Chapter2

DigitalImageFundamentals2.6MathematicalToolsUsedinDigitalImageProcessing2.6.1Array/Matrix2.6.2Linear/NonlinearOperation

Exercise:Givetwoexamplesoflinearoperations&twoexamplesofnonlinearoperations.(inputis1-Dsignalf(x))

2.6.3ArithmeticOperation

s(x,y)=f(x,y)+h(x,y)

d(x,y)=f(x,y)-h(x,y)

p(x,y)=f(x,y)×h(x,y)

v(x,y)=f(x,y)÷h(x,y)

ApplicationofArithmeticOperationAdditiong(x,y)=f(x,y)+n(x,y) n(x,y)isnoiseimage.(2013/10/08)EmulateNoiseEffect[Programming：Rand(),SaturationOperation]ApplicationofArithmeticOperationAveragingKdifferentnoisyimagesSubtractiond(x,y)=f(x,y)-h(x,y)Enhancethedifferencebetween2imagesApplicationofimagesubtraction1Applicationofimagesubtraction2Multiplication g(x,y)=f(x,y)h(x,y) f(x,y)=i(x,y)r(x,y),ImageFormationModel,

i(x,y):illuminationcomponents,0<i(x,y)<∞,r(x,y):reflectancecomponents,0<r(x,y)<1 Emulatelightingeffect. g(x,y)=f(x,y)l(x,y)DivisionShadingCorrectionf(x,y)=g(x,y)/l(x,y); orMultiplicationf(x,y)=g(x,y)*(1/f(x,y))Applicationofimagemultiplication

ordivisionApplicationofImageMultiplication

ROI(regionofinterest)operationOtherApplicationofArithmeticOperationHowtodisplayaimagef(x,y)whichvaluerangeisoutof[0..255]fm=f-min(f);fs=K(fm/max(fm)),whereK=255MixOperationg(x,y)=f1(x,y)*(1-u)+f2(x,y)*u2.6.4SetAndLogicOperation

(1)SetOperation2.6.4SetAndLogicOperation

(2)LogicOperationSetOperation/LogicOperation2.6.5SpatialOperation(1)Singlepixeloperation:g(x,y)=T(f(x,y))g[x,y]=L-1-f[x,y];Lisgraylevels(256)2.6.5SpatialOperation(2)NeighborhoodoperationNeighborhoodoperationLocalaveragingusing8-neighborsg[x,y]=(f[x,y]+f[x-1,y]+f[x+1,y]+f[x,y-1]+f[x,y+1]+f[x-1,y-1]+f[x+1,y-1]+f[x-1,y+1]+f[x+1,y+1])/9ExerciseA:g[x,y]=f[x,y]-f[x-1,y];B:g[x,y]=f[x,y]+10;2.6.5SpatialOperation(3)GeometricImageTransformSpatialTransform2.6.6VectorandMatrixOper