图像与视频处理ver01第二章图像处理基础

图像与处Image 第二讲：图像处理基人工智能与机器InstituteofArtificial ligenceand兰旭图像处Image图像处ImageThehumanvisualLightandtheelectromagneticImagesensingandSampling,sationandImageBasicrelationshipsbetweenMathematicalThehumanvisualLightandtheelectromagneticImagesensingandSampling,sationandImageBasicrelationshipsbetweenMathematical图像图像Image处HumanVisualThebestvisionmodelweKnowledgeofhowimagesformintheeyecanhelpuswithprocessingdigitalWewilltakejustawhirlwindtourofthehumanvisualsystem图像 处理Image 睫状睫状OfThe

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Choroid：nutritiontoeyeIris:colortoeyeRods:generalvisionCones:details(women)HumanVisualThelensfocuseslightfromobjectsontotheretinaTheretinaiscoveredwithlightreceptorscalledcones(6-7million)androds(75-150Conesareconcentratedaroundthefoveaandareverysensitivetocolour,photopicvisionRodsaremorespreadoutandaresensitivetolowlevelsofillumination,scotopicvisionBlind-SpotDrawanimagesimilartothatbelowonapieceofpaper(thedotandcrossareabout6inchesapart)CloseyourrighteyeandfocusonthecrosswithyourlefteyeHoldtheimageabout20inchesawayfromyourfaceandmoveitslowlytowardsyouThedotshouldImageFormationInTheMuscleswithintheeyecanbeusedtochangetheshapeofthelensallowingusfocusonobjectsthatarenearorfarawayAnimageisfocusedontotheretinacausingrodsandconesto eexcitedwhich ysendsignalstothe BrightnessAdaptation&Thehumanvisualsystemcanperceive y1010differentlightintensityHowever,atanyonetimewecanonlydiscriminatebetweenamuchsmallerregionisrelatedtothelightintensitiesoftheregionssurroundingit图像处Image图像处ImageGoodWeberpoorbrightnesspoorbrightness图像 处Image Inlow-levelillumination,ispoor(WeberratioisCarriedoutbyrods-暗光Itimprovessignificantlyasbackgroundcarriedoutbycones—图像处Image图像处ImageBrightnessAdaptation&ErnstPerceivedbrightnessIsPerceivedbrightnessIsnotasimplefunctionofintensityAnexampleofMachUndershootaroundTheboundaryofRegionsUndershootaroundTheboundaryofRegionsOfdifferentAnAnexampleofsimultaneousPerceivedPerceivedbrightnessdoesnotdependSimplyonitsintensityFormoregreatillusionexamplestakealookAvailable图像图像Image处OpticalOurvisualplaylotsoftricksonusMindMapExercise:MindMapForNoteBeauLotto:BeauLotto:OpticalIllusionsShowHowWeThehumanvisualLightandtheelectromagneticImagesensingandSampling,sationandImageBasicrelationshipsbetweenMathematicalLightAndTheElectromagneticIn1666SirIsaacNewtondiscoveredthatlightpassedthroughaprismsplitsintoacontinuousspectrumofLightisjustaparticularpartoftheelectromagneticspectrumthatcanbesensedbythehumaneyeTheelectromagneticspectrumissplitupaccordingtothewavelengthsofdifferentformsofenergyLightandEMc E h:Planck's光谱能波长m光谱能ElectromagneticElectromagneticshorterwaveMoreenergyshorterwaveMoreenergyv图像Image图像Image处LightandEMThecolorsthathumansperceiveinanobjectaredeterminedbythenatureofthelightreflectedfromtheobject.e.g.greenobjectsreflectlightwithwavelengthsMonochromaticlight:voidofIntensityistheonlyattribute,fromblacktoMonochromaticimagesarereferredtoasgray-Chromaticlightbands:0.43to0.79umThequalityofachromaticlightsource:Radiance:totalamountofenergyLuminance(lm):theamountofenergyanobserverfromalightBrightness:asubjectivedescriptoroflightperceptionthatisimpossibletomeasure.Itembodiestheachromaticnotionofintensityandoneofthekeyfactorsindescribingcolorsensation.图像图像Image处ThehumanvisualLightandtheelectromagneticImagesensingandSampling,sationandImageBasicrelationshipsbetweenMathematical图像 处Image Sampling,sationAndInthefollowingslideswewillconsiderwhatisinvolvedincapturingadigitalimageofareal-worldsceneImagesensingandSamplingand图像 处Image ImageingenergylandsonasensormaterialresponsivetothattypeofenergyandthisgeneratesavoltageCollectionsofsensorsarearrangedtocaptureimagesImagingLineofImage ArrayofImage图像处Image图像处ImageImagetolightHighprecision

