IET Image Processing

Research Article

Digital image watermarking using partialpivoting lower and upper triangulardecomposition into the wavelet domain

IET Image Process., pp. 1–9& The Institution of Engineering and Technology 2015

ISSN 1751-9659Received on 10th May 2014Revised on 27th January 2015Accepted on 31st March 2015doi: 10.1049/iet-ipr.2014.0395www.ietdl.org

Nazeer Muhammad1,2 ✉, Nargis Bibi3,4

1Department of Applied Mathematics, Hanyang University, Ansan 426-791, South Korea2Department of Mathematics, COMSATS Institute of Information Technology, Wah Cantt, Pakistan3School of Computer Science, University of Manchester, Manchester, UK4Department of Computer Science, Fatima Jinnah Women University, Rawalpindi, Pakistan

✉ E-mail: nazeer@hanyang.ac.kr

Abstract: A digital image watermarking algorithm using partial pivoting lower and upper triangular (PPLU) decompositionis proposed. In this method, a digital watermark image is factorised into lower triangular, upper triangular andpermutation matrices by PPLU decomposition. The permutation matrix is used as the valid key matrix forauthentication of the rightful ownership of the watermark image. The product of the lower and upper triangularmatrices is embedded into particular sub-bands of a cover image that is decomposed by wavelet transform using thesingular value decomposition. The weightage-based differential evolution algorithm is used to achieve the possiblescaling factor for obtaining the maximum possible robustness against various image processing operations and pirateattacks. The authors experiments show that the proposed algorithm is highly reliable with better imperceptibility of theembedded image and computationally efficient compared with recently existed methods.

1 Introduction

Rapid development of the internet and technology has made it easierto spread and share multimedia information in various formsincluding images, videos and audio contents. However, this hasgiven rise to problems of security and authentication of digitalmultimedia contents. Therefore it is important to employ algorithmsthat provide sufficient security for multimedia contents whileproviding protection against various forms of forgery in an efficientmanner with respect to the speed of the verification process.Ultimately, these needs have led to the development of efficientdigital watermarking techniques that guarantee ownership andmaintain the integrity of digital media at a low computational cost.

Digital watermarking refers to the process of embedding awatermark into a digital document to prevent illegal counterfeiting.When required, embedded data may be extracted from awatermarked document to authenticate its copyright status. Robustsecurity is a key objective of digital watermarking, as it ensuresthat a watermark cannot be fragile by unintentional attacks andaffords sufficient protection for copyright enforcement. Toovercome piracy of digital documents and support claims ofrightful ownership, a number of watermarking techniques havebeen developed by many authors. The majority of existingwatermarking schemes concentrate on robustness, in that they aimto achieve a high imperceptibility of the watermarked image ratherthan focusing on issues of noteworthiness, which refers to theprocess of resolving the rightful ownership of an embeddedwatermark image [1]. Among existing watermarking schemes, it isimportant to mention the method proposed in [2], as it establishedthat determining rightful ownership of watermarked images is acriterion of the utmost importance and provided a non-invertiblescheme that improved on the watermarking method proposed byCox et al. [3]. In this regard, many existing watermarkingtechniques with different attacking strategies are discussed in [2].Such techniques employ numerous claims of ownership in anattempt to discredit the authority of the watermark image byembedding one or more additional watermark images such that itbecomes uncertain which one is the genuine authoritativewatermark [1, 4–14].

In [15–18], the authors have suggested a new approach based onsingular value decomposition (SVD) for reliable watermarking. Theprincipal component of the watermark was embedded in the hostimage instead of singular values. However, the SVD-based methodhas been demonstrated to be non-effective and prone to a highprobability of false detections of watermarks by many authors asdescribed above and also in [5, 11, 14, 19–22].

Here, we propose a novel method that is highly robust and achievesa large embedding capacity and improved security for image-baseddocuments. The proposed method is focused on the digital imagewatermarking issues that have arisen from ownership claims andreducing computational cost. The algorithm is based on partialpivoting lower and upper triangular (PPLU) decomposition, whichis an algebraic method used in many applications such as real-timesignal processing where fast computation is required [23, 24].

