A Multi-bit Robust Watermark for Halftone Images - Semantic Scholar
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➡ A Multi-bit Robust Watermark for Halftone Images Ming Sun Fu, Oscar C. Au* Dept. of EEE, Hong Kong Univ. of Science and Technology Clear Water Bay, Hong Kong, China. Tel: +852 2358-7053 Fax: +852 2358-1485 Email: [email protected], [email protected]*
ABSTRACT In many printer and publishing applications, it is desirable to embed data in halftone images for copyright control and authentication purposes. While intentional attacks on printed matters may not be likely, unintentional attacks such as cropping and distortion due to dirt or human writing/marking are likely. In this paper, we proposed a novel halftone image watermarking method to embed a robust, invisible, multi-bit watermark in the halftone images during halftoning while introducing minimal distortion. 1.
INTRODUCTION
Nowadays, digital images are extremely common. It is often desirable to embed data into the images as value-added content, or for copyright control and authentication purposes. Such embedded data are commonly called watermarks and the method of watermark embedding is called watermarking [1]. Most watermarks of interest are invisible. Some watermarks are fragile and some are robust. Fragile watermarks are designed to be broken easily by common image processing operations and are good for tampering detection and authentication. Robust watermarks are designed to survive hostile and/or un-intentional attack and are good for copyright control. Watermarks can also be classified as private and public watermarks. A private watermark uses the original image in the watermark decoding while a public one does not. In this paper, we are concerned about watermarking for halftone images [2]. Halftone images are binary images appearing routinely in massively distributed printed matters such as books, magazines, newspapers, as well as printouts and fax documents. It is often desirable to hide invisible watermark within the halftone images for copyright protection. There are some existing techniques for watermarking in halftone images. Some use two different dithering matrices for the halftone generation [3] such that the different statistical properties due to the two dithering matrices can be detected. Some use stochastic screen patterns [4] and conjugate halftone screens [5]. In these methods, the embedded pattern cannot be recovered with only one halftone image. It can be viewed only when two halftone images are overlaid. There are also some methods that embed watermarks in one halftone image. Assuming the original gray-scale image is not available, some hide invisible data in halftone images by forcing pixels at pseudo-random locations to toggle and use various methods to minimize the visual degradation [6].
0-7803-7965-9/03/$17.00 ©2003 IEEE
In [7], we proposed a single bit method robust to unintentional attacks such as cropping and distortion due to dirt or human writing/marking are likely. In this paper, we base on it to propose a novel Multi-bit Watermarking Error Diffusion (MWED) for halftone image that is also robust to cropping, and human markings. MWED can generate high quality halftone image. It can embed multi bit (about hundreds) in the halftone images while preserving the same visual quality and robustness compared with [7]. 2.
ERROR DIFFUSION
Error Diffusion is a halftoning technique, which can generate high quality halftone image. Error Diffusion is a causal single-pass sequential algorithm. The 2-D multi-tone image is halftoned line-by-line sequentially. In this algorithm, the past error is diffused back to the current pixel. The relationship between input and output of error diffusion can be described by the following equations (1) – (3): um,n = xm,n -
∑h
k ,l em − k , n −l
bm,n = Q(um,n) em,n =βbm,n - um,n
(1) (2) (3)
1, u m,n ≥ T0 Q (u m , n ) = 0 u m,n < T0 xm,n bm,n em,n um,n
β hk,l Q(.)
= original gray-scale image = binary halftone image = quantization error = state variable = dynamic range of the image, usually 255 = error diffusion kernel 1-bit quantization, T0 = 128 used
The error diffusion kernel controls the feedback weighting of past errors. In this paper, a typical kernel, the Jarvis[2] kernel, is used. 3.
MULTI-BIT WATERMARKING ERROR DIFFUSION (MWED)
The proposed Multi-bit Watermarking error diffusion (MWED) embeds watermark in the line correlation coefficient of the halftone image.
