gabor wavelet in image processing

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1、GABORWAVELETSINIMAGEPROCESSINGDavidBarinaˇDoctoralDegreeProgramme(2),FITBUTE-mail:xbarin02@stud.fit.vutbr.czSupervisedby:PavelZemcíkˇE-mail:zemcik@fit.vutbr.czAbstract:Thisworkshowstheuseofatwo-dimensionalGaborwaveletsinimageprocessing.Convo-lutionwithsuchatwo-dimensionalwaveletcanbes

2、eparatedintotwoseriesofone-dimensionalones.ThekeyideaofthisworkistoutilizeaGaborwaveletasamultiscalepartialdifferentialoperatorofagivenorder.Gaborwaveletsareusedheretodetectedges,cornersandblobs.AperformanceofsuchaninterestpointdetectoriscomparedtodetectorsutilizingaHaarwaveletandad

3、erivativeofaGaussianfunction.TheproposedapproachmaybeusefulwhenafastimplementationoftheGabortransformisavailableorwhenthetransformisalreadyprecomputed.Keywords:Gaborfunction,wavelet,featuredetection,interestpointdetection1INTRODUCTIONAGaboratom(orfunction)wasproposedbyHungarian-born

4、electricalengineerDennisGaborin1946[2].Nowadays,Gaborfunctionsarefrequentlyusedforfeatureextraction,especiallyintexture-basedimageanalysis(e.g.,classification,segmentationoredgedetection)andmorepracticallyinfacerecogni-tion.Manyofimageprocessingtaskscanbeseenintermsofawavelettransfor

5、m.Informallyspeaking,theimagecanbeseenunderthelenswithamagnificationgivenbythescaleofawavelet.Indoingso,wecanonlyseejusttheinformationthatisdeterminedbytheshapeoftheusedwavelet.TheGaboratomscanalsobeseeninthewordsofawavelettransform[8].Specifically,Gaborwaveletsarecreatedfromonepartic

6、ularatombydilation(androtationintwo-dimensionalcase).TheseGaborwaveletsprovideacompleteimagerepresentation[6].Inatwo-dimensionalcase,theabsolutesquareofacorrelationbetweenanimageandthetwo-dimensionalGaborfunctionprovidesalocalspectralenergydensityconcentratedaroundagivenpositionandf

7、re-quencyinacertaindirection.Atwo-dimensionalconvolutionwithacircular(non-elliptical)Gaborfunctionisseparable[7]toseriesofone-dimensionalones.J.G.DaugmandiscoveredthatsimplecellsinthevisualcortexofmammalianbrainscanbemodeledbyGaborfunctions[1].Thus,imageanalysisbytheGaborwaveletsiss

8、imilartoperceptioni