数字图像处理知识点总结

1、基础1.什么是数字图像一副图像可定义为一个二维函数f(X、y),其中x和y是空间(平面)坐标，而在任何一对空间坐标(x、y)处的幅值f称为图像在该点处的强度或灰度。当x、y和灰度值f是有限的离散数值时，我们称该图像为数字图像。Thefunctionfmayrepresentintensity(formonochiomeimages)orcolor(forcolorimages)orotlierassociatedvalues.Digitalimage:animagetliathasbeendigitizedbotliinspatialcoordinatesandassociatedvalueC

2、onsistof2sets:(1)apointsetand(2)avaluesetCanberepresentedintlieformI=(x,a(x):x属于X,a(x)属于FWliydoweneedimagecompression?-Exampledigitalcamera(4Mpixel)Rawdata一24bits,4Mpixels一12Mbytes192Mmemoiycard_16pictures2-图像坐标系笛卡尔坐标不能作为像素坐标最小单位空间分辨率是图像中可辨别的最小细节的度量。灰度分辨率是指在灰度级中可分辨的最小变化。数字图像处理的概念、研究内容数字图像处理是指借助于数字计算

3、机来处理数字图像。数字图像是由有限数量的元素组成的,每个元素都有一个特定的位置和幅值。这些元素成为图画元素、图像元素或像素。Functions:1.Acquisition2.Storage3Processing4Communication5.DisplayimageSamplingandQuantization采样和量化Imagesampling:digitizeanimageinthespatialdomainSpatial/imageresolution分辨率pixelsizeornumberofpixels图像的领域(4,&对角)及连通的概念Neighborhoodrelationisu

4、sedtotelladjacent(邻近，冊匕连)pixelsItisusedinestablishingboundariesofobjectsandcomponentsofregionsinanimageforanalyzingregions.位于坐标(X、y)处的像素p有4个水平和垂直的相邻像素，其坐标由下式给出：(x+1,y),(x-Ey)t(x,y+1),(x,y+1)这组像素成为p的4邻域，用M(P)表示。每个像素距(x,y)一个单位距离。Note:qWN4(p)impliespEN4(q)4-neighborhoodrelationconsidersonlyveitical(垂直)

5、andhorizontal(水平)neighbors.P的4个对角相邻像素的坐标如下：(x-l,y-l),(x,y-1),(x-l,y),(x+ly),(x,y+1),(x+1,y+1),(x+1,y-1),(x-by+1),(x-1,y-1)并用比(p)表示。这些点与4个邻点一起称为p的8邻域，用(P)表示neighborhoodrelationconsidersallneighborpixels.Diagonal-neighborhoodrelationconsidersonlydiagonal(斜的)neighborpixels.(x-1,y-1),(x+1,y-1),(x-1,y+1)

6、,(x+1,y+1)6各不同电磁波谱的图像成像技术，波段划分？7图像数字化过程(打描、采样、量化)及各自含义？图像分辨率(空间、灰度)与质量的关系？（采样间距与数据量的关系、采样间距与质量的关系、量化与数据量的关系、量化与质量的关系）Imagequantization（数字It）digitizecontinuouspixelvaluesintodiscietenumbers空域增强8图像增强的目的（不清晰的图像变得清晰或强调某些感兴趣的特征，改善图像质量，丰富信息量，加强图像判读和识别效果），分类及特点Objective:toprocessannnagesothattheresultismor

7、esuitableforaspecificapplication.PioblemonentedThebestmetliodforenliancingX-rayimagesmaybenotthebestmetliod,evennotsuitableforenliancingpicturesofMars（火星）transmittedbyaspaceprobe（探测器）Theiearetwomaincategoriesoftechniquesforimageenliancement:Spatial（空间的）DomainMetliods-whichoperatedirectlyonpixels.Fre

8、quencyDomainMethods-v/hichoperateontlieFourierTransfoimoftheimage.Combinationalapproacheswithtliesetwocategoriesarenotunusual.9图像增强点到点运算有哪些？特点？优缺点？（对数、乘方率、分段线性、二值化、加法噪声、减法变化）Enhancementatanypointinanimagedependsonlyontliegraylevelatthatpoint.Contraststretching乂寸比度扩展:darkeningthegraylevelsbelownmithe

9、originalimage,bnghtenuigthegraylevelsabovemintlieonginalimageThresholdingI测值ft：thelimitnigcaseistogenerateabinaryimageSomeBasicGrayLevelTransfonnationsNegative（linear）Log（logandinveise-logtiansfbnnations）Powerlaw乘方律（nthpowerandn-tliioottiansfonnations.Theidentitytiansfonnationisatiivial（微不足道的）case:o

