Copyright Protection against Print-and-Scan Operations by Watermarking for Color Images Using Coding and Synchronization of Peak Locations in Frequency Domain
*YEN-CHUNG CHIU1 AND WEN-HSIANG TSAI1,2
1Department of Computer Science National Chiao Tung University
Hsinchu, 300 Taiwan
2Department of Computer Science and Information Engineering Asia Universiy
Taichung, 413 Taiwan
A watermarking method for copyright protection of color images against print-and- scan operations is proposed. A watermark is embedded in an input image as coefficient- value peaks that are circularly and symmetrically distributed in a middle band of the dis- crete Fourier transform (DFT) domain of the input image. By detecting the robust peaks in the DFT domain of a reproduced image obtained by scanning a printed version of a watermarked image, we can extract the embedded watermark to verify the copyright of the reproduced image. Experimental results are given to prove the feasibility of the pro- posed method.
Keywords: digital watermarking, color image, copyright protection, print-and-scan op- erations, discrete Fourier transform, reproduced image
1. INTRODUCTION
Because of the rapid development of electronic products, printers and scanners are commonly used to publish and reproduce documents. Digital images can be printed and distributed. And when a printed image is scanned, the resulting image, called the repro- duced image in this paper, becomes a digital version similar to the original one, though with some distortion occasionally. Such reproduced images can be misused such that the copyright of the original digital image is violated. It is therefore desired to have a means to counteract such illegal print-and-scan operations, sometimes called print-and-scan attacks.
Digital watermarking is a technique that embeds a watermark into a digital image to protect the owner’s copyright of the image. The resulting watermarked digital image is called a stego-image. One way to solve the above-mentioned print-and-scan problem is to make the embedded watermark robust against print-and-scan operations, so that after these operations are applied to a stego-image to yield a reproduced image, the watermark
Received January 1, 2005; accepted August 16, 2005.
Communicated by C. C. Chiang, H. Y. Mark Liao, and K. C. Fan.
* This work was supported in part by the NSC Project Advanced Technologies and Applications for Next Gen- eration Information Networks (II) under Project No. NSC 93-2752-E-009-006-PAEand partially under NSC Project No. NSC 94-2422-H-468-001.
is not fully destroyed and can still be extracted from the reproduced image to verify the copyright of the image.
Some researches on watermarking techniques for copyright protection against print and scan attacks have been reported in recent years. Fleet and Heeger [1] described a human color vision model designed to ensure that the embedded signal is invisible and a method for embedding sinusoidal signals, which act as a grid and provide a coordinate frame for the image. Solachidis and Pitas [2] proposed using a private key, which allows a very large number of possible watermarks, to determine a watermark that is then em- bedded in a ring in the DFT domain. A correlation measure is used for watermark detec- tion. Lefebvre et al. [3] proposed a method that combines an additive watermarking al- gorithm in the spatial domain and a synchronization template in the Fourier domain. In Chotikakamthorne and Pholsomboon [4], a watermark constructed with a ring-shaped constraint is embedded in the spatial domain, and a sinusoidal function with random phases is used to generate each watermark ring.
In a reproduced image, there are two types of distortions, namely, geometric trans- formations and pixel-value changes. The former type includes rotation, scaling, padding, etc., and the latter includes changes of pixel values in luminance, contrast, gamma cor- rection, chrominance, blurring, etc. [5]. Geometric transformations do not cause signifi- cant changes in the visual quality, but pixel-value changes do, as seen in Fig. 1.
(a) The original image “Lena.” (b) Reproduced image of (a) at 100dpi.
Fig. 1. A color image and a reproduced image with degraded quality.
A watermark embedded in a reproduced image must have a certain degree of ro- bustness against pixel-value changes and geometric transformations. In order to embed watermarks in a color image so that the image can survive geometric transformation at- tacks, certain invariant features of the image with respect to geometric operations should be adopted in designing the watermark. In addition, the embedded watermark must be imperceptible.
In this paper, we propose a robust method for embedding a watermark in an input image as a set of coefficient-value peaks that are circularly and symmetrically distributed in a middle band of the discrete Fourier transform (DFT) domain of the input image. The peaks are robust in the DFT of the reproduced image and can be extracted to verify the copyright of the image. Experimental results are given to prove the feasibility of the pro- posed method.