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图像图像Image处ImageImagesaretypicallygeneratedbyenergyreflectedbytheobjectsinthatsceneTypicalnotionsofilluminationandscenecanbewayoff:X-raysofaUltrasoundofanunbornbabyimagesofmoleculesASimpleImageFormationProportionaltoenergyradiatedbyaphysicalsourcef(x,y)i(x,y)rProportionaltoenergyradiatedbyaphysicalsourcewhere0<i(x,y)<and0<r(x,y)<1SomeTypicalRangesofLumen—AunitoflightfloworluminousLumenpersquaremeter(lm/m2)—ThemetricunitofmeasureforilluminanceofasurfaceOnaclearday,thesunmayproduceinexcessof90,000lm/m2ofilluminationonthesurfaceoftheEarthOnacloudyday,thesunmayproducelessthan10,000lm/m2ofilluminationonthesurfaceoftheEarthOnaclearevening,themoonyieldsabout0.1lm/m2ofThetypicalilluminationlevelinacommercialofficeisabout1000SomeTypicalRangesof0.01forblack0.65forstainless0.80forflat-whitewall0.90forsilver-plated0.93for图像 处Image GrayMonochromelf(x0,y0)LminlLmaxLminiminrminLmaximaxrmax[Lmin,Lmax图像图像Image处ThehumanvisualLightandtheelectromagneticImagesensingandSampling,sationandImageBasicrelationshipsbetweenMathematicalImageSamplingAndAdigitalsensorcanonlymeasurealimitednumberofsamplesatadiscretesetofenergysationistheprocessofconvertinga oguesignalintoadigitalrepresentationofthissignalImageSamplingAndImageSampling 图像 处Image ImageSamplingAndRememberthatadigitalimageisalwaysonlyanapproximationofarealworldImagequalityisImagequalityisdeterminedbythenumberofsamplesAnddiscreteintensitylevelsusedinsamplingand 图像图像Image处ImageSamplingAndSamplingisdeterminedbythesensorarrangementusedtogeneratetheSamplingaccuracyrelatestoqualityoftheopticalcomponentsofthesystem.ThehumanvisualLightandtheelectromagneticImagesensingandSampling,sationandImageBasicrelationshipsbetweenMathematical图像处Image图像处ImageImageBeforewediscussimageacquisitionrecallthatadigitalimageiscomposedofMrowsandNcolumnsofpixelseachstoringavaluef(row,f(row,Wewillseelateronthatimagescaneasilyberepresentedas图像Image图像Image处RepresentingDigitalTherepresentationofanM×Nnumericalarrayasf(x,y)

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f(1,N)f(2,N) f(M,N 图像 处Image Saturation:Saturation:upperlimitNose:LowerlimitContrast:Contrast:highest-图像 处Image RepresentingDigitalDiscreteintensityinterval[0,L-1],Thenumberbofbitsrequiredtostorea×Ndigitizedimageb=M×N×k图像 处Image RepresentingDigital60f/s,3.75TB/s,60f/s,3.75TB/s,2h,图像 处Image SpatialdeterminedbyhowsamplingwascarriedSpatialresolutionsimplyreferstothesmallestdiscernabledetailVisionspecialistswilloftentalkaboutpixel

