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Feature Article
Hiding Multitone Watermarks in Halftone Images Jing-Ming Guo and Yun-Fu Liu National Taiwan University of Science and Technology
The authors propose a method for embedding a multitone watermark using low computational complexity. The proposed approach can guard against reasonable cropping or print-and-scan attacks.
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D
igital halftoning1 is a technique for changing grayscale images into two-tone binary images. These halftone images resemble the original images when humans view them from a distance with low-pass filtering. Halftoning is commonly used in printing books, newspapers, and magazines, because these printing processes can only generate two tones—black and white (with and without ink). Halftoning methods include ordered dithering,1 error diffusion (EDF),2-4 least squares,5,6 and dot diffusion.7,8 Of these, EDF offers good visual quality and reasonably low computational complexity. Digital watermarks have many uses, including protecting ownership of an image, preventing the illegal use of an image without permission, and authenticating an image to verify that it hasn’t been altered. Currently, numerous methods exist that use halftones to embed watermarks. These methods primarily fall into two categories: printing security documents (such as ID cards, currency, and confidential documents), and preventing illegal duplication and forgery by further scanning these documents to digital forms. Schemes in the first category embed invisible digital data into halftone images, which we can retrieve by scanning and applying extraction algorithms. These methods include using a number of different dither cells to create a threshold pattern in the halftoning process;9 using vector quantization to embed watermarks into the most-significant bit or least-significant bit of EDF images;10,11 using modified data-hiding error diffusion to embed
1070-986X/10/$26.00 c 2010 IEEE
data into EDF images;12 embedding a message into dithering images using a pair of conjugate halftone screens;13 using smart pair-toggling to embed data into error diffusion images,14 and combining the BCH error-correcting code with data-hiding techniques.15 Methods in the second category embed hidden visual patterns into two or more halftone images so that the viewer perceives them directly when we overlay the halftone images upon each other. These techniques include stochastic screen patterns16 and stochastic EDF.17 The stochastic EDF method hides data by creating a different-phased version of a stochastic EDF image, but leads to poor contrast of the hidden pattern within the image’s high-texture region. Pei and Guo18 proposed noise-balanced error diffusion (NBEDF) to improve the poor contrast problem inherently found in previous attempts.17 However, these methods involve embedding bilevel watermarks. In contrast, we present a method called generalized NBEDF. By ‘‘generalized’’ we mean that we can embed a multitoned grayscale watermark in a host image. Hence, with GNBEDF, embedding a binary watermark is simply a special case of a multitone grayscale watermark. We also propose a single-image, decodable GNBEDF (SID-GNBEDF) to overcome the problem of only having one embedded image available in the decoder. To our knowledge, no other method exists that uses a multitone watermark embedded in halftone images. Most prior work appears to involve a binary watermark that’s embedded in multitone host images. Some methods, however, do embed a multitone watermark in multitone host images.19-23
Multitone watermark embedding Creating and embedding a successful multitone watermark using halftones requires multiple steps. To begin with, we must create two halftone images using two different diffusion methods (the standard method and GNBEDF). We explain the process in greater detail in the following sections. Standard error diffusion Let’s begin by defining standard EDF, because it’s a key element in our overall process. Here we define 255 as a white pixel and 0 as a black pixel. The variable xi,j denotes the current input pixel value and x0i,j denotes the diffused error