10、utput=input,onlyforcompleteness完备性）Piecewise-lineartiansfonnationfunctions（分段线性函数）Bitslicing位切片DefnntionThenegativeofanimagewithgraylevelsintlierange0,L-lcanbedefinedas:s=L-l-ri-L-1,s=0:Wlnte-Black1-0,s=L-l:Black-WhiteFunction:Reversingtheintensitylevelsofanimageintinsmannerproducestlieequivalent（等彳

11、介物）ofaphotogiaphicnegative（照相底片）Applications:Enliancingwhiteorgraydetailsembeddedindarkregions,especiallywhentheblackareasaredominantinsize“Log”Definition:Thegeneralfonnoftlielogtransformationisdefinedass=clog（l+r）L-l=clog（l+L-l）c=L1logLWlierecisaconstant,assumetliatr0uLognFunction:Tomapanairowrange

12、oflowgray-levelvaluesintlieinputimageintoavzideirangeofoutputlevels.Tomapavziderangeofhighgray-levelvaluesintheinputimageintoanairowerrangeofoutputlevels.uLognApplications:Toexpandtlievaluesofdarkpixelsinannnagevzhilecompressingthehigher-levelvaluesTocompressdynamicrangeIngeneral,loga门thmicmappingis

13、usefulifwewishtoenhancedetailinthedarkerregionsoftheimage,attheexpenseofdetailintlieblighterregionsuInverseLognDefinition:Thegeneralformoftlieinverselogtiansfonnationisdefinedass=101L1=gc（L-i）1c=L1WlierecisaconstantInverseLogFunction:TomapavziderangeoflowgrayJevelvaluesintheinputimageintoanairowerra

14、ngeofoutputlevels.Tomapanairowrangeofhighgiay-levelvaluesintlieinputimageintoawiderrangeofoutputlevels.InverseLogApplications:Toexpandthevaluesofbnglitpixelsinanimagewhilecompressingthelowei-levelvalueLogTransfomiationsconckisionNote:Anycuivehavingthegeneralshapeofthelogfunctionscanaccomplishtliesim

15、ilarfunctionofSpreading/Compressingofgraylevels.Comparedwithlogtransformation,Power-Lavztiansfonnations（discussedlater）aremoreversatile（通用的，多而于的）withdifferentparametersHowevei,logfiinctioncancompressthedynamicrangeofimageswithlargevariationsinpixelvalues.Power-LawTransformationsDefnntionsTheBasicfor

16、mofPower-LawTransfomiations:S=CryWlierecandyarepositiveconstantsFunctions:Thecaseofyl:similartothecaseofinveiselogfunctionPiecewise-LinearTransfonnationFunction分段线性Advantage:ThefonnofpiecevziseflinctioncanbearbitranlycomplexDisadvantage:TheirspecificationrequiresmoreuserinputApplicationsContrastStre

17、tching（对比度拉伸）Incieasethedynamicrangeoftliegraylevelsinanlow-confaastnnage.Gray-LevelSlicing（灰度切割/灰度窗II变换）:Highlight吏显著）aspecificrangeofgraylevelsinanimageBit-PlaneSlicing（位平面切割）HighliglittliecontnbutionmadetototalimageappearancebyspecificbitsGraylevelmapping-ConclusionsTheprocessoftakingtheonginalda

18、tanumbersandchangingtliemtonewvaluesiscalledmappuig.Amathematicaldescnptionoftliemappingiscalledamappingfunction.ApplicationBnghtness/contiastenliancementDisplaycalibration(显示标定)/photometiiccalibration(光度学标定)Contourlinedetenmnation(轮廓线确定)Pointprocesses-operationsatapixeldependonlyonthatpixelThesimpl

19、estcaseisthresholdingwheretlieintensityprofileisreplacedbyastepfunction阶跃函数，activeatachosenthresholdvalue.Intinscaseanypixelwithagreylevelbelov/thethresholdintheinputimagegetsmappedto0intheoutputimage.Otlierpixelsaremappedto255加法、减法：Definitionsofaritlimetic/logicoperationsOperationsareperfonnedonapi

20、xel-by-pixelbasisbetweentv/oormoreimages.r(x,y)=gIl(x,y),I2(x,y)Basedonthesoftwareorhardwarebeingused,tlieycanbedoneSequentiallyorinParallelImageSubtractionInputimages:f(x9y)ndh(x9y),subtractionofthem:g(x,刃=f(x9y)h(x,y)Purpose:enliancetliedifferencesbetweenimagesOriginalfractalimageResultofsettingst