Besides, a scaling factor can be optimised by taking advantage ofartificial intelligence techniques such as, genetic algorithm (GA),particle swarm optimisation (PSO), artificial bee colony (ABC)and differential evolution (DE) [15–18, 25]. The PSO algorithm issignificantly affected by the initial values of the parameters [26].The success of the ABC algorithm in finding the global optimumis sensitive to the control parameters of the algorithm [27]. TheDE algorithm has been proposed to overcome the maindisadvantage of poor local search ability of GA [17].

In this paper, the DE is used adaptively to select the strength of thewatermark in the combined domain of PPLU and SVD in the waveletdomain and makes possible the improvement of pixel watermarkingto content watermarking. DE has been used in content-basedwatermarking to effectively lessen the contradiction betweenperceptibility and robustness of conventional watermarkingalgorithms [19].

To authenticate the ownership of host data, the extraction processcan be used to decrypt the product watermark data with the reverseSVD, inverse DE matrix and the genuine key in the form of apermutation matrix. The use of permutation key matrix isconsidered for final authenticity of watermark data. To the best ofour knowledge, the proposed method is the first attempt to use thecombination of PPLU and SVD with weighting control DEparameters in field of digital watermark.

1

In Section 2, the SVD method is briefly reviewed. The PPLUdecomposition algorithm, DE, and their properties are described inSection 3. The same section describes the proposed method andillustrates the embedding and extraction process. Simulation andevaluation results are presented in Section 4. Section 5 concludesthe paper.

2 SVD-based watermarking

Let C and W be matrices representing the cover image andwatermark image, respectively. The SVD is applied to a coverimage C∈ RN×N to embed a watermark W as follows

svd(C) := USV t (1)

where S∈ RN×N is the diagonal matrix with eigenvalues of C, and U,V∈ RN×N are the corresponding unitary matrices. A watermarkW∈ RN×N is embedded with a suitable strength factor intodiagonal matrix S by

Sw = S + aW (2)

where α > 0 controls the embedding strength of the watermark. Fromthe SVD of Sw

svd(Sw) = Uw�SwV

tw (3)

the key matrices are reserved as Uw and Vw and the diagonal matrix�Sw is used along with the principal components of the cover image toobtain a watermarked image Cw given by

Cw = U�SwVt (4)

In the extraction stage, a possibly distorted watermarked image Cwmay be obtained. A corrupted watermark W can be extracted withthe help of the three matrices Uw, S and Vw by reversing theembedding process as follows

svd(Cw) = U �SwV t (5)

with setting Sw = Uw�SwV

tw, the watermark W is estimated by

W = (Sw − S)

a(6)

Since the matrices Uw, S and Vw are assumed to be known for thewatermark extraction process, anyone who uses an arbitrarydiagonal matrix along with known data for Uw and Vw can extractthe watermark image with only the diagonal elements beingdifferent from the original watermark image. Indeed, as logicallypointed out by Zhang and Li, this is a major flaw of SVD-basedwatermarking algorithms [6].

Fig. 1 PPLU decomposition of a watermark image

a Original watermark imageb Lower triangular datac Upper triangular datad Key permutation data of the original watermark image

3 Watermarking based on PPLU decompositionand DE

3.1 PPLU decomposition

PPLU decomposition is a factoring method for the low and uppertriangular matrices of a matrix associated with the partial pivotingprocedure for stable row operations implementing Gauss–Jordanelimination [23, 24]. At each step of row operation, the partialpivoting procedure tries to place the largest absolute value into thepivot position prior to division in order to obtain a leading1. Starting from a given n × n matrix A (0) = A, let A(i), 1≤ j≤ n, beinduced from A(i−1) by selecting the row a(i−1)

jk (1≤ k≤ n) from the

2

rows a(i−1)rk (1≤ k≤ n), i≤ r≤ n, such that for i≤ j≤ n

|a(i−1)ji | = max

n

r=i|a(i−1)

ri | (7)

which is followed by exchanging rows with a(i−1)ik (1≤ k≤ n) and

a(i−1)jk (1≤ k≤ n). In addition, Gauss–Jordan elimination is applied

with the updated pivot row a(i)ik = a(i−1)jk . Finally, this procedure

provides three matrices, namely, a lower triangular matrix L, anupper triangular matrix U and permutation matrix P, where L isthe product of a sequence of elementary matrices induced from thepartial pivoting process, U is a reduced echelon form of A, and Pis induced from the row exchanges performed during the partialpivoting process. According to the partial pivoting processdescribed above, we can define PPLU decomposition as follows

