A NEW TIME-FREQUENCY BASED PRIVATE FRAGILE WATERMARKING SCHEME FOR IMAGE AUTHENTICATION B. Barkat, Member, IEEE and F: Sattar, Member, IEEE Nanyang Technological University School of Electrical and Electronic Engineering Nanyang Avenue, Singapore 639798
[email protected] [email protected] of the original images. In some applications like medical image authentication, the original image should not be changed in some degree afler the embedding. Most of the existing robust image watermarking methods are based on either spatial domain techniques or frequency domain techniques. Only a few methods are based on a joint spatialfrequency domain techniques [SI orajoint time-frequency domain techniques 191. The approach in [SI uses the projections of the 2D Radon-Wigner distribution in order to emphasise the watermark detection process [XI. We should note that for this semi-private watermarking technique, the knowledge of the Radon-Wigner distribution of the original image is necessary in the detection process. The approach in [9] uses the Wigner distribution. Specifically, the Wigner distribution of the image is added to the time-frequency watermark [9]. We note that for this method the detector requires access to the Wigner distribution of the original image. For fmgileisemi-fragile image watermarking, only spatial domain methods or frequency domain methods have been proposed so far, Some examples of these include the works reported in 16, 71. In this paper, we propose a new private fragile watermarking method based on the joint time-frequency analysis. In the proposed method, the fragile watennark consists of an arbitrary nonstationary signal with a particular signature in the time-frequency domain. The watermark signal length (in samples) can be chosen equal up to the total number of pixels in the image. That is, for a given NI x N , image size, we are able to embed a watennark signal o f size less or equal to (NI . N z ) samples. For simplicity, and without loss of generality, we consider in the sequel a square image of size N x N and the non-stationary signal of length N samples only. The locations of the N image pixels used to embed the N watennark samples can be chosen arbitrarily. In what follows, we choose to embed the watermark in the N diagonal pixels of the image. Moreover, in the proposed technique, a pseudo-noise (PN) sequence can be used as a secret key to modulate the watermark signal, making the time-frequency signature harder to see or to modify, In the extraction process, not all pixels of the original image are needed to recover the watermark but only those N pixels where the watermark has been embedded. Here, these N original pixels are inserted in the watermarked image itself. At the receiver, it is assumed that the legal user knows the locations of the watermark samples as well as the locations of the corresponding original pixels and the secret key (if used). Once the watennark is extracted its time-frequency representation is used to confirm the original ownership of the image and verify whether it has been modified or
ABSTRACT
In this paper, a new private fragile image watermarking scheme is proposed for image authentication based on time-frequency analysis. Specifically, the watennark is chosen as an arbitrary nonstationary signal with a particular signature in the time-frequency plane. The proposed technique retains a high quality watermarked image since only a few pixels of the original image are used in the watermarking process. Experimental results show that the pmposed fragile watermark is very sensitive to many attacks such as cropping, scaling, translation and JPEG compression, making it very effective in image authentication. Inder Ternis-Fragile Watermarking, Time-Frequency Analysis, Image Authentication 1. INTRODUCTION
Watemarking techniques for the protection of intellectual property rights have been developed for various areas such as broadcast monitoring, proof of ownership, transaction tracking, content authentication and copy control [I]. In the last two decades a number of watermarking techniques have been proposed 121; however, the requirements that a particular watermarking scheme has to comply with depend on the application purposes. In this paper, we focus on the authentication of images. There are basically two main objectives in image authentication: (i) the verification of the image ownership and (ii) the detection o f any forgery of the original data. For authentication, we check if the embedded information, i.e. the invisible watermark is changed or not in the receiver side. A fragile watermark is readily destroyed ifthe watermarked data has slightly been modified [ I]. Therefore, more attention has been paid recently to a particular watermarking scheme known as thefrugde wwrrermarking [I] for image authentication. As an early work on image authentication, Friedman has pmposed a trusted digital camera, which embeds a digital signature for each captured image. With the digital signature, one can verify that the image is not modified and in the same time can identify the specific camera that pictured the image [3]. Yeung and Mintzer proposed an authentication watermark that uses a pseudo random sequence and a modified ermr diffusion method to protect the integrity of the images 141. Wong and Meinon proposed a secret and a public key image watermarking schemes for grayscale image authentication (51. A l l ofthese methods embed too many information to verify the image’s authenticity. This results in the degradation
0-7803-7946-2/03/$17.00 02003 IEEE
363
arbitrary stari and stop times, as a watermark for our application. We stress here that other non-stationary signals are also feasible to choose and select.