21、hefourlower-orderbitplanestozero.Differencebetween(a)and(b).HistogramequalizeddifferenceimageEvaluatingtlieeffectofsettingto0thelower-orderplanesImageCombiningThisissimilartoadditionbutproportionsofthecoirespondingpixelsofthetwounagesareaddedtogether.Wemaywishtogivemoreemphasistooneimagethantheother

22、.Thiscanbedonebyalphablending1混合g(x,y)=afl(x,y)+(1-a)C(x,y)WliencanthisEquationis05,g(x,y)becomesasimple,evenly-vzeightedaverageoftlietwoinputimages.Itispossibleforaatovaiy,eveiypixelofanunagecanhaveitsowna,storedinaseparatealphachannel.如何设计映射函数？(计算大题)直方图的定义、图像与灰度直方图间的对应关系？不同图像直方图的特点(高调、中调、低调)？Image

23、Histogivam(直方图):BrilitnesshistogramprovidesthefrequencyofthebrightnessvalueintheimageGraylevelmappingandhistogram：D0=axDr+bb0,histogrammovestothenglittomakeimagebrightei*bl,histogramcontiastincreasesal,histogramcontiastdecreases例:Do=1.2xDf+50ExamplesofHistogramsDarkimage-concentiatedonthelowsideoftl

24、iegrayscale.Brightimage-biasedtowardthehighsideoftliegrayscaleLowcontrastimage-narrowandcenteredtowardthemiddleofthegrayscaleHigli-contiastimagecoverabroadrange,thedistnbutionisnottoofarfromunifbim11坐标轴参数的含义？直方图运算(算数、奇与偶的关系)，图像运算与直方图的关系？直方图均衡的基本思想是什么？ContinuousCase:Considerforthecaseofcontinuousimag

25、esandcontinuoustransformationfunctions.LetthetransformationflinctionbeS=T(r),0r1Wlierer=0representsblackandr=lrepresentsvzhite.AssumetliatthefaansfonnationfunctionT(r)satisfiesthefollowingtwoConditions:A9T(r)issingle-valued单值的andmonotonicallyincreasing单调递inOrguaranteetheinveisetiansfonnationwillexis

26、t.T(r)ismonotonicallyincreasnigtopreseivetheincreasingorderfiomblacktowhiteintlieoutputimage.B.T(r)lforOrguaianteestheoutputlevelisinthesamerangeastheinputlevelsDiscreteVersion:Justuseprobabilities概率andsummations总和insteadofprobabilitydensityfunctionsandintegrals.Theprobabilityofoccuirenceofgraylevel

27、inanimageisapproxunatedbyPg=0,1,2,，厶-1ThetransformationfunctionisSk=k=0丄2,.L2inTomapeachpixelwitlilevelintheinputimageintoacoirespondingpixelwithlevelS*intheoutputimageThetransformationgiveninaboveequationiscalledhistogramequalizationorhistogiamlinearization空域滤波、平滑、锐化典型方法、种类、应用特点(平滑均值、平滑中值：锐化拉普拉斯算子，

28、锐化微分算子)Filtersletthroughorattenuate肖ij弱specificrangesofimagedetailseg.slow/gradualorfastchangesinpixelvalueHencetlieclassificationoffiltersintolow-passfiltersAttenuates(变弱)fastchangesnipixelvaluebutletsthroulislow/gradualchangesTypicalapplication:noiseremovalTendstoblurunagehigh-passfiltersAttenuate

29、sslow/giadualchangesinpixelvaluebutletsthrouifastchangesTypicalapplication:edgeenhancementTendstobesensitivetonoiseOutputvaluesmaybeoutsidenumericalrangeofpixelvalueScalingmayberequuedAndotheitypesoffiltersband-passfilteis,band-rejectfilteis,SmootliingSpatialFiltersMotivationbluiring（模糊）andnoiseredu

30、ctionBlurringisusedinpreprocessingstepsRemovalofsmalldetailsfromanimagepriortoobjectextractionBridgingofsmallgaps（MJ隙）inlinesorcuivesReductionoffalsecontours（ducedbyzooming）NoiseReductionCanbeaccomplishedbyblurringwithalinearfilterandalsobynonlinearfiltenng.SmootliingLinearFiltersAveragingfilt

31、er,lowpassfilterIdea:Toreplacethevalueofeveiypixelinanimagebytlieaverageoftliegraylevelsintlieneighboihooddefinedbythefilteimask,whichresultsinanimagewithreduced“sharptransitionsingraylevelsApplicationsNoisereductionHowever,becauseofshaiptiansitionsreduction,edgescanalsobebluired.（Undesirable）Thesmo

