數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03 空域圖像增強課件

DigitalImageProcessingChapter3:ImageEnhancementintheSpatialDomain15June2007數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強SpatialDomainWhatisspatialdomainThespacewhereallpixelsformanimageInspatialdomainwecanrepresentanimagebyf(x,y)wherexandyarecoordinatesalongxandyaxiswithrespecttoanoriginThereisdualitybetweenSpatialandFrequencyDomainsImagesinthespatialdomainarepicturesinthexyplanewheretheword“distance”ismeaningful.UsingtheFouriertransform,theword“distance”islostbuttheword“frequency”becomesalive.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強ImageEnhancementImageEnhancementmeansimprovementofimagestobesuitableforspecificapplications.Example:Note:eachimageenhancementtechniquethatissuitableforoneapplicationmaynotbesuitableforotherapplications.(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強ImageEnhancementExampleOriginalimageEnhancedimageusingGammacorrection(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強=ImageenhancementusingprocessesperformedintheSpatialdomainresultinginimagesintheSpatialdomain.WecanwrittenasImageEnhancementintheSpatialDomainwheref(x,y)isanoriginalimage,g(x,y)isanoutputandT[]isafunctiondefinedintheareaaround(x,y)Note:T[]mayhaveoneinputasapixelvalueat(x,y)onlyormultipleinputsaspixelsinneighborsof(x,y)dependingineachfunction.Ex.Contrastenhancementusesapixelvalueat(x,y)onlyforaninputwhilesmoothingfilteuseseveralpixelsaround(x,y)asinputs.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強TypesofImageEnhancementintheSpatialDomain-Singlepixelmethods -Grayleveltransformations Example -Historgramequalization -Contraststretching -Arithmetic/logicoperations Examples -Imagesubtraction -Imageaveraging-Multiplepixelmethods Examples Spatialfiltering -Smoothingfilters -Sharpeningfilters數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強GrayLevelTransformationTransformsintensityofanoriginalimageintointensityofanoutputimageusingafunction:wherer=inputintensityands=outputintensityExample:Contrastenhancement(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強ImageNegativeWhiteBlackInputintensityOutputintensityOriginaldigitalmammogramL=thenumberofgraylevels0L-1L-1Negativedigitalmammogram(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.BlackWhite數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強LogTransformationsFourierspectrumLogTr.ofFourierspectrumApplication(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強Power-LawTransformations(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強Power-LawTransformations:GammaCorrectionApplicationDesiredimageImagedisplayedatMonitorAfterGammacorrection(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.ImagedisplayedatMonitor數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強Power-LawTransformations:GammaCorrectionApplicationMRIImageafterGammaCorrection(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強Power-LawTransformations:GammaCorrectionApplicationArielimagesafterGammaCorrection(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強ContrastStretchingBeforecontrastenhancementAfterContrastmeansthedifferencebetweenthebrightestanddarkestintensities(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強Howtoknowwherethecontrastisenhanced?NoticetheslopeofT(r)ifSlope>1

ContrastincreasesifSlope<1

ContrastdecreaseifSlope=1

nochangeDrDsSmallerDryieldswiderDs=increasingContrast(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強GrayLevelSlicing(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強Bit-planeSlicingBit7Bit6Bit2Bit1Bit5Bit3(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強HistogramHistogram=GraphofpopulationfrequenciesGradesofthecourse178xxx數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強HistogramofanImage?????pixel?????pixel=graphofno.ofpixelsvsintensities(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.BrightimagehashistogramontherightDarkimagehashistogramontheleft數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強HistogramofanImage(cont.)lowcontrastimagehasnarrowhistogram(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.highcontrastimagehaswidehistogram數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強HistogramProcessing=intensitytransformationbasedonhistograminformationtoyielddesiredhistogram-Histogramequalization-HistogrammatchingTomakehistogramdistributeduniformlyTomakehistogramasthedesire數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強MonotonicallyIncreasingFunction=FunctionthatisonlyincreasingorconstantPropertiesofHistogramprocessingfunction1.Monotonicallyincreasingfunction2.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強ProbabilityDensityFunctionandrelationbetweensandris

