Robust image watermarking based on generalized radon ... · origin for two newly introduced one-dimensional generalized Radon transformations [22]–[24] that are applied to the image.

732 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 13, NO. 8, AUGUST 2003

Robust Image Watermarking Based on GeneralizedRadon Transformations

Dimitrios Simitopoulos, Dimitrios E. Koutsonanos, and Michael Gerassimos Strintzis, Senior Member, IEEE

Abstract—This paper presents a novel watermarking schemeable to resist geometric attacks. The proposed method performsimperceptible watermarking of images in the spatial domain. Togenerate resistance to scaling and rotation attacks, two generalizedRadon transformations of the image are introduced, while resis-tance to translation is accomplished through a localization of thewatermarking method based on feature points of the image. Theoriginal image is not required for the detection process. Experi-mental evaluation demonstrates that the proposed scheme is ableto withstand a variety of attacks including common geometric at-tacks.

Index Terms—Copyright protection, generalized Radon trans-formations, geometric attacks, image watermarking.

I. INTRODUCTION

WATERMARKING of images is a technology that has at-tracted a great deal of attention in recent years. One of

its possible applications is copyright protection. In order for wa-termarking to be used as a means of copyright protection, its ro-bustness to malicious and also to unintentional attacks shouldbe ensured. This can be verified by recording the effects ofa number of common attacks [1]–[3] to watermarked images.Among them, geometric attacks such as scaling, rotation, andtranslation are easy to apply and may lead many watermark de-tectors to total failure due to loss of synchronization betweenthe embedded and the correlating watermark.

Several watermarking methods resistant to geometric attackshave been presented in recent literature. These may be divided inthree main categories. The first category includes watermarkingschemes that perform the watermark detection in a domain thatis invariant to geometric attacks. The authors in [4] derive adomain that is invariant to rotation, scaling and translation at-tacks using the Fourier-Mellin transform, but they fail to com-plete the detection process without using the original image. Themethod described in [5] is also based in the properties of theFourier–Mellin transform and uses a translation and scaling in-variant domain, while resistance to rotations is provided by anexhaustive search.

Another type of watermarking methods that offer resilienceto geometric attacks includes methods that detect and revert thegeometric attack of the watermarked image in order to perform

Manuscript received September 6, 2002; revised March 7, 2003. This workwas supported by the European Union IST Project “ASPIS”.

The authors are with the Informatics and Telematics Institute, 57001 Thermi-Thessaloniki, Greece, and also with the Electrical and Computer EngineeringDepartment of Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece(e-mail: [email protected]; [email protected]; [email protected]).

Digital Object Identifier 10.1109/TCSVT.2003.815947

the detection. This can be achieved by embedding an additionaltemplate and reverting the geometric attack applied to the imagebased on the template’s distortion [6], [7]. However, these tem-plates may be easy to remove [8] since they usually representpeaks in a transform domain. Other approaches of this categoryare based on the autocorrelation function (ACF) of a speciallydesigned watermark as proposed in [9], [10].

Yet another approach for resisting geometric attacks is basedon synchronizing (in terms of position, orientation and scaling)the watermark that is embedded in an image with the correlatingwatermark using image features. This is achieved by geomet-rically transforming a reference watermark based on featuresof the original image content during the embedding process,while in the detection process, features of the watermarked andpossibly distorted image content are used in order to geometri-cally transform the reference watermark or even the image it-self. Such an approach was presented in [11] where principalcomponent analysis was used in order to define the geometrictransformation parameters. Corner points [12], [13] and facialfeature points [14] have also been used for this purpose in otherapproaches of this category.

It should be noted that all methods mentioned above offer (orcould offer in the case of [4]) blind detection of the watermarkwithout the use of the original image. However, nonblind wa-termark detection methods have also been proposed for resis-tance to geometric attacks [15]–[17]. Furthermore, other water-marking approaches have been proposed for resistance to geo-metric attacks, that are not directly linked to any one of the threemain categories described above, e.g. in [18]–[20].

In this paper, a novel image watermarking scheme that canresist geometric attacks is presented. It belongs to the third ofthe categories that were described above. Imperceptible wa-termark embedding and detection are performed in the spatialdomain representation of the image luminance. The embeddingand the correlating watermark are created by geometricallytransforming a reference two-dimensional watermark. For thederivation of the geometric transformation parameters, bothin the embedding and the detection processes, first a cornerdetection method is applied. Using a novel adaptation of thecorner detector proposed in [21] corners in the image contentare detected and the most robust among them, to geometric andother attacks, is determined. Then, this corner is used as anorigin for two newly introduced one-dimensional generalizedRadon transformations [22]–[24] that are applied to the image.According to characteristic values extracted from the two gen-eralized Radon transformations the corresponding geometrictransformation parameters are calculated. In this way, thegeometrically transformed watermark that is embedded in an

1051-8215/03$17.00 © 2003 IEEE

SIMITOPOULOSet al.: ROBUST IMAGE WATERMARKING BASED ON GENERALIZED RADON TRANSFORMATIONS 733

Fig. 1. RIT.

image and may be further transformed by a geometric attackis synchronized with the correlating watermark used for thedetection process. Experimental evaluation of the proposedscheme demonstrates its resistance to geometric as well asother common attacks.