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sum added up from neighboring processed pixels. The variable bi,j denotes binary output at position (i, j) using Jarvis’ EDF kernel hm,n.2 The variable vi,j denotes the modified gray output and ei,j denotes the difference between the modified gray output vi,j and binary output bi,j. We show the organization of the relationships of bi,j, vi,j, and ei,j in Equations 1 and 2: 2 X 2 X
vi;j ¼ xi;j þx0i;j ; where x0i;j ¼
eiþm;jþn hm;n
m¼0 n¼0
ei;j ¼ vi;j bi;j ; where bi;j ¼
0; if vi;j < 128 255; if vi;j 128
(1) (2)
Generalized, noise-balanced error diffusion Now let’s suppose that the watermark’s size is enlarged to fit the host image’s size. We achieve the watermark for the first halftone (EDF1) by processing the original grayscale image with the standard EDF method. (Similarly, EDF2 is the watermark created in the second halftone using the GNBEDF method.) We define the variable WW as the set of locations of all the white pixels in the watermark, and WB as the set of locations of all the black pixels. Similarly, we define (EDF1)W, (EDF1)B, (EDF2)W, and (EDF2)B as white or black sets in the halftones accordingly. Equations 3 and 4 show the reorganized conditions and corresponding processes using NBEDF (note that we don’t introduce the generalizing portion until later): vi;j ¼ 8 x þ x0i;j NA ; if ði; jÞ 2 > > > i;j > < f½W and ðEDF1Þ or ½W and ðEDF1Þ g B W W B > xi;j þ x0i;j þ NA ; if ði; jÞ 2 > > > : f½WW and ðEDF1ÞW or ½WB and ðEDF1ÞB g (3)
(4) Using NBEDF allows us to print EDF1 and EDF2 onto two transparencies, and then superimpose them together to reveal the watermark pattern. If the processing position (i, j) satisfies the condition (i, j) 2 WB and (i, j) 2 (EDF1)W,
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then the corresponding position in EDF2 will be black, thus producing a black overlaid result by EDF1 and EDF2. Consequently, we add NA to the top part of Equation 3. If the processing position (i, j) satisfies the condition (i, j) 2 WW and (i, j) 2 (EDF1)W, then the corresponding position in EDF2 will be white, producing a white overlaid result by EDF1 and EDF2. Consequently, we add þNA to the bottom part of Equation 3. If the processing position (i, j) satisfies the condition (i, j) 2 WW and (i, j) 2 (EDF1)B, the overlaid result is always black, regardless of whether it’s black or white in EDF2. Consequently, we add NA to the top part of Equation 3 to receive a compensating term þNA in the neighborhood in the top part of Equation 4, increasing the probability of the neighbors becoming white. If the processing position (i, j) satisfies the condition (i, j) 2 WB and (i, j) 2 (EDF1)B, then the overlaid result is always black, regardless of whether it’s black or white in EDF2. In general, if a pixel in (i, j) 2 WB, the neighborhood is more likely to be black. Consequently, we add þNA to the bottom part of Equation 3 to receive a compensating term NA to the neighborhood in the bottom part of Equation 4. This increases the probability of the neighbors becoming black. Note that whatever positive or negative additive noise we add in Equation 3, we must also add a compensating term in Equation 4 to preserve the overall brightness. This process then generalizes the two-tone watermark embedding to multitone watermark embedding. Here we show the steps for the proposed GNBEDF. First, we revise Equations 3 and 4 to the following: 8 wi;j > 0 > ; if ði; jÞ 2 ðEDF1ÞB
i;j > :xi;j þ x0i;j þ NA ; if ði; jÞ 2 ðEDF1ÞW 255 (5) 8 wi;j > > ; if ði; jÞ 2 ðEDF1ÞB > : vi;j bi;j NA ; if ði; jÞ 2 ðEDF1ÞW 255 (6)
JanuaryMarch 2010
ei;j ¼ 8 vi;j bi;j þ NA ; if ði; jÞ 2 > > > < f½WB and ðEDF1ÞW or ½WW and ðEDF1ÞB g > vi;j bi;j NA ; if ði; jÞ 2 > > : f½WW and ðEDF1ÞW or ½WB and ðEDF1ÞB g
0:10
where wi,j denotes a grayscale pixel of multitone watermark at position (i, j). Notably, although the watermark is multitoned, the embedded EDF1 and EDF2 remain in binary fashion.
