OBLIVIOUS SCHEMES OF GHOST-BASED WATERMARKING FOR DCT COEFFICIENTS

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1 OBLIVIOUS SCHEMES OF GHOST-BASED WATERMARKING FOR DCT COEFFICIENTS Hiromu KODA, Tomoyuki OGAWA and Shojiro SAKATA Faculty of Electro-Communications The University of Electro-Communications -5- Chofugaoka, Chofu-shi, Tokyo, Japan ABSTRACT In this paper we present oblivious schemes of ghost-based watermarking for DCT coefficients and examine the fundamental resistance to some attacks. First we introduce a bipolar ghost model, which consists of a composite signal and its complementary signal, and formulate the power cepstrum for the model. Next we define the cepstral difference between the composite and complementary signals to improve the cepstral performance, and examine some properties of the cepstral difference. After that, we explain two types of oblivious algorithms for the ghost-based watermarking in DCT domain taking the above properties into account. The experimental results for some test images show that the watermark information in each image can be detected sensitively by our schemes even when the watermarked images are subjected to processing technique such as clipping.. INTRODUCTION The technique of cepstral signal processing has been applied to the analysis of speech and image signals [] [] with success. By exploiting the peculiarity of cepstral technique, we proposed some schemes of ghost-based watermarking [3] []. However the fundamental performance of these schemes was not examined sufficiently from the viewpoint of attacks. In this paper we present oblivious schemes of ghostbased watermarking for DCT coefficients and examine the fundamental resistance to some attacks. First we introduce a bipolar ghost model, which consists of a composite signal and its complementary signal, and then we formulate the power cepstrum for the model. Next we define the cepstral difference between the composite signal and the complementary signal to improve the cepstral performance, and examine some properties of the cepstral difference. After that, we explain two types of oblivious algorithms for the ghost-based watermarking in DCT domain taking the above properties into account. Finally from the experimental results for M-sequence-watermarked images, we show that the watermark information in each image can be detected This work was supported by the Grant-in-Aid for Scientific Research, No.56569, from Japanese MEXT (Ministry of Education, Culture, Sports, Science and Technology). sensitively by our schemes even when the watermarked images are subjected to processing technique such as clipping.. BIPOLAR GHOST MODEL AND ITS CEPSTRUM Now let us consider a composite signal : g(n) =( a)x(n) +ax(n M ) () where x(n); a and M denote an original signal(x(n) = (n < )), mixture ratio (jaj» :5) and time lag, respectively. Then the power cepstrum g pc (q)(= Z [log jz[g(n)]j ]) of g(n) can be given by g pc (q) =a pc (q) +f pc (q) +x pc (q) () where a pc (q) = Z [log jaj ] (Z [ ] : the inverse of z- transform Z[ ]), and then f pc (q) and x pc (q) denote the cepstrums of f (n)(= ffi(n) +Bffi(n M )) and x(n), respectively. Here we note that if x(n) is a random-walk signal (i.e. the spectrum of x(n) x(n ) is white), then x pc (q) = log j j ffi(q) + jqj u(jqj ), where is constant and u(n) =(n ), (otherwise). [5] Next we consider a complementary composite signal : ^g(n) =( μa)x(n) +μax(n M ); μa = a: (3) Then the power cepstrum ^g pc (q) of ^g(n) can be given by ^g pc (q) =a pc (q) +f pc (q) +x pc(q) () where a pc (q) =Z [log ja j ], and fpc (q) denotes the cepstrum of f (n)(= ffi(n) +B ffi(n M )). In this paper we refer to a pair of (g(n); ^g(n)) as a bipolar ghost model, while we refer to a pair of (g(n); ^g(n)ja= = x(n)) as a unipolar ghost model. 3. CEPSTRAL DIFFERENCE FOR BIPOLAR GHOST MODEL The cepstral difference d pc (q) between g(n) and ^g(n) is defined as d pc (q) =g pc (q) ^g pc (q). Then we have ( P ( ) k (B k B k ) k= k ffi(jqj km) (jqj ) d pc (q) = log(jaj=ja j) (q =) (5)

