基于双树复小波变换的图像盲水印算法.docx
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基于双树复小波变换的图像盲水印算法.docx
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基于双树复小波变换的图像盲水印算法
ABlindImageWatermarkingAlgorithmBasedonDualTree
ComplexWaveletTransform
S.Mabtoul,E.Ibn-Elhaj,D.Aboutajdine
Abstract—ThispaperpresentsawatermarkingprocedurefordigitalimageintheComplexWaveletDomain.First,awatermarkimageascopyrightsignispreprocessedwitharandomlocationmatrix.TheoriginalimageistransformedinthecomplexwaveletdomainbyusingDT-CWT,then,accordingtothecharacteristicsoftheimagedata,thepreprocessedwatermarkimageisadaptivelyspreadspectrumandaddedintothehostimageDT-CWTcoefficients.ThesuperiorresultsforimageprocessingapplicationscomparedtotheDWT[5,6].
Intheproposedscheme,weappliedtheDualTreeComplexWaveletTransform;thewatermarkimageispreprocessedwitharandommatrix,adaptivelyspreadspectrum[7]andaddedintothehostimageDT-CWTcoefficients.
proposedwatermarkalgorithmneedstwokeys:
arandomlocationmatrixensuresthesecurityofwatermarkingprocedureandspreadspectrumwatermarksequenceguaranteesitsrobustness.Simulationresultsdemonstratetherobustnessofourimagewatermarkingprocedure,especiallyunderthetypicalattacksofgeometricoperations.
M
I.INTRODUCTION
ultimediawatermarkingtechnologyhasevolvedveryquicklyduringthelastfewyears.Adigitalwatermarkisinformationthatisimperceptiblyandrobustlyembeddedinthehostdatasuchthatitcannotberemoved[1,2].
Thereareseveralwatermarkingalgorithmstransformtheoriginalimageintocriticallysampleddomain(TheDiscreteRealWaveletTransform(DWT,theDiscreteCosineTransform(DCTortheDiscreteFourierTransform(DFT,andaddarandomsequencetothetransformedimagecoefficients[3,4].
Ingeneral,theDWTproduceswatermarkimageswiththebestvisualqualityduetotheabsenceofblockingartifacts.However,ithastwodrawbacks:
--Lackofshiftinvariance,whichmeansthatsmallshiftsintheinputsignalcancausemajorvariationsinthedistributionofenergybetweenDWTcoefficientsatdifferentscales.
--Poordirectionalselectivityfordiagonalfeatures,becausethewaveletfiltersareseparableandreal.
Animportantrecentdevelopmentinwavelet-relatedresearchisthedesignandimplementationof2-DmultiscaletransformsthatrepresentedgesmoreefficientlythandoestheDWT.Kingsbury’scomplexdual-treewavelettransform(DT-CWTisanoutstandingexample[5].TheDT-CWTisanovercompletetransformwithlimitedredundancy(2m:
1form-dimensionalsignals.Thistransformhasgooddirectionalselectivityanditssubbandresponsesareapproximatelyshift-invariant.The2-DDT-CWThasgivenS.MabtouliswiththeGSCM,UniversityMohamedV,Rabat,Morocco(e-mail:
mabtoul_samira@yahoo.fr.
E.Ibn-ElhajiswiththeNationalInstituteofTelecommunication(INPT,Rabat,Morocco(phone:
(+21237773079;fax:
(+21237773044e-mail:
ibnelhaj@inpt.ac.ma.
D.AboutajdineiswiththeGSCM,UniversityMohamedV,Rabat,Morocco(e-mail:
aboutaj@fsr.ac.ma.
II.THEPROPOSEDMETHOD
A.Watermarkimagedisorderpreprocessing
ThefirststepconsiststochangethewatermarkimageW,whichisabinaryimage{-1,1},intoapseudorandommatrixWdbyusingthefollowingequation:
K:
WÎWd,Wd(K(i,j=W(i,j;i,j∈N(1
WhereKpresentthefirstkeyinourwatermarkprocedure,whichisanexclusivekeytorecreatethewatermarkimage.Figure1visualizesanexampleofwatermarkimagedisorder.
OriginalwatermarkimageDisorderwatermarkimage
Fig.1.Theoriginalanddisorderwatermarkimage.
B.Watermarkembedding
TheoriginalimageistransformedinthecomplexwaveletdomainbyusingDT-CWT[5].ThewatermarkimageischangedintoapseudorandommatrixWd,thenitsadaptivelyspreadspectrumWkandaddintolowpasssubbandfromfinallevel.Figure2showsablockdiagramoftheproposedwatermarkembedding.
Fig.3.Imagedetectionscheme
ImagedetectionalgorithmFig.2.Imageembeddingscheme
Imageembeddingalgorithm1DT-CWT:
performa2-levelDualTreeComplexWaveletonoriginalimageIorig.TheDT-CWTcoefficientsaredenotedby~.2GeneratedthespreadspectrumwatermarkWk:
for
eachpixel(i,jofthelowpassimagefromfinallevelin~,thevalueiscomparedwiththoseofitseightneighbors,tdenotesthetotalnumberwhichthevalueislargerthanitsneighbors,asdescribedbythefollowingformula:
≥4andWdd(i,j=1
Wk(i,j=-1
ThespreadspectrumwatermarkWkpresentthesecondkeyofourimagewatermarkingscheme.
3Embeddedwatermark:
thespreadspectrumwatermarksequenceWkisembeddedbythefollowingrule:
ˆI(i,j=~I(i,j+α.W~k(i,j.I(i,j(3
Where:
ˆI:
arethewatermarkedDT-CWTcoefficients.~
I:
aretheoriginalDT-CWTcoefficients.