Graphicdesignerswilltalkaboutdotsperinch(DPI)图像与处Spadeorocsneny图像处Image图像处ImageSpatialResolution图像图像Image处IntensityLevelIntensitylevelresolutionreferstothenumberofintensitylevelsusedtorepresenttheimageThemoreintensitylevelsused,thefinerthelevelofdetaildiscernableinanimageIntensitylevelresolutionisusuallygivenintermsofthenumberofbitsusedtostoreeachintensityNumberofNumberofIntensity120,2400,01,10,40000,0101,8SpatialandIntensitySpatial—Ameasureofthesmallestdiscernibledetailinan—statedwithlinepairsperunitdistance,dots(pixels)perunitdistance,dotsperinch(dpi)IntensityThesmallestdiscerniblechangeinintensitystatedwith8bits,12bits,16bits,图像处Image图像处ImageIntensityLevel256graylevels(8bitsperpixel)128gray(764gray(632gray(516gray(48graylevels(3bpp)4gray(22gray(1图像 处Image IntensityLevel256graylevels(8bitsper 128graylevels(7 64graylevels(6 32graylevels(516graylevels(4 8graylevels(3 4graylevels(2 2graylevels(1图像Image图像Image处Resolution:HowMuchIsThebigquestionwithresolutionisalwayshowmuchisenough?ThisalldependsonwhatisintheimageandwhatyouwouldliketodowithitKeyquestionsDoestheimagelookaestheticallyCanyouseewhatyouneedtoseewithinthe Thepictureontherightisfineforcountingthenumberofcars,butnotforreadingthenumberplate图像 处Image IntensityLevelLow Medium High图像图像Image处IntensityLevelIntensityLevelIntensityLevel图像 处Image PointslyingonanPointslyingonancorrspondtoimagesofequalsubjectivequalityFixedKIncreaseImageswithalargeamountofdetailonlyafewintensitylevelsmaybe图像图像Image处ImageInterpolation—Processofusingknowndatatoestimateunknownvaluese.g.,zooming,shrinking,rotating,andgeometricInterpolation(sometimescalledresampling)—animagingmethodtoincrease(ordecrease)thenumberofpixelsinadigitalimage.SomedigitalcamerasuseinterpolationtoproducealargerimagethanthesensorcapturedortocreatedigitalzoomUsingknowndatatoestimatevaluesatunknown 图像 处Image ImageInterpolation:NearestNeighborf1(x2,y2)f(round(x2),