The paper is organized as follows. In Section II, the proposedone-dimensional generalized Radon transformations and theirproperties are analyzed. Section III describes the concept usedin the proposed watermarking scheme for resisting geometric at-tacks. The proposed corner detector is described in Section IV.The watermark embedding scheme is presented in Section V. InSection VI, the detection process is described. In Section VII,the results of the experimental evaluation are presented, and fi-nally, conclusions are drawn in Section VIII.

II. ONE-DIMENSIONAL GENERALIZED RADON

TRANSFORMATIONS

We propose the use of two one-dimensional GeneralizedRadon transformations to provide resistance to scaling androtation attacks, respectively. The radial integration transform(RIT) will be used for resistance to rotation, while the circularintegration transform (CIT) will be used for resistance toscaling.

A. The RIT and CIT and Their Scaling and Rotation Properties

The RIT of a function is defined as the integral ofalong a straight line that begins from the origin

and has angle with respect to the horizontal axis (see Fig. 1).The RIT is given by the following equation:

(1)

where is the distance from the origin .If is an image and is the

image scaled by in both directions, then the RIT ofimage is easily found to be [23]

(2)

Fig. 2. CIT.

In other words, the RIT amplitude of the scaled image is onlymultiplied by the factor .

If is an image written in polar form andis the image rotated by around the coor-

dinate system’s origin , then the RIT of image is easilydetermined to be [23]

(3)

i.e., the RIT of the rotated image is translated by.The CIT of a function is defined as the integral of

along a circle curve with center and radius(see Fig. 2). The CIT is given by the following equation:

(4)

where is the elementary arc length over the integration pathand is the corresponding elementary angle. The circle center

will be referred to as the origin of the CIT.If is an image and is the

image scaled by in both directions, then the CIT ofimage is easily found to be [23]

(5)

Clearly, the CIT of the scaled image is scaled with the samescaling factor and its amplitude is also multiplied by the factor.If is an image expressed in polar coordinates and

is the image rotated by aroundthe coordinate system’s origin , then the CIT of image

is easily determined to be [23]

(6)

Clearly, the CIT of an image is independent of rotation.


(a)

(b)

Fig. 3. (a) RIT of the original Lena image. (b) RIT of the attacked image.

B. Discrete RIT and CIT

A discrete form of the RIT (1) is given by

(7)

where and are the constant step sizes of the corre-sponding variables, is the number of points that lie on the linewith orientation and are located between the origin and theend of the image in that direction, and .The RIT ( , ) of the original and an attackedLena image ( , , )are shown in Fig. 3(a) and (b), where the scaling and rotationproperties of the proposed transform can be clearly identified.For example, the difference between the values of the parame-ters and which maximize the RIT coefficients of theattacked and the original Lena image, respectively, is 29.93,which means that the divergence from the expected differenceis only 0.07 .

(a)

(b)

Fig. 4. (a) CIT of the original Lena image. (b) CIT of the attacked image.

Similarly, a discrete form of the CIT (4) is given by

(8)

where and are the constant step sizes of the corre-sponding variables, is the radius of the smallest circlethat encircles the image , and . TheCIT ( , ) of the original and an attackedLena image ( , , )are shown in Fig. 4(a) and (b), where the scaling and rotationproperties of the proposed transform can be clearly identified.For example the quotient between the values of the parameters

and which maximize the CIT coefficients of theattacked and the original Lena image, respectively, is 0.705,which means that the divergence from the expected quotient isonly 0.005.

It should be noted that the image samples that appear in(7) and (8) may not coincide with pixels of the original image.This means that interpolation in both dimensions must be used.In our implementation of RIT and CIT bilinear interpolation wasused.


The computational complexity of RIT and CIT are given by

where is the order function.

III. RESISTINGGEOMETRICATTACKS USING RIT AND CIT

The RIT and CIT properties given in (2), (3), (5), and (6) arevery desirable in watermarking applications in which resistanceto geometric attacks on the watermarked image is required. Awatermark embedding and detection scheme that utilizes theseproperties is described in the sequel.