HistogramisanalogoustoProbabilityDensityFunction(PDF)whichrepresentdensityofpopulationLetsandrbeRandomvariableswithPDFps(s)andpr(r)respectivelyWeget數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強HistogramEqualizationLetWeget!數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強HistogramEqualizationFormulainthepreviousslideisforacontinuousPDFForHistogramofDigitalImage,weusenj=thenumberofpixelswithintensity=jN=thenumberoftotalpixels數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強HistogramEqualizationExampleIntensity#pixels0201522531041555610710Total100AccumulativeSumofPr20/100=0.2(20+5)/100=0.25(20+5+25)/100=0.5(20+5+25+10)/100=0.6(20+5+25+10+15)/100=0.75(20+5+25+10+15+5)/100=0.8(20+5+25+10+15+5+10)/100=0.9(20+5+25+10+15+5+10+10)/100=1.01.0數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強HistogramEqualizationExample(cont.)Intensity(r)No.ofPixels(nj)AccSumofPrOutputvalueQuantizedOutput(s)0200.20.2x7=1.41150.250.25*7=1.7522250.50.5*7=3.533100.60.6*7=4.244150.750.75*7=5.255550.80.8*7=5.666100.90.9*7=6.367101.01.0x7=77Total100數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強HistogramEqualization(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強HistogramEqualization(cont.)(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強HistogramEqualization(cont.)(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強HistogramEqualization(cont.)(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強HistogramEqualization(cont.)OriginalimageAfterhistogramequalization,theimagebecomealowcontrastimage(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強HistogramMatching

:AlgorithmConcept:fromHistogramequalization,wehaveWegetps(s)=1WewantanoutputimagetohavePDFpz(z)Applyhistogramequalizationtopz(z),wegetWegetpv(v)=1Sinceps(s)=pv(v)=1thereforesandvareequivalentTherefore,wecantransformrtozbyrT()sG-1()zTotransformimagehistogramtobeadesiredhistogram數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強HistogramMatching:Algorithm(cont.)s=T(r)v=G(z)z=G-1(v)1234(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強HistogramMatchingExampleIntensity(s)#pixels0201522531041555610710Total100InputimagehistogramIntensity(z)#pixels0511021532042051561075Total100DesiredHistogramExampleUserdefineOriginaldata數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強r(nj)SPrs0200.21150.2522250.533100.644150.755550.866100.967101.07HistogramMatchingExample(cont.)1.ApplyHistogramEqualizationtobothtablesz(nj)SPzv050.0501100.1512150.323200.544200.755150.8566100.957751.07sk=T(rk)vk=G(zk)數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強rs0112233445566677HistogramMatchingExample(cont.)2.Getamapvz0011224354657677sk=T(rk)zk=G-1(vk)rsvzsvWegetrz0112223344556576z#Pixels0012023031041551561070ActualOutputHistogram數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強HistogramMatchingExample(cont.)DesiredhistogramTransferfunctionActualhistogram(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強HistogramMatchingExample(cont.)OriginalimageAfterhistogramequalizationAfterhistogrammatching數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強LocalEnhancement:LocalHistogramEqualizationConcept:PerformhistogramequalizationinasmallneighborhoodOrignalimageAfterHistEq.AfterLocalHistEq.In7x7neighborhood(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強LocalEnhancement:HistogramStatisticforImageEnhancementWecanusestatisticparameterssuchasMean,VarianceofLocalareaforimageenhancementImageoftungstenfilamenttakenusingAnelectronmicroscopeInthelowerrightcorner,thereisafilamentinthebackgroundwhichisverydarkandwewantthistobebrighter.Wecannotincreasethebrightnessofthewholeimagesincethewhitefilamentwillbetoobright.(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強LocalEnhancementExample:LocalenhancementforthistaskOriginalimageLocalVarianceimageMultiplicationfactor(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強LocalEnhancementOutputimage(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強LogicOperationsANDORResultRegionofInterestImagemaskOriginalimageApplication:Cropareasofinterest(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強ArithmeticOperation:SubtractionErrorimageApplication:Errormeasurement(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強ArithmeticOperation:Subtraction(cont.)Application:Maskmoderadiographyinangiographywork(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強ArithmeticOperation:ImageAveragingApplication:NoisereductionAveragingresultsinreductionofNoisevarianceDegradedimage(noise)Imageaveraging(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強ArithmeticOperation:ImageAveraging(cont.)(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強SometimeweneedtomanipulatevaluesobtainedfromneighboringpixelsExample:Howcanwecomputeanaveragevalueofpixelsina3x3regioncenteratapixelz?446761922275226445212133429577358222PixelzImageBasicsofSpatialFiltering數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強446761922275226445212133429577358222PixelzStep1.Selectedonlyneededpixels467691334…………BasicsofSpatialFiltering(cont.)數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強467691334…………Step2.Multiplyeverypixelby1/9andthensumupthevalues111111111XMaskorWindoworTemplateBasicsofSpatialFiltering(cont.)數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強Question:Howtocomputethe3x3averagevaluesateverypixels?446761922275226445212133429577Solution:Imaginethatwehavea3x3windowthatcanbeplacedeverywhereontheimageMaskingWindowBasicsofSpatialFiltering(cont.)數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強4.3Step1:Movethewindowtothefirstlocationwherewewanttocomputetheaveragevalueandthenselectonlypixelsinsidethewindow.446761922275226445212133429577Step2:ComputetheaveragevalueSubimagepOriginalimage419223297OutputimageStep3:Placetheresultatthepixelintheoutputimage