f1(x3,y3)f(round(x3),图像图像Image处ImageInterpolation:Bilinearv(x,y)axbycxy444f2(x,(1a)(1b)f(l,k)a(1b)f(l1,k(1a)bf(l,k1)abf(l1,klfloor(x),kfloor(y),axl,byImageInterpolation:BicubicTheintensityvalueassignedtopoint(x,y)isobtainedbythefollowingequation ay f3(x,y) ay i0 jThesixteencoefficientsaredeterminedbyusingthesixteennearestneighbors.PreservemoredetailPreservemoredetail图像 处Image Examples:213*162-72dpi---213*162-72dpi--- 图像 处Image Examples:150dpi---150dpi--- 图像图像处Image Examples:图像Image图像Image处Examples:图像处Image图像处ImageExamples:图像处Image图像处ImageExamples:图像图像Image处ThehumanvisualLightandtheelectromagneticImagesensingandSampling,sationandImageBasicrelationshipsbetweenMathematical图像Image图像Image处BasicRelationshipsBetweenRegionsandNeighborsofapixelpatcoordinates4-neighborsofp,denotedbyN4(p):(x-1,y),(x+1,y),(x,y-1),and(x,y+1).4diagonalneighborsofp,denotedbyND(p):(x-1,y-1),(x+1,y+1),(x+1,y-1),and(x-1,y+1).8neighborsofp,denotedN8(p)=N4(p)ULetVbethesetofintensity4-adjacency:TwopixelspandqwithvaluesfromVare4-adjacentifqisinthesetN4(p).8-adjacency:TwopixelspandqwithvaluesfromVare8-adjacentifqisinthesetN8(p).LetVbethesetofintensitym-adjacency:TwopixelspandqwithvaluesfromVarem-adjacentifqisinthesetN4(p),qisinthesetND(p)andthesetN4(p)∩N4(q)hasnopixelsvaluesarefrom图像 处Image qisinthesetN4(p),qisinthesetND(p)andthesetN4(p)∩N4(q)hasnopixelswhosevaluesarefromV.图像图像Image处BasicRelationshipsBetweenA(digital)path(orcurve)frompixelpwithcoordinates(x0,y0)topixelqwithcoordinates(xn,yn)isasequenceofdistinctpixelswith(x0,y0),(x1,y1),…,(xn,Where(xi,yi)and(xi-1,yi-1)areadjacentfor1≤i≤HerenisthelengthoftheIf(x0,y0)=(xn,yn),thepathisclosedWecandefine4-,8-,andm-pathsbasedonthetypeofadjacency图像Image图像Image处Examples:Adjacencyand

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Them-pathfrom(1,3)to(1,3),(1,2),(2,2),图像Image图像Image处BasicRelationshipsBetweenConnectedinLetSrepresentasubsetofpixelsinanimage.Twopixelspwithcoordinates(x0,y0)andqwithcoordinates(xn,yn)aresaidtobeconnectedinSifthereexistsapath(x0,y0),(x1,y1),…,(xn,Wherei,0in,(xi,yi)ApathbetweenthemconsistingentirelyofpixelsinLetSrepresentasubsetofpixelsinanForeverypixelpinS,thesetofpixelsinSthatareconnectedtopisIfShasonlyoneconnectedcomponent,thenSiscalledConnectedWecallRaregionoftheimageifRisaconnectedTworegions,RiandRjaresaidtobeadjacentiftheirunionformsaconnectedset.Regionsthatarenottobeadjacentaresaidtobe图像 处Image Adjacent图像Image图像Image处QuestionInthefollowingarrangementofpixels,arethetworegions(of1s)adjacent?(if8-adjacencyisused)RegionRegionRegion11Region111101010001111111Inthefollowingarrangementofpixels,arethetwoparts(of1s)adjacent?(if4-adjacencyisused)PartPartPart11Part111101010001111111图像图像Image处RegionRegionInthefollowingarrangementofpixels,thetworegions(of1s)aredisjoint(if4-adjacencyisused)11111101010001111111RegionInthefollowingarrangementofpixels,thetworegions(of1s)aredisjoint(if4-adjacencyisused)111101010001111111图像 处Image BasicRelationshipsBetweenBoundary(orTheboundaryoftheregionRisthesetofpixelsintheregionthathaveoneormoreneighborsthatarenotinR.IfRhappenstobeanentireimage,thenitsboundaryisdefinedasthesetofpixelsinthe andlastrowsandcolumnsoftheimage.ForegroundandAnimagecontainsKdisjointregions,Rk,k=1,2,…,K.LetRudenotetheunionofalltheKregions,andlet(Ru)cdenoteitscomplement.AllthepointsinRuiscalledforeground;Allthepointsin(Ru)ciscalledbackground.图像 处Image InnerboundaryOuter图像Image图像Image处QuestionInthefollowingarrangementofpixels,thecircledpointispartoftheboundaryofthe1-valuedpixelsif8-neighborisused,trueorfalse?00000000000110001100011100111000000图像图像Image处QuestionInthefollowingarrangementofpixels,thecircledpointispartoftheboundaryofthe1-valuedpixelsif4-neighborisused,trueorfalse?00000000110001100011100111000000图像Image图像Image处DistanceGivenpixelsp,qandzwithcoordinates(x,y),(s,t),(u,v)respectively,thedistancefunctionDhasfollowingproperties:D(p,q)≥ [D(p,q)=0,iffp=D(p,q)=D(q,D(p,z)≤D(p,q)+D(q,ThefollowingarethedifferentDistanceEuclideanDistanceDe(p,q)=[(x-s)2+(y-CityBlockDistance:D4(p,q)=|x-s|+|y-t|ChessBoardDistance:D8(p,q)=max(|x-s|,|y-t|)图像Image图像Image处QuestionInthefollowingarrangementofpixels,what’sthevalueofthechessboarddistancebetweenthecircledtwopoints?0000000000011001100010000000000000Inthefollowingarrangementofpixels,what’sthevalueofthecity-blockdistancebetweenthecircledtwopoints?0000000000011001100010000000000000图像Image图像Image处QuestionInthefollowingarrangementofpixels,what’sthevalueofthelengthofthem-pathbetweenthecircledtwopoints?000000011000 11000000000000000图像图像Image处QuestionInthefollowingarrangementofpixels,what’sthevalueofthelengthofthem-pathbetweenthecircledtwopoints? ThehumanvisualLightandtheelectromagneticImagesensingandSampling,sationandImageBasicrelationshipsbetweenMathematicalIntroductiontoMathematicalOperationsinArrayvs.Matrix A a12