In the embedding process, first a two-dimensional arbitraryreference watermark is generated. Then, a specific pointof the image is selected based on properties of the image con-tent. This point serves as the origin for RIT and CIT and alsofor positioning onto the image the geometrically transformedreference watermark, which will be created. Let the orientationof the reference watermark correspond to a reference angleand one of its dimensions (its width, for example) correspond toa reference size . Then, the RIT and CIT are calculated andthe values of the parameters and which maximizethe RIT and CIT coefficients, respectively, define the geometrictransformation that the reference watermark should undergo be-fore additive embedding in the original image. Specifically, thereference watermark is first scaled by the scaling factor

(9)

rotated by the angle

(10)

and positioned using the selected point , and then em-bedded in the image.

Let us assume a scaling and a rotation attack to the water-marked image by and , respectively. Based on the RIT andCIT properties, it is obvious that after the attack, the location ofthe new maximum will be for CIT and forRIT. Subsequently, in the detection process, if the reference wa-termark is scaled by the scaling factor androtated by the angle , the embedding andthe correlating watermark will be synchronized, i.e., acquire thesame scale, orientation, and position which will in turn permita successful detection.

This concept for resisting geometric attacks can only be ap-plied if a specific location of the image content, that will beused as the origin, can be accurately traced both before embed-ding and before detection (possibly after a geometric attack thatcould change its position). The resulting method is highly de-pendent on the location of this origin. For this reason, a methodis defined for the determination of the origin (corner point) so asto be very robust to geometric attacks, as detailed in Section IV.

Furthermore, the value of is selected based on a secret keyof the owner, so as to achieve robustness to collusion attacks.Specifically, is drawn from a uniform distribution in [0,360 ] using a seed derived from the hash value of the owner’ssecret key concatenated, i.e. serially connected, with a unique

image identifier (e.g. its catalog order). The value ofis fixed.In this way, robustness to collusion attacks (as defined in [25])is achieved.

IV. CORNERDETECTION

Before embedding or detecting the watermark in the image,the location of the origin used for positioning the watermark andalso for applying RIT and CIT must be found. For this reason,the corner points in an image are first found using a modifiedHarris corner detector [21], and then the most appropriate isselected as the origin.

A Harris corner detector first calculates the horizontal and thevertical gradients of an image, and , respectively. Then,these two gradient images are low-pass filtered and the images

and are obtained. For each pixel of the originalimage, the matrix is formed

where range over all pixel positions that belong in asquare area centered at the pixel . Using , the Harriscorner detector output [21] for each image pixel is calculated

(11)

The Harris corner detector is a very good tool for extractingthe corner points of an image. However, in our application weneed to ensure that, in addition, the same set of corners is alsoextracted when the corner detector is applied to an attackedimage. Specifically, the corner of the original image with thehighest detector output should at least correspond to one of thecorners of the attacked image that has one of the highest detectoroutputs.

In order to meet the above requirements, the following mod-ifications were carried out so as to enhance the performance ofthe Harris corner detector. First, the terms that are summed inorder to calculate each element of the matrixbelong to cir-cular areas of radius instead of square areas as in [21]. In thisway, the detector output is less prone to significant alteration ifsubjected to a rotation attack.

Furthermore, in order to extract the set of corners, localmaxima in circular areas of the corner detector output imageare detected. Specifically, a pixel is considered a cornerif its corner detector output value is higher than the value of allthe pixels ( , ) that belong to a circular area of radius

centered at the pixel

This modified Harris corner detector is inherently more robustto geometric attacks (especially rotation). Furthermore, due tothe low-pass filtering (Gaussian 5 5) of the image gradients,robustness of the detector to compression and interpolation (be-cause of scaling or rotation) are also achieved. However, in orderto determine which of the found corners will be more robust to apossible attack, a small number of attacks is first applied to theoriginal image before the embedding process. The scheme that


Fig. 5. Extraction of the most robust corner of an image.

is used for generating scaling and rotation attacks to the orig-inal image in order to extract the most appropriate corner as theorigin, is depicted in Fig. 5, and is described in the following.

Consider the original image, its scaled versions ,and its rotated versions , , where and

are, respectively, the total number of the scaling and rotationattacks to be applied to the original image. For everyandimage created, the modified Harris corner detector is appliedand the sets of corners and , respectively, are found. Weshall now define the and operators which are used inorder to register the corners extracted from the attacked imagesto the original image. The argument of theand operatorsis the set of corners and , respectively. Then, the set ofthe most robust corners of the original image is given by

where is the set of corners that are detected by applyingthe modified Harris corner detector to the original image. Usingthe calculated modified Harris detector outputs, the corners thatbelong to each one of the sets , and

are ranked according to the magnitudeof the output. For every corner belonging to , its corre-sponding ranks in the sorted list from all attacked images areaveraged. Normally, the corner with the smallest averaged rankis chosen as the origin used for positioning the watermark andalso for applying the RIT and CIT to the original image. How-ever, if the first corner in the sorted list lies in the outer 20%

part of the image, the next corner in the sorted list is used asthe origin. In this way, possible minor cropping attacks of theouter image part (i.e., meaningful cropping attacks that may notrender the image unusable) will not influence the detection.

