Multiple Watermarking Algorithm Based on Spread Transform Dither Modulation

1.6 MB·

by  Xinchao Li

1
Multiple Watermarking Algorithm Based on Spread
Transform Dither Modulation
∗
Xinchao Li, Ju Liu , Senior Member, IEEE, Jiande Sun, Member, IEEE, Xiaohui Yang, and Wei Liu
Abstract—Multiple watermarking technique, embedding sev- tosimultaneouslyaddressesmedicaldataprotection,archiving,
6 eralwatermarksinonecarrier,hasenabledmanyinterestingap- and retrieval, as well as source and data authentication.
1 plications.Inthisstudy,anovelmultiplewatermarkingalgorithm
Meanwhile, different watermarking techniques and strate-
0 isproposedbasedonthespiritofspreadtransformdithermodu-
gieshavebeenproposedto achievemultiplewatermarking.In
2 lation(STDM).Itcanembedmultiplewatermarksintothesame
regionandthesametransformdomainofoneimage;meanwhile, [6], Sheppard et al. discuss three methods to achieve multi-
n
the embedded watermarks can be extracted independently and ple watermarking: rewatermarking, composite watermarking
a
J blindly in the detector without any interference. Furthermore, and segmented watermarking. Rewatermarking embeds wa-
8 toimprovethefidelityof thewatermarked image, theproperties termarks one after another and the watermark signal could
of the dither modulation quantizer and the proposed multiple
1 only be detected in the corresponding watermarked image
watermarks embedding strategy are investigated, and two prac-
tical optimization methods are proposed. Finally,to enhance the using the former watermarked signal as the original image.
]
M application flexibility, an extension of the proposed algorithm is The watermark embedded previously may be destroyed by
proposed which can sequentially embeds different watermarks the one embedded later. Composite watermarking discusses
M into one image during each stage of its circulation. Compared theextensionofsinglewatermarkingalgorithmstothecaseof
with the pioneering multiple watermarking algorithms, the pro-
multiple watermarking by introducing orthogonalwatermarks
. posed one owns more flexibility in practical application and is
s
c more robust against distortion due to basic operations such as [7], [8]. Being similar to these, CDMA based schemes [9],
[ random noise, JPEG compression and valumetric scaling. [10] use the orthogonal codes to modulate the watermarks

from different users to derive the orthogonal watermarks.
1 Index Terms—Multiple Watermarking, STDM, Constrained
v Quadratic Minimization, Sequential Multiple Watermarking Unfortunately, they cannot guarantee the robustness in the
2 case of blind extraction. Segmented watermarking embeds
2 multiple watermarks into different segments of one image.
5 I. INTRODUCTION Clearly, the number of segments limits the number and size
4 IN recent years, as the rapid development in the field of watermarks to be embedded [11]. The embedding pattern
0
of digitalwatermarking,multiple watermarkingalgorithms chosenformappingwatermarkstosegmentscangreatlyaffect
.
1 which give the possibility of embeddingdifferent watermarks therobustnessofeachwatermarkagainstcroppingattack[12].
0
in the same image, have received widespread attention since Other schemes embed different watermarks into different
6
1 the pioneering contribution [1], where the idea of embedding channels of the host data, e.g., different levels of wavelet
: multiple watermarks in the same image is initially presented. transform coefficients [5], or RGB of the color image [13],
v
Since then, multiple watermarking has enabled many inter- [14]. In fact, the limited quantity of watermarks embedded
i
X esting applications. In [2], Mintzer and Braudaway suggest would somehow constrain their application area.
r that the insertion of multiple watermarks can be exploited In this study, we focus on the techniques that can embed
a
to convey multiple sets of information. Sencar and Memon multiplewatermarksintothesameareaandthesametransform
[3] apply the selective detection of multiple embedded wa- domain of one image, meanwhile, the embedded watermarks
termarks,which can yield lower false-positiverates compared can be extracted independently and blindly in the detector
with embedding a single watermark, to resist ambiguity at- without any interference.
tacks. Boato et al. [4] introduce a new approach that allows To this end, a novel multiple watermarking algorithm is
the tracing and property sharing of image documents by proposed.Itinitiallyextendsthespreadtransformdithermod-
sequentially embedding multiple watermarks into the data. ulation(STDM),a singlewatermarkingalgorithm,to thefield
Giakoumaki et al. [5] apply multiple watermarking algorithm of multiple watermarking. Moreover, through investigating
the properties of the dither modulation (DM) quantizer and
Xinchao Li,JuLiu,JiandeSun,andXiaohuiYangarewiththeSchoolof the proposed multiple watermarks embedding strategy, two
Information Science and Engineering, Shandong University, Jinan, 250100,
optimization methods are presented which can improve the
China(e-mail:[email protected]).