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Table 1. Comparison of sample pixel values with corresponding changes in variables from a watermark created using our process, based on the top parts of Equations 5 and 6. Likelihood that neighboring wij
EDF1ij
vij
eij
pixels will be black
1
Black
þNA (1 1/255)
NA (1 1/255)
Approximately (1 1/255)
80
Black
þNA (1 80/255)
NA (1 80/255)
Approximately (1 80/255)
170
Black
þNA (1 170/255)
NA (1 170/255)
Approximately (1 170/255)
254
Black
þNA (1 254/255)
NA (1 254/255)
Approximately (1 254/255)
Table 2. Comparison of sample pixel values with corresponding changes in variables from a watermark created using our process, based on the bottom parts of Equations 5 and 6. EDF1ij
vij
eij
Likelihood of white pixels
1
White
þNA (1/255)
NA (1/255)
Approximately (1/255)
80
White
þNA (80/255)
NA (80/255)
Approximately (80/255)
170
White
þNA (170/255)
NA (170/255)
Approximately (170/255)
254
White
þNA (254/255)
NA (254/255)
Approximately (254/255)
wij
Tables 1 and 2 present pixel examples from Equations 5 and 6. Table 1 compares pixel values (1, 80, 170, and 254) in the watermark with corresponding modifications in variables vi,j and ei,j. If 0 or 255 occur in the watermark, then we apply the traditional NBEDF. Because (i, j) 2 (EDF1)B, the overlaid result at position (i, j) must be black. Nonetheless, we can control the likelihood of the neighborhood (i, j) 2 (EDF2)B by adding the diffused error term (NA (1 D/255)) in ei,j, where D denotes the watermark’s gray level at position (i, j). Notably, the values in the fifth column of Table 1 simply denote proportions, because we must multiply these values by NA (whose value we discuss shortly), and then diffuse it by multiplying the error kernel inherent in the EDF. Table 2 shows the case of (i, j) 2 (EDF1)W. The values in the fifth column denote the probability of (i, j) 2 (EDF2)W, which is different from the definition in the corresponding fifth column of Table 1.
IEEE MultiMedia
Generalized, noise-balanced error diffusion with a single image In some cases, the decoder might allow only one embedded image. In this section, we present an extension approach based on GNBEDF to solve this problem, called SID-GNBEDF. The GNBEDF is a causal process. Therefore, if (i, j) denotes the current process position, then the pixel at (i Dx, j Dy) was already processed by GNBEDF, where Dx and Dy denote the spatial
displacement, and are set as Dx ¼ 1 and Dy ¼ 0. The processed pixel at (i Dx, j Dy) is considered a pseudo-EDF1 for this particular process, and we apply the GNBEDF to obtain the EDF2. Consequently, Equations 5 and 6 should be modified to Equations 7 and 8, respectively: 8 wiDx ;jDy > ; xi;j þ x0i;j þ NA 1 > > > 255 > > > > < if i Dx ; j Dy ¼ ðEDF1ÞB vi;j ¼ > > x þ x0 þ N wiDx ;jDy ; > A i;j > i;j > 255 > > > : if i Dx ; j Dy ¼ ðEDF1ÞW (7) 8 wiDx ;jDy > > ; > vi;j bi;j NA 1 255 > > > > > < if i Dx ; j Dy 2 ðEDF1ÞB ei;j ¼ wiD ;jD > x y > > ; vi;j bi;j NA > > 255 > > > : if i Dx ; j Dy 2 ðEDF1ÞW
(8)
The EDF2 becomes superimposed in the decoder by its displacement version (i Dx, j Dy). We then apply a Gaussian Difference (GD) approach, so that we can clearly perceive the embedded multitone watermark.
Decoding with Gaussian Difference When the watermark is bilevel, we can easily reveal the decoded result by printing the EDF1 and EDF2 on two different transparencies so that the human eye sees the decoded, superimposed result. However, when we have a
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multitoned watermark, the grayscale of the decoded watermark is difficult to discern from the overlaid transparencies (because of the high texture of the two shared images). Hence, it’s necessary to postprocess the watermark with a computer to help decode it. Figure 1 shows the GNBEDF decoding procedure, where I, W, S, and D denote the original image, watermark, superimposed image, and decoded multitone watermark, respectively. Figure 2a shows the block denoted as a standard EDF. Figure 2b shows the block denoted as the GNBEDF. We can achieve the EDF1, EDF2, and S images by following the procedures we previously outlined. Variables with a subscripted lowercase letter g, such as Sg, EDF1g, Wg, and Dg, indicate the results being processed by the 2D Gaussian filter as 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi g ðx; y Þ ¼ 2x y 1 2 1 2 2ð1 Þ
e
yy y
ðyy Þ2 þ 2 y
I
H 0 ði;jÞ ¼ Sg ði;jÞ EDF1g ði;jÞ
Generalized, noise-balanced error diffusion
Decode procedure
(9)
Threshold bi,j 128 +
1 48 (a)
3 1
hm,n * 7 5 7 5 3 5 3
Dg Wg EDF1g
Calculate correct decode rate
Figure 1. Decoding the proposed generalized, noise-balanced error diffusion.