The remainder of this paper is organized as follows. In section 2, the idea of the pro- posed method is described. In section 3, the proposed watermark embedding process is presented. In section 4, the proposed watermark extraction process is described. In sec- tion 5, some experimental results are given. Finally, some conclusions are drawn in sec- tion 6.
2. IDEA OF PROPOSED METHOD 2.1 Properties of DFT and Color Images
The DFT F(u, v) of an input image f(x, y) of size M × N can be described by
1 1
2 ( / / ) 0 0
( , ) 1 ( , ) .
M N
j ux M vy N
x y
F u v f x y e
MN
− − π
− +
= =
=
∑ ∑
(1)This transform has several properties that are useful for this study. First, it has a symmetry property [6], shown by
F(u, v) = F*(− u, − v), (2) where the symbol F* means the complex conjugate of F. Also, the complex transform F(u, v) can be divided into two parts, the magnitude function (or called spectrum) |F(u, v)| = [R2(u, v) + I2(u, v)]1/2 and the phase function φ(u, v) = tan−1[I(u, v)/R(u, v)], where R(u, v) and I(u, v) are the real and imaginary parts of F(u, v), respectively. For real inputs like images, Eq. (2) leads to
|F(u, v)| = |F(−u, −v)|, (3) which means that a coefficient value and its symmetric version in the DFT domain are equal in magnitude. Both the magnitude and the phase functions are required for recon- struction of an input image from its DFT. The magnitude function is less important than the phase function. The magnitude-only image is unrecognizable, while the phase-only image is barely recognizable [7]. Therefore, we can compute and adjust the magnitudes of the DFT coefficients to embed information without causing significant loss of image quality, as was done in this study.
Furthermore, it is known [5] that the rescaling operation has almost no effect on the DFT coefficients, while image rotation in the spatial domain will cause the coefficient values to have the same rotation in the frequency domain. Figs. 2 (a) and (b) show an image and a rotated version of it. And the corresponding spectrum images, in which each pixel value is taken to be the magnitude of a DFT coefficient, are shown in Figs. 2 (c) and (d), respectively. Notice that the rotation of the spectrum image in Fig. 2 (d) is the same as that of the image in Fig. 2 (b). Finally, it is noted that although we can embed watermark information into all three color channels of an image, experiments have
(a) The image “Lena.” (b) “Lena” after rotation.
(c) Fourier spectrum of “Lena.” (d) Fourier spectrum with the same rotation as in (b).
Fig. 2. Input images and Fourier spectrums of the G channel.
shown that this work can only be conducted in the red and blue channels in the DFT do- main because information hidden in the green channel is easily detected by the human eye [8] and will have perceivable effects.
2.2 Proposed Watermarking Technique Using Coefficient-value Peaks in DFT Domain In the proposed watermarking method, we first shift the zero frequency point F(0, 0) to the center of the DFT domain and select a ring region in a middle band, denoted by B subsequently, in the DFT domain between two circles with two pre-selected radii R1 and R2, where R1< R2, as shown in Fig. 3. Next, we divide B into n equally-spaced concentric circular stripes with outer radii r1, r2, …, rn, and divide each stripe into m angle ranges with starting angles θ1, θ2, …, θm, respectively, as shown in Fig. 4. Then, for watermark embedding, we select n × m locations P = {p1, p2, …, pn×m}, called embeddable positions, in the frequency domain, with coordinates described by
pk = (uk, vk) = (ricosθj, risinθj), (4) where 1 ≤ i ≤ n, 1 ≤ j ≤ m, and 1 ≤ k ≤ with = n × m. We also adjust the coefficient values of some of these positions so that they become local peaks in the frequency do- main, thus forming a desired watermark in the manner described below.
R1
R2
R A
(uk ,vk)
Fig. 3. A ring region in the middle frequency band.
Fig. 4. The ring region in Fig. 3 is divided into concentric circular stripes, and each stripe is divided into angular sectors.