JuLiuandWeiLiuarewith theHisense State KeyLaboratory ofDigital fidelity of the watermarked image significantly. Compared
Multi-Media Technology Co.,Ltd,Qingdao,China. with the pioneering multiple watermarking algorithm [15], it
ThisworkwassupportedpartiallybytheNationalBasicResearchProgram
has considerable advantages, especially in robustness against
of China (973 Program, No.2009CB320905), the National Natural Science
Foundation ofChina (60872024), theCultivation FundoftheKeyScientific Gauss Noise, Salt&Pepper Noise, JPEG Compression and
and Technical Innovation Project (708059), Education Ministry of China Valumetric Scaling. Finally, some potential interesting appli-
forfunding, Nature Science Foundation ofShandongProvince (Q2008G03),
cations are discussed and an application extension of our
Doctoral Program Foundation of Institutions of Higher Education of China
(200804221023). algorithm is proposed to realize image history management
2
by sequentially embedded watermarks. decoder, which finds the quantization point closest to y˜ and
The reminder of this paper is organized as follows. In outputs the estimated message bit m˜ [18].
section II, we briefly describe the main algorithm of spread
m˜ =argmindist(y˜,Ωm) (2)
transform dither modulation. In section III, the proposed
m∈0,1
multiple watermarking algorithm is introduced. In section
IV, to improve the fidelity of the watermarked image, the where dist(y˜,Ωm)=∆ min |y˜−s|.
properties of the dither modulation quantizer and the em- s∈Ωm
bedding strategy of the proposed algorithm are analyzed. In
section V, two practical optimization methods are presented. B. QIM-Dither Modulation
In section VI, the efficiency of the two optimization methods Dither modulation, proposed by Chen and Wornell [16], is
is tested, meanwhile, the robustness of the proposed methods an extensionof the originalQIM. Comparedwith the original
is assessed. Finally, some potential interesting applications QIM, it uses the pseudo-random dither signal, which can re-
of the proposed algorithm and the concluding remarks are duce quantizationartifacts, to producea perceptuallysuperior
summarized in section VII and VIII, respectively. quantizedsignal.Meanwhile,throughtheditherprocedure,the
quantization noise is independent from the host signal. The
II. SPREAD TRANSFORM DITHERMODULATION DM quantizer QDM is as following
As the proposed multiple watermarking algorithm is based y =QDM(x,∆,dm)=Q(x+dm,∆)−dm,m=0,1 (3)
onSpreadTransformDitherModulation,a blindsinglewater-
marking algorithm belonging to the QIM family, introduction wherey isthemarkedsignalofxbyDM quantizer,dm isthe
beginning with the basic QIM is appropriate. dither signal corresponding to the message bit m.
∆
d1 =d0−sign(d0) (4)
A. Quantization Index Modulation 2
whered0 isapseudo-randomsignalandisusuallychosenwith
m=0,Q0 m=1,Q1 a uniform distribution over [−∆/2,∆/2].
In the detecting procedure, the detector firstly applies the
x QDM quantizer (3) to produce two signals S0 and S1, by
embedding“0”and“1”intothereceivedsignaly˜respectively.
D
Fig. 1. Embedding one message bit, m, into one sample x Sm =QDM(y˜,∆,dm)=Q(y˜+dm,∆)−dm,m=0,1 (5)
usingoriginalQIM,wheresetsofcirclesandcrossesrepresent
wheredm mustbeexactlythesameaswhichintheembedding
Ω0 and Ω1, respectively.
procedure. Note that the pseudo-random signal d0 can be
considered as a key to improve the security of the system,
IntheoriginalQIMwatermarking,asetoffeaturesextracted
and in what follows, this secret signal is referenced as the
from the host signal are quantized by means of a quantizer
dither factor, df.
chosen from a pool of predefined quantizers on the basis of
Thedetectedmessagebitisthenestimatedbyjudgingwhich
the to-be-hidden message [16]. In the simplest case, a set
of these two signals has the minimum Euclidean distance to
of uniform quantizers are used leading to lattice-based QIM
the received signal y˜, in the same manner as (2).
watermarking.As illustratedin Fig.1, thebasic QIM usestwo
quantizersQ0 and Q1 to implementthe function,and each of m˜ =argmindist(y˜,Sm) (6)
them maps a value to the nearest point belonging to a class m∈0,1
of predefined discontinuous points, one class (Ω0) represents
bit 0 while the other (Ω1) represents bit 1 [17]. The standard C. QIM-Spread Transform Dither Modulation
quantization operation with step-size ∆ is defined as
As an important extension of the original QIM, STDM
x applies the idea of projection modulation. It utilizes the DM
Q(x,∆)=∆·round( ) (1)
∆ quantizer to modulate the projection of the host vector along
where the function round(.) denotes rounding a value to the a given direction. This scheme combines the effectiveness of
nearest integer. QIM and robustness of spread-spectrumsystem, and provides
In the embedding procedure, according to the message bit significant improvementscompared with DM.
m,Q0 orQ1 ischosentoquantizethesamplextothenearest
quantizationpointy. Forexample,Q0 andQ1 may be chosen x x
p ˜ ¯
in such way that Q0 quantizes x to even integers and Q1
quantizesx to odd integers. If we wish to embed a 0 bit, then u/ u
Q0 is chosen, else Q1. u u/ u ˜ D dm 2
2
In the detecting procedure, it is reasonable to assume the
¯
marked signal y is corrupted by the attacker, resulting in
a noisy signal y˜. The QIM detector is a minimum-distance Fig. 2. Block diagram of spread transform dither modulation
3
Toembedonemessagebitm,ahostvectorx,consistingof Inspired by this, to embed multiple message bits, m1,
samples to be embedded,is projected onto a randomvector u m2,..., mn, into the same host vector x, we can modulate the
to getthe projectionx . Then,the projectionx is modulated projectionofthehostvectorxalongdifferentgivendirections,
p p
according to the message bit m using the DM quantizer (3). u , u ,..., u . The modulatedhost vector g can be expressed
1 2 n
ThisprocedurecanbeillustratedinFig.2,andthewatermarked as follows
vector g is as follows, g =x+UK (12)
QDM(proj(x,u),∆,dm)−proj(x,u)
g=x+( )u (7) where U=[u1,u2,...,un], K=[k1,k2,...,kn]T.