not. If the watermarked image has been attacked or modified the time-frequency ofthe extracted watermark would also be modified significantly, as will be shown later. The paper is organised as follows. In Section 2, we give a brief review of timefrequency analysis and introduce the new watermarking method. In Section 3, we discuss the fragility of the proposed scheme by considering qualitative as well as quantitative measures. Section 4 concludes the paper.
2.2. Watermark Embedding and Extraction As we have seen earlier, we can select one non-stationary signal,
out of an infinite number, as our watermark. It is the particular features of this signal in the time-frequency domain that will be used to identify the watermark and consequently, its ownership. In discrete-time domain, the selected watermark signal can be written as
2. PROPOSED FRAGILE WATERMARKING
TECHNIQUE 2.1. Brief Review of Time-Fmquency Analysis
n = o , i , _ . _N,, , , - I . (2) Here, we assume a unit sampling frequency. In what follows, we set the signal length N,,, equal to N,,, = N = 256 where N x N is the size of the image to be watermarked. In Figure 2, we display the original unwatermarked baboon image used in our analysis.
s(n) =cos[z?r(aon+a,n2+a2n3)1
A given signal can be represented in many ways; however, the most important ones are time and f i q u e n c y domain representations. These two representations and their related classical methods such as autocomlation andior power spectrum proved to be powerful in the analysis of sfationmy signals. However, when the signal is non-stationary these methods fail to fully charaterise it. The use of the joint time-frequency representation gives us a better understanding in the analysis of non-stationary signals. The ability of the time-frequency distribution to display the spectral contents of a given non-stationary signal makes it a very powerful tool in the analysis of such signals [IO]. As an illustration, let us consider the analysis of a non-stationary signal consisting of a quadratic frequency modulated (FM) signal given by s(t) = nT(t - T / Z cos ) [ ~ (aot r
+ a t Z+ a2t3)]
(I)
where n ~ ( tis) 1 for It1 5 T / 2 and zero elsewhere. ao, a1 and az are real coefficients. The signal spectrum, displayed in the bottom plot of Figure I, gives no indication on how the frequency of the signal is changing with time. The time domain representation, displayed in the left plot of Figure 1, is also limited and does not provide full information about the signal. However, a timefrequency representation, displayed in the center plot of the same figure,clearly reveals the quadratic relation between the frequency and time.
Figure 2 The original unwatermarked image used in the analysis. Any arbitrary N pixels (out of the total N 2pixels) of the image are potential candidates to hide the watermark. In this presentation, we choose the main diagonal, from top left to bottom right, pixels as the points of interest. That is, each sample of the quadratic FM watermark signal is added to a diagonal image pixel. Note that if we choose to use the secret key, the watermark signal is fust multiplied by the PN sequence and then added to the original diagonal pixels. Also note that in some cases, the watermark signal may have to be scaled by a real number before it is added to the original pixels. However, in our examples, we have found that a unitary scale coefficient is adequate to perform the task. The watermarked image is displayed in Figure 3. We ohserve that there is no apparent difference between the marked and unmarked images. In addition, the watermark is well hidden and unnoticeable. To extract the watermark, we need to remove the quadratic FM samples from the diagonal pixels of the watermarked image. For that, we need the values of the original image pixels at those particular positions. These original pixels should be known to a legal user. They could he transmitted independently or they can be transmitted in the watermarked image itself. For instance, in the watermarked image in Figure 3, we have inserted these original needed pixels in this very image. We have done so hy augmenting the watermarked image to a new size N x (N+ 1)and allocated the upper diagonal whose elements are indexed by ( i ,i l ) , i = 1 , . . ., N to hold the required original pixels. Obviously, any other N locations (in the watermarked image) can alternatively be used to
Figure 1: Time-frequency representation of a quadratic FM signal: the signal’s time domain representation appears on the left, and its spectrum on the bottom. Note that, theoretically, we have an infinite number of possibilities to generate a quadratic FM. This could be accomplished by just chwsing different combinations of values for ao, a1 and a2. In the sequel, we will select a particular quadratic FM signal, with
+
364