Step4:MovethewindowtothenextlocationandgotoStep2BasicsofSpatialFiltering(cont.)數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強The3x3averagingmethodisoneexampleofthemaskoperationorSpatialfiltering.wThemaskoperationhasthecorrespondingmask(sometimescalledwindowortemplate).wThemaskcontainscoefficientstobemultipliedwithpixelvalues.w(2,1)w(3,1)w(3,3)w(2,2)w(3,2)w(3,2)w(1,1)w(1,2)w(3,1)Maskcoefficients111111111Example:movingaveragingThemaskofthe3x3movingaveragefilterhasallcoefficients=1/9BasicsofSpatialFiltering(cont.)數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強Themaskoperationateachpointisperformedby:1.Movethereferencepoint(center)ofmasktothelocationtobecomputed2.Computesumofproductsbetweenmaskcoefficientsandpixelsinsubimageunderthemask.p(2,1)p(3,2)p(2,2)p(2,3)p(2,1)p(3,3)p(1,1)p(1,3)p(3,1)…………Subimagew(2,1)w(3,1)w(3,3)w(2,2)w(3,2)w(3,2)w(1,1)w(1,2)w(3,1)MaskcoefficientsMaskframeThereferencepointofthemaskBasicsofSpatialFiltering(cont.)數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強Thespatialfilteringonthewholeimageisgivenby:Movethemaskovertheimageateachlocation.Computesumofproductsbetweenthemaskcoefficeints andpixelsinsidesubimageunderthemask.Storetheresultsatthecorrespondingpixelsofthe outputimage.Movethemasktothenextlocationandgotostep2 untilallpixellocationshavebeenused.BasicsofSpatialFiltering(cont.)數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強ExamplesofSpatialFilteringMasksExamplesofthemasksSobeloperators011002-1-2-1-2-11020-1011111111113x3movingaveragefilter-1-1-18-1-1-1-1-13x3sharpeningfilter數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強SmoothingLinearFilter:MovingAverageApplication:noisereductionandimagesmoothingDisadvantage:losesharpdetails(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強SmoothingLinearFilter(cont.)(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強Order-StatisticFilterssubimageOriginalimageMovingwindowStatisticparametersMean,Median,Mode,Min,Max,Etc.Outputimage數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強Order-StatisticFilters:MedianFilter(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強SharpeningSpatialFiltersThereareintensitydiscontinuitiesnearobjectedgesinanimage(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強LaplacianSharpening:HowitworksIntensityprofile1stderivative2ndderivativep(x)Edge數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強LaplacianSharpening:Howitworks(cont.)

Laplaciansharpeningresultsinlargerintensitydiscontinuityneartheedge.p(x)數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強LaplacianSharpening:Howitworks(cont.)p(x)BeforesharpeningAftersharpening數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強LaplacianMasks-1-1-18-1-1-1-1-1-1004-1-10-10111-811111100-411010Application:Enhanceedge,line,pointDisadvantage:EnhancenoiseUsedforestimatingimageLaplacianorThecenterofthemaskispositiveThecenterofthemaskisnegative數(shù)字圖像處理-岡薩雷斯-(英文)Chapter03空域圖像增強Laplacian