kuk
2 To detect the message bits, the modulated vector g is
whereproj(x,u)=∆ hx,ui,hx,uiistheinnerproductofxand projectedontothegivendirections,u1,u2,...,un,respectively.
kuk2 And then, the DM detector is used to estimate each message
u,k·k denotestheL2-normoperation.∆isthequantization
2 bit from the corresponding projection. Thus, in the same
step generated from a pseudo-randomgenerator.
manner as (10), the modulated vector g must be subject to
Inthedetectingprocedure,thedetectorprojectsthereceived
the following equation,
vector˜gontotherandomvectoru.Andthen,itutilizestheDM
detectorto estimate the message bitm˜ fromthe projection,in
the same manner as (5) and (6). This can be expressed as proj(g,u1)=QDM(proj(x,u1),∆1,dm1 1)
follows,  proj(g,u2)=QDM(proj(x,u2),∆2,dm2 2)
.................. (13)
m˜ =amr∈g{m0,1in}dist(proj(g˜,u),QDM(proj(g˜,u),∆,dm))  proj(g,un)=QDM(proj(x,un),∆n,dnmn)
(8) 
Note that, the random vector u and the random positive real
where dmj is the dither signal in the direction u correspond-
number ∆ used in the STDM detector must be exactly the j j
ing to the message bit m .
same as they are in the embedder, and can be considered as j
By substituting (12) into (13), n equationscan be obtained.
twokeyswhichareonlyknowntotheembedderanddetector,
These are expressed as follows in the matrix form,
thereby improving the security of the system.
U K=QDMV−P (14)
I
III. MULTIPLEWATERMARKING ALGORITHM
where
Based on the algorithms mentioned above, we extend the
U =Λ UTU, Λ =[ 1 , 1 ,..., 1 ]
spread transform dither modulation (STDM), a single wa- I U U ku1k ku2k kunk
termarking algorithm, to the field of multiple watermarking P=[proj(x,u1),proj(x,u2),...,proj(x,un)]T
application. The proposed multiple watermarking algorithm, QDMV=[QDMV1,QDMV2,...,QDMVn]T
QDMV =QDM(proj(x,u ),∆ ,dmj)
namelySTDM-MultipleWatermarking(STDM-MW),canem- j j j j
bed multiple watermarks into the same area and the same From(14), the scaling factor sequenceK can be calculated
transform domain of one image, meanwhile, the embedded by
watermarks can be extracted independentlyand blindly in the K=U−1(QDMV−P) (15)
I
detector without any interference.
Finally, according to (12), the watermarked host vector g
A. Fundamental Idea which carries n message bits can be generated. Note that, to
make (15) tenable, the length of the host vector x, namely L,
As mentioned in section II, to embed a single message
must be no less than the number of embedded message bits,
bit, m, STDM modulates the projection of the host vector
n, i.e., L≥n, (see Appendix A).
x alonga givendirectionu. Themodulatedhostvectorg can
Inthedetectingprocedure,wecanapplytheSTDMdetector
be expressed as follows,
(8) to estimate every single bit m from the projection of
j
g=x+ku (9) the received vector g˜ along the corresponding direction u ,
j
independently. This can be expressed as follows,
To detect the message bit, the detector projects the mod- e
ulated vector g onto the given direction u. And then, it
utilizes the DM detector to estimate the message bit from m = argmindist(proj(g˜,u ),QDM(proj(g˜,u ),∆ ,dmj),
j j j j j
the projection. This detection mechanism induces the vector mj∈{0,1}
j =1,2,...,n
g must be subject to e
(16)
proj(g,u)=QDM(proj(x,u),∆,dm) (10)
Thus, the embedding procedure is actually to derive the B. Detailed Implementation
scalingfactork usedin(9)tomakethemodulatedvectorg in
As illustrated in Fig.3 and Fig.4, the proposed scheme,
the form of (10). Substituting (9) into (10), the scaling factor
STDM-MW, consists of two parts, the embedder (Fig.3) and
k can be given by
the detector (Fig.4). In this scheme, each user is given three
QDM(proj(x,u),∆,dm)−proj(x,u) secret keys, STEP KEY, U KEY and Dither KEY, to
k = (11)
kuk implementwatermarkembeddinganddetecting.Itis assumed
2
4
1 2 n
1 2 n
1 2 n
1 2 n
Fig. 3. Block diagram of STDM-Multiple Watermarking embedder
j j j
xɶ
(cid:2)
w
j
Fig. 4. Block diagram of STDM-Multiple Watermarking detector for the jth user
that there are n users and the watermark sequence of the jth w w w ... w ... w
1 11 12 1i 1N
user is wj, wj =[wj1,wj2,...,wjN], with length N. w w w ... w ... w
2 21 22 2i 2N
The embedding procedure is as follows,
(a) Divide the image into disjoint 8 × 8 blocks of pixels, ... ... ... ...
and perform DCT transform to each block to gain its
wj wj1 wj2 ... wji ... wjN jthuser
DCT coefficients. A part of these coefficients will be
selectedtoformasinglevector,denotedasthehostvector
... ... ... ...
xi(i=1,2,...,N),xi =[x1,x2,...,xL],withlengthL.As w w w ... w ... w
illustrated in Fig.5, each host vector x is used to embed n n1 n2 ni nN
i
one bit sequence [w1i,w2i,...,wni], the jth element of
which is corresponding to the jth user’s ith bit.