2 y where A = a, B = a a, A =+a, and B = +a a. Evaluating the above Eq. (5) at short quefrencies (q = ;M) yields d pc () = log j aj j+aj and d pc (M ) = a a. Plots of d pc (q)(q = ;M), d(= d pc (M ) d pc ()) and d (= e pc (M ) e pc ()) are shown in Fig., where d (= e pc (M ) e pc (); e pc (q) = g pc (q) x pc (q)) denotes the result of unipolar ghost model in the literature [3]. From Fig., the following properties can be obtained. () d>when a>, and d<when a< (:sign), () jdj ß3jd pc (M )j (:amplitude), (3) jdj(:bipolar ghost) > jd j (:unipolar ghost), where < jaj»:5. Therefore in this paper, the above property () for the bipolar ghost model is exploited to detect watermarks from watermarked images, and instead of a pair of composite signals (g(n); ^g(n)) in time domain, a pair of composite signals (g(m); ^g(m)) in DCT domain is used to embed watermarks with more energy in an image dpc() dpc(m) dpc(m)-dpc() epc(m)-epc() a Fig. Plots of dpc(q)(q =;M), d(= dpc(m) dpc()) for the bipolar ghost model and d(= epc(m ) epc()) for the unipolar ghost model. log jfft[s i (m)]j ] IFFT[ log jfft[y i (m)]j ], where IFFT[ ] denotes the N -point inverse FFT, and then s i (m) and y i (m) are the weighted versions of g i (m) and ^g i (m), respectively. hs7i Calculate the extracted sequence : d(i) =d (i) pc (M ) d (i) pc (), which is used to detect watermarks by means of cross-correlation. hs8i If i last block then quit, else go to hs6i after i = i +... Methods for Obtaining Two Types of Sequences ) Extract a sequence x i (n)(» n < N = N ) from a set of original signals in the i-th subblock of an image (see Fig. ). ) Calculate the N -point DCT of x i (n) : X i (k) = DCT [x i (n)](» k < N ), and then extract the midsequency components : Xi (k ) = X i (k + 6)(» k < N ). 3) Divide the above components into two types of sequences : ~x i (m) =Xi (m); ^x i(m) =Xi (m+)(» m<n = N ). ) Divide a set of original signals into two types of sequences (x i (n ); x i (n )(» n <N = N )) in the i-th subblock of an image (see Fig. 3). ) Calculate the N -point DCTs of two sequences : X i (k )=DCT [x i (n )]; X i (k )=DCT [x i (n )](» k <N ). 3) Extract the mid-sequency components : ~x i (m) = X i (m + 3); ^x i (m) =X i (m + 3)(» m<n = N ).. OBLIVIOUS WATERMARKING ALGORITHMS.. Basic Algorithm } Generation of Bipolar Ghost in DCT Domain hsi Set i =. hsi Obtain two sequences of DCT coefficients ( ~x i (m); ^x i (m)(» m<n = N ) ) from a set of original signals in the i-th subblock of an image by using either or of.. hs3i Next, calculate two types of composite signals :g i (m) = h(~x i (m);a;m;n ); ^g i (m) = h(^x i (m); μa; M; N ), where μa = a and 8 < x (m) (» m<m); h(x (m);a ;M;N )= _b( a : )x (m) +a x (m M ) c _ (M» m<n ): (6) hsi If i last block then quit, else go to hsi after i = i +. } Calculation of Cepstral Difference hs5i Set i =. hs6i Calculate the cepstral difference: d (i) pc (q) =IFFT[ 6 6 The i-th block 6 56 Extraction of mid-sequency components after DCT x ~ i (m) x ^ i (m) Fig. Diagram of. The i-th block x (n ) i 6 6 x (n ) i Extraction of mid-sequency components after DCT. ~ x i (m) x ^ i (m) Fig. 3 Diagram of. x (n) i X (k ) i