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ICME 2003
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➡ Consider an arbitrary 2-dimensional shape S with a corresponding “origin”. When the origin of the shape is placed at location (i, j ) of the halftone image, it defines a region S (i, j )
around (i, j ) . The local correlation coefficient Pi S, j at location (i, j ) with respect to shape S Pi S, j =
∑
( k ,l )∈S (i , j )
bk ,l mod 2
An example is T1 = 0.4 and T2 = 0.6 . One strong attribute of MWED is that when an image without watermark is subject to watermark detection, it would declare the watermark as undefined. Figure 1 is the block diagram of Multi-bit Watermarking Error Diffusion. The structure of MWED is similar to the normal error diffusion. The major difference is the Noisy Function block N(.) in which the binary output is adaptively toggled.
(4)
In Figure 1, bi , j is the “normal” output without MWED is the correlation coefficient of the halftone pixels within the region S (i, j ) . The mod 2 operation is a mapping function to map the outcomes to 2 events in an unbiased manner. The line correlation coefficient
{
Pi S = average Pi S, j , ∀j
}
(5)
is the average of all the local correlation coefficient in the same line with respect to the shape S. The watermark will be embedded in the line correlation coefficient. It is important to note that the input of line correlation coefficient includes not only the pixel in the same line, but also some previous lines. In this paper, for the sake of simplicity, the shape S is chosen to be an MxN block of pixels with its origin at the lower right corner pixel. In normal error diffusion an image, the local correlation coefficient tends to be quite random, equally likely to be 0 or 1. The local correlation coefficient behaves like a binary random variable, with a mean of 0.5 and variance of 0.25. The line correlation coefficient, or the sample mean, tends to have a binomial distribution. According to the Central Limit Theorem, the line correlation coefficient tends to have a Gaussian distribution with a mean of 0.5 and a variance of 0.25/M, where M is the total number of samples. For a 512x512 image, the effective line width is close to 500 after excluding some boundaries and the variance is 0.25 / 512 ≈ 0 . Thus, the line correlation tends to be very close to 0.5 for typical images. Our method, MWED, works by altering the line correlation coefficient to be significantly different from 0.5 to indicate the presence of a watermark. When the line correlation coefficient is significantly larger or smaller than 0.5, it can represent the presence of a “1” or “0” respectively, or vice versa. For example, we can define the relationship between the global correlation and watermark W as If P S ≤ T1 , then W = 0 . If T1 < P S < T2 , watermark undefined W = X S
If T2 ≤ P , then W = 1 .
(6)
according to error diffusion. With bi , j , the local correlation coefficient Pi S, j is computed using Eqn. (4). If the local correlation coefficient indicates the correct watermark according to (6), no change is applied. And if it gives the wrong watermark, bi , j should be toggled to give the correct watermark. However, this can introduce a huge distortion causing undesirable visual artifacts. As a result, the change would be performed only if the change is acceptable. The change can be controlled by realizing that forced toggling of bi , j is equivalent to adding a distortion to the original image pixel xi , j in Eqn. (2) to distort ui , j such that the quantized output in Eqn. (3) is reverted. xi' , j = xi , j + ∆xi , j ui' , j
=
xi' , j
+
(7)
∑h
k ,l ei − k , j − l
= ui , j + ∆xi , j
bi', j = Q(ui' , j ) = Q (ui , j + ∆xi , j )
(8) (9)
If ui , j ≥ 128 , the minimal distortion ∆xi , j required is 128 − ui , j − 1 < 0 . Otherwise, the minimal ∆xi , j required is 128 − ui , j > 0 . In MWED, if ∆xi , j < T3 for some appropriate threshold T3 , the pixel-wise distortion associated with the forced toggling is considered to be acceptable and thus the toggling would be performed. Otherwise, it would not be performed. Apart from the N(.) block, MWED is the same as regular error diffusion.