x
(b) Use the secret keys, STEP KEY, U KEY and i
Dither KEY,ofeachusertogeneratethestepsizes∆ , Fig.5.Parametersarrangement,thearrangementforprojective
ji
the random projective vectors u and the dither factors vector u, dither factor df and step size ∆ is the same as it is
ji
df for each host vector x , respectively. According to for watermark w.
ji i
the message bit w , the final dither signal dwji can be
ji ji
generated using df .
ji
(c)Embedeachbitsequence[w1i,w2i,...,wni]bymodulating (c) Use the STDM detector to detect every bit w˜ji from each
each host vector xi into gi using the method mentioned hostvectorx˜i,basedontheparameters,uji,dfji and∆ji.
in III-A , based on the parameters, [u1i,u2i,...,uni], Note that, with an eye to the robustness of STDM-MW
[dw1i1i,dw2i2i,...,dwnini],[∆1i,∆2i,...,∆ni],calculatedinstep against valumetric scaling, the step-size ∆ should be multi-
(b). Finally, transform the modified coefficients back to plied by the mean intensity of the whole image.
form the watermarked image.
During the transmission, the watermarked image may sus-
IV. ANALYSIS OF STDM-MULTIPLEWATERMARKING
tain certain attacks, intentional or unintentional, and become
a distorted image at the receiver. Each user can use his own Throughexperiment,itisfoundthatalongwiththeincrease
secret keys to detect his own watermark independently. of the number of watermarks embedded, the quality of the
The detecting procedure of the jth user is as follows imagesdeclinesin varydegrees.To addressthis issue, further
(a)Formeachhostvectorg˜ ofthereceivedimageinthesame analysis of the embeddingstrategy of STDM-Multiple Water-
i
manner as step (a) in the embedding procedure. marking is demanded.
(b) use the secret keys, STEP KEY , U KEY and As is widely known, in the case of Imperceptible & Ro-
j j
Dither KEY , of the jth user to generate the bust watermarking, owning the same robustness, the more
j
step sizes [∆j1,∆j2,...,∆jN], the random projec- imperceptible, the more effective the algorithm is. In most
tive vectors [uj1,uj2,...,ujN] and the dither factors cases, the imperceptibility of the watermark, in other words
[dfj1,dfj2,...,dfjN], respectively. the fidelity of the watermarked image, is measured in PSNR,
5
which varies inversely with the mean squared error, MSE. vector’s projection point p and p’s DM quantization point.
Referencing Appendix B, we have This can be formulated as follows,
MSE ∝kC′−Ck2 (17) dis v =kg−xk2 =kx+ku−xk2 =kkuk2 =dis p
(19)
whereCandC′aretheDCTcoefficientvectorsoftheoriginal As DM quantizer (3) can generate the quantization point
image and the watermarked one. that is closest to the originalpoint, it can find the closest DM
Thus, under the PSNR measurement, the smaller the Eu- quantizationpointtothehostvector’sprojectionpoint,i.e.,the
clidian distance between the watermarked coefficient and the DM quantizer can make dis p minimum. Thus, it is optimal
original one is, the higher the fidelity of the watermarked to use DM quantizer to modulate the host vector x to vector
imagewillbe.Accordingtothisidea,toimprovethefidelityof g by (7). In this way, the minimum dis v can be guaranteed.
the watermarkedimage, we need to produce the watermarked
vector that is closest to the host vector. k u
At the very beginning, as the embedding procedure of g'' 2 g'
STDM-MultipleWatermarkingisbasedonDitherModulation,
it is appropriate to investigate the DM quantizer in a deeper
way.
A. Dither Modulation Based Single Watermarking
p
From section II-B, to embed one message bit m, the
original DM quantizer, QDM, quantizes the point x to D D D
(∆round(x+dm)−dm). However,ignoringthe imperceptible
∆ Fig. 7. Utilizing STDM to embed one message bit m into
constraint(minimumEuclidiandistance),we can quantizethe
one host vector x, where u is the projective vector and g is
point x to any point b , b ∈B.
i i
the watermarked vector. The set of circles represents the DM
B={b|b=β∆−dm, β ∈Z} (18) quantizationpointsoftheprojectionpointp ofthehostvector
x along the direction u.
Definitely, any points in B have the same detection robust-
ness according to the DM detection mechanism, (5) and (6).
In what follows, this kind of points are defined as the DM
quantization points of point x. B. Embedding Strategy of STDM-Multiple Watermarking
As illustrated in Fig.6, in the case of DM single water- As mentioned above, DM quantizer is optimal for STDM
marking, it is optimal to use (3), which is equivalent to in the case of single watermarking. Unfortunately, it seems
β = round(x+dm) in (18), to choose the final quantization that this strategy is not optimal in the case of multiple
∆
point,becausetheselectedoneistheclosestpointtoxamong watermarking.
all the DM quantization points of x,(i.e., points in B). AsmentionedinIII-A,inthecaseofmultiplewatermarking,
if n message bits are embedded, the host vector x must be
modulated along n given directions to form the watermarked
vectorg.Foreachdirection,theprojectionofthewatermarked
vectorg must be the closetDM quantizationpointto the host
vector x’s projection point.
Asillustratedin Fig.8,it isa simpleexamplefortwo users,
D D D
that is embedding two bits into the host vector x. To do this,
hostvectorxmustbeprojectedalongtheprojectivevectorsu
Fig. 6. Utilizing DM to embed one message bit m into point 1
x,wherethesetofcirclesrepresentsquantizationpointsinB, and u2 to gain the projection points p1 and p2, respectively.
