第9章Contourlet变换及其应用

[e-mail]://isip.xmu.edu.cn://isip.xmu.edu.cn2JointLaboratoryofShantouandXiamenUniversity,2008Contourlet„9.1Contourlet„9.1.1LP„9.1.2DFB„9.1.3„9.2Contourlet„9.2.1Contourlet„9.2.2Contourlet„9.3Contourlet„9.3.1NSCT„9.3.2NSCT„9.3.33JointLaboratoryofShantouandXiamenUniversity,20089.1Contourlet„Contourlet(Contoursegment)“”ContourletContourlet“”,9.14JointLaboratoryofShantouandXiamenUniversity,20089.1Contourlet•ab•9.1abContourlet5JointLaboratoryofShantouandXiamenUniversity,20089.1Contourlet„Contourlet(LP)(DFB)9.2CurveletCurvelet„9.2Contourlet(LP)(DFB)6JointLaboratoryofShantouandXiamenUniversity,20089.1.1LP„ba9.3HGMbnNab9.3LPaLPbLP7JointLaboratoryofShantouandXiamenUniversity,20089.1.2DFB)„1992BambergerSmith2-D(DFB)DFBl„MinhN.DoDFBQuincunx9.42-DQ„Q-01111Q−⎛⎞=⎜⎟⎝⎠11111Q⎛⎞=⎜⎟−⎝⎠0Q1Q45458JointLaboratoryofShantouandXiamenUniversity,20089.1.2DFB)„ShearingQuincunxshearing9.5ShearingShearingShearing9.4Quincunx9JointLaboratoryofShantouandXiamenUniversity,20089.1.2DFB)„01101R⎛⎞=⎜⎟⎝⎠11101R−⎛⎞=⎜⎟⎝⎠21011R⎛⎞=⎜⎟⎝⎠31011R⎛⎞=⎜⎟−⎝⎠9.5Shearingl[][]001100111()()()()()()21()()()()()2XHGHGXHGHGXωωωωωωωπωωπωωπ=++++++10JointLaboratoryofShantouandXiamenUniversity,20089.1.2DFB)„„9.4H0,H1,G0,G1QuincunxQuincunx0011()()()()2HGHGωωωω+=0011()()()()0HGHGωπωωπω+++=•ab•9.6DFBal=2bl=311JointLaboratoryofShantouandXiamenUniversity,20089.1.2DFB)„DFBShearingQuincunx9.69.7DFBQuincunx9.6a01239.6a019.6a32QuincunxShearingQuincunxDFB019.8Type1Type29.7DFB)0y00y01y1y10y11y00y01y10y11y0R2R0Q1Q12JointLaboratoryofShantouandXiamenUniversity,20089.1.2DFB)„zoneplateDFB9.7DFB9.8DFB13JointLaboratoryofShantouandXiamenUniversity,20089.1.2DFB)•(a)(b)•9.9‘zoneplate’3DFB14JointLaboratoryofShantouandXiamenUniversity,20089.1.2DFB)„DFB9.6bDFB9.10ES„9.109.10DFB15JointLaboratoryofShantouandXiamenUniversity,20089.1.2DFB)„„DFB„11()11(2,2),02(2,2),22lllkllldiagforkSdiagfork−−−−⎧≤⎪=⎨≤⎪⎩9-1{}2()()02,lllkkkmZdnSm≤∈⎡⎤−⎣⎦9-216JointLaboratoryofShantouandXiamenUniversity,20089.1.3„Coutourlet9.119.11Contourlet17JointLaboratoryofShantouandXiamenUniversity,20089.1.3„9.12contourletwaveletwaveletcontourletcontourletwaveletcontourletDFB0wavelet9.12contourlet18JointLaboratoryofShantouandXiamenUniversity,20089.1.3„PDFBCoutourlet„1.LPDPFPDFB„2.LPDPFPDFB1„3.PDFB4/3„4.DFBLPj(j=12…Jj=1)„„5.FIRNPDFBjl2jwidth≈/22jlength≈()oN19JointLaboratoryofShantouandXiamenUniversity,20089.1.3„contourlet:„9.132contourlet8DFB8Contourletcoefficients(a)(b)20JointLaboratoryofShantouandXiamenUniversity,20089.1.3„9.143contourletpeppers3LP16Contourletcoefficients•(c)(d)•9.13contourlet2(a)c•b(d)21JointLaboratoryofShantouandXiamenUniversity,20089.1.39.14peppers3Contourlet22JointLaboratoryofShantouandXiamenUniversity,20089.2.1Contourlet„1Contourlet„Contourlet„0Contourlet„9.15,{;,1,2,...,;}ijfijnnN=∈,ijf(,)ij,,,{;,1,2,...,;}ijijijgfijnnNε=+=∈,ijεσ,,,{,,1,2,...,;}ijijijgfCCCijnnNε=+=∈(9-3)23JointLaboratoryofShantouandXiamenUniversity,20089.2.1Contourlet„512512BarbaraContourletContourletSNR9.15Contourlet24JointLaboratoryofShantouandXiamenUniversity,20089.2.1Contourlet„„9.1BarbaraSNR„9.1SNR210log10fSNRMSEσ⎛⎞=⎜⎟⎜⎟⎝⎠2,,111()MNijijijMSErfMN===−∑∑,ijf,ijr2fσMN25JointLaboratoryofShantouandXiamenUniversity,20089.2.1Contourletk16.5916.5412.03415.0915.029.50313.3713.036.012Lena14.3714.3512.03413.0512.649.55311.310.466.032BarbaraContourlet(dB)Wavelet(dB)(dB)9.16(a)3Barbara(b)(c)(d)Contourlet26JointLaboratoryofShantouandXiamenUniversity,20089.2.1Contourlet(a)(b)(c)(d)27JointLaboratoryofShantouandXiamenUniversity,20089.2.1Contourlet„9.16Contourlet(a)(b)(c)(d)Contourlet„ContourletSNRContourletContourlet“”Contourlet28JointLaboratoryofShantouandXiamenUniversity,20089.2.1Contourlet„2ContourletCycleSpinning„ContourletContourletContourletGibbs29JointLaboratoryofShantouandXiamenUniversity,20089.2.1Contourlet„ContourletGibbsGibbsContourletContourlet„×(,)Ixy,()ijCI[],()mod(,),mod(,)ijCIIxiNyjN=++9-630JointLaboratoryofShantouandXiamenUniversity,20089.2.1Contourlet„„Sn„DNCTContourlet„fTContourletContourleth1,,()()ijijCICI−−−⎡⎤=⎣⎦9-7^,,((()))ijijICDNCTCS−−=9-81(){[()]}DNCTfThTf−=9-9^I31JointLaboratoryofShantouandXiamenUniversity,20089.2.1Contourlet„:„„12^,,1,1121((()))NNijijijICDNCTCsNN−−===∑9-101N2N32JointLaboratoryofShantouandXiamenUniversity,20089.2.1Contourlet„,,0;1:;1:;();();'();';;;/()ijijSumforiNforjNfCSuDNCTfICuSumISumendendISumNN−−=======+=×33JointLaboratoryofShantouandXiamenUniversity,20089.2.1Contourlet„512512BarbaraLenacontourlet_toolboxContourletContourletCycleSpinning(CS)ContourletLP“pkva”DFBContourletDFB4816CycleSpinningContourlet23459.29.3BarbaraLenaPSNRSNR9.17ContourletContourletPSNRSNR9.18Lena4034JointLaboratoryofShantouandXiamenUniversity,20089.2.1Contourlet9.2BarbaraLenaPSNR====35JointLaboratoryofShantouandXiamenUniversity,20089.2.1Contourlet36JointLaboratoryofShantouandXiamenUniversity,20089.2.1Contourlet9.3BarbaraLenaSNR====37JointLaboratoryofShantouandXiamenUniversity,20089.2.1Contourlet38JointLaboratoryofShantouandXiamenUniversity,20089.2.1Contourl