数字图像处理,冈萨雷斯,课件英文版 Chapter05 图像复原

DigitalImageProcessingChapter5:ImageRestoration23June2006,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,ConceptofImageRestoration,Imagerestorationistorestoreadegradedimagebacktotheoriginalimagewhileimageenhancementistomanipulatetheimagesothatitissuitableforaspecificapplication.,Degradationmodel:,whereh(x,y)isasystemthatcausesimagedistortionandh(x,y)isnoise.,NoiseModels,Noisecannotbepredictedbutcanbeapproximatelydescribedinstatisticalwayusingtheprobabilitydensityfunction(PDF),Gaussiannoise:,Rayleighnoise,Erlang(Gamma)noise,NoiseModels(cont.),Exponentialnoise,Uniformnoise,Impulse(salt&pepper)noise,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,PDF:StatisticalWaytoDescribeNoise,PDFtellshowmucheachzvalueoccurs.,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,ImageDegradationwithAdditiveNoise,Originalimage,Histogram,Degradedimages,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,Originalimage,Histogram,Degradedimages,ImageDegradationwithAdditiveNoise(cont.),(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,PeriodicNoise,PeriodicnoiselookslikedotsInthefrequencydomain,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,EstimationofNoise,WecannotusetheimagehistogramtoestimatenoisePDF.,ItisbettertousethehistogramofoneareaofanimagethathasconstantintensitytoestimatenoisePDF.,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,PeriodicNoiseReductionbyFreq.DomainFiltering,Bandrejectfilter,Restoredimage,Degradedimage,DFT,Periodicnoisecanbereducedbysettingfrequencycomponentscorrespondingtonoisetozero.,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,BandRejectFilters,Usetoeliminatefrequencycomponentsinsomebands,PeriodicnoisefromthepreviousslidethatisFilteredout.,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,NotchRejectFilters,Anotchrejectfilterisusedtoeliminatesomefrequencycomponents.,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,NotchRejectFilter:,Degradedimage,DFT,Notchfilter(freq.Domain),Restoredimage,Noise,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,Example:ImageDegradedbyPeriodicNoise,Degradedimage,DFT(noshift),Restoredimage,Noise,DFTofnoise,MeanFilters,Arithmeticmeanfilterormovingaveragefilter(fromChapter3),Geometricmeanfilter,mn=sizeofmovingwindow,Degradationmodel:,Toremovethispart,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,GeometricMeanFilter:Example,Originalimage,ImagecorruptedbyAWGN,Imageobtainedusinga3x3geometricmeanfilter,Imageobtainedusinga3x3arithmeticmeanfilter,AWGN:AdditiveWhiteGaussianNoise,HarmonicandContraharmonicFilters,Harmonicmeanfilter,Contraharmonicmeanfilter,mn=sizeofmovingwindow,Workswellforsaltnoisebutfailsforpeppernoise,Q=thefilterorder,PositiveQissuitableforeliminatingpeppernoise.NegativeQissuitableforeliminatingsaltnoise.,ForQ=0,thefilterreducestoanarithmeticmeanfilter.ForQ=-1,thefilterreducestoaharmonicmeanfilter.,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,ContraharmonicFilters:Example,Imagecorruptedbypeppernoisewithprob.=0.1,Imagecorruptedbysaltnoisewithprob.=0.1,Imageobtainedusinga3x3contra-harmonicmeanfilterWithQ=1.5,Imageobtainedusinga3x3contra-harmonicmeanfilterWithQ=-1.5,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,ContraharmonicFilters:IncorrectUseExample,Imagecorruptedbypeppernoisewithprob.=0.1,Imagecorruptedbysaltnoisewithprob.=0.1,Imageobtainedusinga3x3contra-harmonicmeanfilterWithQ=-1.5,Imageobtainedusinga3x3contra-harmonicmeanfilterWithQ=1.5,Order-StatisticFilters:Revisit,subimage,Originalimage,Movingwindow,StatisticparametersMean,Median,Mode,Min,Max,Etc.,Outputimage,Order-StatisticsFilters,Medianfilter,Maxfilter,Minfilter,Midpointfilter,Reduce“dark”noise(peppernoise),Reduce“bright”noise(saltnoise),MedianFilter:Howitworks,Amedianfilterisgoodforremovingimpulse,isolatednoise,Degradedimage,Saltnoise,Peppernoise,Movingwindow,Sortedarray,Saltnoise,Peppernoise,Median,Filteroutput,Normally,impulsenoisehashighmagnitudeandisisolated.Whenwesortpixelsinthemovingwindow,noisepixelsareusuallyattheendsofthearray.,Therefore,itsrarethatthenoisepixelwillbeamedianvalue.,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,MedianFilter:Example,Imagecorruptedbysalt-and-peppernoisewithpa=pb=0.1,Imagesobtainedusinga3x3medianfilter,1,4,2,3,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,MaxandMinFilters:Example,Imagecorruptedbypeppernoisewithprob.