(assuming dm > 0). Dotted-lines, L = {l|l = ((2α+1)∆ − And then, points p1 and p2 are quantized into their closet
dm, α ∈ Z}, denote the median point between two adja2cent DMquantizationpoints,Q1andQ2,respectively.Finally,host
vector x is modulated into vector G .
quantization points. 1
However,thisoriginalembeddingstrategy,usingtheclosest
DM quantization point as the final quantization point of the
Inspired by this idea, in the original STDM, as illustrated projectionpoint,cannotproducttheclosetwatermarkedvector
in Fig.7, we can modulate the host vector x to any vector to the hostvector.Actually,vectorsG , G , G andG can
1 2 3 4
(g′′,g′,g),whoseprojectionpointistheDMquantizationpoint all be selected as the watermarkedvectorof the host vector x
of the host vector’s projection point p. while owning the same detection robustness. And, as shown
However, the imperceptible constraint must be considered. in Fig.8, vector G , the original selected one, dose not have
1
Referencing (9), the Euclidian distance dis v between the the minimum Euclidian distance to the host vector x among
watermarked vector g and the host vector x, is proportional the four alternative ones. In practice, vector G is the closest
2
to k, which is actually the distance dis p between the host one.
6
G3 V. OPTIMIZATIONFOR STDM-MULTIPLE
WATERMARKING
D2 As mentioned above,obviously,if all the candidate vectors
p2 in the pool g S are traversed, the one which is closest to the
G2 host vector will be found ultimately. However, as the infinite
D2 G4 size of g S, this procedure is not practical. To address this
Q2
issue, the optimization procedure is divided into two cases,
the special case and the general case.
D2
G1
A. Special Case: Multiple Watermarking using Orthogonal
Projective Vectors
p1 Q1
D D D It has been observed that the goal of our optimization
1 1 1
procedureis to find the closet watermarked vector to the host
vector,i.e., the Euclidian distance between them is minimum.
Fig. 8. Utilizing the original embedding strategy STDM-MW According to (22), the Euclidian distance, dis v, can be
to embed two message bits into one host vector x, where u1 expressed as follows,
andu arethetwoprojectivevectorsdenotingthequantization
2
directions. p1 and p2 are the projection points of x along u1 dis v =kg−xk2 = (Qp−P)TUe(Qp−P) (23)
and u , respectively. The circles along u and u denote the
2 1 2 where U =Λ−1(UTU)−p1Λ−1.
DM quantization points, belonging to the point set B1 and e U U
B2,respectively. Bj ={b|b=βj∆j −dmj j, βj ∈Z}. GrIafmt-hSechpmroijdetcotirvtehovgeocntoarliszauti1o,nu,2t,h..e.,umnatarirxeUprepwroilclebseseIddebny-
e
tity matrix I , and dis v is actually the Euclidian distance
n
between the vector of DM quantization points, Qp, and the
Thus, it is not optimal to use vector G to play as the vector of projection points, P.
1
watermarkedvector. More specifically, once the host vector x
belongsto the shadowedarea in the parallelogramin Fig.8, it dis v =kQp−Pk = (Qp(j)−P(j))2 (24)
2
is notoptimalto use the originalembeddingstrategy to select s j
X
the quantization point along each direction and generate the
As QDM quantizer (3) can minimize each item in (24), the
watermarked vector.
originalembeddingstrategy,usingtheclosestDMquantization
The original multiple watermarks embedding strategy (13)
pointas the final quantizationpoint of the projectionpoint, is
and (15) must be rewritten as
optimalinthecaseofmultiplewatermarkingusingorthogonal
proj(g,u1)=Qp1 projectivevectors.Note that,in thefollowingdescription,this
proj(g,u2)=Qp2 special case will be referred as STDM-MW-Uorth.
 (20)
..................... The simple example for this case is illustrated in Fig.9, if
 proj(g,u )=Qp the host vector x belongs to the rectangle area centered by
n n
 −1 vGeictworithGw.idOtbhv∆io1usalnyd, Gheigishtth∆e2o,pittiwmialllbweatmeromduarlakteeddvtoectthoer
K=U (Qp−P) (21) i i
I for x.
where Qp denotes one DM quantization point in the j-th
j
direction,
B. GeneralCase:MultipleWatermarkingusingUnorthogonal
Qp=[Qp1,Qp2,...,Qpn]T, Projective Vectors
Qp ∈B ,B ={b|b=β ∆ −dmj,β ∈Z}
j j j j j j j
In general,it is notrealistic to expectthe projectivevectors
Substituting (21) into (12), the watermarked vector can be u ,u ,...,u are orthogonal with each other. Thus, taking a
1 2 n
given by tradeoff between PSNR and time efficiency, we propose two
methods for the general case to find the optimized water-
−1
g=x+UU (Qp−P) (22) markedvectorwhichismuchclosertothehostvector,namely
I
STDM-MW-Poptim and STDM-MW-Qoptim.