The Noisy Function is equivalent to adding noise of bounded magnitude to the input image to alter the local correlation. The parameter T3 provides the trade-off between visual quality and the deviation amount of the line correlation coefficient. A large T3 allows more local correlation coefficient to be the correct watermark bit and thus the global correlation, being the sample average, would deviate more from the normal value of 0.5 towards the correct watermark bit. But a large T3 means that the magnitude of the additive noise is large which would translate to large image degradation or lower visual quality.
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➡ 5.
IMPLEMENTATION
7.
In this paper, we use a 3x8 block for calculating coefficient. Ideally, the Maximum capacity of MWED is the total number of lines. For example, for a 512x512, we can embed about 500 bit after discarding some boundary lines. However, in practice it is essential to embed some synchronization bit and using error correction codes or spatial diversity to enhance the robustness. In the following simulations, we only embed 128-bit in a 512 x 512 image. The data bits are duplicated three times and separated by 32-bit synchronization bits. As MWED can embed 3 status according to eqn. (6), the undefined bits (X) can be used as synchronization bits. The watermark message, w, is encoded to be w’ before embedding as shown in Fig. 1. 6.
The proposed Multi-bit Watermarking Error Diffusion (MWED) provides an effective way to embed multi bits robust watermark in the halftone image. It embeds watermark in the line correlation coefficient throughout the whole image while maintains the visual quality of halftone image. The stochastic property is robust to cropping and distortion due to dirt or human writing/marking. 8.
ACKNOWLEDGEMENT
This work has been sponsored by the Research Grants Council of the Hong Kong SAR, China.
SIMULATION RESULTS
9.
Figure 2 is the halftone Lena. In the simulation, the data bit sequence is a 128-bit. For simplicity, the first 64 bits are bit-0 and the rest 64 bits are bit-1. Figure 3 is the extracted bit of halftone Lena by the captioned key. It shows that no data bit can be detected for a normal image. The MWED-watermarked halftoned Lena is shown in Figure 4. Fig. 5 shows the detection results using correct security key. It shows that all bits can be detected successfully. One of attacks, human marking, is simulated in Figure 6. The intentional or unintentional human marking covers a significant area of the image. Figure 7 shows the detection results. Although some detected bits are affected by the marking, the data sequence can still be decoded correctly through the error correction coding. These suggest that the MWED is indeed robust to human marking. When under cropping, some of embed bits are discarded by cropping, but the remaining extracted data bits are nearly unaffected by cropping. Using the synchronization bits, the embedded data bits can be detected correctly.
CONCLUSION
REFERENCES
[1] F. Mintzer, et al., "Effective and Ineffective Digital Watermarks", Proc. of IEEE Int. Conf. on Image Processing, Vol. 3, pp. 9-13, Oct. 1997. [2] R. A. Ulichney, Digital Halftoning, Cambridge, MA, MIT Press, 1987. [3] Z. Baharav, D. Shaked, "Watermarking of Dither Halftoned Images", Proc. of SPIE Security and Watermarking of Multimedia Contents, pp. 307-313, Jan 1999. [4] K.T. Knox, "Digital Watermarking Using Stochastic Screen Patterns", United States Patent Number 5,734,752. [5] S. G. Wang, "Digital Watermarking Using Conjugate Halftone Screens", United States Patent Number 5,790,703. [6] M. S. Fu, O. C. Au, “Data Hiding for Halftone Images”, IEEE Trans. on Image Processing, Vol. 11, Issue 4, pp. 477-484, April 2002. [7] M. S. Fu, O. C. Au, “A robust public watermark for halftone images”, Proc. of IEEE Int. Sym. on Circuits and Systems, Vol. 3, pp. 639-642, 2002.