Wα:
isanintensityparameterofimagewatermark.
k:
isthespreadspectrumwatermarkimagesequence.4IDT-CWT:
bytheinverseDT-CWT,weobtainthewatermarkedimage.
C.Watermarkdetection
Watermarkdetectionisaccomplishedwithoutreferringtotheoriginalimageandtheoriginalwatermarkimage.Figure3showsawatermarkdetectionscheme.
1TheDT-CWTisperformedonwatermarkedimage.ˆI
denotetheDT-CWTcoefficients.2ConstructedWatermarkimagedisorderW
ˆd:
foreachembedwatermarkpixelinˆI
itsvalueiscomparedwiththoseofitseightneighbors;t’denotesthetotalnumberwhichthevalueislargerthanitsneighbors.Disorderwatermarkimagecanbeformedas:
1if(t’≥4andWk(i,j=1
Wˆd(i,j’<4andWk(i,j=-1
3ReconstructedwatermarkimageWˆ:
thereconstructedwatermarkimageW
ˆisobtainedbyusingtheinversetransformofthepreprocessingwiththefirstkey.III.RESULTSANDANALYSISOurproposedschemehasbeentestedundervarious
attacks.WechosetotestthisschemeunderPSNR,medianfilter,JPEGcompression,removelinesandscalingattacksintroducedbyStirmark[8]andalsorotationattack.WehaveperformedthealgorithmunderMatlab6.5environment.Intheexperiments,wehavetestedtreetestimages("Lena","Barbara"and"Cameraman",andtherehavethesimilar
results.Here,weuse"Lena"asanexampleandthewatermarkisabinaryimagewiththesizeof128x128pixels.
Figure4presentstheoriginalimage,thewatermarkedimageandthereconstructedwatermarkimage,inwhichthewatermarkintensityfactorαequal0.004.Weseethatthewatermarkedimageisnotdistinguishablefromtheoriginal
image.OriginalimageWatermarkedimageReconstructedwatermark
(256x256pixels(256x256pixelsimage(128x128pixels
Fig.4.Originalandwatermarkedimageandthereconstructed
watermarkimage.
Therobustnessofwatermarkingismeasuredbythe
similarityofthedetectedwatermarkW
ˆandtheoriginal
watermarkW,whichisdefinedas:
IV.CONCLUSION
Inthispaper,wehaveproposedanovelschemeofimage
ˆ,W=ˆ(i,j.W(i,jSim(W(W(W(i,j(5watermarking.ThisschemeappliestheDualTreeComplex
ijijWaveletTransform;thewatermarkimageispreprocessed
witharandommatrix,adaptivelyspreadspectrumandadded
WetestedthiswatermarkapproachwithDWTtransform;intotheDT-CWTcoefficients.Theexperimentalresultstheresultsaregatheredinfigure6.haveconfirmedthatthisnewschemehashighfidelityandInthefirstsimulation,wetestedthescheme’srobustnessit’srobustagainstJPEGcompression,geometricattacksunderdifferentPSNRsituation.Figure5.ashowatypical(scaling,removelineandrotationwithsmallangleandresult.Resultsshowthatwecanstillcorrectlydetectthesignalprocessing(PSNR,medianfilterintroducedin∑∑∑∑
2
watermarkunderthesetypesofPSNRattacks(figure6.a.TheresultsobtainedwithDT-CWTtransformarebetterthantheresultsobtainedwithDWTtransform.
Wetestedtherobustnessagainstmedianfilter.Figure5.b
hasshownatypicalresult.Thesimilaritiesoforiginalwatermarkandreconstructedwatermarkareshowninfigure6.b.WenoticedthatwecanstillcorrectlydetectthewatermarkwiththealgorithmusedtheDT-CWTtransform.WiththealgorithmusedtheDWTtransform,wecan’tdetect
thewatermarkifthefilterfactorisbiggerthan7.
Wetestedthisschemewhentheimageundergoneascaling(seefigure5.c.Theresultsareshowninfigure6.c.fromtheresultsobtainedwenoticesthatwecandetectthe
watermarkimageifweusedtheDT-CWTortheDWT.Thelinesdropping,whicharesomelinesareremoved
fromthewatermarkedimage.Wetestedthisschemeagainstthistypeofattack(seefigure5.d.Theexperimentresultisplottedinfigure6.d.Theresultsshowthatwecan
reconstructthewatermarkimagecorrectlyifweusedtheDT-CWTortheDWT.
WehavealsotestedtherobustnessagainstJPEGcompression(seeexampleinfigure5.e.Thecorrespondingresultsarepresentedinfigure6.e.thisschemeisrobustness
againstthistypeofattack.
Weevaluatedtherobustnessofthisschemeagainstrotationattacks.Imagerotationmakesthecoordinateaxeschanged.Withoutsynchronizationoforthogonalaxes,wecannotreconstructtheimagemarkcorrectlyFigure5.fillustratestheeffectofthistransformation.Theresultsareshowninfigure5.f.accordingtotheresultswenoticesthatwecanreconstructcorrectlythewatermarkimageifweusedtheDT-CWT.
StirMark.ACKNOWLEDGMENT
TheauthorswouldliketothankDr.NickKingsburyfor
allowingusetousehisDT-CWTalgorithm,andforhis
valuablediscussions.REFERENCES[1]F.P.Gonzalez&JuanR.Hernandez,"Atutorialondigital
watermarking",InIEEEAnnualCarnahanConferenceonSecurity
Technology,1999.[2]IngemarJ.Cox,MattL.Miller,"Thefirst50yearsofelectronicwatermarking",JournalofAppliedSignalProcessing,2,126-132,
2002.
[3]A.Piva,M.Barni,F.Bartolini,andV.Cappellini,"DCT-based
wate
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