AstherearemanyDMquantizationpointsineachdirection, 1) STDM-MW-Poptim: In STDM-MW-Poptim, along each
there are several combinationsto make Qp. This will form a direction, t quantization points, which are near the projection
vector pool for Qp, namely Qp S. Vectors in Qp S can all point of the host vector, are selected to form the point-set for
be chosen as Qp in (22), and correspondingly, a vector pool this direction. This can be expressed as follows
for the watermarked vector g is generated, namely g S. The
x
goal of our optimization procedure is to find the closest one H ={h|h=∆ (floor( )+k)−dmj, k ∈Z} (25)
j j ∆ j
tothehostvectorxfromthisvectorpoolg S,andfinallyuse j
this vector to play as the optimized watermarked vector. where H denotes the point-set of the j-th direction.
j
7
G1
G1 G2 G3
Q6
D2
2 Q6
D
p2 G2
G4
Q5 G4 G5 G6 D2
Q5
2 p2
D
G3
D2
G7 G8 G9 Q4 G5
Q4 G7
2
D
Q1 p1 Q2 Q3
D D D
Q1 p1 Q2 Q3 1 1 G8 1 G6
D D D
1 1 1
Fig. 9. Embeddingtwo message bitsinto one hostvectorx in
the case of u and u are orthogonal projective vectors, and
1 2
G9
G is the optimal watermarked vector for x.
5
Fig. 10. Utilizing STDM-MW-Poptim to embed two message
bits into one host vector x, where u and u are the two
1 2
And then, one point of each point-set is selected to form a projectivevectorsdenotingthequantizationdirections.Q1,Q2
vector PoQp. It can be used to substitute the vector Qp in and Q3 are the selected quantization points, correspondingto
(22), and the watermarked vector can be calculated by the search area k = −1,0,1 in (25). These points form H1,
g =x+UU−1(PoQp −P), i=1,2,...,F (26) the point-set of direction u1. Q4, Q5, Q6 are the same ones.
i I i
where, assuming there are n bits to be embedded in one host
vector, in other words n quantization directions are given for
subject to the constraint in the form of
one host vector, thus there are F = tn ways to choose one
element from n point-sets (of length t) to form the vector A+P∈Qp S (30)
PoQp. And correspondingly, F watermarked vectors g are
produced. To do the optimization, a part of elements in Qp are
Thefinaloptimizedwatermarkedvectorg isthengiven selected as the fixed elements, each of which is generated
optim
by judging which of these watermarked vectors produced in from quantizing the projection point using (3), that is, the
(26) has the minimum Euclidean distance to the host vector closest DM quantization point to the projection point. The
x. other elements in Qp will be optimized to minimize Y in
g = argmin dist(x,g ) (27) (29).
optim i
gi,i∈{1,2,...,F} Assuming the elements to be optimized in Qp are
More specifically, Fig.10 gives an optimization example Qp(o1),Qp(o2),...,Qp(ot) and the elements to be fixed are
for STDM-MW-Poptim, which is the simple case of em- Qp(f1),Qp(f2),...,Qp(fr), thus, in (29), the corresponding
bedding two bits into one host vector. Three quantization elements to be optimized and fixed in A, A = Qp − P,
points are selected in each directions, thus 32 watermarked will be A(o1),A(o2),...,A(ot) and A(f1),A(f2),...,A(fr). By
vectors (G1,G2,...,G9) can be generated. The final optimized differentiatingY withrespecttoeachelementtobeoptimized,
watermarked vector is G2, the one that is closest to the host and setting the derivatives to be zero, t equations will be
vector x among the nine candidate vectors. generated
∂Y
2) STDM-MW-Qoptim: It has been observed that the goal =0, i=1,2,...,t (31)
ofouroptimizationprocedureistofindtheoptimalDMquan- ∂A(oi)
tization pointalong each directionwhichmakes the Euclidian
distance between the optimized watermarked vector and the
t r
host vector is minimum. According to (23), the Euclidian ⇒ U A(o )= U A(f ), i=1,2,...t (32)
distance, dis v, can be expressed as follows, eoioj j eoifk k
j=1 k=1
X X
dis v = ATUeA (28) Solving (32), t optimized elements in A are produced,
consequently,theoptimizedelementsinQpcanbegenerated,
where A=(Qp−P). p
Qp(o )=A(o )+P(o ). Unfortunately,eachQp(o )maynot
Thus, the optimization procedure can be formulated as a i i i i
subjecttotheconstraint(30), inotherwords,Qp(o )dosenot
constrained quadratic minimization problem that minimizes i
belong to the set of quantization points of the o -th direction,
i
Y =ATU A (29) set B , {b|b = β ∆ −dm0i, β ∈ Z}. To satisfy this
e oi oi oi oi oi
8
constraint, the final optimized Qp(o ) can be given by
i
Qp(o )= argmin dist(Qp(o ),b ) (33)
i i j
bj,bj∈Boi
Finally, vector QoQp is generated by assembling Qp(o )
i
andQp(o ), anditcan be usedto substitute the vectorQp in
f
(22). The watermarked vector can be calculated by
g =x+UU−1(QoQp −P), i=1,2,...,F (34)
i I i
where, assuming there are n bits to be embedded in one
host vector, in other words, there are n given quantization
r
directions for one host vector. Thus, there are F =
n
ways to choose r elements from Qp (of length n) (cid:18)to pla(cid:19)y
as the fixed elements. F vectors QoQp are generated, and
correspondingly,F watermarked vectors g are produced.
Thefinaloptimizedwatermarkedvectorg isthengiven Fig. 12. Test images
optim
by judging which of these watermarked vectors produced in
(34) has the minimum Euclidean distance to the host vector
as shown in Fig.12. And all the experimentdata illustrated in
x.
the following section are the averaged ones.
g = argmin dist(x,g ) (35)
optim i
gi,i∈{1,2,...,F} More specifically, for all the proposed algorithms, to be
analyzed in the experiments, the 2nd−8th DCT coefficients,
Morespecifically,Fig.11givesan optimizationexamplefor
in zig-zag-scanedorder, of each 8×8 block are used to form
STDM-MW-Qoptim, which is the simple case of embedding
each host vector which is used to embed severalmessage bits
two bits into one host vector. Thus, there are two elements
in it. The projective vectors and quantization steps are gen-
in Qp, Qp(1) and Qp(2), corresponding to the projection
erated from the Gaussian distribution N(0,16) and N(f ,4),
directions u and u . If Qp(1) is fixed, then Qp(1) is equal g
1 2 respectively. f is adjusted to ensure a given image fidelity.
to Q2. Through (31), actually Path 1 in Fig.11, the optimized g
point of Qp(2) is O2. Finally, according to (33), O2 is
quantized to Q4, and the corresponding watermarked vector A. Experimental Test for the Efficiency of the Optimization
is G1. Correspondingly, if Qp(2) is fixed, Path 2 is used to Methods
optimize Qp(1), and G2 is the corresponding watermarked As mentioned above, to optimize the proposed multiple
vector.ComparingG1 withG2,thefinaloptimalwatermarked watermarking algorithm, two optimization methods, STDM-
vector is G2, the one that is closer to the host vector x. MW-Poptim and STDM-MW-Qoptim,are proposedto realize
image fidelity improvement. To test their performance, 5
Path 1 watermarks,withsize32×32,areembeddedintothestandard
Path 2
image.Meanwhile,the same quantizationsteps, dithersignals
D2 andprojectivevectorsareusedforthetwomethodstocompare
O2 Q4 their performance in PSNR&CPU-time.
p2 G1 As illustrated in Fig.13, both of them have great perfor-
mance in the improvement of the fidelity of the watermarked
D2 G2
Q3 image. The image fidelity is promoted from 41dB to 44dB in
PSNR, compared with the original embedding strategy.
InSTDM-MW-Poptim,alongwiththegrowthofthesearch
D2
area, it takes more time to realize the optimization, whereas,
gives less contribution to the increase in PSNR. Taking a
Q1 O1 p1 Q2 tradeoffbetween CPU-time and PSNR, 2nd point,search area
k = 0,1, is the optimal one for five users in STDM-MW-
D D D
1 1 1
Poptim.
InSTDM-MW-Qoptim,theCPU-timeof2nd&5thpointand
Fig. 11. Utilizing STDM-MW-Qoptimto embed two message 3rd&4th point are almost the same. This is mainly due to the
bits into one host vector x. fact that the number of the watermarked vectors generated
for one host vector, F in (34), are the same, because F =
4 1 3
= for 2nd&5th point, and F = =
5 5 5
VI. EXPERIMENTALRESULTSAND ANALYSIS (cid:18) 2 (cid:19) (cid:18) (cid:19) (cid:18) (cid:19)
for 3rd&4th point. Taking a tradeoff between CPU-
Toevaluatetheperformanceofourproposedmethod,exper- 5
(cid:18) (cid:19)
imentsare performedon standardimageswith size 256×256 time and PSNR, 4th point, fix number r = 2, is the optimal
9
50
45 STDM−MW−Uorth
STDM−MW−Qoptim
44.5
48 STDM−MW−Poptim
44 44.7 STDM−MW−no−optim
44.6
43.5 46
R 44.5
PSN 43 44.4 44
42.5 44.3 NR
S
42 3.5 4 4.5 5 P42
41.5 STDM−MW−Poptim
STDM−MW−Qoptim
41 40
0 2 4 6 8 10 12 14 16
CPU−time (s)
38
Fig. 13. PSNR Vs. CPU-time with different optimization pa-
rameters.Thefirstpointdenotesembeddingwithoutoptimiza-
36
tion, the rest points are corresponding to the different search 1 1.5 2 2.5 3 3.5 4 4.5 5
number of watermarks
areas, k = (0,1),(0,1,2),(−1,0,1),(−1,0,1,2)in (25), for
STDM-MW-Poptim and the fixed numbers, r = 4,3,2,1 in
Fig. 14. PSNR Vs. Number of watermarks
(32), for STDM-MW-Qoptim.
As illustrated in Fig.15, we test four versions, STDM-
one for five users in STDM-MW-Qoptim.
MW-no-optim, STDM-MW-Poptim, STDM-MW-Qoptim and
Comparing the two optimal points in the two methods, STDM-MW-Uorth. And we use the average detection score,
STDM-MW-Poptim has better performance due to less CPU- measuredin bit error rate (BER), to analyze the performance,
time and higher PSNR. and each curve is the average BER of the three detected
Through experiments, for different numbers of users, it is watermarks.
found that k =0,1 and r =floor(user number/2) are the As we expected, according to Fig.15.(d), all the proposed
appropriate optimization parameters for STDM-MW-Poptim schemesdo havegoodperformancein amplitudescaling. The
and STDM-MW-Qoptim. And in what follows, these two rise of BER in scale β ≥ 1.2 is mainly due to the “cutoff
parameters are used to implement the optimization. distortion”,that is, some pixelsof the image are alreadyquite
hugeand will be cutoff to the maximumallowedvalue when
B. Experimental Test for the Proposed Methods in Robust- thereisanscaling.Inthiscase,thepixelswillnotscalelinearly
ness&PSNR with the scaling factor while the quantization step-sizes still
scale linearly as usual. Thus, experimental performance on
To test the impact of multiple watermarks embedding to
bright images will have a worse robustness in this scale.
