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1、&Systems(ICMCS'99),vol.2,pp.530{535.Florence,Italy,Jun.1999OntheRobustnessandImperceptibilityofDigitalFingerprintsJonathanK.SuBerndGirodTelecommunicationsLaboratory,UniversityofErlangen-NurembergCauerstrasse7,D-91058Erlangen,GermanyEmail:[su,girod]@nt.e-technik.uni-erlangen.deonheur
2、isticarguments.Forexample,theauthorsin[3]AbstractsuggestthatanimagewatermarkshouldberestrictedForthemajorityofdigitalwatermarkingapplica-tothelowspatialfrequencies.Thereasoningisthattions,twoofthemostdesirablepropertiesarerobust-imagesaretypicallyassumedtobelowpass,soitisdif-nessand
3、imperceptibility.Thispaperpresentsatheo- cultforanattackertodestroythelowpasswatermarkreticalanalysisofwatermarking,inwhichanattackerwithoutalsodegradingtheimage.Additionalexam-estimatesthewatermarkwiththeWiener lter.Awa-ples,presentedin[2],usefrequency-domainperceptualtermark'srobu
4、stnessandimperceptibilitycanthenbemaskingmodels,motivatedbythenotionthatawa-expressedintermsofitsL-eciency
5、theamountof2termarkthatiswell-matchedtothefrequencycontentwatermarkenergythatanattackercanremove.Itisoftheoriginaldocumentcanbehiddene ectively.demonstratedthatapower-spectrum
6、condition(PSC)mustbesatis edformaximumL-eciency:thewa-22AModelforWatermarkingtermark'spowerspectrumshouldbeascaledversionMostcurrentwatermarkingmethodsareformsofoftheoriginaldocument'spowerspectrum.Amongspread-spectrumcommunications[4,5],inwhichawatermarksthatareindependentoftheori
7、ginaldoc-noise-liketransmittedmessagew[n]issubjecttoad-ument,aPSC-compliantwatermarkismaximallyL-2ditiveinterferencex[n].Asageneralwatermark-ecient.Analysisof1-Dand2-Dsignalmodelsandingmodel,letusrepresenttheoriginaldocumentexperimentswithrealimagesfurtherencouragetheuseandthewater
8、markbythediscrete-timerandompro-ofPSC-compliantwatermarks.cesses(DTRPs)x[n]andw[n],respectively.Bothpro-cessesareergodic,zero-mean,andwide-sensestation-1Introductionary(WSS).WedenotetheirrespectivepowerspectraDigitalwatermarkinghasbeenproposedasawaytoby(!)and(!).Althoughournotatio
9、nim-xxwprotectdigit