First, we select a number of peaks, say h ones, among the ones at the embeddable positions for use to embed a watermark W, which is a pre-selected series number with an integer value w. These peaks may be viewed to code the watermark value w.
To decide which peaks should be used, we apply a combinatorial operation to get all possible codes R = {r1, r2, …, rg}, with each code ri specifying a set of h peak locations, where g = C(, h) with C(, h) being a combinatorial number, that is, the number of ways in which h unordered outcomes can be selected from possibilities. In this study, we set h to be equal to /2 because C(, h) will then have the maximal value for a specific = m
× n. For example, if is equal to four and h is equal to two, then we have P = {p1, p2, p3, p4} and g = C(4, 2) = 6, which means that we have 6 possible codes R = {r1, r2, …, r6} for use as watermarks, where r1 = {p1, p2}, r2 = {p1, p3}, r3 = {p1, p4}, r4 = {p2, p3}, r5 = {p2, p4}, and r6 = {p3, p4}.
Then, after choosing a watermark W with integer value w no larger than g, we get the wth code rw in R and modify the coefficient values M(uk, vk) of the corresponding embeddable positions pk specified by rw as local peaks M′(uk, vk) according to the fol- lowing equation:
M ′(uk, vk) = M(uk, vk) + c, (5) where c is a pre-selected constant that determines the embedded watermark strength.
It should be noted that, when changing the coefficient value to become a peak at each pk = (uk, vk) for the amount of c, we must preserve the positive symmetry property of the DFT [9] by changing the corresponding coefficient value at pk′ = (− uk, − vk) for the same amount c. Otherwise, the peak created at pk will be counteracted by the unchanged symmetric coefficient value at pk′ after applying the inverse DFT. That is, we must per- form, as is done in this study, the operation
M ′(− uk, − vk) = M(− uk, − vk) + c (6) each time we calculate Eq. (5).
2.3 Proposed Technique for Synchronizing Peak Locations for Protection against Rotation and Scaling Attacks
In order to deal with rotation and scaling attacks, an extra local peak Ps, called the synchronization peak, is created in the DFT domain to serve as a signal for synchronizing the peak locations P = {p1, p2, …, pn×m} mentioned previously in a way described later.
Ps is embedded into the middle frequency band B as well at a location ps described by ps = (us, vs) = (rscosθs, rssinθs), (7) where rs is selected to be larger than R2 (the outer radius of the band B) and θs is a pre-selected angle value. We also apply Eqs. (5) and (6) to adjust the DCT value of Ps
and that of its symmetric version so that they become peak values.
We now describe how we use the synchronization peak Ps in the proposed water- mark extraction process to calculate the rotation angle of a suspicious stego-image which possibly suffers from a rotation attack. Because of the DFT properties mentioned previ- ously and illustrated in Fig. 2, if a stego-image is rotated, the location of Ps will also change with the same rotation angle. We can thus calculate the new angle θs′ of Ps and take the difference ∆θ between θs′ and θs to decide whether the stego-image has been rotated in the following way: if ∆θ ≠ 0, then it has been rotated; otherwise, not. If the stego-image is found to have been rotated, then we find the angles θk′ of the other local peaks and recover their original angles θk′′ as follows:
θk′′ = θk′ − ∆θ. (8) On the other hand, as mentioned previously, if a stego-image is rescaled, the DFT coefficient values are unaffected. This means that the radii of the local peaks will not be changed.
2.4 Proposed Technique for Automatically Adjusting Threshold Value for Extracting a Watermark
To extract an embedded watermark in a reproduced image, we have to detect, using a threshold value T, the local peaks in the DFT domain of the image to recover the code representing the watermark. Because the reproduced image has pixel-value changes which degrade the original image quality and counteract the values of the embedded peaks, the threshold value T is difficult to determine. The way adopted in this study to solve this problem is to select first an initial value T0 for T and then adjust T to get a re- fined value in the ith iteration according to the following rule:
1 1
if , if ,
i i
i
i i
T e h
T T e h
δ δ
−
−
+ >
= − < (9)
where Ti is the value for T in the ith iteration, h is the previously-mentioned number of embedded peaks of each code, ei is the number of the peaks detected using the threshold
Ti-1, and δ is a pre-selected constant. This means that if the number of detected peaks is larger than the number of embedded peaks, then the threshold value is incremented by the amount δ to reduce the number of detected peaks in the next iteration, and vice versa.