the fidelity of the image,differentnumbersof watermarksare
With regard to other attacks, both STDM-MW-Poptim
embedded into the image using the four proposed methods
and STDM-MW-Qoptimhave better robustnessagainstGauss
separately.
noise (Fig.15.(a)) and JPEG compression (Fig.15.(b)) com-
As illustrated in Fig.14, along with the increase of the
pared with STDM-MW-no-optim.This mainly due to the fact
numberofwatermarksembedded,thequalityoftheimagesde-
thattheoptimizationprocedurescanimprovethefidelityofthe
clines in vary degrees. STDM-MW-Uorth, which uses Gram-
watermarked image, as shown in Fig.14, in other words, the
Schmidtorthogonalizationtopreprocesstheprojectivevectors,
embeddingstrengthusedinthemcouldberelativelyincreased
has the superior image quality among these methods. This is
while ensuring the given fidelity.
mainly due to STDM-MW-Uorth is optimal in the case of
Although the STDM-MW-Uorth is the best performedone,
orthogonal projective vectors. Unfortunately, in the general
it is not suitable for the applications where independent
case that the projective vectors are not orthogonal, STDM-
detection is required, because all the projective vectors of
MW-no-optim,the quality of the watermarkedimage declines
each users must be gained in the detector to perform Gram-
rapidly using the original embedding strategy without opti-
Schmidt orthogonalization before the detecting procedure.
mization. In contrast, if optimization is applied, e.g., STDM-
Thus, referencing to section VI-A, STDM-MW-Poptim is the
MW-Poptim, the situation will be improved by a large scale,
optimal one to play as the multiple watermarks embedding
which is promotedby 1.03dBfor 3 watermarks, 2.09dBfor 4
strategy in the sense of higher robustness, less CPU-time and
watermarks, and 3.59dB for 5 watermarks.
for general applications.
Fromanotherpointofview,toevaluatetherobustnessofour
proposed multiple watermarking methods, the test images are
C. Comparison with the Pioneering Multiple Watermarking
embeddedinto3watermarks,withsize32×32,undertheuni-
Algorithms
formfidelity,afixedPSNRof42dB.Meanwhile,fourkindsof
attacks, Gauss Noise, JPEG Compression,Salt&PepperNoise To give an objective analysis of the performance of the
and Amplitude Scaling, are used to verify the performanceof proposed method, the optimal one of our proposed schemes,
the schemes. STDM-MW-Poptim, is picked up to be compared with the
10
0.25 STDM−MW−Uorth 0.5
STDM−MW−Uorth
STDM−MW−Qoptim
0.45 STDM−MW−Qoptim
STDM−MW−Poptim
STDM−MW−Poptim
0.2 STDM−MW−no−optim 0.4 STDM−MW−no−optim
bit error rate(BER)0.01.51 bit error rate(BER)00..0023..5523
0.15
0.05 0.1
0.05
0 0
0 1 2 3 4 5 20 30 40 50 60 70 80 90 100
variance of the Gauss Noise x 10−4 JPEG quality
(a) (b)
0.35 0.25
STDM−MW−Uorth STDM−MW−Uorth
STDM−MW−Qoptim STDM−MW−Qoptim
0.3 STDM−MW−Poptim STDM−MW−Poptim
STDM−MW−no−optim 0.2 STDM−MW−no−optim
0.25
R) R)
bit error rate(BE0.01.52 bit error rate(BE0.01.51
0.1
0.05
0.05
0 0
0 0.005 0.01 0.015 0.5 1 1.5
density of the Salt&Pepper Noise scaling factor
(c) (d)
Fig. 15. BER vs. (a) Gaussian Noise, (b) JPEG, (c) Salt&Pepper Noise and (d) Amplitude Scaling
pioneering multiple watermarking algorithms, DA and IA-R nificantly, especially in Salt&Pepper Noise attack, the perfor-
in [15]. Both of them can embed multiple watermarks into manceisalmostimprovedby70%.Suchsuperiorperformance
the same image area, and each watermark can be detected is attributed to the exploitation of the great robustness of
independently, like ours. To correspond with the original the original STDM in single watermarking. In addition, the
paper, the parameters used for them are identical, the keys optimization strategy can provide a significant improvement
K is generated from Gaussian distribution N(0,16) and the inimagefidelity,in otherwords,theembeddingstrengthused
first 10% of the DCT AC coefficients are used to form the inourschemecouldberelativelyincreasedwhileensuringthe
host vector, meanwhile, 3 watermarks are embedded into the given fidelity.
standard images, the same as ours. Note that, the mean of the
keysDismodifiedtomeettheuniformimagefidelity,42dBin
PSNR. The BER curves are illustrated in Fig.16, meanwhile,
to show the subjective visual effect, the detected watermarks VII. APPLICATION DISCUSSION AND EXTENSION
corresponding to different conditions are given in Fig.17.
As illustrated in Fig.16.(d), because DA and IA-R do not As mentioned above, the proposed multiple watermarking
take the amplitude scaling attack into account, they cannot algorithm has the feature that it can embed multiple water-
resist the image process which scales the amplitude of the marks into the same area and the same transform domain
pixels.Incontrast,STDM-MW-Poptimhasgreatadvantagein of one image, meanwhile, the embedded watermarks can be
this field, extractedindependentlyandblindlyinthedetectorwithoutany
In robustness to random noise and JPEG Compression, interference.Tothisend,itmayownsomepotentialinteresting
Fig.16.(a)(b)(c),our proposedscheme outperformsothers sig- applications.