A new adjustable blind Watermarking based on GA and SVD

Hamed Modaghegh, Hossein Khosravi R., Mohammad- R. Akbarzadeh-TDepartment ofElectrical Engineering, Ferdowsi University OfMashhad, Iran

Minimum

Minimum

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image singular values with singular valuedecomposition technique (SVD), and embeddedwatermark data, then rebuilt the image.

After this presentation several papers used andoptimized the technique [4,5], but these techniquessuffer from false-positive drawback (the methodrecognizes non watermarked image as watermarked). 'R. Sun,et al[6] presented another method that solved!he proble~. The method does not use the originalImage and IS so-called blind. Embedding watermark inimage ma~ param:ters causes changes in the image,and more information these parameters carry, yieldsmore changes in image. So, apart from the method weused to embed watermark in the image, there exists atradeoff between perceptibility and robustness againstattacks. This tradeoff results in an optimizationproblem that will be solved in three differentconditions. Based on the following three conditions,we calculate optimized parameters for applyingwatermark using Genetic Algorithm (GA)optimization procedure.• Maximum robustness and

perceptibility. (Robust Watermarking)Minimum robustness andperceptibility. (Fragile Watermarking)Minimum robustness to some attacks whilemaximum robustness to other attacks andMinimum perceptibility. (Semi-FragileWatermarking)

In this paper, we exploit image singular values byusing SVD technique, calculate optimized parametersfor applying watermark by using GA and embedwatermark in the image.

Adjustable watermarking method with minimumperceptibility is attained by mixing the SVD and GAtechniques.SVD and GA are introduced in section 2. The proposedsolution that uses SVD and GA is presented in section3; in section 4, simulation results of proposed methodwithin three conditions: Robust, Fragile, Semi-Fragilear: compared to simulation results based on empiricaladjustment, and we fmally offer a conclusion in section5.

Abstract

Keywords: SVD, blind Watermarking, GA.

1. Introduction

Watermarking was first introduced 700 years ago[l].It was made by impressing a water-coated metalstamp onto the paper during manufacturing.Wat:rmarks have been used by papermakers to identifyspecial products by companies. In general,watermarking is a method for hiding specialinformation (watermark) within cover data in order tosave the author ownership [2].I~ order to protect the rights of the owner against

varIOUS attacks, we should insert owner information inthe image main parameters; One of these mainparameters is singular values [3]. H.zer, et al exploited

As information technology and multimediaproducts become more and more readily available,copyright and other related legal topics become moreand more significant. Embedding copyrightinformation as hidden data into the multimedia product-named watermarking- is one ofthe methods to protectowner rights. Two main concepts in watermarking areimperceptibility and robustness of the watermark. Atradeoff between these two features exists, which canbe introduced as an optimization problem. GeneticAlgorithm (GA) is applied to solve this optimizationproblem. In this paper, a new adjustable watermarkingmethod based on singular value decomposition ispresented so that SVD parameters are adjusted byusing the GA considering image complexity and attackresistance. The proposed watermarking method is alsoan adjustable solution, so that by changing fitnessfunction (cost function), watermarking method can beconverted to each of robust, fragile, or semi-fragiletypes. Simulation results show that the proposedmethod has better results from the case wherewatermarking parameters are adjusted by the userempirically.

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2. Background

2.1. Different Watermarking methods

Considering the amount of robustness to the changes,watermarking techniques can be divided into threecategories: [2].Fragile watermarking: This type of watermarking isdestroyed upon small changes in the image, so it isappropriate to review image authentication. Becausethe smallest change in the watermarked data, willdestroy the watermark and the recipient will be awareof the inserted change.Robust watermarking: This type of watermarking isusually used to apply author ownership on multimediadata and is designed such that it could be robust againstsmall changes, and watermark information could notbe easily destroyed, and more, make it feasible torecognize watermark owner even after changes.Semi-Fragile watermarking: This type ofwatermarking is fragile to some certain changes and isrobust to others. As an example, since white noiseexists in every transmission channel, it is better tochoose a watermarking method that is robust againstwhite noise and is fragile to other changes, whichusually intend abuse.

On the other hand, considering retrieval method, wecan categorize watermarking methods to blind andnon-blind. In order to retrieve watermark data in non­blind methods, in addition to watermarked image, wealso need original image. These methods are moreexposed to false-positive drawback. In blind retrievalmethods, there is no need to original image andwatermark can be extracted only from watermarkedimage. Since the original image is not used in thesemethods, false-positive problem never occurs. Thus,blind methods have more applications than non-blindmethods.

2.2. Watermarking methods by using SVD

Generally for every matrix there exists adecomposition in the form (1), Which is called singularvalue decomposition where U and V are unitarymatrixes so that:

AM N = UM M * DM N * V!vN (1)I = U * U' (2)I = V * V'

The matrix D is a diagonal matrix where the diagonalentries are singular values of matrix A. Many methodsare proposed, which have embedded watermark bySVD. One of the first was presented by H.zer, et al[3].

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By using SVD technique, it first decomposed thematrix in the form of (1).

A = U * D * VT (3)Watermark data (m-by-n matrix) is multiplied to a

constant coefficient a and the result is compoundedwith matrix D.

D' = D + aW (4)a shows strength of watermark insertion in the image

block (4).). We then decompose this matrix to threematrixes by SVD technique one more time, thenreconstruct watermarked image using matrixes Dw, U,and V. (as shown in (5-6)).

D' = Uw * Dw * vX (5)Aw = U * Dw * VT (6)

Watermark retrieval stages are as follows:Suppose that matrix A'w is the watermarked image

so that some changes are applied by the attacker. Firstwe decompose A~ matrix by SVD and obtain D'w:

A' = U' * D:V * V,T (7)Then we multiply this matrix by Uw and Vw to make

D". Watermark is calculated by subtracting matrix Dfrom D":

D" = Uw * D'w * vX (8)W' = D&-D (9)

aVeysel, Aslantas [4] tried to improve the procedure

by merging this method with Genetic Algorithm (GA).The proposed method was robust and non-blind whereparameter "a" was calculated empirically by user. Theresult had very good resistance to attacks, but the maindrawback was that the response to non-watermarkedimages was also positive and declared non­watermarked images as watermarked ones. Thisdrawback is subject to the watermarking method, thatis non-blind and to the watermark data that is too low.In this method, major watermark data are calculated byretrieval of matrixes Uwand Vw. These two matrixesare better to be calculated from attacked watermarkedimage A' rather than original image A.

Other methods were proposed to solve the problem;R.Sun, et al[6] used blocked SVD. Image wasfractioned into 8-by-8 simpler blocks. Then SVD isexecuted for these blocks and we only work on the firstelement that is the maximum singular value of thematrix. In order to get minimum changes in the image,this number is quantized, as shown below:

Z = DCl,l) mod Q (10)ifw = 0 then:

z < 3Q ~ DCl,l)' = DCl,l) + g - z (11)4 4

, SQotherwise ~ DCl,l) = DCl,l) +4 - z

and ifw=l:z < 3Q ~ DCl,l)' = DCl,l) - g + z (12)

4 4

watermark against attacks, three watermarking typeswere introduced, so based on the method that we wantto implement, we should minimize or maximizerobustness. By changing Q, robustness could bechanged against certain attack. There is not a simplelinear relation between Q and robustness, and therelation depends on different criteria like type of theattack and image block complexity; so that it is feasiblethat a particular Q causes high robustness for a certainblock but the same Q results in low robustness inanother block.

Recognizing which block is more affected or lessaffected by the attack is a difficult task, and it will bedifferent with the specifications of each image.Therefore, the diagnosis of this action is better to becarried out for each image and each attack separately.As we see, obtaining the appropriate Q, to gainmaximum or minimum robustness against attacks andminimum perceptibility, can be viewed as anoptimization problem. In order to resolve this problem-that has N input variables (N is total number of imageblocks)-, we use GA algorithm.

k

Yes

atermarkedimage

selection~ -~ - - - --- - - ------ _.

crossover...'riiLifa'tlon" ..

I

3. Proposed Algorithm (using GA tooptimize watermarking algorithm)

, 3Qotherwise ~ D(l,l) =D(l,l) +4 - z

Q is an arbitrary value to quantize D(l,l). As Qincreases, robustness of watermark and so, changes inthe image are increased. After applying watermark datato the maximum singular value, the watermarkedimage can be calculated simply by multiplying these 3matrices:

A = U * D' * VT (13)These steps are taken for other blocks, and as

previously mentioned, SVD value is calculated forthem and other watermark bits are inserted intomaximum singular value. In receiver, we only have tofragment the image into 8-by-8 blocks and run SVDfor each of them. Watermark is extracted using:

Z =D(l,l)' mod Q (14)Ifz<Q/2 then w=O, otherwise w=1.

So all watermark bits can be retrieved from the image;the procedure covered the stated problem and respondscorrectly to non-watermarked images.

The method introduced by R.sun, et al [6] (unlikeother proposed methods) does not need the main imagein order to extract watermark data (blind). So theproblem that occurred in the first method [3] may nothappen in this method, and all information can beexploited from watermarked image. In these methods,knowing Q is enough to extract watermark but, using aconstant Q, to quantize all blocks, remains as adrawback.

As we know, different image blocks do not havesame statistic properties, some have high complexityand some not. The complexity of image block directlyinfluences singular values and increases first singularvalue. From the other hand, perceptibility of insertedchanges, in blocks with higher complexity is lowerthan blocks with simple details. So it is better to reducethe value of inserted changes in singular values forblocks with lower image pixels complexity. In order toreduce perceptibility of the change, value of Q shouldbe small. In blocks with more complexity, we canselect larger values of Q, so that perceptibility ofwatermark would be still low.

Main disadvantage is absence of a uniform relationbetween value of Q and perceptibility; because severalnonlinear elements in the procedure exist. All theseelements have led to lack of ability in computation ofoptimized Q for each block with analysis. In additionto perceptibility, another factor that is effective inselecting Q, is robustness against attacks. Asmentioned in 2-1-2, considering robustness of

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1 Peak Signal to Noise Ratio

Figure 1. Watermarking algorithm block diagram.

Which f is fitness function of i-th populationelement, t represents number of attacks, W*i representsextracted watermark from Iw image and function corrrepresents correlation between the two input matrix.The less corr, function value, the less perceptibility;and the more corrw , the more robustness. Amongfitness functions defmed, the third, converges fasterand results suitable Qs.

But in order to gain a fragile watermarking method,perceptibility and robustness, both should beminimized so that watermark data may not be extractedby small change in watermarked image. Thus weshould defme fitness function so that maximizes corr,and minimizes corrw. We have defmed fitness functionas follows:

Table 1. Sample Obtained Q, from best chromosome forfi t bl k f imase i I t ti

4. Simulation Results

MATLAB software is used for paper simulation andQ is limited between 40 and 100. The attacks used insimulation are Gaussian filter attack (window size 5and variance 1), mean filter attack (window size 3),noise attack (amplitude 4) and move camera attack (3pixels with angle 45). In order to review performanceof GA algorithm, the software is investigated in 2stages and optimized GA parameters for applyingwatermark are obtained.

In the fITst stage, fitness function value is calculatedfor population number 50, crossover rate 0.5, numberof generation 60 and different values of mutation rate.The best result is obtained where mutation rate is 0.03.

Then in second stage fitness function value iscalculated for mutation rate 0.03, same number ofpopulation, different crossover rate values. The bestresult is obtained where crossover rate is 0.5

As mentioned in section (2), semi-fragilewatermarking methods, are robust to some certainattacks and are fragile to others. Therefore the fitnessfunction must be defmed so that maximizes corrw forsome attacks and minimizes for others. We use thefollowing fitness function:

J;. = corrl (I w' I) (19)I 1 II * 1 12 *

t L corrw(w, Wi ) + t L (1- corrw(w, Wi ))

1 i=1 2 i=1

After calculating fitness function for each populationelement, considering ii, we sort them and crossoveroperator is executed. Mutation operator is executed togenerate simple changes and to reconstruct population.The procedure repeats for other populations.

. Calculated coefficients are shown in Table 1, using50 for population number, 0.5 for crossover rate, and0.03 for mutation rate. As shown, Table 1 consists ofdifferent coefficient values with average of 70.Obtained values of Q have high dispersion and this ishappened as a result of differences between imageblocks.

In table 2, results generated using GA are comparedto the case with constant value of Q. As we see, the

Irs oc so Image In as genera Ion<, 1 2 3 4 5 6 7 8

1 65 93 86 97 85 95 99 932 70 48 47 57 80 43 41 463 76 98 65 89 95 62 91 754 81 98 47 47 57 51 65 695 49 72 49 74 63 42 41 466 59 61 81 87 97 41 56 46

(16)

(15)

(17)

(18)

We first produce an initial random population, so thateach element of this population (chromosome) consistsof N variables, each with B bits; and each of thesevariables generates value of Q for one block, so weproduce a random matrix with dimensions: Npop * N *B . We use this matrix to calculate Q for each block andinsert W1xN watermark using calculated Q in theblock. After obtaining watermarked image, we applysome specific attacks on the image to surveywatermark robustness. Then extract watermark fromattacked image and compare with original watermark.Our criteria for the amount of perceptibility, is thePSNR1criterion, and to obtain signal to noise value it'senough to compare original image with watermarkedimage.

Fitness function should be selected in such a way thatincludes both perceptibility and robustness criterions.In order to gain a robust watermarking method, weshould consider minimum perceptibility and maximumrobustness. To provide these two conditions, we candefme fitness function in various forms. Some of themare as follows:

1

;;

9

Table 2. calculated result using GA (Robustwatermarking), compared with constant Q.

GA b.999530.66602 b.718750.63086 0.763673.2752Q=71.3 0.999550.59961 0.650390.58789 0.792972.9202Q= 50 p.9997<; 0.52344p.539060.47656 0.507812.0476Q= 60 0.9997 0.564450.5957 0.51758 0.660162.4059Q=80 0.999430.62695 0.679690.61328 0.849613.2489

::nn g~ 3" correlation between W, W' ~

~~ ?o' ro ~~ Camera~verage~uassian noise g.

mo~ ~

In table 3, simulation results of fragile watermarkingare shown. Fitness function (18) is used to simulatethis method. Similar to Table 2, results are compared tothe case with constant value of Q. As we see GAcalculate Q values so that watermark has shownminimum robustness.

5. Conclusion

As we saw in this paper, using GA, helped us toadjust watermark appliance parameters -in presence ofattacks- such that we obtained maximum efficiency;more clearly we obtained minimum image changewhile having maximum or minimum robustnessagainst attacks .

Another advantage of presented method is thatwatermark applied parameters are optimized withrespect to each specific attack and this gives thedesigner, the ability to generate semi-fragilewatermarking algorithms with desired robustnessagainst different attacks.

Further researches could be done in the field byapplying better criteria (better then PSNR) with moreproximity to human vision.

At last, simulation results of semi-fragilewatermarking are shown in Table 4. In this simulation,the goal is robustness against noise attack and cameramove. On the other hand, we want the watermarkingmethod to be fragile against Gaussian filter attack andmean filter attack. Fitness function: (19) is used tosimulate this method .

The only problem we are faced with, is the existenceof error in watermark retrieval for noise and cameramove attacks. Here, like before we should use codingto correct the error (CorrW=O.78 equivalent toerror=%ll). It should be noted that, applied codingmethod should be able to correct up to %16 of error;because if it corrects more than this value, the methodwill be robust against Gaussian and mean filter attacksso.

6. References

?~o....o'~

correlation between W, W'oo@3~~o' ro~ Cameraaverage~uassian noise

move

Table 3. calculated result using GA (Fragilewatermarking), compared with constant Q.

image obtained from GA method has mmimumperceptibility and maximum robustness compared tothe results when Q is selected empirically. Since corrwis unequal to I, we have some errors in watermarkretrieval. In order to remove the error, we use a codingmethod that corrects errors tcorrw =0.63 equivalent toerror=%18.5)

Table 4. calculated result using GA (semi-fragilewatermarking), compared with constant Q.

GA 0.999560.51758 0.59961b.52539 0.691411.7131Q=68.6 0.999570.603520.63867P.57031 0.781251.5415Q=60 0.999690.564450 .583980.51172 0.673831.7131Q=80 0.999420.619140 .683590.62891 0.859381.4323

[1]Greg Kipper, Investigator's Guide to Steganography ,Auerbach Publications, 2004.[2] Stefan Katzenbeisser and Fabien A. P. Petitco1as ,

Information Hiding Techniques for Steganography andDigital Watermarking , Artech House, Inc,2000.[3] H. zer, B.Sankur, and N.Memon, "An SVD-Based AudioWatermarking Technique," proceedings ofthe 7th workshopon Multimedia and security '05, ACM Press, August 2005.[4] Veyse1 Aslantas, " A singular-value decomposition­based image watermarking usinggenetic algorithm", Int. 1.Electron. Commun. (AE-) 62 (2008).[5] F. H. Huang, Z.H. Guan, "A Hybrid SVD-DCTWatermarking Method Based on PSNR", PatternRecognition Letter, 2004, pp.I769-1775.[6] R. Sun, H. Sun, and T. Yao, "A SVD-and quantizationbased semi-fragile watermarking for image authentication,"in Proc. Int. Coni Signal Processing (ICSP), vol. 2, pp. 26­30,2002.

correlation between W, W '

Camera averageguassian noisemove

0.999510.554690.681640.64063 0.7890612.770.999550 .62109 0.650390 .59961 0.79883~.543

0.9997lJO.50781 0.554690.48828 0.50781~.04350.999670 .58203 0.607420 .55078 0.67188~.2824

0.999430.621090.691410.63672 0.86133~ . 7924

GA71.9506080

10