The iterations stop at the moment when the number of detected peaks equals h. The de- tected peaks are then decoded to recover the embedded watermark value w.
3. WATERMARK EMBEDDING PROCESS
In the proposed watermark embedding process, first we rescale an input image to obtain a pre-selected M × M square image, where M is a radix-2 number. Next, we use radix-2 Fast Fourier Transform (FFT) to transform the input image into the DFT domain in a fast way. Then, we use the DFT domains of the red and blue channels of the input image to embed a series-number watermark. The watermark is transformed into a bit stream, which is then divided into two halves. Each half is transformed back to obtain an integer that serves as a smaller watermark to be embedded in one of the red and blue color channels according to the idea described in the previous section. The detailed algo- rithm for this process is given below.
Algorithm 1 Watermark embedding process Input: a color image C and a watermark W.
Output: a stego-image S.
Step 1: Rescale C to get an M × M square image C ′, where M is a radix-2 number.
Step 2: Transform the red and blue channels of C ′ into the frequency domain by means of the DFT to get Cr′ and Cb′.
Step 3: Transform W into a binary stream, divide the result equally into two substreams, and transform them back into two integers Wr and Wb.
Step 4: Embed Wr as a watermark W ′ into Cr′ by performing the following operations.
4.1 Decide a set of radii R = {r1, r2, …, rn} for n equally-spaced concentric circular stripes in the middle band B of the frequency domain between two pre-selected circles with radii R1 and R2, with R1 < R2.
4.2 Decide m angles Θ = {θ1, θ2, …, θm} equally distributed in the range from 0° to 180°, and take to be m × n.
4.3 Obtain embeddable positions P = {p1, p2, …, p} with pk (k = 1, 2, …, ) being located at (ricosθj, risinθj) and i and j being such that k = (i − 1) × m + j. Obtain also the positions Q = {q1, q2, …, q} symmetric to P with each qk being located at the symmetric location of pk.
4.4 Apply the combinatorial operation mentioned previously to get g codes R = {r1, r2, …, rg}, with each code rk (k = 1, 2, …, g) specifying a set of peak locations, where g = C(, h) with h = /2.
4.5 According to the value w of W′, take rw out of R, and adjust the coefficient value at each location within rw and that of its symmetric location as local peaks by Eqs.
(5) and (6).
4.6 Add a synchronization peak Ps according to the scheme described in section 2.3.
Step 5: Embed Wb as a watermark W′ into Cb′ in a similar way to the above step.
Step 6: Transform Cr′ and Cb′ back into the spatial domain by the inverse DFT.
Step 7: Rescale C′ to the original size of C.
Step 8: Take the final result as the desired stego-image S.
4. WATERMARK EXTRACTION PROCESS
In the proposed watermark extraction process, no information besides the stego- image under suspicion is needed as the input. The stego-image is rescaled to obtain a square image of the pre-selected size M × M, where M is the radix-2 number mentioned previously. The red and blue channels are transformed into the DFT domain by using the FFT. Because of the symmetric property of the DFT coefficient values specified in sec- tion 2.1, we only need to detect local peaks within the range of the upper-half Fourier spectrum image. After all the peaks have been collected, a detected peak with the largest radius is taken as the synchronization peak Ps, which is then used to synchronize the other peak locations. Then, the angles of the remaining h peaks in P = {p1, p2, …, ph} are reconstructed according to Eq. (8) to get their new locations P′ = {p′1, p′2, …, p′h}.
Also, we separate the ring area of the middle frequency band B between the two cir- cles with the previously-mentioned radii R1 and R2 into n equally-spaced concentric cir- cles and into m angle ranges to make B a set of sectors D = {d1, d2, …, d}, where = m
× n , as shown in Fig. 5. Then, P′ and D are compared to collect h sectors to form a set A as follows:
for all k = 1, 2, …, and i = 1, 2, …, h,
if pi′ falls in dk, then regard dk as being in A. (10)
This means that, if there is a peak within an area dk, then dk is taken to into A. Fi- nally, we use a combinatorial operation with D and h as inputs to get g kinds of possible codes R′ = {r1′, r2′, …, rg′}, where g = C(, h) with h = /2. Then, we check if there is any rj′ which is equal to A with 1 ≤ j ≤ g. If there is, the integer number j is then taken as the extracted watermark value. The detailed watermark extraction process is described by the following algorithm.
