Digital Image Processing4Word文档格式.docx
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1）
Computetheforward2DFFTofthe
lenna
imageusingtheMATLABIMAGEPROCESSINGTOOLBOXfunctionFFT2.
2）
LowpassFilterDesign
3）
HighpassFilterDesign
4）
TwoDimensionalFilterDesign
C.Results
Thecommandis:
imglenna=imread（'
lenna.gif'
）;
imgFFT=fft2（double（imglenna）./255）;
imgFFT=fftshift（imgFFT）;
ThefunctionfftshiftisusefulforvisualizingtheFouriertransformwiththezero-frequency（直流分量）componentinthemiddleofthespectrum.
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'
Theresultis:
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））;
Wecangettherowandcolumnoftheimageandusethefunctionfft2toComputetheforward2DFFTofthefilterkernel
c）Fromtheresultsinb）computeandplotthelogmagnitudeandphaseoftheGaussianLowpassFilterkernel.
subplot（121）;
imshow（log（abs（LowpassFFT）+1）,[]）;
LogMagnitude'
subplot（122）;
imshow（angle（LowpassFFT）,[]）;
Phase'
Figure2:
logmagnitudeandphaseoftheGaussianLowpassFilterkernel
Fromtheresult,wecanfindthecenteroflogmagnitudeisbrightandthephaseisalternatinglightanddarkstripes.
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
Fromtheresult,wecanfindtheimageafterlowpassfiliterisfuzzyandthehigh-frequencycomponentsoftheimagearelost.
a）UsetheMATLABIMAGEPROCESSINGTOOLBOXfunctionFSPECIALtodesignalaplacianhighpassfilter.
HighpassFilter=fspecial（'
laplacian'
HighpassFFT=fftshift（fft2（HighpassFilter,imgRows,imgCols））;
c）Fromtheresultsinb）computeandplotthelogmagnitudeandphaseoftheLaplacianhighpassFilterkernel.
imshow（log（abs（HighpassFFT）+1）,[]）;
imshow（angle（HighpassFFT）,[]）;
Figure5:
logmagnitudeandphaseoftheLaplacianhighpassFilterkernel
Fromtheresult,wecanfindthecenterofthelogmagnitudeisdarkandthereisacleardividinglineinphase.
d）Utilizingtheresultsin1）and3b）performthefilteringfunctionG（u,v）=H（u,v）*F（u,v）,whereH（u,v）=2DFFToftheGaussianFilterKernel,andF（u,v）=2DFFTofthelennaimage.Plotthelogmagnitudeandphaseofthelowpassfilteredimage.Thecommandis:
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
Fromtheresult,wecanfindtheimageafterHighpassFilteronlycontainsthecontourwithfrequencycomponents.
Theobjectiveofthisexerciseidtoutilizethefilterdesignfunctions:
1.
Use[f1,f2]=freqspace（21,'
meshgrid'
commandtodesignthesamplinggridforthefilter.
2.
Once1）iscompletedcomputetheradiusvectorsforthefollowingfilterdesignsforthefilterdesignfunctions:
Theradiusvectorsarethefollowing:
Bandpass:
（r<
0.1）|（r>
0.6）
Lowpass:
r>
0.6
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<
Foreachofthefilteringalgorithmsdothefollowing:
Designabandpass,lowpass,andhighpassfilter
Computetheforward2DFFTofthefilterkernelsusingthesamesizeFFTasthatofthelennaimage.
Utilizethe
SIZE
functionfromtheexampleonthewebsite.
Usetheresultsin2）computeandplotthelogmagnitudeandphaseofeachrespectivefilterkernel.
Utilizingtheresultsin2）performthefilteringfunctionG（u,v）=H（u,v）*F（u,v）,whereH（u,v）=2DFFToftherespectivefilterkernel,andF（u,v）=2DFFTofthelennaimage.
Plotthelogmagnitudeandphaseofthefilteredimage.
5）
Computeandplottheinverse2DFFTofeachfilteredimage.
Withthefilterdesignfunctionsfsamp2,thecommandis:
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））;
Theresultsare:
Figure8:
LogMagnitudeandPhaseofbandpass,lowpass,andhighpassfilter
Figure9:
logmagnitude,phaseandinverse2DFFTofeachfilteredimage
Fromtheresults,wecanfindthattheimageafterLowpassFilterisfuzzy.TheimageafterHighpassandBandpassisdistortionbutretaindifferentfrequencycomponentsoftheimage.
Withthefilterdesignfunctionsfwind1,thecommandis:
BandpassFilter=fwind1（Bandpass,hamming（21））;
HighpassFilter=fwind1（Highpass,hamming（21））;
LowpassFilter=fwind1（Lowpass,hamming（21））;
Theresultsare:
Figure10:
LogMagnitudeandPhaseofbandpass,lowpass,andhighpassfilter
Figure11:
Fromtheresults,wecanfindthatimageafterLowpassFilterisbetter.TheimageafterHighpassFilterretainsminimalinformation.TheimageafterBandpassFilterretainpartofinformation.
Withthefilterdesignfunctionsfwind2,thecommandis:
window=fspecial（'
21,2）;
window=window./max（max（window））;
BandpassFilter=fwind2（Bandpass,window）;
HighpassFilter=fwind2（Highpass,window）;
LowpassFilter=fwind2（Lowpass,window）;
Figure12:
Figure13:
Fromtheresults,wecanfindthattheimageafterHighpassFilterretainhighfrequencycomponentsoftheimagecontour.TheimageafterLowpassFilterlostlessinformationcomparedwiththeoriginalimage.AndtheimageafterBandpassFilterisdarkcomparedwiththeoriginalimage.
D.Conclusions
TheeffectofLowpassFilterinFrequencydomainistoremovethehighfrequencynoiseoftheimage,andtheabilitydependsontheformandcutofffrequencyofthefilter.LowpassFilterwillal
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