圖像與處Image 第二講：圖像處理基人工智能與機(jī)器InstituteofArtificial ligenceand蘭旭圖像處Image圖像處ImageThehumanvisualLightandtheelectromagneticImagesensingandSampling,sationandImageBasicrelationshipsbetweenMathematicalThehumanvisualLightandtheelectromagneticImagesensingandSampling,sationandImageBasicrelationshipsbetweenMathematical圖像圖像Image處HumanVisualThebestvisionmodelweKnowledgeofhowimagesformintheeyecanhelpuswithprocessingdigitalWewilltakejustawhirlwindtourofthehumanvisualsystem圖像 處理Image 睫狀睫狀OfThe

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纖纖維肌視網(wǎng)角視網(wǎng)

玻璃狀盲盲

神經(jīng)

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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圖像處Image圖像處ImageGoodWeberpoorbrightnesspoorbrightness圖像 處Image Inlow-levelillumination,ispoor(WeberratioisCarriedoutbyrods-暗光Itimprovessignificantlyasbackgroundcarriedoutbycones—圖像處Image圖像處ImageBrightnessAdaptation&ErnstPerceivedbrightnessIsPerceivedbrightnessIsnotasimplefunctionofintensityAnexampleofMachUndershootaroundTheboundaryofRegionsUndershootaroundTheboundaryofRegionsOfdifferentAnAnexampleofsimultaneousPerceivedPerceivedbrightnessdoesnotdependSimplyonitsintensityFormoregreatillusionexamplestakealookAvailable圖像圖像Image處OpticalOurvisualplaylotsoftricksonusMindMapExercise:MindMapForNoteBeauLotto:BeauLotto:OpticalIllusionsShowHowWeThehumanvisualLightandtheelectromagneticImagesensingandSampling,sationandImageBasicrelationshipsbetweenMathematicalLightAndTheElectromagneticIn1666SirIsaacNewtondiscoveredthatlightpassedthroughaprismsplitsintoacontinuousspectrumofLightisjustaparticularpartoftheelectromagneticspectrumthatcanbesensedbythehumaneyeTheelectromagneticspectrumissplitupaccordingtothewavelengthsofdifferentformsofenergyLightandEMc E h:Planck's光譜能波長(zhǎng)m光譜能ElectromagneticElectromagneticshorterwaveMoreenergyshorterwaveMoreenergyv圖像Image圖像Image處LightandEMThecolorsthathumansperceiveinanobjectaredeterminedbythenatureofthelightreflectedfromtheobject.e.g.greenobjectsreflectlightwithwavelengthsMonochromaticlight:voidofIntensityistheonlyattribute,fromblacktoMonochromaticimagesarereferredtoasgray-Chromaticlightbands:0.43to0.79umThequalityofachromaticlightsource:Radiance:totalamountofenergyLuminance(lm):theamountofenergyanobserverfromalightBrightness:asubjectivedescriptoroflightperceptionthatisimpossibletomeasure.Itembodiestheachromaticnotionofintensityandoneofthekeyfactorsindescribingcolorsensation.圖像圖像Image處ThehumanvisualLightandtheelectromagneticImagesensingandSampling,sationandImageBasicrelationshipsbetweenMathematical圖像 處Image Sampling,sationAndInthefollowingslideswewillconsiderwhatisinvolvedincapturingadigitalimageofareal-worldsceneImagesensingandSamplingand圖像 處Image ImageingenergylandsonasensormaterialresponsivetothattypeofenergyandthisgeneratesavoltageCollectionsofsensorsarearrangedtocaptureimagesImagingLineofImage ArrayofImage圖像處Image圖像處ImageImagetolightHighprecision