3 5. EXPERIMENTAL CONDITIONS The standard images SIDBA/ GIRL and MOON (N N = pels, 56 gray levels) are used for our simulation, of which the conditions are summarized as follows. () Ghost-based modulation of M-sequence : In this study, we use M-sequence as watermark information and generate watermarked images by means of the following procedure. hsi An original M-sequence A i (= "(or +); " (or )) with period N (= 8 ) is calculated to produce an extended M-sequence fa ;A ;:::;A N ; "g (period N =56). hsi The above extended M-sequence is embedded into an original image by using the ghost parameters (a; M), and then the conversion rule that a =+a (binary symbol = "); a (otherwise), where <a» :5, is used subblock by subblock at the step hs3i of.. () Objective measure of image quality : To evaluate the quality of ghost images objectively, we use the SNR (Signal to Noise Ratio) defined as SNR = log (55 =MSE) [db] (7) where MSE is the mean square error between the gray levels of original and watermarked images. P (3) Cross-correlation function(ccf) : r dp (fi )= N N i= d(i) p(i + fi ), where d(i)(= d (i) pc (M ) d (i) pc ()) is the extracted sequence in the i-th subblock and p(i) is the original pattern of M-sequence f+; g. () Decision rule : Output levels b(i) =+:(d(i) >T), :(otherwise), where threshold T =. (5) Fundamental attacks : AWGN(Additive White Gaussian Noise), clipping and lossy coding (JPEG, JPEG) [6] [7]. 6. EXPERIMENTAL RESULTS 6.. Basic Results () Number of errors vs. mixture ratio Figures (a) and (b) show the error properties of watermarked images for GIRL and MOON, respectively, where Methods I and II denote the processing methods described in.. From Fig. (a), it is found that the performance of is superior to that of. From Fig. (b), it is found that the performance of is relatively superior to that of when jaj :9. Next we examined the lower bound (a lb ) of mixture rate a such that the M-sequence pattern can been detected from the sharp peak of CCF, and it has been confirmed that a lb =:5 (Methods I and II) in Fig.. Here we note that the patterns of embedded M-sequence (watermarks) can be estimated by CCF when the number of errors is less than errors (i.e. BER < 3[%])[3]. () SNR vs. mixture ratio Figures 5(a) and (b) show the SNR properties of watermarked images for GIRL and MOON, respectively. From Fig. 5, it is found that the value of SNR in each method decreases as the value of jaj increases. (3) Watermarked images and their CCFs Figures 6 and 7 show examples of watermarked images for GIRL by means of Methods I and II, respectively, and the corresponding error images are shown in Figs. 8 and 9, respectively. From Figs. 6 and 7, it is found that the degradations in watermarked images are quite invisible since SNR > [db]. From error images (Figs. 8 and 9), we can observe that most image degradations introduced by watermarks are located around edges and in textured areas. Here we note that in the spatial masking areas [8] such as edges and textured areas, the human visual system (HVS) is less sensitive to image degradations than in smooth areas. Next Figs. and show the CCFs for Figs. 6 and 7, respectively and it is found that we can sensitively detect the sharp peaks y of Figs. and at the delay fi =(or56). As another example, we also produced the watermarked images (Figs. and 3) for MOON. Then it is found that the image degradations in Figs. and 3 are quite invisible, and that we can sensitively detect the peaks of Figs. 6 and 7 at the delay fi =(or56). 6.. Results of Resistance Tests () AWGN (Additive White Gaussian Noise) test Figures 8(a) and (b) show the error properties of AWGNadded images for GIRL and MOON, respectively, where the standard deviation (ff) of AWGN is 6. From Fig. 8, it is found that the performance of in Fig. 8(a) is superior to that of when :5»jaj» :5, while the performance of in Fig. 8(b) is relatively superior to that of when :5»jaj» :7. Furthermore it has been confirmed that a lb = : (), :6 () in Fig. 8(a), while a lb =: (), :8 () in Fig. 8(b). Next Fig. 9 shows an example of AWGN-added version of Fig. 7, where ff =6, and its error image is shown in Fig.. In Fig. 9, the image degradation due to granular noise is visible. Figure shows the CCF for Fig. 9, and it is found that we can still detect the sharp peak of CCF. Furthermore it has been confirmed that we can detect the M- sequence pattern even when the severe noises that ff =3 (), 35 () are added to Fig. 7. () Clipping test Figures (a) and (b) show the error properties of clipped images for GIRL and MOON, respectively, where the removal ratio (») of watermarked image is 5[%]. From Fig., it is found that the performance of is relatively superior to that of. Furthermore it has been confirmed that a lb = :9 (), :6 () in Fig. (a), while a lb = :5 (Methods I and II) in Fig. (b). Next Figs. 3(a) and (b) show examples of clipped images of Fig. 7, where» = 5[%] (Fig. 3(a)), 75[%] (Fig. 3(b)). Figures (a) and (b) show their CCFs. From Fig., it is found that we can still detect the sharp peaks of CCFs. Furthermore it has been confirmed that we can detect the M-sequence pattern even when 7[%] () and 96[%] () of the data are removed from Fig. 7 because the M-sequence is used as the pattern of pseudonoise (PN) sequence. y By comparing with the previous result [3] in time domain, it is confirmed that the peak value of CCF in Fig. is about two times as much as that of CCF in the previous result, where M =; jaj =:;SNR = :8[dB], because the mixture ratio that jaj = : is used in Fig. 7.

