Reversible data hiding based on multilevel histogram modification and sequential recovery

International

Journal

of

Electronics

and

Communications

(AEÜ)

jo u rn al h om e p a g e :w w w . e l s e v i e r . d e / ae u e

Reversible

data

hiding

based

on

multilevel

histogram

modification

and

sequential

recovery

Zhenfei

Zhao

a,b

_,

_Hao

_Luo

c,∗

_,

_Zhe-Ming

_Lu

c

_,

_Jeng-Shyang

_Pan

d a_{SchoolofInformationScienceandTechnology,SunYat-senUniversity,Guangzhou,China}

b_{HeilongjiangInstituteofScienceandTechnology,Harbin,China}

c_{SchoolofAeronauticsandAstronautics,ZhejiangUniversity,No.38ZheDaRoad,Hangzhou310027,China} d_{DepartmentofElectronicEngineering,NationalKaohsiungUniversityofAppliedSciences,Kaohsiung,Taiwan}

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received14January2010 Accepted21January2011

Keywords:

Reversibledatahiding

Multilevelhistogrammodification Sequentialrecovery

a

b

s

t

r

a

c

t

Thispaperproposesareversibledatahidingmethodfornaturalimages.Duetothesimilarityofneighbor pixels’values,mostdifferencesbetweenpairsofadjacentpixelsareequalorclosetozero.Inthiswork, ahistogramisconstructedbasedonthesedifferencestatistics.Inthedataembeddingstage,amultilevel histogrammodificationmechanismisemployed.Asmorepeakpointsareusedforsecretbitsmodulation, thehidingcapacityisenhancedcomparedwiththoseconventionalmethodsbasedononeortwolevel histogrammodification.Moreover,asthedifferencesconcentricityaroundzeroisimproved,the distor-tionsonthehostimageintroducedbysecretcontentembeddingismitigated.Inthedataextractionand imagerecoverystage,theembeddinglevelinsteadofthepeakpointsandzeropointsisused. Accord-inglytheaffiliatedinformationismuchsmallerthaninthosemethodsofthekind.Asequentialrecovery strategyisexploitedforeachpixelisreconstructedwiththeaidofitspreviouslyrecoveredneighbor. Experimentalresultsandcomparisonswithothermethodsdemonstrateourmethod’seffectivenessand superiorperformance.

© 2011 Elsevier GmbH. All rights reserved.

1. Introduction

Datahiding,alsocalledinformationhiding,playsanimportant roleininformationsecurity.Itaimsatembeddingimperceptible confidentialinformationincovermediasuchasstillimages,videos, audios,3D meshes, etc. It consists of severalbranches suchas steganography,watermarking,visualcryptography,etc.Thedata hidingschemeproposedinthisworkcanbeclassifiedintothe cat-egoryofsteganography.Steganographyisusuallyusedforcovert communications.Thusthehighembeddingcapacity isthemain concernin this kindof technique. In contrast,watermarking is usually usedfor copyright protection and announcement. Thus researchersaimatimprovingtherobustnessofwatermark con-tentagainstintentionalorunintentionalattacks.Therefore,most availabledatahidingmethodscanprovideahighercapacitythan thatprovidedbywatermarkingschemes.Thisadvantagebroadens theapplicationscenariosofdatahiding.

Nowadays,variousdatahidingtechniqueshavebeenreportedin literatures[1,2,29–31].Asaburgeoningbranch,reversibledata hid-inghasdrawnmuchattentionamongresearchers.Itskeyproperty isnotonlythesecretdatabutalsothehostimagecanbeaccurately

∗ Correspondingauthor.Tel.:+8615858259064;fax:+8657186971612. E-mailaddress:luohao@zju.edu.cn(H.Luo).

recoveredindecoder.Therefore,itcanbeusedinthoseapplications wherethehostimages(e.g.,militarymaps,remotesensingimages, medicalimages[11],digitalizedartpictures,etc.)mustbeexactly reconstructed.Incontrast,theconventionalirreversibledatahiding methodsarenotappropriateanylonger.

Availablereversibledatahidingtechniquescanbedividedinto spatialdomain,transformdomainandcompresseddomain meth-ods.Inthespatialdomainbasedmethods[3–20],thesecretdatais usuallyembeddedbypixels’valuesmodification.Inthetransform domainmethods,somereversibility-guaranteedtransforms(e.g., integerdiscretecosinetransform[21,22],integerwavelet trans-form[23])are exploitedand thedata embeddingisreduced to coefficientsmodulation.Inthecompresseddomainmethods,some popularusedimagecompressiontechniques(e.g.,vector quantiza-tion[24–26],blocktruncationcoding[27],MPEGcoding[28])are involved.

