全面的图像滤波方面课件PPT

Whatisnoise?s=1,3,5Gaussianfilters=2s=4Gaussiansmoothingp1p2p1p1p1p2P2P1GxGGaussianandits2derivativesLOGoperatorLocalimagecharacteristicsbasedon:•Scale•Frequency•DirectionxGsyGsyGxGsssincosFourierbasisSpatialdomainFrequencydomain1/s1/sssEven(Symmetric)Odd(antisymmetic)GaborFilterExampleHighfrequencyalongaxisLowerfrequencyoff-axisEvenlowerfrequencyScalesmallcomparedtoinversefrequencys=2f=1/6OddGaborfilterFirstDerivativeEvenGaborfilterLaplacianyGxGguFxgFgFfFgfFdudveyxgvugFyyxGxyxGyxGyGxGGyeyyxGxexyxGeyxGvyuxityxyxyxssssssssssssssssincos)()()().()*(),(),)((),(),(),(),(),(21),()(2222222222222222222Separable,low-passfilterNot-separable,approximatedbyAdifferenceofGaussians.OutputofconvolutionisLaplacianofimage:Zero-crossingscorrespondtoedgesSeparable,outputofconvolutionisgradientatscales:sGII*GaussianDerivativesofGaussianDirectionalDerivativesLaplacianFourierTransformF(g)(u,v)=componentofimageatfrequencysqrt(u2+v2)indirection(u,v)TransformofGaussiansisGaussian1/sOutputofconvolutionismagnitudeofderivativeindirection.Filterislinearcombinationofderivativesinxandyuuueykxkseykxkannyxyxyxyxiii2,...,2,2,...,2,)(2(in:odd)(2cos(:even22222222sssssSteerability(可操控性)Generalizationofpropertyofderivatives:issteerableiftherotatedfiltercanbeexpressedasalinearcombinationofbasisfilters.GaborFiltersComputethelocalcontributionoffrequencyinthedirection(kx,ky)atscales.Forslargecomparedto1/f,evenfiltersapproximate2ndderivative,oddfiltersapproximate1stderivative.22yxkkfSpecialcaseofGaborwaveletsifsandfrestrictedtopowersof2GaussianPyramids),,(**11yxfIGSILIGSIkkkkksssGaussiansmoothimageandsubsampleateachstageComputeLaplacianbydifferenceofGaussianateachstageLaplacianPyramidsScale-SpaceConverttheimagef(x,y)toacontinuousfunctionofscale222222121122ssybxaybxaeDirectionalsmoothingSmoothwithdifferentscalesinorthogonaldirections