A = PPLU(A) = PA = LU (8)

The efficiency of PPLU decomposition is viewed in terms ofcomputational cost and storage of the algorithm. Since oneapplication of the Gauss–Jordan elimination phase gives thefactorisation PA = LU: the PPLU decomposition asymptoticallyrequires only 1/3n3 long operations (multiplication and division),which is lower than for SVD decomposition. Moreover, from astorage point of view, PPLU decomposition is very compact,because it can overwrite entries of L and U. For a givenwatermark image matrix A, the PPLU processed matrix A gives ascrambled image where the permutation matrix P is the key matrixfor recovering the watermark. To reconstruct A from the scrambleddata, A is simply permuted inversely using P. PPLUdecomposition of an image l(m, n) with m = 1, 2, .., M and n = 1,2, .., N is shown in Fig. 1.

The product LU is embedded into the transformed domains of ahost image and the permutation matrix P is reserved forauthenticating the watermark during the reconstruction process.For robust watermarking, the data of LU must be embedded intoparticular sub-bands of the wavelet domain of the host.

3.2 Differential evolution

We have used the commonly used version of DE ‘DE/rand/1/bin’ inour method and explained here [17, 18]. The basic operators of DEare briefly explained in the following sections.

Initial population: If initially there is no information about theproblem to be optimised, the target vector xi,G can be generated

IET Image Process., pp. 1–9& The Institution of Engineering and Technology 2015

randomly as follows

xi,G = xi,(L) + randi[0, 1](xi,(H) − xi,(L)) (9)

where xi,(L) is used to represent the lower boundaries and xi,(H) is usedto represent the higher boundaries of vector xi = {xj,i} = {x1,i, x2,i, ...,xD,i}T, respectively. The ranges i and j over the number ofindividuals in terms of population and dimension of problem arerepresented as: i = 1, …, NP and j = 1, …, D, respectively.

Mutation: For each xi,G, a vector vi,G+1 is generated in terms ofmutation of randomly chosen vectors at generation G from thecurrent population as follows

vi,G+1 = xr1,G + F(xr2,G − xr3,G) (10)

where i, r1, r2 and r3 are mutually random integer indices such thatr1≠r2≠r3≠1 and r1r1, r2, r3∈ {1, 2,…, NP}. The population size NPis considered to be higher than the number of selected randomindices F [22]. For greater values of F, the generated mutatedpopulation has higher diversity and the lower values of F result infaster convergence. Mutation operator is used to expand the searchspace. This way of generating a mutant vector is called DE1.Another popular scheme is named as DE2 in which mutant vectorsare produced with an influence from the best vector xbest,G of thecurrent generation as

vi,G+1 = xr3,G + K(xbest,G−x − xr2,G)+ F(xr1,G − xr2,G) (11)

where K is the combination factor that provides increased greedinessof the search process.

Crossover: The crossover operation is applied to increase thediversity of the mutated vector, vi,G+1. It is a swapping operationbetween the elements of the target vector xi,G and the elements ofmutated vector vi,G+1, to produce trial vector ui,G+1. Cr is used tocontrol the cross over rate

xi,G = xi,(L) + randi[0, 1](xi,(H) − xi,(L)) (12)

u j,i,G+1 =v j,i,G+1 if rand j,i ≤ Cr or j = Irandx j,i,G if rand j,i . Cr or j = Irand

{(13)

where = 1, 2, …, D; randj,i∈ [0;1] is the random number; Cr is usedto control the cross over rate such that Cr∈ [0;1] is predefinedcrossover constant and Irand∈ [1, 2, …, D] is a randomly chosenindex. Irand makes sure that vi,G+1≠ xi,G.

Selection: Selection rule is applied to decide between the trial vectorand the target vector and the one with maximum function is selectedto enter to the next generation. This selection rule is called objectivefunction. If the value returned by the objective function for the trialvector uj,i,G+1 is greater than or equal to the value obtained for thetarget vector xi,G, the latter is replaced by the former otherwise thelatter is reserved in the next generation

xi,G+1 =ui,G+1 if f (ui,G+1) ≤ f (xi,G), i = 1, 2, . . . , NPxi,G otherwise

{(14)

3.2.1 DE implementation approach: Owing to the advantagesof simplicity, fast convergence and less parameters, DE has beenapplied to solve a wide range of real-life application problems[15–18, 22]. Mutation factor and cross-over rate are two veryimportant control parameters of DE [15]. There are quite differentconclusions about the optimal setting of the mutation factor F andcrossover rate Cr [15–18]. It has been suggested in [16] that thevalue of F should be in the range [0.4, 1] and the reasonablechoice of Cr may be 0.1. However, in [17] it is recommended thatthe values of F should be 0.6, while Cr should be in the range

IET Image Process., pp. 1–9& The Institution of Engineering and Technology 2015

[0.3, 0.9]. Moreover, different parameter settings are discussedin [22] such that a possible best choice of the F = 0.9 lying in[0.4, 0.95] and that Cr typically lies in [0, 0.2] when the functionis separable, while in [0.9, 1] when the function’s parameters aredependent. Most of the adaptation schemes that are available applysome sort of random change to the parameters irrespective of thequality of the current parameters [15–18, 22].

3.3 Embedding process

The proposed watermark embedding process comprises two startingmodules: a watermark image and a cover image. For the watermarkprocess, PPLU decomposition (P) of a watermark image is obtainedas described in (15). We consider the application of DE in findingscaling factor to achieve a better performance [15]. For a givencover image, a wavelet transform is applied to obtain sub-bandimages [28, 29] in which the coded watermark data is embeddedas explained in following steps:

1. Wavelet transform has become an important tool in imageprocessing and watermarking because of its good energycompaction properties. The basic idea of discrete wavelettransforms (W) is to separate frequency detail [29]. Apply onelevel W on cover image (C) to decompose it into four sub-bands

Ck such that k [ C(ll)j−1, C

(hl)j−1, C

(lh)j−1, C

(hh)j−1

{ }. These four sub-bands,

namely a lower resolution approximation component (C(ll)j−1) and

three other corresponding to horizontal (C(lh)j−1), vertical (C

(hl)j−1) and

diagonal (C(hh)j−1) detail components. Apply again W at level second

on C(ll)j−1 and C(hh)

j−1 to decompose it into four sub-bands of

respective sub-bands: C(ll)pk and C(hh)

qk such that pk [ C p(ll)j−1 , C

p(hl)j−1 ,

{C p(lh)

j−1 , Cp(hh)j−1 } and qk [ Cq(ll)

j−1, Cq(hl)j−1 , C

q(lh)j−1 , C

q(hh)j−1

{ }.

2. Apply the SVD (S) to each sub-band at level second on matricesC(ll)

pk and C(hh)qk to partition it into three matrices U, V and S such

that (1)

svd(C(ll)pk ) := UpkSpkV

tpk

svd(C(ll)qk ) := UqkSqkV

tqk

3. For the watermark process, PPLU decomposition of a watermarkimage (W) is obtained as described in (8)

PwWK = LwUw = Yw (15)

where Pw is the permutation matrix associated withW containing therow swapping information and Lw, Uw are the lower and uppertriangular matrices of W, respectively. Furthermore, thepermutation matrix Pw is reserved as a security key to validate theoriginal watermark at the extraction stage. Apply one level W onproduct data Yw of lower Lw and upper Uw triangular matrices todecompose it into four sub-bands Ywk such that

k [ Y (ll)j−1, Y

(hl)j−1, Y

(lh)j−1, Y

(hh)j−1

{ }. Subsequently, perform S operation

on matrix Ywk to partition it into three matrices U, V and S such that

svd(Ywk) := UwkSwkVtwk (16)

Dw = UwkSwk (17)

the coded watermark data Δw (principal components of eachsub-band) is properly scaled down by multiplying with scalingfactor DE using (14) for embedding into a chosen sub-band imageset of the cover image C using the SVD application, as explainedin step 2.4. From step 2, modify the singular values of diagonal matrices Sk ofall sub-bands of C(ll)

pk and C(hh)qk with the coded watermark data Δw

3

from (17) and then apply S to reconstruct them respectively

Swk(p,q) = Sk(p,q) + lℓ ⊙ Dw,

ℓ [ C p(ll)j−1 , C

q(ll)j−1, C

q(ll)j−1

{ }Cq(ll)

j−1 [ C p(hl)j−1 , C

p(lh)j−1 , C

p(hh)j−1 , Cq(hl)

j−1 , Cq(lh)j−1 , C

q(hh)j−1

{ }(18)

where scaling factor lℓ is used in the form of diagonal matrix andobtained from DE algorithm [15], explained in Section 3. SVDapplication to reconstruct the C using the Swk is shown as

Ck(p,q) = Uk(p,q)Swk(p,q)Vtk(p,q), p, q [ C(ll)

kp , C(hh)kq

{ }

Furthermore, by employing inverse W on C(ll)kp and C(hh)

kq the

modified C(ll)J−1 and C(hh)

J−1 sub-bands are reconstructed.5. Watermarked image CJ is obtained by replacing the originalC(ll)

j−1 and C(hh)j−1 sub-bands of cover image (as discussed in step 1)

by modified C(ll)J−1 and C(hh)

J−1 sub-bands using inverse wavelet

Fig. 2 Watermarking flowchart

a Embedding processb Extracting process

4

transform from the following combination of sub-band data

C(ll)j−1, C

(lh)j−1, C

(hl)j−1, C

(hh)j−1

Importantly, embedding the same watermark in the approximateddata and detailed data at the lower resolution level enhancescorrelations against certain image processing operations [28, 29].

3.4 Extraction process

The watermarked image Cj is subjected to various distortions. Awavelet transform is applied to decompose a possibly distortedwatermarked image C∗

j as well as the original cover images C intothe four sub-band data as discussed in step 1 of Section 3.3. Thedistorted watermarked image is decomposed into the approximated

sub-band C∗(ll)j−1 , the horizontal sub-band C∗(lh)

j−1 , vertical sub-band

C∗(hl)j−1 and diagonal sub-band data C∗(hh)

j−1 , respectively. Further Wdecomposition of C∗(ll)

j−1 and C∗(hh)j−1 are obtained same as in

embedding process. Application of SVD is used for obtaining thedistorted product data X ∗

wk with an appropriate scaling factor lℓ,exactly same as that used during the embedding process. The X ∗

wkresults demonstrate the reliability of the proposed method forprotection of digital images with respect to rightful ownershipusing only a genuine permutation key matrix of the original

IET Image Process., pp. 1–9& The Institution of Engineering and Technology 2015

watermark image. If C∗j is distorted watermarked image then a

possibly corrupted watermark W* can be extracted performing thefollowing steps:

1. Apply steps 1 and 2 of the embedding process on the corruptedwatermarked image C∗

j to obtain S∗wk.

2. Extract the possibly corrupted watermark

D∗wk =

(S∗wk − Sk )

lℓ(19)

The extracted data are the estimated product data of the lower andupper triangular matrices, which is embedded during theembedding process through (8).3. Compute possibly corrupted sub-bands detail of product of lowerand upper triangular matrices of watermark image D∗

wk using reserve

Fig. 3 Visual quality of watermarked and extracted watermark images:watermarked with embedded data Xw

a Lenab Manc Scenej Hillk Boatl Barbarad–i and m–r watermark images extracted from the C∗(ll)

j−1 and C∗(hh)j−1

Table 1 Comparison of the proposed method and [17] by evaluations of differe

Test images/method MSSIM (index) PSNR, dB

Our [17] Our [17]

Lena 0.9752 0.9716 40.7832 38.477Man 0.9813 0.9773 40.783 38.456Scene 0.9804 0.9779 40.7834 38.471Hill 0.9841 0.9816 40.7833 38.418Boat 0.9815 0.9785 40.7864 38.424Barbara 0.9827 0.9794 40.7839 38.414

IET Image Process., pp. 1–9& The Institution of Engineering and Technology 2015

vector V tw from (16)

Y ∗wk = D∗

wkVtwk, D∗

wk [ U∗wS

∗w (20)

W ∗k = inv(P)∗Y ∗

wk, k [ C(ll)j−1 and C(hh)

j−1

{ }(21)

4. Apply inverse W on W ∗k to obtain the possibly corrupted

watermarks using matrix P from (15). As a result, we obtain two

watermark images from (21): W1 from C∗(ll)j−1 and W2 from C∗(hh)

j−1 ,respectively, as shown in Fig. 2. Experimentally, retrieving thewatermark with W1 is robust against various image processingoperations such as against Gaussian noise, and resizing. Theretrieving the watermark with W2 is also robust against theblurring, histogram, contrast and gamma correction.

4 Simulation and evaluation

The proposed scheme is examined with respect to its ability toprovide security for certain digital documents, and is found to bemore convenient than existing methods. In addition, the proposedmethod performs without delay and huge computationalrequirement, and verifies the identity of the true ownership.Specifically, we examine the visual quality of watermarked imagesby using mean structure similarity index measurement (MSSIM)and peak signal-to-noise ratio (PSNR) [23–32]. To evaluate thecorrelation between the original watermark image and theextracted watermark image, the coefficient correlation CC [28]which is a number between 0 and 1 is used to specify theconfidence level between the two images.

As shown below in the following figures, our experiments indicatethat the proposed watermarking scheme exhibits highimperceptibility and good robustness. We perform experiments ondifferent standard test images from SIPI image database,University of Southern California, ranging from the relatively lesscomplicated images (Lena, Scene and Barbara) to the morecomplicated images (Hill, Man and Boat) shown in Fig. 3. In allexperiments, the sizes of the test images are 512 × 512. Likewise,the size of the DDNT watermark image is 256 × 256. We use thereasonable higher embedding capacity to test our proposedmethod: capacity = 20 888 bit. For general analysis of the proposedmethod, simple and unique watermark-based perceptualobservations of watermarked images are performed asdemonstrated in the following figures.

The proposed method is examined by measuring the quality ofwatermarked test images as shown in Table 1. The MSSIM andPSNRs as shown in Table 1 are maintained the good level ofimperceptibility of watermarked images and the correspondingcorrelation coefficient CC values for the extracted watermarkimages are highly reliable for high-end security as shown inFig. 4. In addition, the less computational time (s) of theextraction process shows the efficiency of the PPLUdecomposition process as shown in Fig. 4c.

To provide a general comparison of the proposed method with themethod described in [17] in terms of imperceptibility of watermarkedimages, quality of extracted watermark, and computational time ofthe extraction process using bench mark test images are

nt test images

CC (index) Extraction time, s

C∗(ll)J−1 C∗(hh)

J−1 [17] Our [17]

1 0.9988 0.9798 0.9968 111.59 344.042 0.9986 0.9804 0.9968 112.99 345.363 0.9987 0.9796 0.9965 114.28 346.143 0.9988 0.9796 0.9966 111.32 344.048 0.9986 0.9792 0.9966 112.99 345.369 0.9987 0.9818 0.9967 114.28 346.14

5

Fig. 4 Comparison of proposed method (dark grey bars) with the method described in [17] (light grey bars) is represented

a Imperceptibility of watermarked images on the basis of MSSIM (index)b PSNR (dB) valuesc Computational time of the extraction processd Extracted watermark quality using CC (index) values of different test images are shown

demonstrated visually using Fig. 3 and numerically shown inTable 1.

The imperceptibility of watermarked images, the best CC valuesof the extracted watermark images W1 and W2 from the particular

sub-band data C∗(ll)j−1 and C∗(hh)

j−1 , and the correspondingcomputational time of the extraction process are analysednumerically and reported in Table 1 and Fig. 4. Experiments areperformed on an Intel ® Core (TM) i3-2120 CPU @ 3.30 GHzwith 8 GB of RAM running a 64-bit Windows 8.1 System. Toanalyse the effects of common image processing and geometricaloperations [17], we use the Stir Mark test from [33]. A jointphotographic experts group (JPEG) compression operation, wherethe compression ratio is varied from 70 to 90 is performed.

In Table 2, the CCLL and CCHH are the coefficient correlation

values for watermark images extracted from C∗(ll)j−1 and C∗(hh)

j−1 ,

Table 2 Robustness against JPEG compression operation

Test images Methods 90% 85% 80% 75% 70%

Lena CCLL 0.9849 0.9729 0.9596 0.9430 0.9266CCHH 0.1937 0.1180 0.1066 0.1049 0.0956[17] 0.9804 0.9681 0.9543 0.9389 0.9259

Man CCLL 0.9838 0.9686 0.9526 0.9323 0.9128CCHH 0.1296 0.0707 0.0703 0.0722 0.0659[17] 0.9789 0.9616 0.9442 0.9246 0.9049