In our implementation, four scaling and three rotation attacksare applied to the image. The scaling factors used are 0.5, 0.75,1.25 and 1.5, and the rotation angles are 22.5, 45 , and 67.5.In Fig. 6(a), the corners that belong to the setfor the imageLena are depicted (for , ). In Fig. 6(b), thecorners belonging to the set and the corner selected as theorigin (white cross) are given.

Furthermore, in order to test the robustness of the proposedcorner extraction scheme for the determination of the origin,the following experiment was conducted. The proposed mod-ified Harris corner detector was used to extract a corner fromeach of some standard images, including the 512512 Lena,Fishing Boat, Peppers, and F16 images. Then, the images werewatermarked and all combinations of rotation (0to 90 witha step of 10), scaling (scale factors ranging from 0.5 to 1.5,with a step of 0.05), jpeg compression and low-passfiltering were implemented. For each attacked image the Harriscorner detector was used to find a set of corners and their rank inthe sorted list. Then, it was determined whether any of the foundcorners corresponds to the corner found before the attack. In allexperiments, the sought corner was found and its rank in the listwas always lower than 7, as can be seen in Fig. 7.

V. WATERMARK EMBEDDING

A. Watermark-Embedding Process

The proposed watermarking scheme, based on the conceptdescribed in Section III, performs the watermark embedding inthe following steps (see Fig. 8).

• A random two-dimensional sequence of the values1 and1 is created based on a cryptographically secure proce-

dure. Each value of the sequence is spread in blocks sized. This block-based watermark will be used as the

reference watermark.• The proposed corner detector is applied to the image. The

detector extracts a set of corner points from which themost robust to geometric and other attacks is determinedas described in Section IV.

• Using the location of the most robust corner as theorigin, the RIT and CIT are applied to the image. Then,

and are found and by using (9) and (10) thescaling parameter and the rotation parameter , re-spectively, are calculated.

• The reference watermark is geometrically transformedusing the , and parameters for the rotation,the scaling and the translation, respectively.

• The amplitude of the watermark for each image pixelis determined as described in [26] in order to

perform imperceptible watermark embedding. Then, thewatermark is additively embedded in the spatial-domainrepresentation of the image luminance.

The embedding process is analyzed in the subsections thatfollow.


(a) (b)

Fig. 6. (a) The set of corners that are detected by applying the modified Harris corner detector to the original image Lena (marked with small white squares).(b) The most robust corners of the original Lena image and the corner selected as origin (marked with a white cross), extracted using the corner detection schemedepicted in Fig. 5.

Fig. 7. Histogram of the ranks of the found corners.

B. Generation of the Initial Watermark

We shall assume the use of the following procedure for thegeneration of the embedding watermark: the values of the em-bedding watermark sequence are either 1 or 1. This se-quence is produced from an integer random number generatorby setting the watermark coefficient to 1 when the generator out-puts a positive number and to1 when the generator output isnegative. The result is a zero mean, unit variance process. Therandom number generator is seeded with the result of a hashfunction. The MD5 algorithm [27] is used in order to producea 128-bit integer seed from a meaningful message (owner ID).The watermark generation procedure is depicted in Fig. 9. Asexplained in [28], the watermark is generated so that even if anattacker finds a watermark sequence that leads to a high corre-lator output, the attacker still cannot find a meaningful owner IDthat would produce the watermark sequence through this proce-dure and therefore cannot claim to be the owner of the image.This is ensured by the use of the hashing function included inthe watermark generation.

The set of values that comprise the one-dimen-sional watermark sequence are positioned on a square

image in raster scan order. The origin of the watermark is thepoint that corresponds to the center of the square. The water-mark generation process is completed by spreading the water-mark values in blocks sized . The resulting watermark

has size , where , and

where and are the indices of the watermark image andin-dicates downward truncation. This watermark is block based;that is, the watermark is divided into blocks of size ,having the same value for all elements of the block. This is illus-trated in Fig. 10 for , i.e., for 2 2 blocks. This resultingwatermark is the reference watermark described in Section III.

The existence of a block-based watermark will compensatefor possible de-synchronization between the embedded and thecorrelating watermark due to small errors in estimating the geo-metric transformation parameters for the correlating watermarkduring the detection process.

C. Watermark Transformation

First, the RIT and CIT of the image are calculated usingthe extracted most robust corner as the origin with coordinates

. Then, the values of the parameters andwhich maximize the RIT and CIT coefficients, respectively, arefound. These are used in order to calculate the scaling param-eter and the rotation parameter using (9) and (10), respec-tively. In this way, the parameters for the geometric transforma-tion of the watermark are found and the affine transforma-tion matrix is formed

(12)

This affine transformation matrix is used for the rotation, scalingand translation (for positioning the watermark’s origin on thedetected corner point) of the watermark. Using, the geomet-rically transformed watermark is created. In our imple-


Fig. 8. Embedding process based on RIT and CIT.

Fig. 9. Watermark generation.

mentation, linear interpolation was used, hence is valuedin [ 1, 1]. Therefore, in order to preserve the watermark en-ergy after the interpolation, we choose the embedding water-mark by

(13)

D. Imperceptible Watermark Embedding

Every pixel of the image is watermarked by addingthe corresponding value of the embedding watermarkmul-

Fig. 10. Portion of a 2� 2 block-based watermark. The black and gray pointsrepresent watermark pixels which have the value+1 and�1, respectively.

tiplied by the strength factor . The watermarked pixelis given by

(14)

The strength factor for every pixel should be calculated in sucha way that the watermark embedding leads to imperceptible vi-sual degradation of the image. This is achieved by taking into


(a) (b) (c)

Fig. 11. (a) Original Lena image. (b) Watermarked Lena image(PSNR = 41:9 dB). (c) Amplified difference between the original and the watermarked Lenaimage.

account the local variance of the image luminance, which servesas a measure of the watermark magnitude that could be imper-ceptibly embedded in each image pixel. For this reason, first thevariance in a square area of pixels for eachimage pixel is calculated. Then the maximum variance is foundand used for the normalization of the variances in the range [0,1]. Specifically, is given by

(15)

where is the strength of the watermark that will be em-bedded in the case of a pixel whose neighborhood has zero vari-ance (smooth area) and is the maximum strength that thefirst term of the right hand side of (15) will contribute to the finalwatermark strength factor . After experimenting with sev-eral combinations of values for and , we selected thevalues and . In fact, in a set of 500 pho-tographic images, taken from [29], where the watermark wasembedded, these values produced no noticeable degradation ofthe image quality and the minimum and average PSNR observedwere 39.97 and 41.76 dB, respectively. Fig. 11 presents the orig-inal 512 512 Lena image, the corresponding watermarkedimage and their difference.

Alternatively, other methods for additive watermark embed-ding in the spatial domain that use sophisticated perceptualmodels, like the ones presented in [30] and [31], may be used, atthe expense, however, of additional computational complexity.

VI. DETECTION

A. Description of the Detection Process

For the detection of the watermark, a correlation-based detec-tionscheme is applied [32]–[34]. The detection process can bedivided in the following steps (see Fig. 12).

1) The watermark is created using the owner’s ID and isthen transformed to a block-based watermark, as inthe embedding process.

2) The modified Harris corner detector is applied to theimage.

3) The RIT and CIT of the image are calculated using thelocation of the corner detector output maximum as theorigin. Then, the values of the parameters andthat maximize the RIT and CIT coefficients, respectively,are found.

4) Using , , and the values of , that were usedin the embedding, the scaling parameterand the rotation parameter that willbe used to geometrically transform the correlating water-mark are calculated.

5) The correlating watermark is created by first geomet-rically transforming the watermark using (12), andthen by applying the sign function to the values of the ge-ometrically transformed watermark as in the embeddingprocess.

6) The local mean of the luminance of eachpixel of the test image is calculated

(16)

where and are integers such that each pixelbelongs to an area and is the number

of pixels included in . This area contains all testimage pixels belonging to a windowcentered at , for which does notbelong to the same watermark block as . This isdone in order to exclude from the local mean thepixel values that correlate with ,which would decrease the detector performance for thereasons described in [35].

7) The correlation value between the watermarked andthe, possibly distorted, image pixel values ,reduced by the local mean , and the watermarkvalues is calculated

(17)

8) The correlation value is compared to an image adap-tive threshold, which is defined as is described in the fol-lowing.


Fig. 12. Detection process based on RIT and CIT.

B. Calculation of the Image Adaptive Threshold

The detection can be formulated as the following statisticalhypothesis test:

: the test image is not watermarked.: the test image is watermarked.

In order to determine which of the above hypotheses is true,the correlation-based detection expressed in (17) is applied andthen the correlation value is compared to a threshold. In order todefine the threshold, we first performed a statistical analysis ofthe correlator output similar to the one performed in [36]. Inthe following, the results of this analysis are presented. Specifi-cally, the mean values and the variances of the correlatoroutput corresponding to each hypothesis, are givenby the following equations:

(18)

(19)

and (20)–(21), as shown at the bottom of the page, whererange over all pixel positions within the test image,, are inte-gers such that the pixel belongs to the block of thecorrelating watermark containing pixel , , , and ,are integers such that the pixels and

belong to the areas and , respec-tively, and is the number of pixels included in .