R’1 R’2
d1 d2 d3 d4
d5 d6
Fig. 5. The middle frequency band is divided into concentric sectors.
Algorithm 2 Watermark extraction process Input: a stego-image S.
Output: a watermark W.
Step 1: Rescale S to get an M × M square image S′ where M is a radix-2 number.
Step 2: Transform the red and blue color channels of S′ into the DFT domain to get Fou- rier spectra Sr′ and Sb′.
Stpe 3: Detect peaks within the upper-half areas of Sr′ and Sb′, respectively, by perform- ing the following operations.
3.1 Use an adjusted threshold value T to detect peaks in the middle-frequency band according to the method described in section 2.4.
3.2 Select the peak with the largest radius as the synchronization peak and calculate its angle change ∆θ with respect to the original angle of the synchronization peak.
3.3 Reconstruct the angles of the remaining h peaks using Eq. (8) to get their new locations P′ = {p′1, p′2, …, p′h}.
3.4 Divide the middle frequency band between R1 and R2 into n equally-spaced con- centric circles and into m angle ranges to change the middle band into several sectors D = {d1, d2, …, d}, where = m × n.
3.5 Compare P′ and D to select h areas as a set A according to the method specified by Eq. (10), where h = /2.
3.6 Apply a combinatorial operation to get g codes R′ = {r1′, r2′, …, rg′}, with each code rj′ (j = 1, 2, …, g) specifying a set of h areas of D, where g = C(, h). Then, check if there is any rj′ equal to A with 1 ≤ j ≤ g. If there is, take j as the desired serial number.
Step 4: Link two serial numbers in binary form from Sr′ and Sb′ sequentially.
Step 5: Transform the linked bit stream into a serial number.
Step 6: Take the final result as the desired watermark W.
5. EXPERIMENTAL RESULTS
Some experimental results obtained by applying the proposed method will be dis- cussed in this section. A serial number 888 was used as a watermark. The factor c that determines the embedded watermark strength was set to be 1.5. Fig. 6 shows an input
Fig. 6. The input image “Lena.”
image of size 512 × 512. Fig. 7 (a) shows the stego-image of Fig. 5 after embedding the watermark. In addition, Figs. 7 (b) and (c) show the corresponding Fourier spectrum im- age and the detected locations of the peaks, indicated by red and green marks. The green mark is the synchronization peak. Fig. 7 (d) shows a reproduced version of Fig. 7 (a) obtained by printing (a) at 600dpi on an HP Color LaserJet 5500 laser printer and scan- ning the result at 100dpi using a Microtech Scanmaker 9800XL flatbed scanner. And the corresponding Fourier spectrum image and the detected peak locations are shown in Figs.
7 (e) and (f), respectively. The embedded peaks can be successfully detected in our ex- periments.
(a) Stego-image “Lena.” (d) Reproduced image with a resolution of 100dpi.
(b) Fourier spectrum of (a). (e) Fourier spectrum of (d).
(c) Peak locations of (b). (f) Peak locations of (e).
Fig. 7. Output stego-images with the watermark, reproduced image, and Fourier spectra.
Figs. 8 (a) and (b) show two other color images, both of size 512 × 512. The corre- sponding stego-images after embedding the watermark are shown in Figs. 8 (c) and (d), respectively. The corresponding PSNR values are shown in Table 1, which shows that the quality of each of the stego-images is still good. The embedded watermark is imper- ceptible to the human eye.
(a) Image “Pepper.” (c) Stego-image after embedding the watermark in (a).
(b) Image “Jet.” (d) Stego-image after embedding the watermark in (b).
Fig. 8. Input images and stego-images with watermark.
Table 1. The PSNR values of recovered images after embedding watermarks.
