最新计算机图形学与图像处理04-digitalimage课件PPT.ppt 60页

'计算机图形学与图像处理04-digitalimage Chapter4:4.1background4.2IntroductiontotheFourierTransformandtheFrequencyDomain 1.Whyweneedit?2.TheoriginalmathematicfunctionFromonedimensiontotwodimension3.ForimageprocessingapplicationFromcontinuoussignaltodiscretesignal4.Specificapplication 4.2IntroductiontotheFourierTransformandtheFrequencyDomain 4.2IntroductiontotheFourierTransformf(x):continuousfunctionofarealvariablexFouriertransformoff(x):whereEq.1 (u)isthefrequencyvariable.TheintegralofEq.1showsthatF(u)iscomposedofaninfinitesumofsineandcosinetermsand…Eachvalueofudeterminesthefrequencyofitscorrespondingsine-cosinepair.4.2IntroductiontotheFourierTransform 4.2IntroductiontotheFourierTransforminverseFouriertransform:TheabovetwoequationsaretheFouriertransformpair. 4.2IntroductiontotheFourierTransformFouriertransformpairforafunctionf(x,y)oftwovariables:andwhereu,varethefrequencyvariables. DiscreteFourierTransformAcontinuousfunctionf(x)isdiscretizedintoasequence:bytakingMsamplesxunitsapart.M DiscreteFourierTransformWherexassumesthediscretevalues(0,1,2,3,…,M-1)thenThesequence{f(0),f(1),f(2),…f(M-1)}denotesanyMuniformlyspacedsamplesfromacorrespondingcontinuousfunction. DiscreteFourierTransformThediscreteFouriertransformpairthatappliestosampledfunctionsisgivenby:Foru=0,1,2,…,M-1Forx=0,1,2,…,M-1and DiscreteFourierTransformEachtermoftheFT(F(u)foreveryu)iscomposedofthesumofallvaluesoff(x) DiscreteFourierTransformFourierspectrum:Phase:Powerspectrum: DiscreteFourierTransformIna2-variablecase,thediscreteFTpairis:Foru=0,1,2,…,M-1andv=0,1,2,…,N-1Forx=0,1,2,…,M-1andy=0,1,2,…,N-1AND: 4.2DiscreteFourierTransformBasicPropertiesA.F(0,0):Conclusion:F(0,0)----theaveragegrayleveloftheimage.F(0,0)----dccomponentofthespectrum(直流分量) 4.2DiscreteFourierTransformBasicPropertiesB:F(0,0)isatu=M/2andv=N/2ShiftstheoriginofF(u,v)to(M/2,N/2),i.e.Frequencyrectangle:fromu=0tou=M-1,andv=0tov=N-1(u,vintegers,M,Nevennumbers) 4.2DiscreteFourierTransformBasicPropertiesC.discerptible(拆分) 4.2DiscreteFourierTransform 4.2DiscreteFourierTransform Iff(x,y)isanimage,thevalueoftheFouriertransformattheorigin(F(0,0))isequaltotheaveragegrayleveloftheimage.F(0,0)sometimesiscalledthedccomponentofthespectrum. 4.2DiscreteFourierTransform1.Multiplytheinputimageby(-1)x+ytocentrethetransform,asindicatedin(4.2.21)2.ComputeF(u,v),theDFToftheimagefromstep1.3.MultiplyF(u,v)byafilterfunctionH(u,v).4.ComputetheinverseDFToftheresult3.5.Obtaintherealpartoftheresult4.6.Multiplytheresultin5by(-1)x+y. Basicstepsforfilteringinthefrequencydomain P159Theimportantpointtokeepinmindisthatthefilteringprocessisbasedonmodifyingthetransformofanimageinsomewayviaafilterfunction,andthentakingtheinverseoftheresulttoobtaintheprocessedoutputimage. Somebasicfiltersp159Thefilterjustdiscussediscalledanotchfilter(陷波滤波器)becauseitisaconstantfunctionwithahole(notch)attheorigin.Afterfilter,theaveragegraylevelofthisimageshouldbezero. SomebasicfiltersLowfrequenciesintheFouriertransformareresponsibleforthegeneralgray-levelappearanceofanimageoversmoothareas.Highfrequenciesareresponsiblefordetail,suchasedgesandnoise. SomebasicfiltersAfilterthatattenuateshighfrequencieswhile“passing”lowfrequenciesiscalledalowpassfilter.(低通滤波器)Afilterthathastheoppositecharacteristicisappropriatelycalledahighpassfilter.(高通滤波器) SomebasicfiltersAlowpass-filteredimagewillhavelesssharpdetailthantheoriginalbecausethehight-frequencieshavebeenattenuated.Ahighpass-filteredimagewillhavelessgraylevelvariationsinsmoothareasandemphasizedtransitionalgray-leveldetail,andtheimageappearsmoresharper. CorrespondencebetweenFilteringintheSpatialandFrequencyDomainsThemostfundamentalrelationshipbetweenthespatialandfrequencydomainsisestablishedbyawell-knownresultcalledtheconvolution(卷积)theorem. CorrespondencebetweenFilteringintheSpatialandFrequencyDomains CorrespondencebetweenFilteringintheSpatialandFrequencyDomains 4.3SmoothingFrequency-DomainFiltersTheobjectiveistoselectafiltertransferfunctionH(u,v)thatyieldsG(u,v)byattenuatingthehigh-frequencycomponentsofF(u,v).p167 4.3.1IdealLowpassFiltersThesimplestlowpassfilterwecanenvisionisafilterthat“cutsoff”allhigh-frequencycomponentsoftheFouriertransformthatareatadistancegreaterthanaspecifieddistanceD0fromtheoriginofthetransform. IdealLowpassFilters IdealLowpassFilters IdealLowpassFilters IdealLowpassFiltersExplanationofblurringandringingpropertiesoftheILPF GFdesignu,varethecoordinateinfrequencydomainH(-1,-1)H(-1,0)H(-1,1)H(0,-1)H(0,0)H(0,1)H(1,-1)H(1,01)H(1,1) 4.4SharpeningFrequencyDomainFiltersImagesharpeningcanbeachievedinthefrequencydomainbyahighpassfilteringprocess,whichattenuatesthelow-frequencycomponentswithoutdisturbinghigh-frequencyinformationintheFT.p180 HighpassFilters HighpassFilters HighpassFilters HighpassFilters HomomorphicFilters(同态滤波器) HomomorphicFilters(同态滤波器) 普洒阳光心语，甘泉滋润人心——学会做一个快乐的人四（6）中队 同学们好，大家都想和快乐在一起，天天快乐，时时快乐。可是生活、学习中我们总会遇上这样那样不顺心的事。这不，今天早晨我来上班，在快到拐弯处时横冲出来一个人，老师赶快捏闸险些摔倒了。谁知此人丝毫没有察觉，扬长而去。这使我非常生气，这人既不遵守交通规则，又不珍惜自己的生命，太不应该了。老师心里很不愉快。是啊，生活中，让人生气、让人烦恼、让人痛苦的事情太多了，同学们，在你的生活中，遇到过不快乐的事情吗? 听故事：《国王长了一只兔耳朵》 观看心理小品，评析是非： 情境游戏：《猜一猜》 享用“心理快餐” 生活中常用的能创造快乐,发泄不良情绪的办法：★读有趣的书；★至少培养自己有一种兴趣爱好；★经常与家人、同学、朋友在一起，谈心、玩耍；★照镜子，与镜中的人说说话；★到没有人的地方大声喊叫；★在劳动创造中体会快乐…… 再见'