The correlation value, in (17) has mean and variance givenby (18) and (20) under hypothesis , and (19) and (21) underhypothesis . In addition, since the last twoterms on the right-hand side of the sum (21) were experimen-tally found to have very small values compared to other terms.

The watermark detection system error probabilityis givenby , where is the false positiveprobability (detection of the watermark under ), is thefalse negative probability (failure to detect the watermark under

) and equala priori probabilities for both hypotheses are as-sumed. As argued in [28], if the number is large enough, thesum (17) will contain enough independent terms for the cen-tral limit theorem [37] to be applicable. Thus,will be approx-

(20)

(21)


imately normally distributed and the analytical expressions ofand will be given by

(22)

(23)

where is the threshold against which the correlator output iscompared and is defined as

(24)

Since , it can be easily proven that the threshold selec-tion which minimizes the detection error probability(maximuma posterioricriterion) is given by

(25)

However, as noted in [32] for the case of watermarking DCTcoefficients, this is not an accurate expression for the bestthreshold, mainly because in case of attacks the mean value

is not accurately estimated using (19). In fact, experimentalresults have shown that in case of attacks the experimental meanof the correlation value under is smaller than the theoreticalmean calculated using (19). For this reason, the threshold

is selected which leads to the minimum probabilityof false negative errors while keeping false positive errors at anacceptable rate (Neyman-Pearson criterion). By solving (22)for T, we obtain

(26)

Equation (26) can be used for the calculation of the threshold fora fixed , since and can be reliably calculated using(18) and (20), respectively.

If the point with the maximum corner detector output duringdetection is not the same with the one used as origin in the em-bedding, the detection will fail. In such cases, the correct corneris usually one of the subsequent corners in the list where thedetected corners are ranked according to the magnitude of thedetector output. For this reason, the detection process in Sec-tion VI-A is repeated, starting from the third step and using thelocation of a small number of the subsequent corners of thelist as the origin for the RIT and CIT.

Furthermore, during embedding, the global RIT (or CIT)maximum may be very close to one or more local RIT (or CIT,respectively) maximum. Following an attack the latter may be-come a global maximum which will lead to a detection failure.Thus, when during detection a global and a local maximum ofRIT or CIT are found to be very close, the detection process isrepeated starting from the fourth step and using also the localmaximum position as or , respectively. As a result,the number of corners tested will slightly increase.

The detection procedure will be performed times and themaximum of correlation values will be the final detector

output. Since the event is equivalent to the eventthat at least one of the correlation values is larger than, thetotal false positive probability of the detection systemis found, using the binomial distribution, by:

(27)

If (27) is solved for , the final threshold is obtainedby:

(28)

Given a fixed total false positive probability, (28) is used fordetermining the image adaptive threshold for the wa-termark detection, based on the Neyman-Pearson criterion.

VII. EXPERIMENTAL EVALUATION

A. Setting of Parameters

The experiments presented in the following were all per-formed using the following values for the parameters of thewatermarking system: , for the modifiedHarris corner detector, , for the discreteRIT, , for the discrete CIT,for the calculation, , for the block-basedreference watermark, , , forthe determination of the embedding strength, and ,

and for the detection process. Linearinterpolation was used for the geometric transformations of thewatermark.

B. Implications of the Watermark Interpolation

As described in Section V-C linear interpolation is used forthe geometrical transformation of the watermark. In the absenceof an attack the correlating watermark will be identical tothe embedded. In case of geometric attacks however, the em-bedded watermark is corrupted and hence not identical to thecorrelating watermark . In order to evaluate the mismatchof embedded and correlating watermarks the following experi-ment was conducted: the embedding procedure was applied forvarious test images and the values of were de-termined; then all combinations of rotation (ranging from 0to 90 with a step of 5) and scaling attacks (scale factorsranging from 0.5 to 2.0 with a step of 0.05) were implemented,using linear interpolation for each geometric attack. The cor-responding correlating watermark was also created usinglinear interpolation. The sign of the values ofof the attacked embedded watermark was compared to the signof the values of the correlating watermark. Fig. 13presents the percentage of the corresponding values of the twowatermarks that had the same sign for image Lena. Similar re-sults were also obtained for other test images. As can be seen inFig. 13, in all cases of attacks this percentage is very high, al-ways above 93%, demonstrating robustness of the detection pro-cedure to geometric attacks. This is partly due to the block-basedstructure of the embedded watermark. Robustness is further ver-ified by the results of the next subsection.


