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1、GaborwavelettransformanditsapplicationWei-lunChaoR98942073AbstractThistermprojectreportintroducesthewell-knowGaborwavelettransformanditsapplications.Wavelettransformcouldextractboththetime(spatial)andfrequencyinformationfromagivensignal,andthetunablek
2、ernelsizeallowsittoperformmulti-resolutionanalysis.Amongkindsofwavelettransforms,theGaborwavelettransformhassomeimpressivemathematicalandbiologicalpropertiesandhasbeenusedfrequentlyonresearchesofimageprocessing.1.IntroductionFromthelastthreelecturesof
3、the“time-frequencyanalysisandwavelettransform”course[3],wehavelearnedthatthewavelettransformcouldperformmulti-resolutiontime-frequencyanalysis.Thetunablekernelsizeresultsindifferenttime-frequencyresolutionpairandthesizeisrelatedtotheanalyticalfrequenc
4、y.Forexample,smallerkernelsize(intimedomain)hashigherresolutionintimedomainbutlowerresolutioninfrequencydomain,andisusedforhigherfrequencyanalysis;whilebiggerkernelsizehashigherresolutioninfrequencydomainbutlowerresolutionintimedomain,andisusedforlowe
5、rfrequencyanalysis.Thisgreatpropertymakeswavelettransformsuitableforapplicationssuchasimagecompression,edgedetection,filterdesign,andsomekindsofimageobjectrecognition,etc.Amongvariouswaveletbases,Gaborfunctionsprovidetheoptimalresolutioninboththetime(
6、spatial)andfrequencydomains,andtheGaborwavelettransformseemstobetheoptimalbasistoextractlocalfeaturesforseveralreasons[2]:Biologicalmotivation:Thesimplecellsofthevisualcortexofmammalianbrainsarebestmodeledasafamilyofself-similar2DGaborwavelets.Mathe
7、maticalandempiricalmotivation:Gaborwavelettransformhasboththemulti-resolutionandmulti-orientationpropertiesandareoptimalformeasuringlocalspatialfrequencies.Besides,ithasbeenfoundtoyielddistortiontolerancespaceforpatternrecognitiontasks.Basedontheseadv
8、antagesofGaborwavelettransform,ithasbeenusedinmanyimageanalysisapplications,andthisreportfocusit’sapplicationsonfacerecognition,textureclassification,facialexpressionclassification,andsomeotherexcellentresearches.Thereportisorganizedasfollows:
