One of the problems arising from the use of digital media is the ease of identical copies of digital images or audio files, allowing manipulation and unauthorized use. Copyright is an effective tool for preserving intellectual
property of those documents but authors and publishers need effective techniques that prevent from copyright modification, due to the straightforward access to multimedia applications and the wider use of digital publications through the www. These techniques are generally called watermarking and allow the introduction of side information (i.e. author
identification, copyrights, dates, etc.). This work concentrates on the problem embedding and optimum blind detection of data in color images through the use of spread spectrum techniques, both in space (Direct Sequence Spread Spectrum or DSSS) and frequency (Frequency Hopping). It is applied to RGB and opponent color component representations. Perceptive information is considered in both color systems. Some
tests are performed in order to ensure imperceptibility and to assess detection quality of the optimum color detectors.Peer ReviewedPostprint (published version

Madueño Ruíz, María Isabel

Sayrol Clols, Elisa

Vidal Manzano, José

English

One of the problems arising from the use of digital media is the ease of identical copies of digital images or audio files, allowing manipulation and unauthorized use. Copyright is an effective tool for preserving intellectual

property of those documents but authors and publishers need effective techniques that prevent from copyright modification, due to the straightforward access to multimedia applications and the wider use of digital publications through the www. These techniques are generally called watermarking and allow the introduction of side information (i.e. author

identification, copyrights, dates, etc.). This work concentrates on the problem embedding and optimum blind detection of data in color images through the use of spread spectrum techniques, both in space (Direct Sequence Spread Spectrum or DSSS) and frequency (Frequency Hopping). It is applied to RGB and opponent color component representations. Perceptive information is considered in both color systems. Some

tests are performed in order to ensure imperceptibility and to assess detection quality of the optimum color detectors.Peer Reviewe

UPCommons

Data hidding in color images using perceptual models

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Workshop on friendly exchanging through the net March 22-24, 2000DATA HIDDING IN COLOR IMAGES USING PERCEPTUAL MODELS1Josep Vidal, Elisa Sayrol, Maribel MadueñoDept. Teoría de la Señal y Comunicaciones, Universitat Politècnica de CatalunyaCampus Nord, Módulo D5, c/ Jordi Girona 1-308034 Barcelona, SPAINEmail: {elisa,pepe}@gps.tsc.upc.es                                                          1 This work was partially supported by the European Commission under ACTS, AC347 SUNBEAM, the Spanish National Plan of Research, throughthe projects CICYT, TIC98-0412 and TIC98-0703, the AECI and Generalitat de Catalunya, through the project CIRIT, 1998SGR-00081.ABSTRACTOne of the problems arising from the use of digitalmedia is the ease of identical copies of digital images oraudio files, allowing manipulation and unauthorized use.Copyright is an effective tool for preserving intellectualproperty of those documents but authors and publishersneed effective techniques that prevent from copyrightmodification, due to the straightforward access tomultimedia applications and the wider use of digitalpublications through the www. These techniques aregenerally called watermarking and allow theintroduction of side information (i.e. authoridentification, copyrights, dates, etc.). This workconcentrates on the problem embedding and optimumblind detection of data in color images through the useof spread spectrum techniques, both in space (DirectSequence Spread Spectrum or DSSS) and frequency(Frequency Hopping). It is applied to RGB andopponent color component representations. Perceptiveinformation is considered in both color systems. Sometests are performed in order to ensure imperceptibilityand to assess detection quality of the optimum colordetectors.Keywords: watermarking, CIE-lab models, directsequence spread spectrum.1. INTRODUCTIONThe watermark system described in [2] was successfullyapplied to gray scale images [1] and could be easilyextended to color images by embedding the watermarkin the luminance component or in each of the threecomponents. Some efforts have been done to derivewatermark systems specifically considering colorimages. Thus, in [3] the watermark is added in the bluechannel motivated by the fact that the human visualsystem is less sensitive to this component.In [4] a model of human color vision based on theCIELAB standard is used and the hidden information isembedded in the yellow-blue opponent component.Nevertheless, there is no need to limit the system towatermark only one component, the perceptual modelwill correctly weight the amplitude of the embeddedsignal in each component in order to preserveimperceptibility. The objectives may be the introductionof more information in the mark or the decrease in theprobability of error by the diversity of including themark in three components.In [1][8] optimum detectors were derived in the MLsense for the case of gray-scaled images. However theextension to color images is not straightforward whenthe watermark is added to each component. In this workwe derive optimum detectors for color images departingfrom an experimental model for the density function ofthe images that has been found to fit well in all studiedimages. Perceptual models are also used to ensure theinvisibility of the watermark, in particular the perceptualmodels described in [3] and [4] are considered.2. DIGITAL WATERMARKSThere are some techniques that successfully embedhidden information in an image. In particular, spreadspectrum techniques in space (DSSS) and in frequency(FH) adapt specifically to the different requirements of awatermarking system [5]. It is interesting to attack theproblem by considering the watermark as a signal buriedin noise, that is the image. The signal design may beobtained as a compromise between the followingfactors:a) The watermark has to be difficult to detect by a non-authorised user, therefore some kind of encriptionhas to be done, if possible both in space andfrequency. Spread spectrum techniques in space(DSSS) and in frequency (FH) adapt specifically tothe requirement.b) Visual quality of the marked image should beindistingeable from the original. The paper [2] is apioneering work on the use of psycovisual criteria inthe watermark embedding process, by modeling thebehavior of human visual system with Gabor filters[9]. The well known masking effect is used there: awatermark whose bandwidth is less than or equal tothe Gabor filter bandwidth will be invisible providedthat its energy be lower than the image energy in thatband. On the other hand the S-CIELAB system is anextension of CIELAB which is based onpsychophysical studies of color discriminability andtakes spatial structure also into account [3]. Thissystem will be used to measure and reduceperceptibility in watermarked color images.c) The amount of information this signal can convey:large amounts might increase the signal bandwidth,that implies either an increase in the probability oferror or a noticeable watermark.d) The probability of error in the detection of eachsymbol constituting the watermark should be as lowas possible, conveying high power for the mark and,at the same time, noticeable effect on the markedimage. DSSS techniques again allow the use of lowpower signals while maintaining probability of errorin reasonable levels thanks to the processing gain.e) The watermark should be robust enough to low-passfiltering, compression, or any other not noticeablemodification of the image. In particular the centralfrequency of the watermark should be placed atfrequencies that are generally preserved by a lowcompression JPEG procedure.Having those conditions in mind, a possible space-basedwatermarking scheme is illustrated in figure 1: it consistin a series of K=31 orthogonal symbols being each ofthem a pseudorandom minimum length sequence (MLS)(see figure 1).832 pixels832 x  31 pixelscSymbol #131·TcTSymbol #2     . . .MLSE sequencesFigure 1. Watermarking on the spatial domain usingDSSS sequences.Each series of symbols is modulating in amplitude abidimensional carrier whose frequencies are randomlychosen. The set of available frequencies has to be suchthat the carriers be orthogonal in the integration intervalof size 8x992 pixels. Horizontal normalized frequenciesof values kx/992 (k=0,1,…,991) fit the requirements.The value of kx cannot be too low to give noticieableresults nor too high to be eliminated in a JPEGcompression. In practice, the values chosen are [1] in theinterval 0,1 y 0,2 in which we can accomodate around100 different frequencies.This scheme might be reproduced for each colorcomponent, thus obtaining a system in which either threetimes the information can be added, or the same symbolsare encountered in each component so as to obtaincolor-diversity and hence reduction in probability oferror. The use of optimum detectors exclusivelydesigned for a model of image and for color images willalso reduce the errors with respect to the conventionaldetector based on the correlation.3. OPTIMUM WATERMARK DETECTIONIN COLOR IMAGESIt is required that the authorized user be able to recoverthe watermark with low probability of error. Gooddetection schemes allow the watermark embedding withlow power and hence, low visual impact. Beforederiving the detector, let us formulate a model for thewatermark: if we do represent the watermarked colorimage in vector notation, as  r = p+mo qi  whereúúúûùêêêëé=úúúûùêêêëé=úúúûùêêêëé=BiBGiGRiRiBGRµµµµqqqqpppprrrrBGRo (1)and o  stands for element-to element vector product.r : Watermarked image with three components. In thefollowing derivations, RGB components are usedalthough the same derivations apply when other colorcomponents are used, for example opponentcomponents.p : Original three components image.m : Amplitude that controls the total power for eachcomponent.qi : Weighted symbol, that is, for each component X wehave: qXi=fxo si  where fx corresponds to the perceptualmask and si stands for the original symbol to code,which is a pseudorandom minimum length sequence [1].3.1  Optimum linear detectorThe optimum detector has to take into account thedensity function of the noise, that is, the image p. Theconventional and computationally simple approach is toconsider the noise to be Gaussian and stationary. In thiscase, the log-likelihood function of r is given by:)()( iTi ?HrC?Hr --=Y-1RGB          (2)The detectors derived in the following make theapproximation that the fx amplitudes are constant, (notspace dependant) which is a rough approximation if aperceptual mask is used (see sections below). Thistranslates into 3-components for the vector q:[ ]CC?sssHÄL==úúúûùêêêëé=RGBi BGRTiiiAAA000000      (3)C represents the covariance matrix that takes intoaccount spatial correlation, and L is the correlationmatrix between the three-color components. The symbolÄ represents kronecker product between matrices. Notethat spatial correlation is assumed equal in the threecomponents.The decision function has to be minimized over thepossible symbols si, and q. It is easy to show that this iscompletely equivalent to maximize the decision functionover i:( ) rCHHCHHCr?HCr1RGBTii1RGBTii1-RGBii-1RGB---===Y1TTiˆ      (4)A first-order Markov model is assumed for C (thecovariance of the original image) and although a closedform of the inverse can be derived, it is more convenientto use a pre-whitening filter playing the role of C-1/2.Analogously L-1/2 represents the pre-whitening amongthe RGB components. Thus, the decision function issimplified to:i2/1swiB,G,R2/1B,G,wRswiTswi2swiTwB2swiTwG2swiTwRi)(sCsrC?rsssrsrsr--=Ä=++=Y     (5)rwX  is a whitened version of the X component of thewatermarked image in space and color dimensions andsswi is the symbol si that is whitened in the spatialdimension only.3.2 Cauchy detectorAlthough a Gaussian model yields to reasonablesolutions, the distribution of the whitened image tends toexhibit a slower decay in the tails of the distribution. Wecan model this behavior with alpha-stable distributions[6], which concentrate around the mean but are alsocharacterized by heavier tails. In particular we considera Cauchy distribution. Figures 2 to 4 show thedistribution of the whitened RGB components for acertain image. As it can be seen the Cauchy distributionis closer to the histogram than the Gaussian distribution.This result has been found to be general for all testedreal images.Considering the Cauchy distribution, we derive anoptimum receiver in the maximum likelihood sense todecide which symbol is present in a region of thewatermarked image, that is:[ ]å=+g=YNkisCi kzmini 122                    )(log        (6)where N is the number of pixels in the block in which asymbol is present, g is the distribution dispersion (whichcan be estimated according to the lines in [8] on thewhitened components) and zi(k) are the N componentsof the vector:( )úúúúûùêêêêëé-==-= -wBTwsiwsiwGTwsiwsiwRTwsiwsiwsiTwsi rssrssrssssr?HrCz1wDi1/2RGBi            (7)This detector greatly improves the probability of errorwith respect to the Gaussian.GaussianCauchyHistogramlog(pdf)Figure 2: Histogram of the whitened R component,Gaussian pdf and Cauchy pdf for a given imageGaussianCauchyHistogramlog(pdf)Figure 3: Histogram of the whitened G component,Gaussian pdf and Cauchy pdf for a given imageGaussianCauchyHistogramlog(pdf)Figure 4: Histogram of the whitened B component,Gaussian pdf and Cauchy pdf for a given image4. COLOR PERCEPTUAL MODELSFor a watermark to be really imperceptible it has to bespatially windowed in a way that accounts for theperceptual characteristics of the human visual system. Astraightforward approach is to the use the Gabor filtermodel used in [2] for each color component. A morerigurous approach is to use the advanced perceptualmodel for color images given by the S-CIELAB. Theinterest of this model is twofold: it takes into account thespatial information of the image, and it translates thethree color components to a basis in which a linearincrement is linearly perceived as a color change. Thewatermark generation scheme based on S-CIELAB [4]is shown in figure 5.RGB¯XYZLPF1LPF2LPF3WatermarkedimageCIELAB DEalfaDE ³ thresholdDE < thresholdLPF3LPF1LPF2LPF3LPF1LPF2XYZ¯OPPZXYZ¯RGBRGBXY OPP¯XYZWatermarkattenuationFigure 5: Watermark Embedding using S-CIELABThe watermark is applied to the opponent colorcomponents, which are yellow-blue (YB), red-green(RG) and luminance (L). Nevertheless numericaldifferences that correspond to perceptual differences aremeasured in the Lab space. Thus, for each pixel theperceptual difference between the original image and thewatermarked image is given by :222 baLE D+D+D=D    (8)Although usually DE should be lower than 3 to beunnoticeable, a more restrictive measure of DE<1 issometimes used. Those pixels that are above the selectedthreshold are attenuated until a high percentage ofpixels, usually 99%, are under the threshold. Figure 6shows how the perceptual measure is computed.DECIELABLPF1OriginalimageRGB¯XYZXYZ¯OPPXYZ¯OPPRGB¯XYZWaterm.imageLPF1LPF2LPF3LPF2LPF3Figure 6: Computation of the error measure in theS-CIElab model5. RESULTSIn order to assess the performance of the differentdetectors using different perceptual models, the errorrate has been computed by marking several color imageswith a set of symbols. The images were obtained fromthe Petitcolas’ benchmark database [10], where one canfind different synthetic and real images with diversespatial and luminance characteristics. First, Gabormodels are considered and two tests have been made:luminance-only watermarking and RGB componentswatermarking, using the same info in the threecomponents. This allows some kind of diversity that willsurely be used by the detector to decrease theprobability of error in the symbol detection. Additionaland significant gain is obtained from the use of theCauchy detector with respect to the conventionalGaussian (with whitening), as seen in table 1. 7500symbols were added to the set of images, so reliableestimations of the probability of error are above 10-3 .The three LAB components have been also markedusing the S-CIELAB model with a perceptual DE=1.Somewhat better visual results were obtained. Thewatermark exhibited structural differences as shown infigure 7. However, the probability of error showedminor differences with respect to the RGB and havebeen associated to the first column in table 1.Table 1: Error rate when watermarking the RGB/LABand luminance components, for the two detectorsRGB/LAB LuminanceGaussian 2,6e-3 1,4e-2Cauchy 1,7e-3 9,6e-3Robustness with respect to the JPEG compression hasbeen tested for the luminance and the three componentswatermarking. Results in table 2 also show that ingeneral, it is better to watermark the RGB componentsthan the luminance component, specially under JPEGcompression. On the other side, the Cauchy detectorgives better results compared to the optimum lineardetector. In all cases the original image and the markedimage were visually equivalent.Table 2: Error rate when watermarking the RGB/LABand luminance components for the two detectors whenimage is compressedJPEG RGB/LAB LuminanceCauchy Gaussian Cauchy GaussianQ=50 9,5e-2 5,8e-2 1,6e-1 1,9e-1Q=70 2,9e-2 5,5e-2 1,2e-1 1,5e-1Q=90 3,7e-2 7,8e-2 5,8e-2 6,6e-26. CONCLUSIONSA watermark embedding and detecting system for colorimages that relies on perceptual models has beenproposed. Consequently, comparison between theoriginal and the watermarked image showsimperceptible differences by the human eye. Anoptimum detector has been developed showing lowerprobability of error with respect to: 1) optimum lineardetector thanks to a better adaptation to the imagemodel, and 2) luminance watermarking, due to thediversity allowed by the use of three color components.These observations are reproduced, although lessevidently, when the image suffers high degradation viaJPEG compression. It has also been assesed that the S-CIELAB model gives slightly better visual results.Work is in progress to use redundant coding to reducethe probability of error and modulations in thefrequential domain so as to avoid synchronizationproblems when the image is cropped.7. REFERENCES[1] Josep Vidal, Elisa Sayrol, “Optimum Watermark Detectionand Embedding in Digital Images”, Proc. of IEEE Workshopon Multimedia Signal Processing, Los Angeles, CA,December 1998, pp. 285-290.[2] J.F. Delaigle, et al., “Low Cost Watermarking Based on aHuman Visual Model”, Proc. ECMAST 97, 1997.[3] M. Kutter, F. Jordan, F. Bossen, “Digital watermarkingof color images using amplitude modulation”, Journal ofElectronic Imaging 7(2), pp. 326-332, April 1998.[4] David J. Fleet, David J. Heeger, "Embedding InvisibleInformation in Color Images", Proc. of ICIP '97, SantaBarbara, October 1997, pp 532-535[5] I. J. Cox, et al., “Secure Spread Spectrum Watermarkingfor Multimedia”, IEEE Trans. on Image Processing, vol. 6, no12, Dec. 1997[6] M. Shao and C. L. Nikias, ”Signal Processing withfractional Lower Order Moments: Stable Processes and theirApplications”, Proc. of IEEE, V-81, No. 7, July 93.[7] G. A. Tsihrintzis and C. L. Nikias, “Performance ofOptimum and Suboptimum Receivers in the Presence ofImpulsive Noise Modeled as an Alpha-Stable Process”, IEEETrans. on Comm., V-43, No. 2/3/4, February 1995.[8] J.R. Hernández, F. Pérez-González, “Statistical Analysisof Watermarking Schemes for Copyright Protection ofImages”, Proc. of IEEE, vol. 87, no. 7, July 1999, pp. 1142-1166.[9] S. Mallat “Multifrequency Channel Decompositions ofImages and Wavelet Models”, IEEE Trans. on ASSP. Vol 37,No 12, pag 2091-2094.[10]http://www.cl.cam.ac.uk/~fapp2/watermarking/benchmark/image_database.htmlFigure 7. Original image (top) and the watermarksobtained using the Gabor perceptual ponderation(middle) and the S-CIElab (bottom). Most of thewatermark information is placed on the image contours.

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Data hidding in color images using perceptual models

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