sk ¼ T ðrk Þ ¼L
k X
Pr rj ; k ¼ 0; 1; 2; . . . ; L 1
(12)
j¼0
Noise substrating (NA) +
Figure 2. Algorithms
vi,j
Threshold 128
Noise adding (NA)
Error diffusion kernel hm,n
− ei,j
5 3 1
Sg
+
where H0 (i, j) denotes the compensated result. The overlaid result Sg is expected to be darker than EDF1g, which corresponds to those areas with dark gray levels in the watermark. Hence, subtracting both of them can eliminate the black dots corresponding to the watermark’s white background. To correctly display the decoded result, we must scale the image pixels to the positive value using Equation 11. Because this decoding procedure cannot guarantee the best output dynamic range, we apply a histogram equalization in Equation 12 over the decoded watermark H(i, j), as
x ´i,j
+
Gaussian filter
−
xi,j
vi,j
Superimposed processing
D
+
x ´i,j
S
EDF 2
W
(11)
Hði;jÞ ¼ H ði;jÞ þ jminðH ði;jÞÞj
+
W
Watermark
(10)
0
EDF 1
Standard error diffusion
where the variable m in Equation 9 denotes the mean of x or y; the variable r denotes the relation coefficient, and the variable s denotes the standard deviation. Later we’ll discuss the values of the parameters r and s, as well as the size of the filter. The overlaid result S attempts to characterize the watermark’s fluctuation. However, the original black pixels in EDF1 and EDF2 interfere with the decoded image contrast. Therefore, in Equations 10 and 11 we adopt the following GD to compensate for interferences:
xi,j
Encoder
Original image
Decoder
ðxx Þ2 x 2 x x 2 x
0
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bi,j
for (a) standard error diffusion, and (b) generalized, noisebalanced error diffusion.
+
−
Noise adding (NA) Noise substrating (NA)
ei,j
(b)
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both pairs of grayscale images, such as using EDF or ordered dithering to produce the set. In Equations 14 through 18 we use an LMS approach to derive w:
Figure 3. Least-meansquare-trained human visual filter
0.1
x-axis and y-axis stand
0.08 0.06 0.04
for pixels, and the
0.02
(7 7 pixels). The
z-axis stands for the coefficient value.
wm;n biþm;jþn
(14)
m;n2R
0 –0.02 8
X X
x^i;j ¼
2 e2i;j ¼ xi;j x^i;j 6 4 2
2
0 0
4
8
6
@e2i;j @wm;n
where Pr() denotes the probability density function of the corresponding pixel value, and L denotes the total number of possible gray level in the image. The T() denotes the transformation function; rk denotes the gray level in the decoded watermark, and sk denotes the reconstructed gray level. We can use this approach to prevent unauthorized leaking of a copyright-protected image. Consider a scenario where someone embeds different EDF2s with different watermarks. If the owner wants to prevent the EDF2 image from being accessed by unauthorized people, she can give an EDF2 to a particular person, and keep the original EDF1 image. The EDF2 contains the particular watermark. If this watermarked image gets leaked without authorization, then the owner can discover who is responsible for it by computing the watermark after superimposing EDF2 with EDF1.