Lowcost:UsingSensorStripsand

圖像圖像Image處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圖像 處Image GrayMonochromelf(x0,y0)LminlLmaxLminiminrminLmaximaxrmax[Lmin,Lmax圖像圖像Image處ThehumanvisualLightandtheelectromagneticImagesensingandSampling,sationandImageBasicrelationshipsbetweenMathematicalImageSamplingAndAdigitalsensorcanonlymeasurealimitednumberofsamplesatadiscretesetofenergysationistheprocessofconvertinga oguesignalintoadigitalrepresentationofthissignalImageSamplingAndImageSampling 圖像 處Image ImageSamplingAndRememberthatadigitalimageisalwaysonlyanapproximationofarealworldImagequalityisImagequalityisdeterminedbythenumberofsamplesAnddiscreteintensitylevelsusedinsamplingand 圖像圖像Image處ImageSamplingAndSamplingisdeterminedbythesensorarrangementusedtogeneratetheSamplingaccuracyrelatestoqualityoftheopticalcomponentsofthesystem.ThehumanvisualLightandtheelectromagneticImagesensingandSampling,sationandImageBasicrelationshipsbetweenMathematical圖像處Image圖像處ImageImageBeforewediscussimageacquisitionrecallthatadigitalimageiscomposedofMrowsandNcolumnsofpixelseachstoringavaluef(row,f(row,Wewillseelateronthatimagescaneasilyberepresentedas圖像Image圖像Image處RepresentingDigitalTherepresentationofanM×Nnumericalarrayasf(x,y)

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

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

f1(x3,y3)f(round(x3),圖像圖像Image處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圖像 處Image Examples:213*162-72dpi---213*162-72dpi--- 圖像 處Image Examples:150dpi---150dpi--- 圖像圖像處Image Examples:圖像Image圖像Image處Examples:圖像處Image圖像處ImageExamples:圖像處Image圖像處ImageExamples:圖像圖像Image處ThehumanvisualLightandtheelectromagneticImagesensingandSampling,sationandImageBasicrelationshipsbetweenMathematical圖像Image圖像Image處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圖像 處Image qisinthesetN4(p),qisinthesetND(p)andthesetN4(p)∩N4(q)hasnopixelswhosevaluesarefromV.圖像圖像Image處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圖像Image圖像Image處Examples:Adjacencyand

V={1,

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Them-pathfrom(1,3)to(1,3),(1,2),(2,2),圖像Image圖像Image處BasicRelationshipsBetweenConnectedinLetSrepresentasubsetofpixelsinanimage.Twopixelspwithcoordinates(x0,y0)andqwithcoordinates(xn,yn)aresaidtobeconnectedinSifthereexistsapath(x0,y0),(x1,y1),…,(xn,Wherei,0in,(xi,yi)ApathbetweenthemconsistingentirelyofpixelsinLetSrepresentasubsetofpixelsinanForeverypixelpinS,thesetofpixelsinSthatareconnectedtopisIfShasonlyoneconnectedcomponent,thenSiscalledConnectedWecallRaregionoftheimageifRisaconnectedTworegions,RiandRjaresaidtobeadjacentiftheirunionformsaconnectedset.Regionsthatarenottobeadjacentaresaidtobe圖像 處Image Adjacent圖像Image圖像Image處QuestionInthefollowingarrangementofpixels,arethetworegions(of1s)adjacent?(if8-adjacencyisused)RegionRegionRegion11Region111101010001111111Inthefollowingarrangementofpixels,arethetwoparts(of1s)adjacent?(if4-adjacencyisused)PartPartPart11Part111101010001111111圖像圖像Image處RegionRegionInthefollowingarrangementofpixels,thetworegions(of1s)aredisjoint(if4-adjacencyisused)11111101010001111111RegionInthefollowingarrangementofpixels,thetworegions(of1s)aredisjoint(if4-adjacencyisused)111101010001111111圖像 處Image BasicRelationshipsBetweenBoundary(orTheboundaryoftheregionRisthesetofpixelsintheregionthathaveoneormoreneighborsthatarenotinR.IfRhappenstobeanentireimage,thenitsboundaryisdefinedasthesetofpixelsinthe andlastrowsandcolumnsoftheimage.ForegroundandAnimagecontainsKdisjointregions,Rk,k=1,2,…,K.LetRudenotetheunionofalltheKregions,andlet(Ru)cdenoteitscomplement.AllthepointsinRuiscalledforeground;Allthepointsin(Ru)ciscalledbackground.圖像 處Image InnerboundaryOuter圖像Image圖像Image處QuestionInthefollowingarrangementofpixels,thecircledpointispartoftheboundaryofthe1-valuedpixelsif8-neighborisused,trueorfalse?00000000000110001100011100111000000圖像圖像Image處QuestionInthefollowingarrangementofpixels,thecircledpointispartoftheboundaryofthe1-valuedpixelsif4-neighborisused,trueorfalse?00000000110001100011100111000000圖像Image圖像Image處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|)圖像Image圖像Image處QuestionInthefollowingarrangementofpixels,what’sthevalueofthechessboarddistancebetweenthecircledtwopoints?0000000000011001100010000000000000Inthefollowingarrangementofpixels,what’sthevalueofthecity-blockdistancebetweenthecircledtwopoints?0000000000011001100010000000000000圖像Image圖像Image處QuestionInthefollowingarrangementofpixels,what’sthevalueofthelengthofthem-pathbetweenthecircledtwopoints?000000011000 11000000000000000圖像圖像Image處QuestionInthefollowingarrangementofpixels,what’sthevalueofthelengthofthem-pathbetweenthecircledtwopoints? ThehumanvisualLightandtheelectromagneticImagesensingandSampling,sationandImageBasicrelationshipsbetweenMathematicalIntroductiontoMathematicalOperationsinArrayvs.Matrix A a12