Fig. 13. Percentage of thea(i; j)W (i; j) values of the attacked embeddedwatermark of image Lena that correlate with theW (i; j) values of thecorrelating watermark. The rotation angles and the scaling factors used forattacking the embedded watermark were in the range [0, 90 ] and [0.5,2],respectively.

Fig. 14. Total false positive probability for the image Lena.

C. Detection Performance

In our experiments, first the calculation of the mean and thevariance of the correlation valueunder using (18) and (20),and also the validation of these results by estimating the aboveparameters through detection experiments with a large numberof different watermarks were performed. For this reason, firstthe theoretical mean and variance for the case of hypothesiswere calculated for the image Lena using (18) and (20). Thenthe detection procedure described in Section VI-A was appliedto the original unwatermarked Lena image for 10 000 differentwatermarks and the empirical mean and variance values werefound. The theoretical and experimental values of the means andvariances were identical and equal to and .On replacing these values in (27) the total false positive prob-ability versus the threshold for the image Lena wasobtained. The corresponding plot is shown in Fig. 14 where thetotal false positive probability for different values of is given.The bold solid line corresponds to which was the valueused in the rest of the experiments, since this number of corners

proved sufficient for reliable detection and at the same time itdid not severely influence the total false positive probability.

In order to evaluate the detector performance under, de-tection experiments based on 500 different watermarks for thewatermarked and attacked Lena image were performed. The at-tacks applied to the watermarked Lena images included rotation,scaling, JPEG compression, JPEG2000 compression, Gaussiannoise addition and Gaussian low-pass filtering. Fig. 15 illus-trates the distribution of the correlation value for each attackand also for the case where no attack was present. In all casesof attacks the correlation value was above the image adaptivethreshold for the selected total false positive proba-bility . In addition, the correlation value for thewatermarked image Lena using 500 different correlating water-marks is given in Fig. 16.

For the last class of experiments, the Stirmark 3.1.79 water-mark removal software [1], [38] was used. TheLena, Peppers,Bear, andF16 images were first watermarked and then usedin the tests. The PSNR of all images was higher than 41.6 dB.The following classes of attacks were implemented: signal en-hancement, JPEG compression, scaling, rotation, row/columnremoval, random geometrical distortions, general linear geo-metric transformations, and shearing. The effects of each attackwere also evaluated following JPEG compression at a qualityfactor of 90. To each image a score of 1 is assigned if the wa-termark is detected and 0 if not detected. In Table I the av-erage score for each class of attacks is given. In particular, in allsignal enhancement attacks apart from sharpening, the water-mark was successfully detected. Signal enhancement includedgaussian lowpass filtering, sharpening, frequency mode Lapla-cian removal attack, and also median filtering with kernels 2

2, 3 3 and 4 4. The compression attacks included JPEGcompression with quality levels of 10, 15, 20, 25, 30, 40, 50, 60,70, 80, and 90. In most cases, the watermark was detected evenfor the lowest quality factors resulting in a 0.83 score. The wa-termark was detected in all downscaling and upscaling attacksperformed by Stirmark. In case of rotation attacks the schemealso performed very well. Finally, the scheme’s performancewas satisfactory under row/column removal attacks (the 11,1 5, 5 1, 5 17 and 17 5 cases were tested).

The last three rows of Table I include attacks that performlocal geometric attacks (Random Geometric Distortions),nonuniform scaling (General Linear Geometric Transforma-tions) and shearing. Although the proposed watermarkingscheme is not designed for resistance to such attacks, thewatermark was detected in most cases. More specifically, thewatermark was detected after all General Linear GeometricTransformations and all shearing attacks in which the shift ineach direction is up to 1% of the image’s corresponding dimen-sion. The watermark was also detected after applying randomgeometric distortions to three out of the four watermarked testimages. The correct detection in all these cases is due to theblock-based structure of the watermark which compensatesfor the errors in the estimation of the scaling, rotation, andpositioning parameters of the correlating watermark.

It should finally be noted that the proposed watermarkingscheme is inherently robust to translation attacks, due to thepositioning of the watermark according to the image content


(a) (b)

(c) (d)

(e) (f)

(g)

Fig. 15. Distribution of the correlation valuec for each attack applied on the 500 watermarked Lena images: (a) no attack, (b) rotation by 10, (c) downscalingwith scaling factor 0.7, (d) JPEG2000 compression to 0.8 bits/pixel (the original image has 8 bits/pixel), (e) JPEG compression withQuality = 70, (f) additionof Gaussian noise with� = 5, and (g) Gaussian filtering (5� 5).

before embedding or detection. Furthermore, collusion attacksusing images of the same owner are not possible because they

are watermarked with different geometric transformations of thesame watermark.