¼ 2ei;j biþm;jþn
8 if wm;n > > < w m;n > if w m;n > : wm;n
(15) (16)
> wm;n;opt ; slope > 0, should be decreased < wm;n;opt ; slope < 0; should be increased
ðkþ1Þ
k wm;n ¼ wm;n þ eiþm;jþn biþm;jþn
(17)
(18)
where wi,j,opt denotes the optimum LMS coefficient, e2i;j denotes the mean square error (MSE) between xi,j and x^i;j , @ denotes partial differentiation, and m denotes the adjusting parameter used to control the convergent speed of the LMS optimum procedure, which we set at 105. Figure 3 shows the trained LMS filter. Note that this filter has some basic humanvisual-system characteristics:
the diagonal has less sensitivity than the vertical and horizontal directions, and
the center portion has the highest sensitivity Performance evaluations We evaluated the performance of our work by measuring the peak signal-to-noise ratio (PSNR) and correct decoding rate (CDR). For an image of size P Q , in Equation 13 we define the quality evaluation of halftone images as PSNR ¼ 10 log10
P Q 2552 Q h P P P
xi;j
i¼1 j¼1
P P
wm;n biþm;jþn
i2
m;n2R
(13)
IEEE MultiMedia
where xi,j is the original grayscale image, bi,j is the halftone image, wm,n is the least-meansquare (LMS)-trained coefficient at position (m, n), and R is the support region of the human visual system coefficients. In this work, we fixed R at size 7 7. We can obtain the LMS-trained filter w with psychophysical experiments.24 The other way to derive w is to use a training set and good halftone results of
and it decreases while moving away from the center. The other way of evaluating our method’s performance—CDR—determines the similarity between the original watermark and the corresponding decoded watermark. Normally, a decoded watermark’s quality is judged by the naked human eye. Therefore, first we processed the decoded and original watermarks with the Gaussian filter to imitate human vision. Note that we don’t use the LMS filter here because it’s trained for use with halftone images, and some of the watermarks had a multitone format. Hence, we used the well-known Gaussian filter in this case without loss of generality. In Equation 19, we define the CDR as
1 Dg ði; jÞ Wg ði; jÞ =255 CDR ¼ PQ 100 percent
(19)
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where D g and W g denote the Gaussianprocessed decoded watermark and the corresponding original watermark, respectively.
Experimental results We tested eight different kinds of images that measured 2048 2048 pixels. We used the well-known mandrill, milk, peppers, Tiffany, airplane, Earth, lake, and Lena sample images. Figure 4 shows the results of the NBEDF, where Figure 4a shows the original bilevel watermark. Figures 4b and 4c have a PSNR of 31.1 and 30.85 decibels (dB), which we obtained using traditional EDF and NBEDF, respectively. Figure 4d has a CDR of 92.64 percent, which we obtained by superimposing Figures 4b and 4c. Figure 4f shows the results of superimposing two totally different images from Figures 4b and 4e. The PSNR of Figure 4e is 33.34 dB and the CDR of Figure 4f is 70.98 percent. It’s interesting to note that the nose portion of the Mandrill image is black, as Figure 4d shows. The corresponding regions in Figures 4b and 4c are significantly different. This region changes drastically after superimposition. For this, we used a ramped image and bilevel watermark (as Figures 5a and 5b show) for conducting the NBEDF. Figure 5c shows the overlaid result. The middle-left region of the lower part of Figure 5c is almost entirely black. If a white pixel has the value 255 and a black pixel has the value 0, then the middle-left region of Figure 5a is less than or equal to 128, and the lower part associates to the black region of the watermark. When we overlay the EDF1 and EDF2 of Figure 5a, two groups of sufficient black pixels with inconsistent positions controlled by the additive noise NA make up almost all the black region in the middle-left region of the lower part of Figure 5c. The nose part of the Mandrill image has a value of around 128 and, as with Figure 4d, the resulting overlaid nose result is almost entirely black. Conversely, the upper parts of Figure 5c have either large or small white clusters except for the left end, because the position-consistent black pixels in EDF1 and EDF2 associate to the white region of the watermark that’s controlled by the additive noise NA. Figure 6 (next page) shows some of the results achieved by the proposed GNBEDF. Figure 6a
(a)
(b)
(c)
(d)
(e)
(f)
shows the original 256-tone watermark, and Figure 6b shows the embedded EDF2 with a PSNR of 30.99 dB. Figure 6c shows the results superimposed by Figures 4b and 6b. Obviously, the contrast is poor, making the embedded watermark difficult to reveal. Hence, we applied the proposed GD decoding to obtain Figure 6d. The quality improved significantly with a CDR of 85.48 percent. The gray levels are mostly preserved compared to the original watermark. Notably, the EDF1 and EDF2 in Figures 4b and 6b are still halftones. Figures 6e through 6h show three-tone and seven-tone decoding results with CDRs of 85.06 percent and 85.74 percent, respectively. Clearly, the original gray levels are also mostly preserved in these cases. Moreover, we were able to embed a 256-tone watermark in two totally different images, as Figures 4b and 6i show. Figure 6j shows the overlaid result. We then further enhanced the overlaid result using the proposed GD decoding, and Figure 6k shows the decoded result.