4 (3) Lossy coding test Figures 5(a) and (b) show the error properties of compressed images for GIRL and MOON, respectively, where original watermarked images via Methods I and II are compressed between.5[bpp] and.[bpp] by using the JPEG coding. From Fig. 5, it is found that the performance of is relatively superior to that of. Next Fig. 6 shows an example of JPEG- compressed image of Fig. 7, where compression ratio is /8, and its error image is shown in Fig. 7. Figure 8 shows the CCF for Fig. 6, and from this figure, it is found that we can still detect the peak of CCF at the delay fi =(or56). From the results of previous experiments [], it has been confirmed that our methods have the resistance to JPEG coding. 7. CONCLUSION In this paper we have presented oblivious schemes of ghostbased watermarking for DCT coefficients, and then we have examined the fundamental resistance to some attacks. Experimental results for some test images show that the watermark information in each image can be detected sensitively by our schemes even when the watermarked images are subjected to AWGN, clipping and lossy coding. In this paper M-sequences are used as PN sequences, but we can also use Gold sequences [9] to increase the number of sequences. Hereafter we will introduce the Gold sequences in our schemes. 8. REFERENCES [] D.G. Childers, et al., The cepstrum ; a guide to processing, Proc. of the IEEE, vol. 65, no., pp. 8-3, Oct [] H. Koda and H. Tanaka, A new method of measuring the blocking effects of images based on cepstral information, IEICE Trans. Fundamentals, vol. E79- A, no. 8, pp. 7-8, Aug [3] H. Koda, T. Ogawa and S. Sakata, Non-oblivious and oblivious schemes of ghost-based watermarking via cepstral difference and M-sequence, Proc. SMMSP3, Spain, pp. -8, Sept. 3. [] T. Ogawa, H. Koda and S. Sakata, A note on a scheme of ghost-based watermarking in DCT domain, Proc. Symposium on Information Theory and Its Applications (SITA3), pp , Dec. 3. [5] H.Koda, M.Kubo and S.Sakata, Lag detection of digital ghost images based on cepstral analysis, Proc. IWAIT, Korea, pp , Feb.. [6] D.S. Taubman et al., JPEG:Image Compression Fundamentals, Standards, and Practice, Kluwer Academic Publishers,. [7] W.B. Pennebaker et al., JPEG Still Image Data Compression Standard, Kluwer Academic Publishers, 3. [8] A. Hanjalic, et al., Image and Video Databases : Restoration, Watermarking and Retrieval, Elsevier,. [9] M. K. Simon, et al., Spread Spectrum Communications Handbook, McGraw- Hill,99. SNR[dB] SNR[dB] Fig. The number of errors vs. mixture ratio a (M =) Fig. 5 SNR vs. mixture ratio a (M =).

5 Fig. 6 Watermarked image I Fig. 7 Watermarked image II (M =; jaj =:; 3:[dB]). (M =; jaj =:; :[db]). Fig. Watermarked image I Fig. 3 Watermarked image II (M =; jaj =:; :[db]). (M =; jaj =:; 3:[dB]). Fig. 8 Error image ( 5) Fig. 9 Error image ( 5) for Fig. 6. for Fig. 7. Fig. Error image ( 5) Fig. 5 Error image ( 5) for Fig.. for Fig , =., M= 5 3, =., M= Fig. CCF for Fig. 6. Fig. 6 CCF for Fig.. 5, =., M= , =., M= Fig. CCF for Fig. 7. Fig. 7 CCF for Fig. 3.

6 Fig. 9 AWGN-added version of Fig. 7 (; ff =6;SNR =:[db]) Fig. Error image ( 5) for Fig , =., M=, AWGN(SD=6) Fig. 8 The number of errors vs. mixture ratio a after AWGN-addition (M =, ff =6) Fig. CCF for Fig. 9.

7 5 3 9 (a)» = 5[%]; SNR=:[dB] (b)» = 75[%]; SNR=:5[dB]. Fig. 3 Clipped version of Fig. 7..5, =., M=, clip:9.5% (a) CCF for Fig. 3(a). Fig. The number of errors vs. mixture ratio a after clipping (M =,» = 5[%]) , =., M=, clip:75.% (b) CCF for Fig. 3(b). Fig. CCFs for clipped images.

8 BIT RATE [bpp] Fig. 6 Compressed version of Fig. 7 (; :[bpp]; 35:9[dB];JPEG). 8 6 Fig. 7 Error image ( 5) for Fig BIT RATE [bpp] Fig. 5 The number of errors vs. bit rate (M =, jaj =:, JPEG)., =., M=, JPEG(/8) Fig. 8 CCF for Fig. 6.