1、基礎1.什么是數字圖像一副圖像可定義為一個二維函數f(X、y),其中x和y是空間(平面)坐標，而在任何一對空間坐標(x、y)處的幅值f稱為圖像在該點處的強度或灰度。當x、y和灰度值f是有限的離散數值時，我們稱該圖像為數字圖像。Thefunctionfmayrepresentintensity(formonochiomeimages)orcolor(forcolorimages)orotlierassociatedvalues.Digitalimage:animagetliathasbeendigitizedbotliinspatialcoordinatesandassociatedvalueC

2、onsistof2sets:(1)apointsetand(2)avaluesetCanberepresentedintlieformI=(x,a(x):x屬于X,a(x)屬于FWliydoweneedimagecompression?-Exampledigitalcamera(4Mpixel)Rawdata一24bits,4Mpixels一12Mbytes192Mmemoiycard_16pictures2-圖像坐標系笛卡爾坐標不能作為像素坐標最小單位空間分辨率是圖像中可辨別的最小細節的度量。灰度分辨率是指在灰度級中可分辨的最小變化。數字圖像處理的概念、研究內容數字圖像處理是指借助于數字計算

3、機來處理數字圖像。數字圖像是由有限數量的元素組成的,每個元素都有一個特定的位置和幅值。這些元素成為圖畫元素、圖像元素或像素。Functions:1.Acquisition2.Storage3Processing4Communication5.DisplayimageSamplingandQuantization采樣和量化Imagesampling:digitizeanimageinthespatialdomainSpatial/imageresolution分辨率pixelsizeornumberofpixels圖像的領域(4,&對角)及連通的概念Neighborhoodrelationisu

4、sedtotelladjacent(鄰近，冊匕連)pixelsItisusedinestablishingboundariesofobjectsandcomponentsofregionsinanimageforanalyzingregions.位于坐標(X、y)處的像素p有4個水平和垂直的相鄰像素，其坐標由下式給出：(x+1,y),(x-Ey)t(x,y+1),(x,y+1)這組像素成為p的4鄰域，用M(P)表示。每個像素距(x,y)一個單位距離。Note:qWN4(p)impliespEN4(q)4-neighborhoodrelationconsidersonlyveitical(垂直)

5、andhorizontal(水平)neighbors.P的4個對角相鄰像素的坐標如下：(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。這些點與4個鄰點一起稱為p的8鄰域，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各不同電磁波譜的圖像成像技術，波段劃分？7圖像數字化過程(打描、采樣、量化)及各自含義？圖像分辨率(空間、灰度)與質量的關系？（采樣間距與數據量的關系、采樣間距與質量的關系、量化與數據量的關系、量化與質量的關系）Imagequantization（數字It）digitizecontinuouspixelvaluesintodiscietenumbers空域增強8圖像增強的目的（不清晰的圖像變得清晰或強調某些感興趣的特征，改善圖像質量，豐富信息量，加強圖像判讀和識別效果），分類及特點Objective:toprocessannnagesothattheresultismor

7、esuitableforaspecificapplication.PioblemonentedThebestmetliodforenliancingX-rayimagesmaybenotthebestmetliod,evennotsuitableforenliancingpicturesofMars（火星）transmittedbyaspaceprobe（探測器）Theiearetwomaincategoriesoftechniquesforimageenliancement:Spatial（空間的）DomainMetliods-whichoperatedirectlyonpixels.Fre

8、quencyDomainMethods-v/hichoperateontlieFourierTransfoimoftheimage.Combinationalapproacheswithtliesetwocategoriesarenotunusual.9圖像增強點到點運算有哪些？特點？優缺點？（對數、乘方率、分段線性、二值化、加法噪聲、減法變化）Enhancementatanypointinanimagedependsonlyontliegraylevelatthatpoint.Contraststretching乂寸比度擴展:darkeningthegraylevelsbelownmithe

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

10、utput=input,onlyforcompleteness完備性）Piecewise-lineartiansfonnationfunctions（分段線性函數）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門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分段線性Advantage:ThefonnofpiecevziseflinctioncanbearbitranlycomplexDisadvantage:TheirspecificationrequiresmoreuserinputApplicationsContrastStre

17、tching（對比度拉伸）Incieasethedynamicrangeoftliegraylevelsinanlow-confaastnnage.Gray-LevelSlicing（灰度切割/灰度窗II變換）:Highlight吏顯著）aspecificrangeofgraylevelsinanimageBit-PlaneSlicing（位平面切割）HighliglittliecontnbutionmadetototalimageappearancebyspecificbitsGraylevelmapping-ConclusionsTheprocessoftakingtheonginalda