Lena Pepper Jet
PSNR 33.0 33.0 32.4
In addition, two reproduced images of Figs. 8 (a) and (b) are shown in Figs. 9 (a) and (b), with resolutions of 100dpi and 150dpi, respectively. The watermarks can be ex- tracted successfully from each of these images by the proposed watermark extraction process in our experiments.
Finally, we tested 120 reproduced images, which were generated from twenty digi- tal color images by printing at 600dpi and scanning at 85dpi, 100dpi, 150dpi, 200dpi, 250dpi, and 300dpi, respectively. The probability of successfully extracting the water- marks was 91.67%. The errors were mainly due to the use of improper image resolutions when rescanning the printed versions of the original input images.
(a) Reproduced image with a resolu- tion of 100dpi.
(b) Reproduced image with a resolu- tion of 150dpi.
Fig. 9. Some reproduced images of different quality levels.
6. CONCLUSIONS
In this paper, we have proposed a method for embedding a watermark into a color image by coding and synchronization of coefficient-value peak locations in the DFT do- main. According to the properties of the image coefficients in the DFT domain, we em- bed the watermark by creating peaks circularly and symmetrically in the middle frequen- cies. We also use a combinatorial operation to code the peak locations. In addition, an extra synchronization peak is added to synchronize the peak locations. In the watermark extraction process, the positions of the coefficient-value peaks are detected and mapped into a combinatorial operation to get a watermark. The embedded watermark is shown to be robust and able to survive print-and-scan operations. The proposed method can achieve the goal of protecting the image copyright of the owner.
However, by the proposed watermark embedding method, the capacity of a nor- mal-size image is not large enough for hiding a common logo image. In future works, we may attempt to solve this problem.
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Yen-Chung Chiu (邱彥中) received the B.S. degree in Computer Science from National Chengchi University, Taipei, Taiwan, in 2002 and the M.S. degree in Computer and Informa- tion Science from National Chiao Tung University, Hsinchu, Taiwan, in 2004. Mr. Chiu has worked at the Foxlink Image Technology Co. in Taipei, Taiwan, as a research engineer since July, 2004. His current research interests include data hiding for image watermarking, image copyright protection, color image processing, and pattern recognition.
Wen-Hsiang Tsai (蔡文祥) received the B.S. degree in Electrical Engineering from National Taiwan University in 1973, the M.S. degree in Electrical Engineering from Brown University in 1977, and the Ph.D. degree in Electrical Engineering from Pur- due University in 1979. Dr. Tsai joined the faculty of National Chiao Tung University (NCTU) in Taiwan in November, 1979, and was an NCTU Chair Professor in the Department of Com- puter and Information Science. Since August, 2004, he has been the President of Asia University in Taiwan. At NCTU, Professor Tsai was the Head of the Department of Computer and Informa- tion Science from 1984 to 1988, the Dean of General Affairs from 1995 to 1996, the Dean of Academic Affairs from 1999 to 2001, and Vice President from 2001 to 2004. He served as the Chairman of the Chinese Image Processing and Pattern Recognition Soci- ety of Taiwan from 1999 to 2000. He has been the Editor of several academic journals, including Journal of the Chinese Engineers, International Journal of Pattern Recognition and Artificial Intelligence, Journal of Information Science and Engineering, and Pattern Recognition. He was the Editor-in-Chief of Journal of Information Science and Engi- neering from 1998 to 2000.
Professor Tsai has received many awards, including one Distinguished Research Award, four Outstanding Research Awards, two Special Researcher Awards, and one
Outstanding Researcher Award, all from the National Science Council, between 1987 and 2001. He was the recipient of the 13th Annual Best Paper Award from the Pattern Recognition Society of the U.S.A. He also received the Academic Award form the Min- istry of Education in 2002. Finally, he was the recipient of the ISI Citation Classic Award in 2001.
Professor Tsai’s major research interests include image processing, pattern recogni- tion, computer vision, virtual reality, and information copyright and security protection.
So far he has published 311 academic papers, including 121 journal papers. Dr. Tsai is a senior member of IEEE and is currently the Chair of the Computer Society of IEEE Taipei Section in Taiwan.