32、othingoffalsecontoursThefalsecontoursresultfiomusinganinsufficientnumberofgraylevelsThereductionofciirelevant1detailinanimagecIrrelevantdetailnmeanspixelregionstliataresmallwithrespecttothesizeoffilteimask.SharpeningSpatialFiltersObjectiveofSharpeningTohighlightfinedetailToenliancedetailthathasbeenb

33、luiTed（模糊）EitherinerrorOrasanaturaleffectofaparticularimageacquisition（采集）methodApplicationsElectronprinting（电子E卩刷）andmedicalimagingIndustrialinspection匸业检测andautonomousguidance自制导inmilitaiysystemsLaplacianhfasksIsotiopic各向同性的filtersRotationmvanantCoefficientsThecenteicoefficientoftlieLaplacianmaski

34、snegative,theothersarepositive,orviceversa.Thesumofcoefficientsis0Themaskcontainingthediagonalteimsusuallyarealittleshaiper.TheLaplaciancanhighlightsgrayleveldiscontinuitiesanddeemphasizeregionwithslowlyvaiyinggraylevelsItproducesgrayishedgelinesandotlierdiscontinuities.Howevei;tliesefeaturesaresupe

35、rimposedonadark,featurelessbackground.Howcanwerecovertheonginalbackgioundwhilepreseivingthesharpeningeffect?Theanswerissunpie,justaddbacktheonginalimageasfollowsSharpeningspatialfilterSmoothingspatialfilterLinearfilter(meanfilter)NoisereductionblurringBlur(smooth)ApplicationsSmoothingNoiseReductiona

36、ndObjectDetectionExample2ndDerivative(Laplacian)EnhancedetailDeblur(sharpen)Non-linear(Medianfilter)1stDerivative(gradient)尺寸与滤波效果的关系？滤波器系数的特点？滤波器形状？滤波器的结构，滤波算法的实现SmootliingLinearFiltersThelargeitliesize,themorebluiredtheunageandtlielesstliedetailsCoefficients(系数)Largertlian0Averaging/vzeiglited(red

37、ucingeffectofborder)Nonnalization：Smootliingmasksarenomiallyadjustedtopreseiveaveragevalue(Ewi=1)频域增强16傅里叶变换公式、定义、性质，有哪些特点？谱与空域特征的关系？17.频域滤波（理想、巴特沃斯、高斯）（低通、高通）特点？振铃效应？各个滤波器之间的比较，适用情况ButterworthfiltersOrder=2Thereislessnngingeffectcomparedtotlioseofideallowpassfilters!Ringingeffect振铃效应Ringingiscaused

38、asthelow-passfilteiingintioducesthesin（r）/nnthekernel.复原18图像质量退化的原因？模型？SimplifiedassumptionsNoiseisindependentofsignalNoisetypesIndependentofspatiallocationImpulsenoiseAdditivewhiteGaussiannoiseSpatiallydependentPeiiodicnoise处理技术？（中值一孤立点、椒盐；带阻、陷波一去除图像中某一频率分量、周期噪声）PeriodicNoiseSource:electncalorelect

39、romechanicalinterferenceduringimageacquisitionCharacteristicsSpatiallydependentPeiiodic-easytoobseiveinfrequencydomainProcessingmetliodSuppressingnoisecomponentinfrequencydomainPeriodicnoisecanbereducedbysettingfrequencycoinponentscoirespendingtonoisetozero.BandRejectFilters频带抑制（带阻）滤波器Usetoeluninate

40、fiequencycomponentsinsomebandsPenodicNotchRejectFilters陷波滤波器Anotchrejectfilterisusedtoeliminatesomefrequencycomponents.增强与复原的关系？彩色几个彩色系统（RGB、CMY、CMYK、HSI）各自特点？各分量含义？RGBmodel:Red,Green,BlueColormonitors,colorvideocamerasBasicknowledgeofRGBBasedonCartesiancoordinatesystemColorsaredefinedbyvectorsexten

41、dingf?omtlieongininR,GandBcomponentsAllvaluesofR,GandBarenoimalizedintherange0,1ImagesrepresentedintheRGBmodelConsistsof3coinponents,R,GandBIftliepixeldepthofeachcomponentis8bits,thereare24bitsinRGBcolorpixelFull-colorunageisoftenusedtodenotea24-bitRGBcolorimageAndtotalnumberofcolorsoftheimageis（28）3=16,777,216Indigitalimages,weoftenusetheintegerrange0,1,2,.,255,ratlierthantlienonnalizedrealrange0,1foreachcolorcoinponent.CMYandCMYKmodels:CMY:Cyan青,Magenta品红,Yellow,CMYK：Cyan,Magenta,Yellow,BlackColorprin