Most spatial domain reversible data hiding are developed basedontwoprinciples,i.e.,differenceexpansion(DE)[3–12]and histogram modification [13–20]. In general,the former kindof methodscanprovideahighercapacitywhilethelattercanproduce abetterqualitymarkedimage.

Thispaperproposesareversibledatahidingschemebasedon histogrammodification.Itsprincipleistomodifythehistogram constructedbasedontheneighborpixeldifferencesinsteadofthe hostimage’shistogramasin[13].Manypeakpointsexistaround

1434-8411/$–seefrontmatter © 2011 Elsevier GmbH. All rights reserved. doi:10.1016/j.aeue.2011.01.014

Z.Zhaoetal./Int.J.Electron.Commun.(AEÜ)65 (2011) 814–826 815 Original histogram … 0 1 2 … PP+1 Z-1Z … 255 … … … … … 0 1 2 …PP+1 … Z-1Z… 255 … … … 0 1 2 … PP+1 … Z-1Z… 255

“0” “1”

Shifted histogram Histogram with data embedded Fig.1.Principleofreversibledatahidingbasedonhistogrammodification.

thebinzerointhishistogramduetothesimilarityofadjacentpixel values.Besides,manyzeropointsexistinbothsidesofthebinzero. Herethepeakpointreferstotheheightofhistogrambinwiththe largeststatisticalvalue(i.e.,thecountfallinginthe correspond-ingbin),and thezeropointmeansthehistogrambin withzero value.Inourcase,allthedifferencesareclassifiedintolevelsof [−255,255]andeachlevelcorrespondstoahistogrambin.Hence itisreasonabletomodifythehistogramwithamultilevel mecha-nismforhidingmoresecretdata.Indecoder,thehostimagepixels arerecoveredonebyone.Thatis,eachpixelisrecoveredaidedby itspreviouslyrecoveredneighbor.Meanwhile,thesecretdatais extractedfromthemarkedadjacentpixels’differences.

Thispaperisorganizedasfollows.Section2reviewstherelated work.Section 3 describes theproposed schemeincluding data embedding,extractionandimagerecoveryprocedures.Section4 discussesthecapacity estimation, overflowand underflow pre-vention.Experimentalresultsandperformancecomparisonswith otheralgorithmsareshowninSection5.Finally,conclusionsare giveninSection6.

2. Relatedwork

In[13],Nietal.proposedareversibledatahidingmethodbased onhistogrammodification.Inthescheme,partofthecoverimage histogramisshiftedrightwardorleftwardtoproduceredundancy fordataembedding.Theprinciplecanbeillustratedasshownin Fig.1.First,thepeakandzeropointbinsoftheoriginalhistogram arefounddenotedasb(P)andb(Z),respectively.Thenallthebins belongingtob(P)andb(Z)areshiftedrightwardonelevel.Inthis way,thebinofb(P)isemptiedandb(P+1)becomesthenewpeak point.Next,theconfidentialdatacanbeembeddedbymodulating thepixelvaluesequalingP+1.Thatis,ifencounterapixelwith valueequalingP+1,thenonebitconfidentialdatacanbehidden. Forexample,ifthecurrentprocessingconfidentialbitis“0”,we modifythepixelvalueasP;whereasifthecurrentprocessing con-fidentialbitis“1”,thepixelwithvalueP+1iskeptnochanged. Indecoder,thedataextractionandimagerecoveryistheinverse processingofdataembedding.

In[16],Lietal.proposedareversibledatahidingmethodnamed adjacentpixeldifference(APD)basedontheneighborpixel differ-encesmodification.Inthismethod,aninverse“S”orderisadopted toscantheimagepixels.AsshowninFig.2,a3×3imageblockis usedtoillustratethisprinciple.Thescandirectionismarkedasthe blueline,andtheblockcanberearrangedintoapixelsequenceas p1,p2,...,p9.

SupposethehostimageIisan8-bitgraylevelimagesizedas M×N.Thena pixelsequence p1,p2,...,pM×N areobtainedvia

theinverse“S”orderscan.Thedifferencesofadjacentpixelsare computedas: di=



p1 i=1 pi−1−pi 2≤i≤M×N (1)

p

1

p

6

p

2

p

5

p

3

p

4

p

7

p

8

p

9

Fig.2. Inverse“S”scanofa3× 3imageblock.