=0.1,Imagecorruptedbysaltnoisewithprob.=0.1,Imageobtainedusinga3x3maxfilter,Imageobtainedusinga3x3minfilter,Alpha-trimmedMeanFilter,wheregr(s,t)representtheremainingmn-dpixelsafterremovingthed/2highestandd/2lowestvaluesofg(s,t).,Thisfilterisusefulinsituationsinvolvingmultipletypesofnoisesuchasacombinationofsalt-and-pepperandGaussiannoise.,Formula:,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,Alpha-trimmedMeanFilter:Example,Imagecorruptedbyadditiveuniformnoise,Imageobtainedusinga5x5arithmeticmeanfilter,Imageadditionallycorruptedbyadditivesalt-and-peppernoise,1,2,2,Imageobtainedusinga5x5geometricmeanfilter,2,Alpha-trimmedMeanFilter:Example(cont.),Imagecorruptedbyadditiveuniformnoise,Imageobtainedusinga5x5medianfilter,Imageadditionallycorruptedbyadditivesalt-and-peppernoise,1,2,2,Imageobtainedusinga5x5alpha-trimmedmeanfilterwithd=5,2,Alpha-trimmedMeanFilter:Example(cont.),Imageobtainedusinga5x5arithmeticmeanfilter,Imageobtainedusinga5x5geometricmeanfilter,Imageobtainedusinga5x5medianfilter,Imageobtainedusinga5x5alpha-trimmedmeanfilterwithd=5,AdaptiveFilter,FilterbehaviordependsonstatisticalcharacteristicsoflocalareasinsidemxnmovingwindowMorecomplexbutsuperiorperformancecomparedwith“fixed”filters,Statisticalcharacteristics:,Generalconcept:,Localmean:,Localvariance:,Noisevariance:,Adaptive,LocalNoiseReductionFilter,Purpose:wanttopreserveedges,1.Ifsh2iszero,Nonoisethefiltershouldreturng(x,y)becauseg(x,y)=f(x,y)2.IfsL2ishighrelativetosh2,Edges(shouldbepreserved),thefiltershouldreturnthevalueclosetog(x,y)3.IfsL2=sh2,AreasinsideobjectsthefiltershouldreturnthearithmeticmeanvaluemL,Formula:,Concept:,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,AdaptiveNoiseReductionFilter:Example,ImagecorruptedbyadditiveGaussiannoisewithzeromeanands2=1000,Imageobtainedusinga7x7arithmeticmeanfilter,Imageobtainedusinga7x7geometricmeanfilter,Imageobtainedusinga7x7adaptivenoisereductionfilter,Algorithm:,LevelA:A1=zmedianzminA2=zmedianzmaxIfA10andA20andB20,returnzxyElsereturnzmedian,AdaptiveMedianFilter,zmin=minimumgraylevelvalueinSxyzmax=maximumgraylevelvalueinSxyzmedian=medianofgraylevelsinSxyzxy=graylevelvalueatpixel(x,y)Smax=maximumallowedsizeofSxy,where,Purpose:wanttoremoveimpulsenoisewhilepreservingedges,LevelA:A1=zmedianzminA2=zmedianzmaxElseWindowisnotbigenoughincreasewindowsizeIfwindowsize0andB20andA20,gotolevelB,LevelB:,Determinewhetherzmedianisanimpulseornot,Determinewhetherzxyisanimpulseornot,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,AdaptiveMedianFilter:Example,Imagecorruptedbysalt-and-peppernoisewithpa=pb=0.25,Imageobtainedusinga7x7medianfilter,ImageobtainedusinganadaptivemedianfilterwithSmax=7,Moresmalldetailsarepreserved,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,EstimationofDegradationModel,Degradationmodel:,Purpose:toestimateh(x,y)orH(u,v),Methods:1.EstimationbyImageObservation2.EstimationbyExperiment3.EstimationbyModeling,or,Why?,Ifweknowexactlyh(x,y),regardlessofnoise,wecandodeconvolutiontogetf(x,y)backfromg(x,y).,EstimationbyImageObservation,f(x,y),f(x,y)*h(x,y),g(x,y),Subimage,ReconstructedSubimage,DFT,DFT,Restorationprocessbyestimation,Originalimage(unknown),Degradedimage,EstimatedTransferfunction,Observation,Thiscaseisusedwhenweknowonlyg(x,y)andcannotrepeattheexperiment!,EstimationbyExperiment,Usedwhenwehavethesameequipmentsetupandcanrepeattheexperiment.,Inputimpulseimage,SystemH(),Responseimagefromthesystem,DFT,DFT,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,EstimationbyModeling,Usedwhenweknowphysicalmechanismunderlyingtheimageformationprocessthatcanbeexpressedmathematically.,AtmosphericTurbulencemodel,Example:,Originalimage,Severeturbulence,k=0.00025,k=0.001,k=0.0025,Lowturbulence,Mildturbulence,EstimationbyModeling:MotionBlurring,Assumethatcameravelocityis,Theblurredimageisobtainedby,whereT=exposuretime.,EstimationbyModeling:MotionBlurring(cont.),Thenweget,themotionblurringtransferfunction:,Forconstantmotion,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,MotionBlurringExample,Forconstantmotion,Originalimage,Motionblurredimagea=b=0.1,T=1,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,InverseFilter,afterweobtainH(u,v),wecanestimateF(u,v)bytheinversefilter:,Fromdegradationmodel:,NoiseisenhancedwhenH(u,v)issmall.,Toavoidthesideeffectofenhancingnoise,ponent(u,v)withinaradiusD0fromthecenterofH(u,v).,Inpractical,theinversefilterisnotPopularlyused.,InverseFilter:Example,Originalimage,BlurredimageDuetoTurbulence,Resultofapplyingthefullfilter,ResultofapplyingthefilterwithD0=70,ResultofapplyingthefilterwithD0=40,ResultofapplyingthefilterwithD0=85,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,WienerFilter:MinimumMeanSquareErrorFilter,Objective:optimizemeansquareerror:,WienerFilterFormula:,where,H(u,v)=DegradationfunctionSh(u,v)=PowerspectrumofnoiseSf(u,v)=Powerspectrumoftheundegradedimage,ApproximationofWienerFilter,WienerFilterFormula:,ApproximatedFormula:,Difficulttoestimate,Practically,Kischosenmanuallytoobtainedthebestvisualresult!,WienerFilter:Example,Originalimage,BlurredimageDuetoTurbulence,Resultofthefullinversefilter,ResultoftheinversefilterwithD0=70,ResultofthefullWienerfilter,WienerFilter:Example(cont.),Originalimage,ResultoftheinversefilterwithD0=70,ResultoftheWienerfilter,BlurredimageDuetoTurbulence,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,Example:WienerFilterandMotionBlurring,Imagedegradedbymotionblur+AWGN,Resultoftheinversefilter,ResultoftheWienerfilter,sh2=650,sh2=325,sh2=130,Note:Kischosenmanually,Degradationmodel:,Writteninamatrixform,ConstrainedLeastSquaresFilter,Objective:tofindtheminimumofacriterionfunction,Subjecttotheconstraint,Wegetaconstrainedleastsquarefilter,where,P(u,v)=Fouriertransformofp(x,y)=,where,ConstrainedLeastSquaresFilter:Example,Constrainedleastsquarefilter,gisadaptivelyadjustedtoachievethebestresult.,Resultsfromthepreviousslideobtainedfromtheconstrainedleastsquarefilter,ConstrainedLeastSquaresFilter:Example(cont.),Imagedegradedbymotionblur+AWGN,ResultoftheConstrainedLeastsquarefilter,ResultoftheWienerfilter,sh2=650,sh2=325,sh2=130,ConstrainedLeastSquaresFilter:Adjustingg,Define,Itcanbeshownthat,Wewanttoadjustgammasothat,wherea=accuracyfactor,SpecifyaninitialvalueofgComputeStopifissatisfiedOtherwisereturnstep2afterincreasinggifordecreasinggifUsethenewvalueofgtorecompute,1,1,ConstrainedLeastSquaresFilter:Adjustingg(cont.),Forcomputing,Forcomputing,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.,ConstrainedLeastSquaresFilter:Example,Originalimage,BlurredimageDuetoTurbulence,Resultsobtainedfromconstrainedleastsquarefilters,Usewrongnoiseparameters,Correctparameters:Initialg=10-5Correctionfactor=10-6a=0.25sh2=10-5,Wrongnoiseparametersh2=10-2,Usecorrectnoiseparameters,GeometricMeanfilter,Thisfilterrepresentsafamilyoffilterscombinedintoasingleexpression,a=1theinversefiltera=0theParametricWienerfiltera=0,b=1thestandardWienerfilterb=1,a0.5MoreliketheWienerfilter,Anothername:thespectrumequalizationfilter,GeometricTransformation,Thesetransformationsareoftencalledrubber-sheettransformations:Printinganimageonarubbersheetandthenstretchthissheetaccordingtosomepredefinesetofrules.,Ageometrictransformationconsistsof2basicoperations:1.Aspatialtransformation:Definehowpixelsaretoberearrangedinthespatiallytransformedimage.2.Graylevelinterpolation:Assigngraylevelvaluestopixelsinthespatiallytransformedimage.,GeometricTransformation:Algorithm,Distortedimageg,Selectcoordinate(x,y)inftoberestoredCompute,3.Gotopixelinadistortedimageg,Imageftoberestored,4.getpixelvalu