Figure 1 Block Diagram of Multi-bit Watermarking Error Diffusion
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Figure 2 Halftone Lena
Figure 3 Detection results of Halftone Lena
Figure 4 Watermarked Halftone Lena by MWED
Figure 5 Detection results of Fig. 4
Figure 6 Corrupted Watermarked Halftone Lena by MWED
Figure 7 Detection results of Fig. 6
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➡ A Multi-bit Robust Watermark for Halftone Images Ming Sun Fu, Oscar C. Au* Dept. of EEE, Hong Kong Univ. of Science and Technology Clear Water Bay, Hong Kong, China. Tel: +852 2358-7053 Fax: +852 2358-1485 Email: [email protected], [email protected]*
ABSTRACT In many printer and publishing applications, it is desirable to embed data in halftone images for copyright control and authentication purposes. While intentional attacks on printed matters may not be likely, unintentional attacks such as cropping and distortion due to dirt or human writing/marking are likely. In this paper, we proposed a novel halftone image watermarking method to embed a robust, invisible, multi-bit watermark in the halftone images during halftoning while introducing minimal distortion. 1.
INTRODUCTION
Nowadays, digital images are extremely common. It is often desirable to embed data into the images as value-added content, or for copyright control and authentication purposes. Such embedded data are commonly called watermarks and the method of watermark embedding is called watermarking [1]. Most watermarks of interest are invisible. Some watermarks are fragile and some are robust. Fragile watermarks are designed to be broken easily by common image processing operations and are good for tampering detection and authentication. Robust watermarks are designed to survive hostile and/or un-intentional attack and are good for copyright control. Watermarks can also be classified as private and public watermarks. A private watermark uses the original image in the watermark decoding while a public one does not. In this paper, we are concerned about watermarking for halftone images [2]. Halftone images are binary images appearing routinely in massively distributed printed matters such as books, magazines, newspapers, as well as printouts and fax documents. It is often desirable to hide invisible watermark within the halftone images for copyright protection. There are some existing techniques for watermarking in halftone images. Some use two different dithering matrices for the halftone generation [3] such that the different statistical properties due to the two dithering matrices can be detected. Some use stochastic screen patterns [4] and conjugate halftone screens [5]. In these methods, the embedded pattern cannot be recovered with only one halftone image. It can be viewed only when two halftone images are overlaid. There are also some methods that embed watermarks in one halftone image. Assuming the original gray-scale image is not available, some hide invisible data in halftone images by forcing pixels at pseudo-random locations to toggle and use various methods to minimize the visual degradation [6].
0-7803-7965-9/03/$17.00 ©2003 IEEE
In [7], we proposed a single bit method robust to unintentional attacks such as cropping and distortion due to dirt or human writing/marking are likely. In this paper, we base on it to propose a novel Multi-bit Watermarking Error Diffusion (MWED) for halftone image that is also robust to cropping, and human markings. MWED can generate high quality halftone image. It can embed multi bit (about hundreds) in the halftone images while preserving the same visual quality and robustness compared with [7]. 2.
ERROR DIFFUSION
Error Diffusion is a halftoning technique, which can generate high quality halftone image. Error Diffusion is a causal single-pass sequential algorithm. The 2-D multi-tone image is halftoned line-by-line sequentially. In this algorithm, the past error is diffused back to the current pixel. The relationship between input and output of error diffusion can be described by the following equations (1) – (3): um,n = xm,n -
∑h
k ,l em − k , n −l
bm,n = Q(um,n) em,n =βbm,n - um,n
(1) (2) (3)
1, u m,n ≥ T0 Q (u m , n ) = 0 u m,n < T0 xm,n bm,n em,n um,n
β hk,l Q(.)
= original gray-scale image = binary halftone image = quantization error = state variable = dynamic range of the image, usually 255 = error diffusion kernel 1-bit quantization, T0 = 128 used
The error diffusion kernel controls the feedback weighting of past errors. In this paper, a typical kernel, the Jarvis[2] kernel, is used. 3.
MULTI-BIT WATERMARKING ERROR DIFFUSION (MWED)
The proposed Multi-bit Watermarking error diffusion (MWED) embeds watermark in the line correlation coefficient of the halftone image.
