数字图像处理课件英文Chapter03-空域图像增强

DigitalImageProcessingChapter3:ImageEnhancementintheSpatialDomain15June2007,SpatialDomain,Whatisspatialdomain,Thespacewhereallpixelsformanimage,Inspatialdomainwecanrepresentanimagebyf(x,y)wherexandyarecoordinatesalongxandyaxiswithrespecttoanorigin,ThereisdualitybetweenSpatialandFrequencyDomains,Imagesinthespatialdomainarepicturesinthexyplanewheretheword“distance”ismeaningful.,UsingtheFouriertransform,theword“distance”islostbuttheword“frequency”becomesalive.,ImageEnhancement,ImageEnhancementmeansimprovementofimagestobesuitableforspecificapplications.Example:Note:eachimageenhancementtechniquethatissuitableforoneapplicationmaynotbesuitableforotherapplications.,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,ImageEnhancementExample,Originalimage,EnhancedimageusingGammacorrection,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,=ImageenhancementusingprocessesperformedintheSpatialdomainresultinginimagesintheSpatialdomain.Wecanwrittenas,ImageEnhancementintheSpatialDomain,wheref(x,y)isanoriginalimage,g(x,y)isanoutputandTisafunctiondefinedintheareaaround(x,y),Note:Tmayhaveoneinputasapixelvalueat(x,y)onlyormultipleinputsaspixelsinneighborsof(x,y)dependingineachfunction.Ex.Contrastenhancementusesapixelvalueat(x,y)onlyforaninputwhilesmoothingfilteuseseveralpixelsaround(x,y)asinputs.,TypesofImageEnhancementintheSpatialDomain,-Singlepixelmethods-GrayleveltransformationsExample-Historgramequalization-Contraststretching-Arithmetic/logicoperationsExamples-Imagesubtraction-Imageaveraging-MultiplepixelmethodsExamplesSpatialfiltering-Smoothingfilters-Sharpeningfilters,GrayLevelTransformation,Transformsintensityofanoriginalimageintointensityofanoutputimageusingafunction:,wherer=inputintensityands=outputintensity,Example:Contrastenhancement,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,ImageNegative,White,Black,Inputintensity,Outputintensity,Originaldigitalmammogram,L=thenumberofgraylevels,0,L-1,L-1,Negativedigitalmammogram,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,Black,White,LogTransformations,Fourierspectrum,LogTr.ofFourierspectrum,Application,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,Power-LawTransformations,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,Power-LawTransformations:GammaCorrectionApplication,Desiredimage,ImagedisplayedatMonitor,AfterGammacorrection,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,ImagedisplayedatMonitor,Power-LawTransformations:GammaCorrectionApplication,MRIImageafterGammaCorrection,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,Power-LawTransformations:GammaCorrectionApplication,ArielimagesafterGammaCorrection,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,ContrastStretching,Beforecontrastenhancement,After,Contrastmeansthedifferencebetweenthebrightestanddarkestintensities,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,Howtoknowwherethecontrastisenhanced?,NoticetheslopeofT(r)ifSlope1ContrastincreasesifSlope1ContrastdecreaseifSlope=1nochange,Dr,Ds,SmallerDryieldswiderDs=increasingContrast,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,GrayLevelSlicing,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,Bit-planeSlicing,Bit7,Bit6,Bit2,Bit1,Bit5,Bit3,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,Histogram,Histogram=Graphofpopulationfrequencies,Gradesofthecourse178xxx,HistogramofanImage,pixel,pixel,=graphofno.ofpixelsvsintensities,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,Brightimagehashistogramontheright,Darkimagehashistogramontheleft,HistogramofanImage(cont.),lowcontrastimagehasnarrowhistogram,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,highcontrastimagehaswidehistogram,HistogramProcessing,=intensitytransformationbasedonhistograminformationtoyielddesiredhistogram,-Histogramequalization,-Histogrammatching,Tomakehistogramdistributeduniformly,Tomakehistogramasthedesire,MonotonicallyIncreasingFunction,=Functionthatisonlyincreasingorconstant,PropertiesofHistogramprocessingfunction,1.Monotonicallyincreasingfunction2.,ProbabilityDensityFunction,andrelationbetweensandris,HistogramisanalogoustoProbabilityDensityFunction(PDF)whichrepresentdensityofpopulation,LetsandrbeRandomvariableswithPDFps(s)andpr(r)respectively,Weget,HistogramEqualization,Let,Weget,!,HistogramEqualization,FormulainthepreviousslideisforacontinuousPDF,ForHistogramofDigitalImage,weuse,nj=thenumberofpixelswithintensity=jN=thenumberoftotalpixels,HistogramEqualizationExample,HistogramEqualizationExample(cont.),HistogramEqualization,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,HistogramEqualization(cont.),(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,HistogramEqualization(cont.),(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,HistogramEqualization(cont.),(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,HistogramEqualization(cont.),Originalimage,Afterhistogramequalization,theimagebecomealowcontrastimage,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,HistogramMatching:Algorithm,Concept:fromHistogramequalization,wehave,Wegetps(s)=1,WewantanoutputimagetohavePDFpz(z),Applyhistogramequalizationtopz(z),weget,Wegetpv(v)=1,Sinceps(s)=pv(v)=1thereforesandvareequivalent,Therefore,wecantransformrtozby,r,T(),s,G-1(),z,Totransformimagehistogramtobeadesiredhistogram,HistogramMatching:Algorithm(cont.),s=T(r),v=G(z),z=G-1(v),1,2,3,4,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,HistogramMatchingExample,Inputimagehistogram,DesiredHistogram,Example,Userdefine,Originaldata,HistogramMatchingExample(cont.),1.ApplyHistogramEqualizationtobothtables,sk=T(rk),vk=G(zk),HistogramMatchingExample(cont.),2.Getamap,sk=T(rk),zk=G-1(vk),rs,vz,sv,Weget,ActualOutputHistogram,HistogramMatchingExample(cont.),Desiredhistogram,Transferfunction,Actualhistogram,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,HistogramMatchingExample(cont.),Originalimage,Afterhistogramequalization,Afterhistogrammatching,LocalEnhancement:LocalHistogramEqualization,Concept:Performhistogramequalizationinasmallneighborhood,Orignalimage,AfterHistEq.,AfterLocalHistEq.In7x7neighborhood,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,LocalEnhancement:HistogramStatisticforImageEnhancement,WecanusestatisticparameterssuchasMean,VarianceofLocalareaforimageenhancement,ImageoftungstenfilamenttakenusingAnelectronmicroscope,Inthelowerrightcorner,thereisafilamentinthebackgroundwhichisverydarkandwewantthistobebrighter.,Wecannotincreasethebrightnessofthewholeimagesincethewhitefilamentwillbetoobright.,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,LocalEnhancement,Example:Localenhancementforthistask,Originalimage,LocalVarianceimage,Multiplicationfactor,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,LocalEnhancement,Outputimage,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,LogicOperations,AND,OR,ResultRegionofInterest,Imagemask,Originalimage,Application:Cropareasofinterest,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,ArithmeticOperation:Subtraction,Errorimage,Application:Errormeasurement,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,ArithmeticOperation:Subtraction(cont.),Application:Maskmoderadiographyinangiographywork,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,ArithmeticOperation:ImageAveraging,Application:Noisereduction,AveragingresultsinreductionofNoisevariance,Degradedimage,(noise),Imageaveraging,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,ArithmeticOperation:ImageAveraging(cont.),(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,SometimeweneedtomanipulatevaluesobtainedfromneighboringpixelsExample:Howcanwecomputeanaveragevalueofpixelsina3x3regioncenteratapixelz?,4,4,6,7,6,1,9,2,2,2,7,5,2,2,6,4,4,5,2,1,2,1,3,3,4,2,9,5,7,7,3,5,8,2,2,2,Pixelz,Image,BasicsofSpatialFiltering,4,4,6,7,6,1,9,2,2,2,7,5,2,2,6,4,4,5,2,1,2,1,3,3,4,2,9,5,7,7,3,5,8,2,2,2,Pixelz,Step1.Selectedonlyneededpixels,4,6,7,6,9,1,3,3,4,BasicsofSpatialFiltering(cont.),Step2.Multiplyeverypixelby1/9andthensumupthevalues,X,MaskorWindoworTemplate,BasicsofSpatialFiltering(cont.),Question:Howtocomputethe3x3averagevaluesateverypixels?,4,4,6,7,6,1,9,2,2,2,7,5,2,2,6,4,4,5,2,1,2,1,3,3,4,2,9,5,7,7,Solution:Imaginethatwehavea3x3windowthatcanbeplacedeverywhereontheimage,MaskingWindow,BasicsofSpatialFiltering(cont.),4.3,Step1:Movethewindowtothefirstlocationwherewewanttocomputetheaveragevalueandthenselectonlypixelsinsidethewindow.,Step2:Computetheaveragevalue,Subimagep,Originalimage,Outputimage,Step3:Placetheresultatthepixelintheoutputimage,Step4:MovethewindowtothenextlocationandgotoStep2,BasicsofSpatialFiltering(cont.),The3x3averagingmethodisoneexampleofthemaskoperationorSpatialfiltering.wThemaskoperationhasthecorrespondingmask(sometimescalledwindowortemplate).wThemaskcontainscoefficientstobemultipliedwithpixelvalues.,Maskcoefficients,Example:movingaveraging,Themaskofthe3x3movingaveragefilterhasallcoefficients=1/9,BasicsofSpatialFiltering(cont.),Themaskoperationateachpointisperformedby:1.Movethereferencepoint(center)ofmasktothelocationtobecomputed2.Computesumofproductsbetweenmaskcoefficientsandpixelsinsubimageunderthemask.,Subimage,Maskcoefficients,Maskframe,Thereferencepointofthemask,BasicsofSpatialFiltering(cont.),Thespatialfilteringonthewholeimageisgivenby:Movethemaskovertheimageateachlocation.Computesumofproductsbetweenthemaskcoefficeintsandpixelsinsidesubimageunderthemask.Storetheresultsatthecorrespondingpixelsoftheoutputimage.Movethemasktothenextlocationandgotostep2untilallpixellocationshavebeenused.,BasicsofSpatialFiltering(cont.),ExamplesofSpatialFilteringMasks,Examplesofthemasks,Sobeloperators,3x3movingaveragefilter,3x3sharpeningfilter,SmoothingLinearFilter:MovingAverage,Application:noisereductionandimagesmoothing,Disadvantage:losesharpdetails,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,SmoothingLinearFilter(cont.),(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,Order-StatisticFilters,subimage,Originalimage,Movingwindow,StatisticparametersMean,Median,Mode,Min,Max,Etc.,Outputimage,Order-StatisticFilters:MedianFilter,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,SharpeningSpatialFilters,Thereareintensitydiscontinuitiesnearobjectedgesinanimage,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,LaplacianSharpening:Howitworks,Intensityprofile,1stderivative,2ndderivative,p(x),Edge,LaplacianSharpening:Howitworks(cont.),Laplaciansharpeningresultsinlargerintensitydiscontinuityneartheedge.,p(x),LaplacianSharpening:Howitworks(cont.),p(x),Beforesharpening,Aftersharpening,LaplacianMasks,Application:Enhanc