Consideringthepixelvaluessimilaritybetweenp_i−1andpi,alarge

quantityofdi(2≤i≤M×N)isequalorcloseto0.Thedifference

histogramisconstructedbasedontheseM×N−1difference statis-tics.Supposethehistogrambinsfromlefttorightaredenotedby b(−255),b(−254),...,b(−1),b(0),b(1),...,b(254),b(255).Fig.3 showsthe512×512Lenaimage’sdifferencehistogram.Obviously mostdifferencesareconcentratedaroundb(0).Whenthecurve spreadsawaytobothsides,itdropsdramatically,andnodifferences fallintothosebinsfarfromb(0).

Basically,APDselectsonepairofbinsb(p1)andb(z1)(suppose

p1<z1)whereb(p1)andb(z1)denotethepeakpointandzeropoint,

respectively.Thenthebinsbetween[b(p1+1),b(z1−1)]areshifted

rightwardonelevel.Thusb(p1+1)areemptiedfordataembedding.

Thatis,ifasecretbit“1”isembedded,thedifferencesequalingp1

areaddedby1.If“0”isembedded,theyarenotchanged.

Toenhancethecapacity,APDcanalsoselecttwopairsof peak-zeropoints,e.g. [b(p1), b(z1)]and [b(z2), b(p2)] (supposep1<z1

-250 -200 -150 -100 -50 0 50 100 150 200 250 0 0.5 1 1.5 2 2.5 3x 10 4

4 0 -4 4 0 -4 4 0 -4 -4 0 4

c

d

Fig.4.HistogrammodificationforEL=0.

andz2<p2).Thenthebinsbetween[b(p1+1),b(z1−1)]areshifted

rightwardone level,andthose between[b(z2+1),b(p2−1)]are

shiftedleftwardonelevel.Thusb(p1+1)andb(p2−1)areemptied

fordataembedding.Thesecretbitsmodulationissimilarasthatin onepairofpeak-zeropointsembedding.Notetherangesof[b(p1),

b(z1)]and[b(z2),b(p2)]mustnotbeoverlapped.

3. Proposedscheme

3.1. Motivation

However,thedisadvantageofAPDmethodisthattheprovided capacityisnotveryhighduetoonlytwopairsofpeak-zeropointsat mostareemployedfordatahiding.Thislimitsitsscopeof applica-tionwherealargequantityofdataistobeembedded.Infact,more pairsofpeak-zeropointscanbeutilized.Motivatedfromthis,this workdesignedamultilevelhistogrammodificationmechanismfor alargecapacitydatahiding.

3.2. Dataembedding

In ourscheme,theinverse“S” order is adoptedtoscan the imagepixelsfordifferencegeneration.Thesecretdataarebinary sequencesproducedbypseudorandomnumbergenerator.Inthe dataembeddingstage,amultilevelhistogrammodificationstrategy isutilized.AnintegerparametercalledembeddinglevelEL(EL≥0) isinvolvedtocontrolthehidingcapacity.AlargerELindicatesmore secretdatacan beembedded. Astheembeddingoperationsfor EL>0aremorecomplicatedthanthoseofEL=0,wedescribethem forEL=0andEL>0separately.

Step1.Inverse“S”scanIintoapixelsequencep1,p2,...,pM×N.

Step2.Computethedifferencesdi(1≤i≤M×N)accordingtoEq.

(1)andconstructahistogrambasedondi(2≤i≤M×N).

Step3.SelectanEL.IfEL=0,executeStep4.IfEL>0,gotoStep5. Step4.DataembeddingforEL=0.

Step4.1.Shifttherightbinsofb(0)rightwardonelevelas:

d_i=



p1 if i=1 di if di≤0,2≤i≤M×N di+1 if di>0,2≤i≤M×N (2)

Step4.2.Examined_i=0(2≤i≤M×N)onebyone.Eachdifference equaling0canbeusedtohideonesecretbit.Ifthecurrent

pro-4 0 -4 4 0 -4 4 0 -4 4 0 -4 4 0 -4 4 0 -4 4 0 -4 4 0 -4

c

d

e

f

g

h

Fig.5.HistogrammodificationforEL=2.

cessingsecretbitw=0,itisnotchanged.Ifw=1,itisaddedby 1.Theoperationisas:

d_i =



p1 if i=1 d_i+w if d_i=0,2≤i≤M×N d_i if d_i /=0,2≤i≤M×N (3)

The histogram modification strategy for EL=0 is shown in Fig.4(a)–(d)wheretheredandbluearrowsindicateembedding “0”and“1”,respectively.Afterthat,gotoStep6.(For interpreta-tionofthereferencestocolourinthetext,thereaderisreferred tothewebversionofthearticle.)