18、tanumbersandchangingtliemtonewvaluesiscalledmappuig.Amathematicaldescnptionoftliemappingiscalledamappingfunction.ApplicationBnghtness/contiastenliancementDisplaycalibration(顯示標定)/photometiiccalibration(光度學標定)Contourlinedetenmnation(輪廓線確定)Pointprocesses-operationsatapixeldependonlyonthatpixelThesimpl

19、estcaseisthresholdingwheretlieintensityprofileisreplacedbyastepfunction階躍函數，activeatachosenthresholdvalue.Intinscaseanypixelwithagreylevelbelov/thethresholdintheinputimagegetsmappedto0intheoutputimage.Otlierpixelsaremappedto255加法、減法：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.如何設計映射函數？(計算大題)直方圖的定義、圖像與灰度直方圖間的對應關系？不同圖像直方圖的特點(高調、中調、低調)？Image

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

24、iegrayscale.Brightimage-biasedtowardthehighsideoftliegrayscaleLowcontrastimage-narrowandcenteredtowardthemiddleofthegrayscaleHigli-contiastimagecoverabroadrange,thedistnbutionisnottoofarfromunifbim11坐標軸參數的含義？直方圖運算(算數、奇與偶的關系)，圖像運算與直方圖的關系？直方圖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單值的andmonotonicallyincreasing單調遞inOrguaranteetheinveisetiansfonnationwillexis

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

27、inanimageisapproxunatedbyPg=0,1,2,，厶-1ThetransformationfunctionisSk=k=0丄2,.L2inTomapeachpixelwitlilevelintheinputimageintoacoirespondingpixelwithlevelS*intheoutputimageThetransformationgiveninaboveequationiscalledhistogramequalizationorhistogiamlinearization空域濾波、平滑、銳化典型方法、種類、應用特點(平滑均值、平滑中值：銳化拉普拉斯算子，

28、銳化微分算子)Filtersletthroughorattenuate肖ij弱specificrangesofimagedetailseg.slow/gradualorfastchangesinpixelvalueHencetlieclassificationoffiltersintolow-passfiltersAttenuates(變弱)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（電子E卩刷）andmedicalimagingIndustrialinspection匸業檢測andautonomousguidance自制導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)尺寸與濾波效果的關系？濾波器系數的特點？濾波器形狀？濾波器的結構，濾波算法的實現SmootliingLinearFiltersThelargeitliesize,themorebluiredtheunageandtlielesstliedetailsCoefficients(系數)Largertlian0Averaging/vzeiglited(red

37、ucingeffectofborder)Nonnalization：Smootliingmasksarenomiallyadjustedtopreseiveaveragevalue(Ewi=1)頻域增強16傅里葉變換公式、定義、性質，有哪些特點？譜與空域特征的關系？17.頻域濾波（理想、巴特沃斯、高斯）（低通、高通）特點？振鈴效應？各個濾波器之間的比較，適用情況ButterworthfiltersOrder=2Thereislessnngingeffectcomparedtotlioseofideallowpassfilters!Ringingeffect振鈴效應Ringingiscaused

38、asthelow-passfilteiingintioducesthesin（r）/nnthekernel.復原18圖像質量退化的原因？模型？SimplifiedassumptionsNoiseisindependentofsignalNoisetypesIndependentofspatiallocationImpulsenoiseAdditivewhiteGaussiannoiseSpatiallydependentPeiiodicnoise處理技術？（中值一孤立點、椒鹽；帶阻、陷波一去除圖像中某一頻率分量、周期噪聲）PeriodicNoiseSource:electncalorelect

39、romechanicalinterferenceduringimageacquisitionCharacteristicsSpatiallydependentPeiiodic-easytoobseiveinfrequencydomainProcessingmetliodSuppressingnoisecomponentinfrequencydomainPeriodicnoisecanbereducedbysettingfrequencycoinponentscoirespendingtonoisetozero.BandRejectFilters頻帶抑制（帶阻）濾波器Usetoeluninate

40、fiequencycomponentsinsomebandsPenodicNotchRejectFilters陷波濾波器Anotchrejectfilterisusedtoeliminatesomefrequencycomponents.增強與復原的關系？彩色幾個彩色系統（RGB、CMY、CMYK、HSI）各自特點？各分量含義？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品紅,Yellow,CMYK：Cyan,Magenta,Yellow,BlackColorprin