Figure 4. Experimental results of noisebalanced error diffusion (NBEDF). (a) Watermark of 2,048 2,048 pixels. (b) The first watermarked halftone (EDF1) obtained by traditional EDF. (c) The first watermarked halftone (EDF2) obtained by NBEDF. (d) Overlaid result. (e) The EDF2 obtained by NBEDF. (f ) Overlaid result.
Figure 5. Bilevel watermark embedded
(a)
into ramped image. (a) Ramped host image. (b) Bilevel watermark. (c) Overlaid result by
(b)
EDF1 and EDF2.
(c)
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Figure 6. Embedding result using the GNBEDF. (a) A 256tone watermark. (b) The EDF2 image obtained by GNBEDF. (c) Superimposed result by Figures 4b and 6b. (d) A 256-tone decoded
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
result using Gaussian Difference (GD). (e) Three-tone watermark. (f ) Threetone decoded result using GD. (g) Seventone watermark. (h) Seven-tone decoded result using GD. (i) The EDF2 image obtained by GNBEDF. (j) Superimposed result from Figures 4b and 6i. (k) Enhanced result from Figure 6j using GD.
(i)
Figure 7. Embedding result using the singleimage decodable (SID)-GNBEDF. (a) Halftone image obtained by SID-GNBEDF. (b) Superimposed result from Figure 7a with its displacement version. (c) Enhanced result using GD from Figure 7b.
(a)
(j)
The PSNR of Figure 6i is 34.38 dB, and the CDR of Figure 6k is 85.42 percent. Finally, we obtained Figure 7a with a PSNR of 30.99 dB using the SID-GNBEDF. Figure 7b shows the superimposed result. Figure 7c shows the GD-enhanced result with a CDR of 86.02 percent. We conducted extensive experiments to characterize the performance of the GNBEDF with watermarks in different tones, as Figure 8 shows. We employed 10 different watermarks and eight different host images to conduct simulations for each tone.
(b)
(c)
(k)
Figure 8a shows the average PSNR of the EDF2 versus additive noises with different watermark tones using the test images. As expected, the PSNR decreases as additive noise increases. It’s interesting that the PSNR increases with increasing tones in the watermark. Figure 8b shows the average CDR of the GDdecoded result versus additive noises with different watermark tones using the test images. The standard deviation s ¼ 0.9, and the Gaussian filter is 7 7 pixels. Experimental results indicate that a little value in additive noise can cause a significant improvement in CDR, as the left ends of the curves show. Hence, additive noise indeed plays a significant role in the GNBEDF. Figure 8c shows the average CDR versus the standard deviation with different watermark tones using the test images. On average, we achieved the best CDR with a standard deviation of around 0.9. Hence, unless specified otherwise, we adopted a standard deviation value of 0.9 in the experiments.
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Correct decoding rate
Peak signal-to-noise ratio
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0
10
20
30
40
50
60
70
80
90
100
80 75 70 65 60 55 50
0
10
20
30
Additive noise
60
70
80
90
100
(b) 80 Correct decoding rate
Correct decoding rate
50
Additive noise
(a) 81 79 77 75 73 71 69 67 65 0.45
40
0.55
0.65
0.95 0.75 0.85 Standard deviation
1.05
(c)
1.15
75 70 2-tone 3-tone 7-tone 15-tone 256-tone
65 60 55 50
1×1
3×3
5×5
7 × 7 9 × 9 11 × 11 13 × 13 15 × 15 17 × 17 Gaussian filter size
(d)
Figure 8. Testing all the parameters in the proposed algorithm (using the averages from eight test images using different watermark tones). (a) The peak signal-to-noise ratio versus additive noises. (b) The correct decoding rate (CDR) versus additive noises. (c) The CDR versus standard deviations. (d) The CDR versus Gaussian filter sizes.
