数字图像处理作业.docx

数字图像处理作业.docx

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数字图像处理作业

数字图像处理实验报告

学号:

16S051049

姓名:

代烁

专业:

计算机科学与技术

日期:

2017.4.15

1Introduction1

2HistogramEqualization1

2.1CentralIdeas1

2.2ApplicationScenario1

2.3CumulativeDistributionFunction1

2.4AdvantagesandDisadvantages2

2.5Algorithm2

2.6Theresults3

3NoiseReduction5

3.1TypeofthisNoise5

3.2MedianFilter5

3.2.1MainIdea5

3.2.2ApplicationScenario6

3.2.3Algorithm6

3.2.4Theresults6

3.3AveragingFilter8

3.3.1Introduction8

3.3.2Algorithm8

3.3.3Theresults9

4Gaussianhighpassfilters10

4.1Introduction10

4.2Algorithm11

4.3Theresults11

5Conclusion15

1Introduction

Inthisprojectwemainlysolvethreeproblemsaboutimageenhancement.Thefirstquestionishistogramequalization,thesecondquestionisnoisereduction,andthethirdquestionisGaussianhighpassfilters.Isolvethethreequestionbyusingpythonprogramminglanguage.

2HistogramEqualization

2.1CentralIdeas

Thehistogramisbasedonthestatisticsofthegreylevelsofpixels.Histogramequalizationisamethodofadjustingthecontrastusingimagehistogramsinthefieldofimageprocessing.Histogramequalizationisdonebyusingthecumulativedistributionfunctiontoadjustthegrayvaluetoachievethepurposeofcontrastenhancement.Thecentralideaof​​histogramequalizationistochangethegrayhistogramoftheoriginalimagefromarelativelyconcentratedgrayscaletoauniformdistributionovertheentiregrayscale,whichincreasesthedynamicrangeofthepixelgrayscalevaluesoastoachievetheeffectofenhancingtheoverallcontrastoftheimage.Histogramequalizationisthenon-linearstretchingoftheimage,redistributeofimagepixelvalues,tomakethenumberofpixelsinacertaingrayscalerangeapproximatelythesame.Histogramequalizationistochangethehistogramdistributionofagivenimagetoauniformdistributionhistogramdistribution.

2.2ApplicationScenario

Thismethodisoftenusedtoincreasethelocalcontrastofmanyimages,especiallywhenthecontrastoftheusefuldataoftheimageisfairlyclose.Inthisway,thebrightnesscanbebetterdistributedoverthehistogram.Thiscanbeusedtoenhancethelocalcontrastwithoutaffectingtheoverallcontrast,histogramequalizationbyeffectivelyexpandingthecommonlyusedbrightnesstoachievethisfunction.Thismethodisveryusefulforbackgroundsandprospectsthataretoobrightortoodark,forexample,skeletalstructuresinX-rayimages,overexposureorunderexposurephotos.

2.3CumulativeDistributionFunction

Equalizationprocess,wemustensurethatthetwoconditions:

nomatterhowthepixelmap,wemustensurethatthegraysizerelationshipoforiginalimagekeepunchanged,thebrightareaisstillbrighter,darkstilldark,butthecontrastincreases.

Ifitisaneight-bitimage,thenthevalueofthepixelmappingfunctionshouldbebetween0and255,donotcrosstheborder.

Basedontheabovetwoconditions,thecumulativedistributionfunctionisagoodchoice,becausethecumulativedistributionfunctionisamonotonicallyincreasingfunction（Toensurethattheenhancedprocessingdoesnotdisruptthegrayscaleorderoftheoriginalimage）,andtherangeis0to1.

2.4AdvantagesandDisadvantages

Advantages

Itisafairlyintuitivetechniqueandisareversibleoperation.Iftheequalizationfunctionisknown,thentheoriginalhistogramcanberestoredandtheamountofcomputationisnotlarge.

Disadvantages

1.Thegrayscaleofthetransformedimageisreducedandsomedetailsdisappear

2.Someimages,ifthehistogramhaveapeak,aftertreatment,thecontrastisunnatural.

3.Itdoesnotselectthedatatobeprocessed,itmayincreasethecontrastofthebackgroundandreducethecontrastoftheusefulsignal

2.5Algorithm

Thehistogramequalizationalgorithmisdividedintothreesteps.

1.Countthenumberofpixelsineachappearinggraylevel.Thenmap（graylevel,thenumberofpixelsofthisgraylevel）.

2.Sortbythegraylevel

3.Foreverygraylevel,Sumallthenumberofpixelsofgraylevelbeforeitincludingthenumberofpixelsofit.Thenmap（graylevel,sumthenumberofpixelsstilltocurrentgraylevel）

4.Foreverygraylevel,normalize“sumthenumberofpixelsstilltocurrentgraylevel”

5.everynormalizedresult*255

2.6Theresults

Figure1thehistogramoforiginalimage

Figure2histogramafterhistogramequalization

Figure3originalimage

Figure4imageafterhistogramequalization

Wegettheuniformdistributionhistogramovertheentiregrayscale,comparedtothegrayhistogramoftheoriginalimagefromarelativelyconcentratedgrayscale.Weachievetheeffectofenhancingtheoverallcontrastoftheimage.

