19RobotVision-Transformation2012/9/11ROBOTVISIONHuang-NanHuang2012/9/112012/9/112012AutumnContentsDiscreteTransform32012/9/1142012/9/11
Imagetransform
DiscreteTransform
FourierTransform
DiscreteCosineTransform
WaveletTransform
Here,theimagedataaremappedfromthespatialdomaintothefrequencydomain,alsoviewedasthefactthatatransformmapsimagedataintoadifferentmathematicalspaceviaatransformationequation;whereallthepixelsintheinput(spatialdomain)contributetoeachvalueintheoutput(frequencydomain).IntroductiontotheFourierTransform52012/9/1162012/9/11
Thediscreteformofthosetransformiscreatedbysampling
TheOne-DimensionalFourierTransformanditsInversethecontinuousarebased,i.e.,thebasisfunctions,andsuchfunctionsaretypicallysinusoidalorrectangular.
Eachvalueinthefrequencydomainisalinearsumofbasisfunctions.
Thebasicfunctionsaresampledandthenprovideduswithbasisvectorfor1-Dcase.Ifweextendtheseinto2-Dcase,asforimage,suchdiscretebasicfunctionsarecalledbasismatricesorbasisimages.
Theprocessoftransformingtheimagedataintoanotherdomainamountstoprojectingtheimageontobasisimages.Why?Two-DimDiscreteFourierTransform72012/9/1182012/9/11Filteringinthefrequencydomain92012/9/11102012/9/112012/9/112012/9/111112FastFourierTransform132012/9/11142012/9/11DiscreteFourierTranform2012/9/11162012/9/1115Fourierspectrum172012/9/11182012/9/11Matlab-fft2,fftshift,ifft2DiscreteCosineTranform192012/9/11202012/9/112012/9/112012/9/1121222D232012/9/112012/9/11242012/9/112012/9/112526272012/9/112012/9/11
“f(x,y)–128”modifies[0,255]to[-128,127]inordertoreducethemaximumbitnumberneededtorepresenttheDC(i.e.,c(0,0))term.28Featuresof2D-DCTMatlab-dct2,idct2292012/9/11302012/9/11
Frequency:number(ordegree)ofalternating(交錯)ofbasisimagesthedistributionoffrequencyforbasisimage.WaveletTransform312012/9/112012/9/11
Similartosub-bandcoding.
Advantages:1.Thecompressionefficiencyofeachsubbandsignalismo