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HissaidtobealinearHissaidtobeanonlinearoperatorifitdoesnotmeettheabovequalification.圖像 處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)÷圖像 處Image AnExampleofImageLeastsignificantbitLeastsignificantbit圖像Image圖像Image處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圖像 處Image Example:AdditionofNoisyImagesforNoiseInastronomy,imagingunderverylowlightlevelsfrequentlycausessensornoisetorendersingleimagesvirtuallyuselessfor Inastronomicalobservations,similarsensorsfornoisereductionbyobservingthesamesceneoverlongperiodsoftime.Imageaveragingisthenusedtoreducethenoise. 1020 50 100圖像 處Image AnExampleofImageSubtraction:MaskModeMaskh(x,y):anX-rayimageofaregionofapatient’sLiveimagesf(x,y):X-rayimagescapturedatTVratesafterinjectionofthecontrastmediumg(x,y)=f(x,y)-TheproceduregivesamovieshowinghowthecontrastmediumpropagatesthroughthevariousarteriesintheareabeingLiveEnhanced

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

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

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

IRCompositeafter圖像 處Image 圖像配參考圖像（主圖像 待配準(zhǔn)圖像（輔圖像 圖像圖像Image處AffinevsNon-Non-Non-AverageAnatomicalImagesfrom10Subjectsdisplayedat1.5x1.5x1.5Image 圖像Image Imageregistration圖像 處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-圖像Image圖像Image處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.圖像 處Image Example:ImageDenoisingbyUsingDCTDifferentDifferentsinusoidal圖像 處Image FourierFT圖像圖像Image處圖像圖像Image處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)

ej2(ux/Mvy/N2-DFourierM1NT(u,v) f(x,y)ej2(ux/Mvy/Nx0yTAFA[ej2ux/M][image][ej2vy/Nf(x,y)

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wherenkisthenumberoftimesthatintensityp(zk)kThemean(average)intensityisgivenm zkp(zkk

occursinthe圖像 處Image ProbabilisticThevarianceoftheintensitiesisgiven2 =(zkm)2p(zk2kThenthmomentoftheintensityvariablezun(z)=(zkk

m)np(zk圖像 處Image Example:ComparisonofStandardDeviation

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