is similar to that used for monocomponent signals. Consequently, one can select any arbitrary pattern in the time-frequency domain as a signature without any additional computational load compared to the quadratic FM signal example illustrated earlier. 3. RESULTS AND PERFORMANCE In this section, we evaluate the performance of the proposed fragile
watermarking technique. For that, we consider the analysis of the time-frequency of the extracted watermark when the watermarked image has been subjected to some common attacks such as crop ping, scaling, translation and JPEG compression. For the cropping, we choose to crop only the first row of pixels of the watermarked image (leaving all the other rows untouched); for the scaling we choose the factor value I .1; for the translation we choose to translate the whole watermarked image by only I column to the right; for the compression we choose a JPEG compression at quality level equal to 99%. Visually, the effect of these attacks on the watermarked image is unnoticeable. This is because the chosen values are very close to the values 1 (i.e., no scaling), 0 (i.e., no translation) and 100% (i.e., no compression). For space limitations, the various attacked watermarked images are not shown here (they look very similar to the unattacked watermarked image displayed in Figure 3). Before presenting the results for the images subjected to attacks, let us present here the extracted watermarks when there has been no attack. In Figure 5 (left plot), we display the TFD of the extracted watermark when the PN has not been dealt with yet and in the same figure (right plot) we display the TFD of the extracted watermark after we decode the watermark using the correct PN code. It is clear from these two figures that any attempt by an illegal user to identify the owner of the image from the TFD without knowing the correct PN code (i.e., the secret key) will be a total failure.
Figure 3: Watermarked image. insert the original N pixels. Similarly, if the PN sequence is used, it should also be known to the legal user at the receiving end in order to extract the watermark. This sequence can also be transmitted independently or hidden in the watermarked itself (using a similar procedure to the one used forthe needed original pixels). Once, we have extracted the watermark samples, we use a time-frequency distribution (TFD) to analyse their content. In the literature, we can find many TFDs. The choice of a particular one depends on the specific application at hand and the representation propaties that are desirable for this application. Since we select a monocomponent quadratic FM signal as the watermark (refer to Figure I), thus, we can clearly and unambiguously recognise our time-frequency signature by using a windowed Wigner-Ville distribution (WVD) of the signal. The windowed WVD is defined as [IO]
where ~ ( tis) the analytic signal associated with the watermark signal .(t) and W ( T ) is the considered window. lfwe decide to use a more complicated watermark signal such as the multicomponent signal displayed in Figure 4, the WVD would not be appropriate as it will have cross-terms which might hide the real feature ofour signature. In this case, a reduced interference TFD is more appropriate to use [ I I , 121.
Figure 5 : TFDs of the extracted wate-k with no attack (lefl plot) before removing the PN effect and (right plot) after removing the PN effect. In the examples displayed below, we have not used the PN in the watermarking process in order to focus on the effect of the
attacks only. When the PN is considered, we obtained similar reSUltS. From each attacked image, we extract the watermark signal, as discussed in the previous section, and analyse it using a windowed WVD. The results of this operation are shown in Figure 6. These TFDs are drastically distorted in comparison with the TFD of the watermark signal extracted from the unattacked watermarked image (see Figure 5 (right plot)).
Figure 4 Reduced-interference distribution of a multicomponent signal consisting of 2 quadratic FM components (with opposite instantaneous frequencies). The watermarking procedure used for multicomponent signals
365
4. CONCLUSION l i t this paper, we propoacd a novel private .md fragile uatermark1 In this scheme, the watermark coning scheme for ~ 1 1 1 images. si>ts of an abitraty non-stationary signal with J particular signature i n the time-frequency plane. The scheme can allow the use of a secret key to enhince security and pn\acy. To ven(L the im3ge ownetship and check whether it has been s u h p t c d to any attack. u e crploit the pirttculnr signdture of the watermark in the timefrequency domain. ‘The advantages of our scheme ure twofold. Fit% we can detect changes resulting from attacks such as ruintion. scaling. translation. and compression. Secondly. the image quality IS retained quite high kcause only a few pixels ofthe orig1m1image arc affected in the uatermarkng process.
l
I
IbJ
5. REFEKENCES
:
-
_-_
..-
c---__-
[ I ] 1. J. Cox, M. I . . Miller. and J A. Hloom, “Digital Wntermarking:’ .Mowm Kaalmann Publishers, A n Imprint of Acadcmic I’rcss. USA, X W 2 .