Figure 8d shows the CDR versus Gaussian filter sizes with different tones of watermarks. The Gaussian filter of 7 7 pixels achieves the highest CDR according to the experimental results. Filters of sizes larger than 7 7 do not significantly improve the CDR, and moreover increase the computational complexity. We therefore used a 7 7 filter for applications in this study. Figure 9 shows the decoded watermark quality achieved by different filter sizes, where s ¼ 0.9 and NA ¼ 25. Figures 9a through 9f, respectively, show the decoded watermark using Gaussian filters of 1 1 (except no Gaussian filter is involved here, because the filter only appears in instances with multiple pixels), 3 3, 5 5, 7 7, 9 9, and 11 11. Among these, Figures 9e and 9f show slightly better results than that of Figure 9d. Nonetheless, the 7 7 filter is the starting point in CDR saturation, as indicated in Figure 8d. In fact, the 7 7 filter has the same CDR when rounded to a decimal hundredth, yet the computational complexity is greatly lower than filters larger than 7 7. Hence, we fixed the Gaussian filter size at 7 7 in this study.
(a)
(b)
(c)
(d)
(e)
(f)
Figure 9. The 256-tone decoded result using different Gaussian filter mask sizes. (a) A 1 1 size, with no Gaussian filter and the correct decoding rate (CDR) ¼ 56.41 percent). (b) A 3 3 size and the CDR ¼ 83.94 percent. (c) A 5 5 size and the CDR ¼ 85.4 percent. (d) A 7 7 size and the CDR ¼ 85.48 percent. (e) A 9 9 size and the CDR ¼ 85.48 percent. (f) An 11 11 size and the CDR ¼ 85.48 percent.
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Figure 10. Cropping attack. Average correct decoding rate versus an attack with a cropping rate of 0 to 40 percent of the whole image (s ¼ 0.9 and NA ¼ 25).
mmu2010010034.3d
Correct decoding rate
[3B2-9]
scan attack. Average correct decoding rate compared to different print-and-scan resolutions (s ¼ 0.9 and NA ¼ 25).
Correct decoding rate
Figure 11. Print-and-
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85.5 85 84.5 84 83.5 83 82.5 82
0
5
10
15 20 25 30 Cropping rate
86
35
40
Scan dots per inch
84
150 600
82
300 1,200
80 78 76 74 72
150
300 Print (in dots per inch)
600
We also tested for the two most-likely forms of attacks—cropping (tampering) and printing and scanning—to analyze robustness. The cropping rates range from 0 to 40 percent in the EDF2. To avoid losing clusters of information by cropping, we pseudopermutated the watermark before embedding it. We then
repermutated the embedded EDF1 and EDF2 before using the computer to decode. Figure 10 shows the superimposed decoded results. Notably, the CDRs in Figure 10 are the averaged results of the eight testing images. The print-and-scan attack involves several configurations, namely printing at 150, 300, and 600 dpi, and scanning at 150, 300, 600, and 1,200 dpi. We found it difficult to perfectly decode the watermark, because the print-andscan procedure involves slight rotation, a dotgain darkening effect, and shifting. Additionally, the bending of the scanned result causes geometric distortions. In our experiments, we manually rerotated the scanned EDF1 and EDF2 and scaled them with Adobe Photoshop 7.0, but we decoded them automatically. Figure 11 shows the average CDR compared to different configurations of print-and-scan resolutions using eight test images. Among these, the results printed with 600 dpi were difficult to decode, because they involved serious dot gains. Figure 12 shows some decoded Lena images. Notably, because an image of 2,048 2,048 pixels printed at 150 dpi exceeds the area of an A4 paper, we printed EDF1 and EDF2 on four pieces of paper, respectively, and then superimposed them together. This explains why the visible vertical and horizontal artifacts occur in the middle of the decoded results. Overall, the experimental results demonstrate that our proposed approach can guard against reasonable attacks in protected printed halftone images.
Conclusion
(a)
(b)
(c)
(d)
(e)
(f)
This article provides a technique for a multitone watermark embedded into a halftone image, which relieves the traditional limitations of embeddable data types. A problem with this approach is that the contrast of the decoded watermark is somewhat unclear because of the interference with the original image’s texture. Thus, any solution for increasing the contrast and clarity would significantly benefit this technique. MM
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Figure 12. The 256-tone decoded result with an attack using different
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