Step5.DataembeddingforEL>0.

Step5.1.Shifttherightbinsofb(EL)rightwardEL+1levels,and shifttheleftbinsofb(−EL)leftwardELlevelsas:

d_i=

⎧

⎪

⎨

⎪

⎩

p1 if i=1 di if −EL≤di≤EL,2≤i≤M×N di+EL+1 if di>EL,2≤i≤M×N di−EL if di<−EL,2≤i≤M×N (4)

Step5.2.Examined_i=0(2≤i≤M×N)intherangeof[−EL,EL] onebyone.Themultileveldataembeddingstrategyisdescribed asfollows.

Step5.2.1.Embedthesecretdataas:

d_i =

⎧

⎪

⎨

⎪

⎩

p1 if i=1 d_i if −EL<d_i<EL,2≤i≤M×N 2×EL+w if d_i=EL,2≤i≤M×N −2×EL−w+1 if d_i=−EL,2≤i≤M×N (5) Step5.2.2.ELisdecreasedby1.

Z.Zhaoetal./Int.J.Electron.Commun.(AEÜ)65 (2011) 814–826 817

Fig.6. ExampleofdataembeddingforEL=0.

Fig.7. ExampleofdataextractionandimagerecoveryforEL=0.

Fig.23.MarkedCarimagesobtainedbyourscheme(left:220801bitshidden,33.05dB)andKimetal.’sscheme[17](right:171244bitshidden,31.40dB)withEL=9.

andAPD2denoteoneandtwopairsofpeak-zeropointsareused

respectively.ThecomparisonresultsarealsogiveninTable1.Our schemecanprovideahighercapacitythanLietal.’smethodwith goodmarkedimagesquality.

Next,ourschemeiscomparedwithKimetal.’smethod[17]. Althoughboth are based onmultilevel histogram modification, the histogram construction mechanisms are different. In gen-eral,thecapacityof differencehistogram modificationis jointly affectedby the total number of differences and the their con-centricity tob(0). In [17], the differences are computed based onsubimages’correlation andhence thenumberof differences is determined by the number of subimages. For example, if a 512×512hostimageissubsampledinto16 equal-sized subim-ages,thereare512×512×15/16=245760differencesproduced. Incontrast,thereare512×512−1=262143differencesproduced inourscheme.The histogrambinsbelongingto[b(−30),b(30)] obtainedby [17] and our schemeare shown in Fig. 11. Obvi-ously,moredifferencesinourhistogramsareconcentratedaround b(0).Asaresult,alargercapacitycanbeprovidedinourscheme thanin[17].Moreover,b(−1)isemptiedafterembeddingin[17] for the shifting leftward is one level farther than that in our scheme,and consequently theintroduced distortions are more serious.

Theperformancecomparisonsofourscheme(markedasblue) andKimetal.’smethod(markedasred)areshowninFigs.12–17. The horizontal axisdenotes the EL setfrom 0 to 9. The verti-calaxesofcapacityandPSNRarenormalizedas[0,1.0]bpp(bit perpixel)and[30,55]dB,respectively.Intheseexperiments,the hostimagesarepartitionedinto16equal-sizedsubimagesin[17]. ThesixmarkedimagesobtainedbyourschemeandKimetal.’s schemeareshowninFigs. 18–23.Alltheseresultsdemonstrate not only the capacities but also the PSNRs in our method are improved.Inotherwords,eventhoughmoresecretdataembedded inourscheme,themarkedimagesqualityisstillbetterthanthose in[17].

6. Conclusions

Areversibledatahidingschemeisproposedinthispaper.The multilevelhistogram modificationisemployedfor data embed-ding.Ononehand,ahighercapacityisprovidedcomparedwithone ortwolevelhistogrammodificationbasedmethods.Ontheother hands,assecretdataisembeddedindifferencesofadjacentpixels values,themarkedimagesqualityisimprovedcomparedwiththat inpreviousmultilevelhistogrammodificationbasedwork.

Acknowledgments

Theauthorsthanktheeditorandtheanonymousreviewersfor theirconstructivecommentsandvaluablesuggestionsfor readabil-ityimprovement.ThisworkisfinanciallysupportedbytheNational ScientificFundofChina(Nos.61003255and61071128).

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