f

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.Wealsodiscusstheeectsofvariousparametersonourclassi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.Thereisaconsiderabledierenceintheappearanceacrossimages.theresultantimage(seegure1).Thiscausesalargevariabilityintheimagedappearanceofatextureanddealingwithitsuccessfullyisoneofthemaintasksofanyclassicationalgorithm.Anotherfactorwhichcomesintoplayisthat,quiteoften,twotextureswhenphotographedunderverydierentimagingconditionscanappeartobequitesimilar,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,belongtodierentclasses.Similarly,inthebottomrow,theimagesappearsimilarandyettherearethreedierenttextureclassespresent.AStatisticalApproachtoTextureClassicationfromSingleImages3clusteringisinaverylowdimensionalspaceandisalsorotationallyinvariant.Thesecondinnovationistoclassifytexturesfromsingleimageswhilerepresentingeachtextureclassbyasmallsetofmodels.OurapproachismostcloselyrelatedtothoseofLeungandMa-lik(LeungandMalik,2001),Schmid(Schmid,2001)andCulaandDana(CulaandDana,2004).LeungandMalik'smethodisnotro-tationallyinvariantandrequiresasinputasetofregisteredimagesacquiredundera(implicitly)knownsetofimagingconditions.Schmid'sapproachisrotationallyinvariantbuttheinvarianceisachievedinadif-ferentmannertoours,andtextonclusteringisinahigherdimensionalspace.CulaandDanaclassifyfromsingleimages,butthemethodisnotrotationallyinvariantandtheiralgorithmformodelselectiondiersfromtheonedevelopedinthispaper.Thesepointsarediscussedinmoredetailsubsequently.Thepaperisorganisedasfollows:insection2,thebasicclassica-tionalgorithmisdevelopedwithinarotationallyinvariantframework.Theclustering,learningandclassicationstepsofthealgorithmaredescribed,andtheperformanceoffourltersetsiscompared.ThesetsincludethoseusedbySchmid(Schmid,2001),LeungandMalik(LeungandMalik,2001),andtworotationallyinvariantsetsbasedonmaximallterresponses.Insection3,methodsaredevelopedwhichminimisethenumberofmodelsusedtocharacterisethevarioustextureclasses.Section4thendealswithvariousmodicationsandgeneralisationsofthebasicalgorithm.Inparticular,theeectofthechoiceoftextondictionaryandtrainingimagesupontheclassierisinvestiga