Chapter2X-1GeometricImageTransform

SpatialTransform2.x.1Fundamentals2.x.1.1SpatialTransformInputimage:f(u,v)Outputimage:g(x,y)g(x,y)=f(u,v)(x,y)=T[(u,v)],2013/9/162.x.1Fundamentals2.x.1.2ForwardMapping (x,y)=(X(u,v),Y(u,v)) example:Zoomout (x,y)=(u/2,v/2) [Programming]2.x.1Fundamentals2.x.1.3InverseMapping (u,v)=(U(x,y),V(x,y))

example:Zoomout (u,v)=(x*2,y*2) [Programming]

2.x.1Fundamentalsexample:Zoomin FM:(x,y)=(u*2,v*2)

IM:(u,v)=(x/2,y/2)

[Programming]2.x.1FundamentalsUsuallyImageProcessing(SpatialTransform)usingIMComputerGraphics(GeometricsRender)usingFM2.x.2AffineTransform2.x.2.1DefinitionofAffineTransformA(x)=L(x)+c2.x.2.2GeneralForm

2.x.2AffineTransform2.x.2AffineTransform2.x.2.3OthersExerciseFlipTransformFlipHorizontalFlipVerticalZoomAt(x0,y0)LocalZooming[Programming]ExerciseFlipVExerciseFlipHExercise（2014.9.22）Byte[,]ZoomAt(byte[,]f,intx0,inty0,floatK)Exercisebyte[,]localZooming(byte[,]f,intx0,inty0,floatR,floatK)Exercisebyte[,]localZooming2(byte[,]f,intx0,inty0,floatR,floatK)CompostedAffineTransformBasicAffineTransformTranslation,Scaling,RotationCompostedAffineTransform eg.ZoomingAtAffineTransformPropertiesCompostedAffineTransformisAffineTransformInverseAffineTransformisAffineTransform2.x.3ImageInterpolation2.x.3.1Background[ProgrammingofZoomin4X4]2.x.3ImageInterpolation2.x.3.2Sampling&Interpolation

Samplingf(X)f[n]f[n]Interpolation2.x.3ImageInterpolation2.x.3.2Sampling&Interpolationf[n]=f(n),f[n]=int(f(n))h(x):InterpolationKernal2.x.3ImageInterpolation2.x.3.2NearestNeighborhoodInterpolation2D:x’=(int)(x+0.5),y’=(int)(y+0.5)2.x.3ImageInterpolation2.x.3.2BilinearInterpolationi<=x<i+1a=x-if(x)=f[i]*(1-a)+f[i+1]*a;2.x.3ImageInterpolation2.x.3.2BilinearInterpolation2D i<=x<i+1,j<=y<j+1, a=x-i,b=y-jf(x,j)=f[i,j]*(1-a)+f[i+1,j]*a;f(x,j+1)=f[i,j+1]*(1-a