Digital Image Processing4Word下载.docx

Digital Image Processing4Word下载.docx

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imageusingtheMATLABIMAGEPROCESSINGTOOLBOXfunctionFFT2.

2） 

LowpassFilterDesign

3） 

HighpassFilterDesign

4） 

TwoDimensionalFilterDesign

C.Results

Thecommandis:

imglenna=imread（'

lenna.gif'

）;

imgFFT=fft2（double（imglenna）./255）;

imgFFT=fftshift（imgFFT）;

a） 

Computethelogmagnitudeandphase（i.e.,MATLABIMAGEPROCESSINGTOOLBOXfunction 

ANGLE.

imgLogMag=log（abs（imgFFT）+1）;

imgPhase=angle（imgFFT）;

b） 

Computetheinverse2DFFTofthe 

imageusingtheMATLABIMAGEPROCESSINGTOOLBOXfunction 

IFFT2.

imgIFFT=abs（ifft2（imgFFT））

c） 

Plottheoriginal 

image,logmagnitude,phase,andinversetransformedimages.

figure;

subplot（221）;

imshow（imglenna）;

title（'

OriginalImage'

subplot（222）;

imshow（imgLogMag,[]）;

LogMaganitudeofFFT'

subplot（223）;

imshow（imgPhase,[]）;

PhaseofFFT'

subplot（224）;

imshow（imgIFFT,[]）;

InverseFFT'

Figure1:

Original,logmagnitude,phase,andinversetransformedimages

a.）UsetheMATLABIMAGEPROCESSINGTOOLBOXfunctionFSPECIALtodesignan11x11Gaussianlowpassfilterwithavalueofsequalto1.3.

LowpassFilter=fspecial（'

gaussian'

[1111],1.3）;

b.）Computetheforward2DFFTofthefilterkernelusingthesamesizeFFTasthatofthelennaimage.UtilizetheSIZEfunctionfromtheexampleonthewebsite.

imgSize=size（imglenna）;

imgRows=imgSize

（1）;

imgCols=imgSize

（2）;

LowpassFFT=fftshift（fft2（LowpassFilter,imgRows,imgCols））;

c.）Fromtheresultsinb.）computeandplotthelogmagnitudeandphaseoftheGaussianLowpassFilterkernel.

subplot（121）;

imshow（log（abs（LowpassFFT）+1）,[]）;

LogMagnitude'

subplot（122）;

imshow（angle（LowpassFFT）,[]）;

Phase'

Figure2:

logmagnitudeandphaseoftheGaussianLowpassFilterkernel

d.）Utilizingtheresultsin1.）and2b.）performthefilteringfunctionG（u,v）=H（u,v）*F（u,v）,whereH（u,v）=2DFFToftheGaussianFilterKernel,andF（u,v）=2DFFTofthelennaimage.Plotthelogmagnitudeandphaseofthelowpassfilteredimage.imgFiltered=LowpassFFT.*imgFFT;

imshow（log（abs（imgFiltered）+1）,[]）;

imshow（angle（imgFiltered）,[]）;

Figure3:

logmagnitudeandphaseofthelowpassfilteredimage

e.）Computeandplottheinverse2DFFTofthelowpassfilteredimage.

imgLowpassFiltered=abs（ifft2（imgFiltered））;

imgLowpassFiltered=circshift（imgLowpassFiltered,[-1.*floor（length（LowpassFilter）/2）-1.*floor（length（LowpassFilter）/2）]）;

imshow（imgLowpassFiltered,[]）;

InverseFFTofLowpassFilteredImage'

Figure4:

theinverse2DFFTofthelowpassfilteredimage

a.）UsetheMATLABIMAGEPROCESSINGTOOLBOXfunctionFSPECIALtodesignalaplacianhighpassfilter.

HighpassFilter=fspecial（'

laplacian'

HighpassFFT=fftshift（fft2（HighpassFilter,imgRows,imgCols））;

c.）Fromtheresultsinb.）computeandplotthelogmagnitudeandphaseoftheLaplacianhighpassFilterkernel.

imshow（log（abs（HighpassFFT）+1）,[]）;

imshow（angle（HighpassFFT）,[]）;

Figure5:

logmagnitudeandphaseoftheLaplacianhighpassFilterkernel

d.）Utilizingtheresultsin1.）and3b.）performthefilteringfunctionG（u,v）=H（u,v）*F（u,v）,whereH（u,v）=2DFFToftheGaussianFilterKernel,andF（u,v）=2DFFTofthelennaimage.Plotthelogmagnitudeandphaseofthelowpassfilteredimage.imgFiltered=HighpassFFT.*imgFFT;

Figure6:

e.）Computeandplottheinverse2DFFTofthehighpassfilteredimageusingtheIFFT2function.

imgHighpassFiltered=abs（ifft2（imgFiltered））;

imgHighpassFiltered=circshift（imgHighpassFiltered,[-1.*floor（length（HighpassFilter）/2）-1.*floor（length（HighpassFilter）/2）]）;

imshow（imgHighpassFiltered,[]）;

InverseFFTofHighpassFilteredImage'

Figure7:

InverseFFTofHighpassFilteredImage

a.） 

Theobjectiveofthisexerciseidtoutilizethefilterdesignfunctions:

1. 

