數(shù)字圖像處理-第四章4

數(shù)字圖像處理-第四章4第一頁，共53頁。ObjectiveVeryoften,asignalorimagehasthemajorityofitsenergyinthelow-andmid-frequencyrangeofitsamplitudespectrum.Atthehigherfrequencies,theinformationofinterestisoftenburiedbynoise.Thus,afilterthatreducestheamplitudeofhigh-frequencycomponentscanreducethevisibleeffectsofnoise.4.1LowpassFilters第二頁，共53頁。第三頁，共53頁。4.1Low-passFilters4.1.1Linearfilter--TheboxFilterArectangularpulse,calledamoving-averagefilter.第四頁，共53頁。ItsFouriertransformisasincfunctionsin(s)/s.Itcanbeseenthatthelowerfrequenciesgetrelativehigheroutput.第五頁，共53頁。Bythesimilaritytheorem,thewidthofthetransferfunctionisreverselyproportionaltothewidthoftheimpulseresponse.Thewiderthewidthofthepulse,thelessthehighfrequencycomponentspass,andthemorethedangerofreversalphaseforsmallstructures.第六頁，共53頁。Sometimescalledaweighted-averagefilter.In2dimensions,ittakesontheappearanceofapyramid.Thespectrumofthetriangularpulsehastheformof[sin(s)/s]2.Itissafewithoutfearofphasereversal,becauseofthenon-negativespectrum.4.1Low-passFilters4.1.2Linearfilter—TheTriangularFilter第七頁，共53頁。DirectlymakethefrequenciesoutsideD0zero.Theimpulseresponseofthetransferfunctionisasinc.4.1LowpassFilters4.1.3Linearfilter--TheIdealLow-passFilter(ILPF)HighFrequencyCuttoff第八頁，共53頁。ringingeffectf(x)h(x)g(x)第九頁，共53頁。Thedrawbackofthisfilterfunctionisaringingeffectthatoccursalongtheedgesofthefilteredspatialdomainimage.Forthisreason,sharpcutoffinthefrequencydomainisoflimitedusefulness.第十頁，共53頁。第十一頁，共53頁。4.1Low-passFilters4.1.4Linearfilter--TheGaussianLow-passFilter

第十二頁，共53頁。4.1Low-passFilters4.1.6Non-Linearfilter–

Butterworthfilter第十三頁，共53頁。Impulseresponse第十四頁，共53頁。D0=10Morecomparison第十五頁，共53頁。第十六頁，共53頁。4.1LowpassFilters4.1.5Non-Linearfilter--

TheMedianFilter第十七頁，共53頁。Ingeneral,themedianfilterallowsagreatdealofhighspatialfrequencydetailtopasswhileremainingveryeffectiveatremovingnoiseonimageswherelessthanhalfofthepixelsinasmoothingneighbourhoodhavebeeneffected.Oneofthemajorproblemswiththemedianfilteristhatitisrelativelyexpensiveandcomplextocompute.第十八頁，共53頁。

then’thiterativeimageatpixelj

theneighborsystemofpixelj

Parameter,Euclidiandistancebetweenpixelj’andkThestrongertheedge,thelessimpactinsmoothing.Wheniterationconverges,largeedgeispreserved,andsmoothareabecomesmoresmooth.4.1LowpassFilters4.1.6Non-Linearfilter--

Edgepreservedadaptivesmoothing第十九頁，共53頁。第二十頁，共53頁。第二十一頁，共53頁。Mostofthedesignmethodsdescribedinthissectionworkbycreatingatwo-dimensionalfilterfromaone-dimensionalfilterorwindowcreatedusingfunctionsfromtheSignalProcessingToolbox.Althoughthistoolboxisnotrequired,youmightfinditdifficulttodesignfiltersintheImageProcessingToolboxifyoudonothavetheSignalProcessingToolboxaswell.濾波器設計是一個創(chuàng)建滿足指定濾波要求的濾波器參數(shù)的過程。濾波器的實現(xiàn)包括濾波器結構的選擇和濾波器參數(shù)的計算。4.1LowpassFilters4.1.7MatlabToolbox__FilterDesign第二十二頁，共53頁。原型：B=FIRPM(N,F,A)；例子：b=firpm(10,[00.40.61],[1100]);[H,w]=freqz(b,1,64,'whole‘);colormap(jet(64))plot(w/pi-1,fftshift(abs(H)))figure,freqz2(h,[3232])FrequencyTransformationMethod第二十三頁，共53頁。FrequencySamplingMethodThefrequencysamplingmethodcreatesafilterbasedonadesiredfrequencyresponse.Givenamatrixofpointsthatdefinetheshapeofthefrequencyresponse,thismethodcreatesafilterwhosefrequencyresponsepassesthroughthosepoints.Hd=zeros(11,11);Hd(4:8,4:8)=1;[f1,f2]=freqspace(11,'meshgrid');mesh(f1,f2,Hd),axis([-11-1101.2]),colormap(jet(64))h=fsamp2(Hd);figure,freqz2(h,[3232]),axis([-11-1101.2])第二十四頁，共53頁。第二十五頁，共53頁。WindowingMethodTransformingasingleone-dimensionalwindowtocreateatwo-dimensionalwindowthatisnearlycircularlysymmetric,byusingaprocesssimilartorotationCreatingarectangular,separablewindowfromtwoone-dimensionalwindows,bycomputingtheirouterproductHd=zeros(11,11);Hd(4:8,4:8)=1;[f1,f2]=freqspace(11,'meshgrid');mesh(f1,f2,Hd),axis([-11-1101.2]),colormap(jet(64))h=fwind1(Hd,hamming(11));figure,freqz2(h,[3232]),axis([-11-1101.2])第二十六頁，共53頁。第二十七頁，共53頁。CreatingtheDesiredFrequencyResponseMatrix[f1,f2]=freqspace(25,'meshgrid');Hd=zeros(25,25);d=sqrt(f1.^2+f2.^2)<0.5;Hd(d)=1;mesh(f1,f2,Hd)第二十八頁，共53頁。4.2BandpassandBandstopFilters4.2.1TheIdealBandpassFilter第二十九頁，共53頁。第三十頁，共53頁。4.2BandpassandBandstopFilters4.2.2TheIdealBandstopFilter第三十一頁，共53頁。第三十二頁，共53頁。4.2BandpassandBandstopFilters4.2.3TheGeneralBandpassFilter第三十三頁，共53頁。第三十四頁，共53頁。4.2.4TheDifference-of-Gaussiansfilter第三十五頁，共53頁。Theimpulseofthefilter第三十六頁，共53頁。RulesforbandpassfilterdesignMaximumItcanbegreaterthanA-B第三十七頁，共53頁。G(0)canbetakenas1,topassthe0frequencycomponent.Itmeansthatthelowfrequencycomponentswillpersist.Frequencyatzero第三十八頁，共53頁。第三十九頁，共53頁。Ahighpassfilterisusedindigitalimageprocessingtoremoveorsuppressthelowfrequencycomponent,resultinginasharpenedimage.Highpassfiltersareoftenusedinconjunctionwithlowpassfilters第四十頁，共53頁。4.3High-FrequencyEnhancementFilters4.3.1Theidealhighpassfilter第四十一頁，共53頁。4.3.2TheButterworthhighpassfilter第四十二頁，共53頁。4.3.3Theexponentialhighpassfilter第四十三頁，共53頁。LaplacianofGaussian(L