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HissaidtobealinearHissaidtobeanonlinearoperatorifitdoesnotmeettheabovequalification.图像 处Image ArithmeticArithmeticoperationsbetweenimagesarearrayoperations.Thefourarithmeticoperationsaredenoteds(x,y)=f(x,y)+d(x,y)=f(x,y)–p(x,y)=f(x,y)×v(x,y)=f(x,y)÷图像 处Image AnExampleofImageLeastsignificantbitLeastsignificantbit图像Image图像Image处Example:AdditionofNoisyImagesforNoiseNoiselessimage:Noise:n(x,y)(ateverypairofcoordinates(x,y),thenoiseisuncorrelatedandhaszeroaveragevalue)Corruptedimage:g(x,y)=f(x,y)+ReducingthenoisebyaddingasetofnoisyKig(x,y)1g(x,iKKg(x,y)1g(x,

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2n(x,y图像 处Image Example:AdditionofNoisyImagesforNoiseInastronomy,imagingunderverylowlightlevelsfrequentlycausessensornoisetorendersingleimagesvirtuallyuselessfor Inastronomicalobservations,similarsensorsfornoisereductionbyobservingthesamesceneoverlongperiodsoftime.Imageaveragingisthenusedtoreducethenoise. 1020 50 100图像 处Image AnExampleofImageSubtraction:MaskModeMaskh(x,y):anX-rayimageofaregionofapatient’sLiveimagesf(x,y):X-rayimagescapturedatTVratesafterinjectionofthecontrastmediumg(x,y)=f(x,y)-TheproceduregivesamovieshowinghowthecontrastmediumpropagatesthroughthevariousarteriesintheareabeingLiveEnhanced

Theproceduregivesamovieshowinghowthecontrastmediumpropagatesthroughthevariousarteriesintheareabeingobserved.图像 处Image AnExampleofImageShadedShadedShadedShadedG(x,y)=f(x,y)h(x,y):f(x,y)perfectimage;h(x,y)shaded 图像 处Image IntensityGivenimagef,guaranteethefullrangeofanarithmeticoperationbetweenimagesiscapturedintoafixednumberofbits0-255,sum:0-

fmfmin(ffsK[fm/max(fm)]0fmK8bit8bit图像 处Image SpatialSingle-pixelAlterthevaluesofanimage’spixelsbasedonthesT(z)图像处Image图像处ImageSpatial NeighborhoodThevalueofthispixelisdeterminedbyaspecifiedoperationinvolvingthepixelsintheThevalueofthispixelisdeterminedbyaspecifiedoperationinvolvingthepixelsintheinputimagewithcoordinatesinSxy图像图像Image处GeometricSpatialGeometrictransformation(rubber-sheet—Aspatialtransformationof(x,y)T{(v,—intensityinterpolationthatassignsintensityvaluestothespatiallytransformedpixels.Affine