I - 213
ICME 2003
➡
➡ Consider an arbitrary 2-dimensional shape S with a corresponding “origin”. When the origin of the shape is placed at location (i, j ) of the halftone image, it defines a region S (i, j )
around (i, j ) . The local correlation coefficient Pi S, j at location (i, j ) with respect to shape S Pi S, j =
∑
( k ,l )∈S (i , j )
bk ,l mod 2
An example is T1 = 0.4 and T2 = 0.6 . One strong attribute of MWED is that when an image without watermark is subject to watermark detection, it would declare the watermark as undefined. Figure 1 is the block diagram of Multi-bit Watermarking Error Diffusion. The structure of MWED is similar to the normal error diffusion. The major difference is the Noisy Function block N(.) in which the binary output is adaptively toggled.
(4)
In Figure 1, bi , j is the “normal” output without MWED is the correlation coefficient of the halftone pixels within the region S (i, j ) . The mod 2 operation is a mapping function to map the outcomes to 2 events in an unbiased manner. The line correlation coefficient
{
Pi S = average Pi S, j , ∀j
}
(5)
is the average of all the local correlation coefficient in the same line with respect to the shape S. The watermark will be embedded in the line correlation coefficient. It is important to note that the input of line correlation coefficient includes not only the pixel in the same line, but also some previous lines. In this paper, for the sake of simplicity, the shape S is chosen to be an MxN block of pixels with its origin at the lower right corner pixel. In normal error diffusion an image, the local correlation coefficient tends to be quite random, equally likely to be 0 or 1. The local correlation coefficient behaves like a binary random variable, with a mean of 0.5 and variance of 0.25. The line correlation coefficient, or the sample mean, tends to have a binomial distribution. According to the Central Limit Theorem, the line correlation coefficient tends to have a Gaussian distribution with a mean of 0.5 and a variance of 0.25/M, where M is the total number of samples. For a 512x512 image, the effective line width is close to 500 after excluding some boundaries and the variance is 0.25 / 512 ≈ 0 . Thus, the line correlation tends to be very close to 0.5 for typical images. Our method, MWED, works by altering the line correlation coefficient to be significantly different from 0.5 to indicate the presence of a watermark. When the line correlation coefficient is significantly larger or smaller than 0.5, it can represent the presence of a “1” or “0” respectively, or vice versa. For example, we can define the relationship between the global correlation and watermark W as If P S ≤ T1 , then W = 0 . If T1 < P S < T2 , watermark undefined W = X S
If T2 ≤ P , then W = 1 .
(6)
according to error diffusion. With bi , j , the local correlation coefficient Pi S, j is computed using Eqn. (4). If the local correlation coefficient indicates the correct watermark according to (6), no change is applied. And if it gives the wrong watermark, bi , j should be toggled to give the correct watermark. However, this can introduce a huge distortion causing undesirable visual artifacts. As a result, the change would be performed only if the change is acceptable. The change can be controlled by realizing that forced toggling of bi , j is equivalent to adding a distortion to the original image pixel xi , j in Eqn. (2) to distort ui , j such that the quantized output in Eqn. (3) is reverted. xi' , j = xi , j + ∆xi , j ui' , j
=
xi' , j
+
(7)
∑h
k ,l ei − k , j − l
= ui , j + ∆xi , j
bi', j = Q(ui' , j ) = Q (ui , j + ∆xi , j )
(8) (9)
If ui , j ≥ 128 , the minimal distortion ∆xi , j required is 128 − ui , j − 1 < 0 . Otherwise, the minimal ∆xi , j required is 128 − ui , j > 0 . In MWED, if ∆xi , j < T3 for some appropriate threshold T3 , the pixel-wise distortion associated with the forced toggling is considered to be acceptable and thus the toggling would be performed. Otherwise, it would not be performed. Apart from the N(.) block, MWED is the same as regular error diffusion.