Fig. 16. Correlator values for the watermarked image Lena using 500 differentcorrelating watermarks. The 100th watermark was embedded in the image. Thethreshold corresponds toP = 10 .

TABLE ISTIRMARK RESULTS

D. Bitstream Embedding and Extraction

Watermarking is a technology that can be used for variousdata hiding applications. Apart from its use for proving thecopyright ownership described in the previous sections, addi-tional information (small bitstreams) can be embedded in animage using a variation of the proposed watermarking tech-nique (data hiding). For example, such additional informationcould be the identification number of a buyer. By using thisinformation “malicious buyer tracking” can be achieved, i.e.,when copyrighted material is found to be used by unauthorizedusers, the initial buyer, who allowed the unauthorized use ofthe copyrighted material to a third party, can be traced.

One way to embed such bitstreams into images is to modulatethe reference watermark with thebits of the bitstream beforeembedding it to the host image. Specifically, after transformingall 0-bit values to 1, every bit of the bitstream is used to mul-tiply the reference watermark values in selected positionsand then the modulated watermark is geometrically transformedand embedded in the image as described in Section V.

In order to extract the bit values from a watermarkedimage, first the first six steps of the detection procedure de-scribed in Section VI are applied. Then, for each bit, the sum

is calculated

(29)

where and are integers such that each corresponds toa location where the bit is expected to be embedded. Finally,

is assigned the value 0 if is negative and the value 1 ifis positive.

Using the above described procedure for bitstream embed-ding, 64 bits were embedded in the image Lena. The attacks ap-plied to the watermarked Lena image included rotation by 10,downscaling with scaling factor 0.7, JPEG2000 compression to0.8 bits/pixel, JPEG compression with , additionof Gaussian noise with and gaussian filtering (5 5). Inall cases of attacks, all 64 bits were successfully extracted.

VIII. C ONCLUSION

A novel watermarking scheme for copyright protectionwhich is robust to geometric transformations was presented.The scheme is based on the properties of the RIT and CIT gen-eralized Radon transformations and manages to synchronizethe watermark that is embedded in an image with the corre-lating watermark in case of geometric attacks. Furthermore,the watermark detection process was proven to be robust togeometric attacks (rotation, scaling, translation), as well asother attacks such as compression, low-pass filtering, and noiseaddition.

Future work will focus on applying the proposed method toregions of the image instead of the entire image. These regionsmay be defined using the extracted set of robust corners in orderto form Voronoi diagrams or Delaunay tessellations, as pro-posed in [13] and [12], respectively. In this way, further robust-ness to attacks may be achieved.

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Dimitrios Simitopoulos was born in Komotini,Greece, in 1977. He received the Diploma inelectrical and computer engineering in 1999 fromAristotle University of Thessaloniki, Thessaloniki,Greece, where he is currently working toward thePh.D. degree in the Department of Electrical andComputer Engineering, where he holds a TeachingAssistantship position.

Since 2000, he has been a Research Assistantwith the Informatics and Telematics Institute,Thessaloniki, Greece. His research interests include

watermarking and multimedia security and image indexing and retrieval. He isa member of the Technical Chamber of Greece.

Dimitrios E. Koutsonanos was born in Kozani,Greece, in 1976. He received the B.Sc. degree incomputer science from the University of Ioannina,Ioannina, Greece, in 1999.

In June 2001, he joined the Informatics andTelematics Institute, Thessaloniki, Greece, where heis currently a Developer and Research Assistant. Hiscurrent interests include image and video processing,virtual and augmented reality.

Michael Gerassimos Strintzis (M’70–SM’80)received the Diploma degree in electrical engi-neering from the National Technical Universityof Athens, Athens, Greece, in 1967, and the M.A.and Ph.D. degrees in electrical engineering fromPrinceton University, Princeton, NJ, in 1969 and1970, respectively.

He then joined the Electrical Engineering Depart-ment at the University of Pittsburgh, Pittsburgh, PA.,where he served as Assistant Professor (1970–1976)and Associate Professor (1976–1980). Since 1980, he

has been Professor of electrical and computer engineering at the University ofThessaloniki, Thessaloniki, Greece, and, since 1999, Director of the Informaticsand Telematics Research Institute, Thessaloniki. His current research interestsinclude 2-D and 3-D image coding, image processing, biomedical signal andimage processing, and DVD and Internet data authentication and copy protec-tion.

Dr. Strintzis has been serving as Associate Editor for the IEEETRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY

since 1999. In 1984, he was awarded one of the Centennial Medals of the IEEE.

Robust image watermarking based on generalized radon ... · origin for two newly introduced one-dimensional generalized Radon transformations [22]–[24] that are applied to the image.

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