..
.A.
\“I
[2] S. Lee and S. Jung, “A Survey of Watermarking Techniques Applied to Multimedia,” Proc. IEEE Int. Symposium on Industrial Electronics, vol. I, pp. 272-277, 2001. [3] G. Friedman, “The Trustworthy Digital Camera: Restoring Credibility to the Photographic Image,” IEEE Trans. ConsumerElecfron.,vol. 39, pp. 905-910, 1993. [4l M. Yeung and E Mintzer, “Invisible Watermarking Technique for Image Verification,” Pmc. IEEE Int. ConJ on Image pmc. (KIP)),vol. 2, pp. 680-683, 1997. [SI P. Wong and N.Memon, “Secret and Public Key Image Watermaking Schemes for Image Authentication and Ownership Verification:’ IEEE Trans. on Image Processing, vol. IO, pp. 1593-1601,2001.
Figure 6: TFDs of the extracted watermark for (a) a P E G compression attack, @) a scaling attack (factor 1.1) (c) a translation attack and (d) a cropping attack.
Table 1: Similarity measure between the TFD of original the watermark and that of the extracted watermark subjected to some attacks. Attack function Scaling (factor I . I) Translation P E G (QF=99?h)
Correlation coefficient, T -0.0027 -0.0453 0.2027
[6] S. C. Byun, S. K. Lee, A. H. Tewf&, and B. H. Ahn, “A SVD-based fragile watermarking scheme for image authentication,” Proc. of International Workshop on Digital Watermarking, pp. 211-219, 2002. [7] 1. Hu, J. Huang, D. Huanf, and Y. Q. Shi, “A DWT-based Fragile watermarking tolerant of P E G compression,’’ Proc. of International Workshop on Digital Watermarking, pp. 22%229,2002. [8] S. Stankovic, 1. Djurovic, and 1. Pitas, “Watermarking in the spaceispatial-frequency domain using twdimensional Radon-Wigner distribution:’ IEEE Trans. on Image Processing,vol. IO, no. 4, pp. 65M58, April 2001. [9] B. G. Mobasseri, “Digital watermarking in joint timefrequency domain,” Proc. of fhe IEEE Internafional Conference on Image Processing, vol. 3, pp. 481484, 2002. [IO] F. Hlawatsch and G. F Boudreaux-Bartels, “Linear and quadratic time-frequency signal representations,” IEEE SignalPmcessingMagazine, Vol. 9(2), pp. 21-67, Apr. 1991. [ I I] H.I. Choi and W.J. Williams, “Improved Time-Frequency representation of multicomponent signals using the exponential kernels,” IEEE Trans ASSP, Vol. 37, No. 6, pp. 862-87 I , June 1989. [ I21 J. Jeong and W.J. Williams, “Kemel Design for Reduced Interference Distributions,’’IEEE Trans. on Signal Processing, Vol. 40,No. 2, pp. 402-412, Feb. 1992.
Although the plots in Figure 6 show the visual impact of the considered attacks on the watermark time-frequency representations, they do not quantify the amount of distortion caused to the watermark or image. In order to quantify the distortion, we evaluate the similarity, expressed in terms of the normalized correlation coegicient, r, between the TFD of the extracted watermark and that of the original watermark. This similarity measure is defined
as
where w is obtained by reshaping the 2-D TFD of the original watermark as a I-D vector hom which we remove its mean, w‘ is obtained in a similar way from the TFD of the extracted watermark. p is the total number of time-frequency points in these respective TFDs. The magnitude range of r is [-],I] and the unity holds if the TFD of the extracted watermark perfectly matches that of the Original watermark. Table 1 shows the performance index r for some attacks considered earlier. The values of r found are quite low, indicating that our watermarking scheme is quite sensitive to small changes resulting from various types of attacks.
366