Scene CCLL 0.9818 0.9647 0.9483 0.9290 0.9090CCHH 0.1083 0.0623 0.0532 0.0504 0.0535[17] 0.9753 0.9562 0.9371 0.9182 0.8992

Hill CCLL 0.9824 0.9667 0.9510 0.9314 0.9126CCHH 0.1082 0.0722 0.0662 0.0703 0.0696[17] 0.9764 0.9584 0.9401 0.9211 0.9021

Boat CCLL 0.9834 0.9690 0.9535 0.9344 0.9161CCHH 0.1071 0.0675 0.0653 0.0725 0.0731[17] 0.9783 0.9624 0.9460 0.9282 0.9103

Barbara CCLL 0.9841 0.9693 0.9546 0.9345 0.9143CCHH 0.1982 0.1357 0.1016 0.1033 0.1027[17] 0.9798 0.9627 0.9466 0.9268 0.9070

6

respectively. These C∗(ll)j−1 and C∗(hh)

j−1 have different levels ofresistance against certain image processing operations. Specifically,

the C∗(ll)j−1 is robust to common image processing operations

including JPEG image compression as shown in Fig. 5.

Furthermore, the C∗(hh)j−1 enhances the quality of the watermark

extracting from C∗(ll)j−1 since the same watermark is embedded in

both C(ll)j−1 and C(hh)

j−1. In order for watermark embedding to beefficient, it robustness against various image processing andgeometrical operations has determined as shown in Fig. 6 andTable 3.

The bold values of numerical results shown in Table 1 to Table 3and filled squares lines in Fig. 6 confirm the robustness of theproposed method. With respect to the blurring operation, testimages are analysed using a Gaussian low-pass filter. We observedthat the CC values of the watermark images extracted with CT,

GM and JPEG operation from the C∗(ll)j−1 are higher compared with

the C∗(hh)j−1 and those extracted from C∗(hh)

j−1 exhibits more robustresistance to (BL), (NS), and (RS) operations. However, in thecase of blurring tests with a low-pass Gaussian filter with a

standard deviation of 0.3, the C∗(ll)j−1 shows sufficient robustness

compared with the C∗(hh)j−1 . The noise addition test is conducted by

adding salt and pepper noise (noise density = 0.001) to thewatermarked image.

4.1 False positive detection analysis

False positive detection problem is a problem of rightful ownership.The main purpose of a watermark is to protect the owner’s copyright.However, for many existing watermarking schemes, an attacker caneasily confuse one by manipulating the watermarked image and

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Fig. 5 Comparison of JPEG compression ratio

CC values of extracted watermark from standard listed images are demonstrated corresponding to the different levels of JPEG compression ratioCircles represent the proposed method and the squares represent the recent existing method [17]

Fig. 6 Comparison of image processing operations

CC values of extracted watermark from three different standard images: Lena, Man and Scene, are demonstrated corresponding to the different nature of image processing operations:noise (NS), rescaling (RS), histogram (HS), blurring (BL), contrast (CT) and gamma correction (GM)Filled squares represent the proposed method and the filled circles the existing method [17]

Table 3 Robustness against fragile watermarking operations

Test images Methods NS RS BL HS CT GM

Lena CCLL 0.8697 0.8505 0.9827 0.0508 0.0311 0.0601CCHH 0.6805 0.0814 0.9971 0.8953 0.9765 0.9928[17] 0.8431 0.7918 0.9913 0.6216 0.7782 0.8427

Man CCLL 0.8724 0.7806 0.9827 0.0600 0.0430 0.0557CCHH 0.6972 0.0797 0.9970 0.8501 0.9619 0.9897[17] 0.8656 0.6790 0.9966 0.6726 0.8994 0.8448

Boat CCLL 0.8735 0.7484 0.9827 0.1144 0.0333 0.0805CCHH 0.4020 0.0607 0.9967 0.7093 0.8828 0.9829[17] 0.8464 0.6645 0.9904 0.5795 0.7431 0.8144

NS: noise, RS: rescaling, HS: histogram, BL: blurring, CT: contrast and GM: gamma correction.

IET Image Process., pp. 1–97& The Institution of Engineering and Technology 2015

Fig. 7 Correct and false positive detection analysis flowchart

claim that he or she is the legitimate owner or the watermarked imagebelongs to him [1, 2]. Some authors have claimed and showed thatthere is ambiguity in the SVD-based watermarking schemes [15–18].

