lec6_7 Image Enhencement in Frequency Domain

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1、ImageAnalysisandComputerVisionLecture6,7!ImageEnhencementinFrequencyDomainWeiqiangWangSchoolofInformationScienceandEngineering,GUCASSeptember30,2010W.Q.Wang(SISE,GUCAS)ImageAnalysisandComputerVisionSeptember30,20101/48Outline12-DDiscreteFourierTransform2Filt

2、eringintheFrequencyDomain3ObtainingFrequencyDomainFiltersfromSpatialFilters4GeneratingFiltersDirectlyintheFrequencyDomain5SharpeningFrequencyDomainFiltersW.Q.Wang(SISE,GUCAS)ImageAnalysisandComputerVisionSeptember30,20102/482-DDiscreteFourierTransform2-DFour

3、ierTransformAnyfunctionthatperiodicallyrepeatsitselfcanbeexpressedasthesumofsinesand/orcosinesofdierentfrequencies,eachmultipliedbyadierentcoecient(Fourierseries).Evenfunctionsthatarenotperiodic(butwhoseareaunderthecurveisnite)canbeexpressedastheintegral

4、ofsinesand/orcosinesmultipliedbyaweightingfunction(Fouriertransform).ThefrequencydomainreferstotheplaneofthetwodimensionaldiscreteFouriertransformofanimage.ThepurposeoftheFouriertransformistorepresentasignalasalinearcombinationofsinusoidalsignalsofvariousfre

5、quencies.W.Q.Wang(SISE,GUCAS)ImageAnalysisandComputerVisionSeptember30,20103/482-DDiscreteFourierTransform2-DContinuousFourierTransformTheone-dimensionalFouriertransformanditsinverseFouriertransformR1pF(u)=f(x)ej2uxdx;wherej=11InverseFouriertransform:R1f

6、(x)=F(u)ej2uxduej=cos+jsin1Thetwo-dimensionalFouriertransformanditsinverseFouriertransformF(u)=R1R1f(x;y)ej2(ux+vy)dxdy11InverseFouriertransform:f(x;y)=R1R1F(u;v)ej2(ux+vy)dudv11W.Q.Wang(SISE,GUCAS)ImageAnalysisandComputerVisionSeptember30,20104/

7、482-DDiscreteFourierTransform2-DDiscreteFourierTransformTheone-dimensionalDiscreteFouriertransform(DCT)anditsinverseFouriertransform1PM1j2uxF(u)=x=0f(x)eMforu=0;1;2;:::;M1MInverseFouriertransform:PM1j2uxf(x)=u=0F(u)eMforx=0;1;2;:::;M1Sinceej=cos+jsi

8、n,thenDCTcanberedenedas1PM12ux2uxF(u)=f(x)[cosjsin]Mx=0MMforu=0;1;2;:::;M1Frequency(time)domain:thedomain(valuesofu)overwhichthevaluesofF(u)range;becauseudeterminesthefrequencyofthecompon