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t31 图像 处Image IntensityForward(x,y)T{(v,It’spossiblethattwoormorepixelscanbetransformedtothesamelocationintheoutputimage.Inverse(v,w)T1{(x,ThenearestinputpixelstodeterminetheintensityoftheoutputpixelInversemapsaremoreefficienttoimplementthan 图像 处Image Example:ImageRotationandIntensityRotate21-图像Image图像Image处Image Inputandoutputimagesareavailablebutthetransformationfunctionisunknown.Goal:estimatethetransformationfunctionanduseittoregisterthetwoimages. Oneoftheprincipalapproachesforimage Thecorrespondingpointsareknownpreciselyintheinputandoutput(reference)images.Asimplemodelbasedonbilinearxc1vc2wc3vwycvcwcvw Where(v,w)and(x,y)arethecoordinatesoftiepointsintheinputandreferenceimages.mIm图像 处ImageImageImageEOCompositebeforeIR

IRCompositeafter图像 处Image 图像配参考图像（主图像 待配准图像（辅图像 图像图像Image处AffinevsNon-Non-Non-AverageAnatomicalImagesfrom10Subjectsdisplayedat1.5x1.5x1.5Image 图像Image Imageregistration图像 处Image ImageAparticularlyimportantclassof2-Dlineartransforms,denotedT(u,v)M1NT(u,v) f(x,y)r(x,y,u,x0wheref(x,y)istheinputr(x,y,u,v)istheforwardtransformationkernel,variablesuandvarethetransformvariables,u=0,1,2,...,M-1andv=0,1,...,N-图像Image图像Image处ImageGivenT(u,v),theoriginalimagef(x,y)canberecoveredusingtheinversetransformationofT(u,v).M1Nf(x,y) T(u,v)s(x,y,u,u0wheres(x,y,u,v)istheinversetransformation x=0,1,2,...,M-1andy=0,1,...,N-1.图像 处Image Example:ImageDenoisingbyUsingDCTDifferentDifferentsinusoidal图像 处Image FourierFT图像图像Image处图像图像Image处ForwardTransformM1NT(u,v) f(x,y)r(x,y,u,x0yThekernelr(x,y,u,v)issaidtobeSEPERABLEr(x,y,u,v)r1(x,u)r2(y,Inaddition,thekernelissaidtobeSYMMETRICr1(x,u)isfunctionallyequaltor2(y,v),sor(x,y,u,v)r1(x,u)1(y,TheKernelsfor2-DFourierTheforwardr(x,y,u,v)ej2(ux/Mvy/NWhere Theinverses(x,y,u,v)

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图像 处Image BackgroundmathematicsMatrixalgebra图像图像Image处Review:MatricesandSomeAnm×n(read"mbyn")matrix,denotedbyA,isarectangulararrayofentriesorelements(numbers,orsymbolsrepresentingnumbers)enclosedtypicallybysquarebrackets,wheremisthenumberofrowsandnthenumberofcolumns.图像Image图像Image处Review:MatricesandDefinitionsAissquareifm=Aisdiagonalifalloff-diagonalelementsare0,andnotalldiagonalelementsare0.Aistheidentitymatrix(I)ifitisdiagonalandalldiagonalelementsare1.Aisthezeroornullmatrix(0)ifallitselementsareThetraceofAequalsthesumoftheelementsalongitsmainTwomatricesAandBareequaliffthehavethesamenumberofrowsandcolumns,andaij=bij.图像Image图像Image处Review:MatricesandDefinitionsThetransposeATof