Recently, Mohammad et al. [9] proposed a technique that reformstechnique in [4] to solve this issue; however, it is susceptible to bothgeometric and common image processing operation. It is importantto note that none of the above-mentioned watermarkingtechniques, which are based on singular vectors, are capable ofpreserving the orthogonal properties of the left or right singularvectors of corresponding matrices, since the transformation used toembed the watermark image is non-linear [10]. Indeed, it isexceedingly difficult to embed a watermark image into the singularvectors of a cover image while preserving orthogonality [11–14].

The high robustness of these schemes is due to the fact that theSVD subspace (singular vector matrices) can preserve thesignificant amount of the watermark and this information isprovided by the owner not extracted from the image being

Fig. 8 False positive detection analysis

a Watermarked Man image embedded with Fig. 1a using the method [17]b Arbitrary watermark imagec Watermark extraction from (Fig. 8a) by Ali and Ahn [17] with true singular vector Vwk; CCd, eWatermark extraction from the watermarked image (Fig. 3b) using the proposed method wit0.9988 and CCHH = 0.9804

f, g To extract the embedded watermark from (Fig. 3b) with the help of arbitrary permutation m

C∗(hh)j−1 ; CCLL = 0.3140 and CCHH = 0.0389 using the proposed method

h Watermark extraction from (Fig. 8a) with arbitrary singular vector Vwk watermark image of

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protected. As was shown in [2], extracting the watermark from awatermarked image is not enough to prove ownership. Authors of[6] gave a set of sufficient conditions that watermarks andwatermarking schemes must meet in order to resolve the problemof ownership proof. To overcome above-mentioned problems, thewatermark image is decomposed using PPLU and subsequentlythe principal component of product data of lower and uppertriangular matrices are embedded in the cover image instead ofsingular values or simple principle component of watermark imageas performed in recent existed method [14].

It is clear from Figs. 8f and g that the original watermark imagecannot be detected using arbitrary reference watermark imagesusing the proposed method. Thus, the proposed algorithm canhandle the false claim of illegal ownership, efficiently. However,in comparison to this, the method in [17] cannot handle theproblem of false positive detection accurately, particularly in cases,where the arbitrary reference watermark image is composed on

= 0.9968h true permutation matrix Pw and true singular vector Vwk from C∗(ll)

j−1 and C∗(hh)j−1 ; CCLL =

atrix Pw and arbitrary singular vector Vwk watermark image of Fig. 8b from C∗(ll)j−1 and

Fig. 8b using [17]; CC = 0.5610

IET Image Process., pp. 1–9& The Institution of Engineering and Technology 2015

some similar data value as like to original watermark image, asshown in Fig. 8b. Specially, in case of digital documents, theusual pattern of watermark is repeated often in terms of differentsequence of numeric or alphabetical data set, as can be observedin Fig. 7d. Hence, to keep the uniqueness of singular values ofcorresponding unitary matrices of watermark images are notpossible as shown in Fig. 7. This flaws occurred because of basicpitfall encountered by the strategy adapted using SVD applicationas mentioned in [5, 11, 14, 20], where the watermark wasmodified only along the diagonals, leading to the extraction of areference watermark that is being searched using an arbitraryimage. Hence, our method utilises the property of SVD-basedwatermarking algorithms along with PPLU decomposition andensures rightful ownership of the digital watermark image. PPLUis used to reduce the rounding error growth factor [34]. In therounding error problem, it is not easy to decide all of them sincethere is no relation between a pixel and its neighbours. However,with slight change in pattern while using the arbitrary watermarkfor extracting process, illegally, the arbitrary watermark cannot begenerated falsely as shown in Fig. 8.

5 Conclusion

In this paper, a comparatively new watermarking scheme with PPLUdecomposition of watermark image is proposed as a method forembedding the watermark data into a cover image using the DEalgorithm as a scaling factor and for extracting of watermarkuniquely and to avoid the false positive problem. The effectivenessof the proposed algorithm is numerically analysed and confirmedby simulation results. On the basis of the mathematical propertiesof the PPLU decomposition method, the proposed method isfound to provide good imperceptibility of watermarked images,preserving the high-end security of watermarks, and exhibits fastcomputation. This method is tested successfully against a numberof spiteful image processing operations and pirated attacks.

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