The Noisy Function is equivalent to adding noise of bounded magnitude to the input image to alter the local correlation. The parameter T3 provides the trade-off between visual quality and the deviation amount of the line correlation coefficient. A large T3 allows more local correlation coefficient to be the correct watermark bit and thus the global correlation, being the sample average, would deviate more from the normal value of 0.5 towards the correct watermark bit. But a large T3 means that the magnitude of the additive noise is large which would translate to large image degradation or lower visual quality.
I - 214
➡
➡ 5.
IMPLEMENTATION
7.
In this paper, we use a 3x8 block for calculating coefficient. Ideally, the Maximum capacity of MWED is the total number of lines. For example, for a 512x512, we can embed about 500 bit after discarding some boundary lines. However, in practice it is essential to embed some synchronization bit and using error correction codes or spatial diversity to enhance the robustness. In the following simulations, we only embed 128-bit in a 512 x 512 image. The data bits are duplicated three times and separated by 32-bit synchronization bits. As MWED can embed 3 status according to eqn. (6), the undefined bits (X) can be used as synchronization bits. The watermark message, w, is encoded to be w’ before embedding as shown in Fig. 1. 6.
The proposed Multi-bit Watermarking Error Diffusion (MWED) provides an effective way to embed multi bits robust watermark in the halftone image. It embeds watermark in the line correlation coefficient throughout the whole image while maintains the visual quality of halftone image. The stochastic property is robust to cropping and distortion due to dirt or human writing/marking. 8.
ACKNOWLEDGEMENT
This work has been sponsored by the Research Grants Council of the Hong Kong SAR, China.
SIMULATION RESULTS
9.
Figure 2 is the halftone Lena. In the simulation, the data bit sequence is a 128-bit. For simplicity, the first 64 bits are bit-0 and the rest 64 bits are bit-1. Figure 3 is the extracted bit of halftone Lena by the captioned key. It shows that no data bit can be detected for a normal image. The MWED-watermarked halftoned Lena is shown in Figure 4. Fig. 5 shows the detection results using correct security key. It shows that all bits can be detected successfully. One of attacks, human marking, is simulated in Figure 6. The intentional or unintentional human marking covers a significant area of the image. Figure 7 shows the detection results. Although some detected bits are affected by the marking, the data sequence can still be decoded correctly through the error correction coding. These suggest that the MWED is indeed robust to human marking. When under cropping, some of embed bits are discarded by cropping, but the remaining extracted data bits are nearly unaffected by cropping. Using the synchronization bits, the embedded data bits can be detected correctly.
CONCLUSION
REFERENCES
[1] F. Mintzer, et al., "Effective and Ineffective Digital Watermarks", Proc. of IEEE Int. Conf. on Image Processing, Vol. 3, pp. 9-13, Oct. 1997. [2] R. A. Ulichney, Digital Halftoning, Cambridge, MA, MIT Press, 1987. [3] Z. Baharav, D. Shaked, "Watermarking of Dither Halftoned Images", Proc. of SPIE Security and Watermarking of Multimedia Contents, pp. 307-313, Jan 1999. [4] K.T. Knox, "Digital Watermarking Using Stochastic Screen Patterns", United States Patent Number 5,734,752. [5] S. G. Wang, "Digital Watermarking Using Conjugate Halftone Screens", United States Patent Number 5,790,703. [6] M. S. Fu, O. C. Au, “Data Hiding for Halftone Images”, IEEE Trans. on Image Processing, Vol. 11, Issue 4, pp. 477-484, April 2002. [7] M. S. Fu, O. C. Au, “A robust public watermark for halftone images”, Proc. of IEEE Int. Sym. on Circuits and Systems, Vol. 3, pp. 639-642, 2002.
Figure 1 Block Diagram of Multi-bit Watermarking Error Diffusion
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Figure 2 Halftone Lena
Figure 3 Detection results of Halftone Lena
Figure 4 Watermarked Halftone Lena by MWED
Figure 5 Detection results of Fig. 4
Figure 6 Corrupted Watermarked Halftone Lena by MWED
Figure 7 Detection results of Fig. 6
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