Use[f1,f2]=freqspace（21,'

meshgrid'

commandtodesignthesamplinggridforthefilter.

2. 

Once1.）iscompletedcomputetheradiusvectorsforthefollowingfilterdesignsforthefilterdesignfunctions:

Theradiusvectorsarethefollowing:

1.） 

Bandpass:

（r<

0.1）|（r>

0.6）

2.） 

Lowpass:

r>

0.6

3.） 

Highpass:

r<

[f1,f2]=freqspace（21,'

r=sqrt（f1.^2+f2.^2）;

Hd=ones（size（f1））;

Bandpass=Hd;

Lowpass=Hd;

Highpass=Hd;

Bandpass（（r<

0.1）|（r>

0.6））=0;

Lowpass（r>

0.6）=0;

Highpass（r<

b.） 

Foreachofthefilteringalgorithmsdothefollowing:

Designabandpass,lowpass,andhighpassfilter

Computetheforward2DFFTofthefilterkernelsusingthesamesizeFFTasthatofthelennaimage. 

Utilizethe 

SIZE 

functionfromtheexampleonthewebsite.

Usetheresultsin2.）computeandplotthelogmagnitudeandphaseofeachrespectivefilterkernel.

4.） 

Utilizingtheresultsin2.）performthefilteringfunctionG（u,v）=H（u,v）*F（u,v）,whereH（u,v）=2DFFToftherespectivefilterkernel,andF（u,v）=2DFFTofthelennaimage. 

Plotthelogmagnitudeandphaseofthefilteredimage.

5.） 

Computeandplottheinverse2DFFTofeachfilteredimage 

thefilterdesignfunctions:

fsamp2

BandpassFilter=fsamp2（Bandpass）;

LowpassFilter=fsamp2（Lowpass）;

HighpassFilter=fsamp2（Highpass）;

BandpassFilterFFT=fftshift（fft2（BandpassFilter,imgRows,imgCols））;

LowpassFilterFFT=fftshift（fft2（LowpassFilter,imgRows,imgCols））;

HighpassFilterFFT=fftshift（fft2（HighpassFilter,imgRows,imgCols））;

subplot（321）;

imshow（log（abs（BandpassFilterFFT）+1）,[]）;

LogMagnitudeofBandpassFilter'

subplot（322）;

imshow（angle（BandpassFilterFFT）,[]）;

PhaseofBandpassFilter'

subplot（323）;

imshow（log（abs（LowpassFilterFFT）+1）,[]）;

LogMagnitudeofLowpassFilter'

subplot（324）;

imshow（angle（LowpassFilterFFT）,[]）;

PhaseofLowpassFilter'

subplot（325）;

imshow（log（abs（HighpassFilterFFT）+1）,[]）;

LogMagnitudeofHighpassFilter'

subplot（326）;

imshow（angle（HighpassFilterFFT）,[]）;

PhaseofHighpassFilter'

%Applicationoffilterstoimage.

imgFiltered=imgFFT.*BandpassFilterFFT;

subplot（331）;

imshow（log（1+abs（imgFiltered）））;

LogMagnitudeofBandpassFilteredImage'

subplot（332）;

imshow（angle（imgFiltered））;

PhaseofBandpassFilteredImage'

subplot（333）;

imgLennaFiltered=abs（ifft2（imgFiltered））;

imgLennaFiltered=circshift（imgLennaFiltered,[-1.*floor（length（BandpassFilter）/2）-1.*floor（length（BandpassFilter）/2）]）;

imshow（imgLennaFiltered）;

InverseFFTofBandpassFilteredImage'

imgFiltered=imgFFT.*LowpassFilterFFT;

subplot（334）;

imshow（log10（1+abs（imgFiltered）））;

LogMagnitudeofLowpassFilteredImage'

subplot（335）;

imagesc（angle（imgFiltered））;

PhaseofLowpassFilteredImage'

subplot（336）;

imgLennaFiltered=circshift（imgLennaFiltered,[-1.*floor（length（LowpassFilter）/2）-1.*floor（length（LowpassFilter）/2）]）;

imgFiltered=imgFFT.*HighpassFilterFFT;

subplot（337）;

LogMagnitudeofHighpassFilteredImage'

subplot（338）;

PhaseofHighpassFilteredImage'

subplot（339）;

imgLennaFiltered=abs（ifft2（imgFiltered））;

imgLennaFiltered=circshift（imgLennaFiltered,[-1.*floor（length（HighpassFilter）/2）-1.*floor（length（HighpassFilter）/2）]）;

Figure8:

LogMagnitudeandPhaseofbandpass,lowpass,andhighpassfilter

Figure9:

logmagnitude,phaseandinverse2DFFTofeachfilteredimage

fwind1

BandpassFilter=fwind1（Bandpass,hamming（21））;

HighpassFilter=fwind1（Highpass,hamming（21））;

LowpassFilter=fwind1（Lowpass,hamming（21））;