3NoiseReduction

3.1TypeofthisNoise

Figure5imageb

Wewillremovethenoisefromtheimageb.Filteringisoftenusedtoremovenoisefromimages.Wecanknowthenoiseinimagebissaltandpepper.Salt-and-peppernoisealsocalledimpulsenoise,itpresentsitselfassparselyoccurringwhiteandblackpixels.Salt-and-peppernoiseisproducedbytheimagesensor,transmissionchannel,decodingprocessing.Aswecanthoseblackorwhitepointsareverydifferentfromthepixelsaroundit,soweregardthemasexceptionvalue.Sowecanreplaceexceptionvaluewithpixelsaroundit.Aneffectivenoisereductionmethodforthistypeofnoiseisamedianfilter.Inaddition,wetrytheeffectofaveragingfilter.

3.2MedianFilter

3.2.1MainIdea

Medianfilterisanonlineardigitalfilteringtechnique.Thebasicprincipleofmedianfilteristhatwereplacethevalueofapointinthedigitalimageorasequenceofdigitwiththemedianofeachpointinneighborsofthepointinordertoeliminateisolatednoisepoints.Themethodistousetwo-dimensionalslidingtemplate,thetemplateiscalledthe“window”.Ifthewindowhasanoddnumberofpoints,itisjustthemiddlevalueafterallthepixelsinthewindowaresortednumerically.

3.2.2ApplicationScenario

Medianfilterisparticularlyeffectiveinthepresenceofsalt-and-peppernoise

3.2.3Algorithm

edge=step/2

foriinrange（edge,imageheight-edge）

forjinrange（edge,imagewidth-edge）

sum=[]

forkinrange（-edge,edge+1）:

forminrange（-edge,edge+1）:

sum.append（image[i+k][j+m]）

sum.sort（）

image[i][j]=sum[int（step*step/2）+1]

3.2.4Theresults

Figure6

medianfilter

Figure7

medianfilter

Figure8

medianfilter

WecanseefromtheFigure6-8thatmedianfilterisparticularlyeffectiveinthepresenceofsalt-and-peppernoiseandthelargerthesizeofthewindow,themoreblurrytheimagebecomes.Wecanfindthatmedianfiltercan’tfiltertheedgenoise.

3.3AveragingFilter

3.3.1Introduction

Averagingfilterisatypicallinearfilteringalgorithm.Itsprincipleisthatreplacetheoriginalpixelvaluewiththeaveragepixelofallpixelsaroundit.Averagingfilterdestroysthedetailsoftheimagewhilereducenoiseoftheimage,sothattheimagebecomesblurredandthenoiseisnotwellremoved.ForGaussiannoise,theeffectofthemeanfilteringisbetterthanthatofthemedianfilter.

3.3.2Algorithm

edge=step/2

foriinrange（edge,imageheight-edge）

forjinrange（edge,imagewidth-edge）

sum=[]

forkinrange（-edge,edge+1）:

forminrange（-edge,edge+1）:

sum.append（image[i+k][j+m]）

image[i][j]=sum.sum/（step*step）

3.3.3Theresults

Figure9

averagingfilter

WecanseefromtheFigure9thattheimageisveryblurry.Forsalt-and-peppernoise,themedianfilterisbetterthanaveragingfilter.

4Gaussianhighpassfilters

4.1Introduction

Figure10imagec

AGaussianfilterisaclassoflinearsmoothingfiltersthatselectweightsbasedontheshapeoftheGaussianfunction.TheGaussiansmoothingfilterisveryeffectiveinsuppressingnoisefromthenormaldistribution.GaussianSharpencanmakeimagelookclearerbymodifyingthedifferencebetweenthelightanddarkpoints,andcanproducemoreobviouscontrastbetweenbrightanddarkpixels.InFouriertransform,thelowfrequenciesareresponsibleforthegeneralgreylevelappearanceofanimageoversmoothareas.Thehigherfrequenciesbegintocorrespondtofasterandfastergraylevelchangesintheimage.Highpassfiltersonlypassthehighfrequencies,dropthelowones.Detailssuchasedgesandnoisesinimagesareassociatedwithhighfrequencycomponents,sowecangetedgesandfinedetailinformationbyhighpassfilters.Wewillenhancetheimageinthefrequencydomain,firstlywewillgetthediscreteFouriertransformoftheimage.

ThetransferfunctionofaGaussianhighpassfilterisdefinedas:

isthecut-offfrequency,

isthesquareofthedistancefromthepointintheimagetothecenterpoint.

4.2Algorithm

1.ThefastFouriertransformalgorithmisusedtoobtainthefrequencydistribution

2.Thedefaultresultcenterpointpositionisintheupperleftcorner,moveittothemiddleposition,getfshift

3.Getthewidthandheightofthisimage

4.MakethecutoffdistanceD0equal15,30,80

5.Getcenterpointcoordinate（m,n）ofthisimage

6.Traverseeachpointcoordinate（i,j）intheimage

7.d=thesquareof（i-m）+thesquare（n-j）

8.h=exp（-d/（2*thesquareofD0））

9.Result[i][j]=（1-h）*fshift[i][j]

10.Thenbacktothespatialdomaintorestoretheimage

4.3Theresults

Figure11Fourierspectrumoftheimagec

Figure12ResultsofGaussianhighpassfilteringwithD0=15

Figure13FourierspectrumofimageofGaussianhighpassfilteringwithD0=15

Figure14ResultsofGaussianhighpassfilteringwithD0=30

Figure15FourierspectrumofimageofGaussianhighpassfilteringwithD0=30

Figure16ResultsofGaussianhighpassfilteringwithD0=80

Figure17Fourierspect