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.ConceptofImageRestorationImagerestorationistorestoreadegradedimagebacktotheoriginalimagewhileimageenhancementistomanipulatetheimagesothatitissuitableforaspecificapplication.Degradationmodel:),(),(),(),(yxyxhyxfyxgwhereh(x,y)isasystemthatcausesimagedistortionand(x,y)isnoise.NoiseModelsNoisecannotbepredictedbutcanbeapproximatelydescribedinstatisticalwayusingtheprobabilitydensityfunction(PDF)Gaussiannoise:222/)(21)(zezpRayleighnoiseazfor0for)(2)(/)(2azeazbzpbazErlang(Gamma)noise0zfor00for)()!1()(1zeazbzazpazbbNoiseModels(cont.)ExponentialnoiseUniformnoiseImpulse(salt&pepper)noiseazaezp)(otherwise0afora-b1)(bzzpotherwise0forfor)(bzPazPzpba(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.PDF:StatisticalWaytoDescribeNoisePDFtellshowmucheachzvalueoccurs.(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.ImageDegradationwithAdditiveNoiseOriginalimageHistogramDegradedimages),(),(),(yxyxfyxg(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.OriginalimageHistogramDegradedimagesImageDegradationwithAdditiveNoise(cont.)),(),(),(yxyxfyxg(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.PeriodicNoisePeriodicnoiselookslikedotsInthefrequencydomain(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.EstimationofNoiseWecannotusetheimagehistogramtoestimatenoisePDF.ItisbettertousethehistogramofoneareaofanimagethathasconstantintensitytoestimatenoisePDF.(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.PeriodicNoiseReductionbyFreq.DomainFilteringBandrejectfilterRestoredimageDegradedimageDFTPeriodicnoisecanbereducedbysettingfrequencycomponentscorrespondingtonoisetozero.(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.BandRejectFiltersUsetoeliminatefrequencycomponentsinsomebandsPeriodicnoisefromthepreviousslidethatisFilteredout.(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.NotchRejectFiltersAnotchrejectfilterisusedtoeliminatesomefrequencycomponents.(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.NotchRejectFilter:DegradedimageDFTNotchfilter(freq.Domain)RestoredimageNoise(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.Example:ImageDegradedbyPeriodicNoiseDegradedimageDFT(noshift)RestoredimageNoiseDFTofnoiseMeanFiltersArithmeticmeanfilterormovingaveragefilter(fromChapter3)xyStstsgmnyxf),(),(1),(ˆGeometricmeanfiltermnStsxytsgyxf1),(),(),(ˆmn=sizeofmovingwindowDegradationmodel:),(),(),(),(yxyxhyxfyxgToremovethispart(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.GeometricMeanFilter:ExampleOriginalimageImagecorruptedbyAWGNImageobtainedusinga3x3geometricmeanfilterImageobtainedusinga3x3arithmeticmeanfilterAWGN:AdditiveWhiteGaussianNoiseHarmonicandContraharmonicFiltersHarmonicmeanfilterxyStstsgmnyxf),(),(1),(ˆContraharmonicmeanfilterxyxyStsQStsQtsgtsgyxf),(),(1),(),(),(ˆmn=sizeofmovingwindowWorkswellforsaltnoisebutfailsforpeppernoiseQ=thefilterorderPositiveQissuitableforeliminatingpeppernoise.NegativeQissuitableforeliminatingsaltnoise.ForQ=0,thefilterreducestoanarithmeticmeanfilter.ForQ=-1,thefilterreducestoaharmonicmeanfilter.(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.ContraharmonicFilters:ExampleImagecorruptedbypeppernoisewithprob.=0.1Imagecorruptedbysaltnoisewithprob.=0.1Imageobtainedusinga3x3contra-harmonicmeanfilterWithQ=1.5Imageobtainedusinga3x3contra-harmonicmeanfilterWithQ=-1.5(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.ContraharmonicFilters:IncorrectUseExampleImagecorruptedbypeppernoisewithprob.=0.1Imagecorruptedbysaltnoisewithprob.=0.1Imageobtainedusinga3x3contra-harmonicmeanfilterWithQ=-1.5Imageobtainedusinga3x3contra-harmonicmeanfilterWithQ=1.5Order-StatisticFilters:RevisitsubimageOriginalimageMovingwindowStatisticparametersMean,Median,Mode,Min,Max,Etc.OutputimageOrder-StatisticsFiltersMedianfilter),(median),(ˆ),(tsgyxfxyStsMaxfilter),(max),(ˆ),(tsgyxfxyStsMinfilter),(min),(ˆ),(tsgyxfxyStsMidpointfilter),(min),(max21),(ˆ),(),(tsgtsgyxfxyxyStsStsReduce“dark”noise(peppernoise)Reduce“bright”noise(saltnoise)MedianFilter:HowitworksAmedianfilterisgoodforremovingimpulse,isolatednoiseDegradedimageSaltnoisePeppernoiseMovingwindowSortedarraySaltnoisePeppernoiseMedianFilteroutputNormally,impulsenoisehashighmagnitudeandisisolated.Whenwesortpixelsinthemovingwindow,noisepixelsareusuallyattheendsofthearray.Therefore,it’srarethatthenoisepixelwillbeamedianvalue.(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.MedianFilter:ExampleImagecorruptedbysalt-and-peppernoisewithpa=pb=0.1Imagesobtainedusinga3x