Watermarking in halftone images with parity-matched error diffusion

Signal Processing 91 (2011) 126–135

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Watermarking in halftone images with parity-matched error diffusion Jing-Ming Guo a,n, Soo-Chang Pei b, Hua Lee c a b c

Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan, R.O.C Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan, R.O.C. Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106-9560, USA

a r t i c l e i n f o

abstract

Article history: Received 2 September 2009 Received in revised form 11 June 2010 Accepted 17 June 2010 Available online 23 June 2010

In this paper, a halftone watermarking technique of high watermark rate, robustness, and watermark-rate flexibility is presented. This technique, namely the parity-matched error diffusion (PMEDF) method, is capable of achieving an embedded watermark rate as high as 6.25–25% with good image quality and without the need for the original image as the reference for the decoding. The proposed PMEDF method employs the high efficient parity-matching strategy to spread a watermark bit to each pixel of a block of the host image. Thus, the majority voting mechanism can be applied for decoding to achieve an advantage of high robustness. As documented in the experimental results, this technique is capable of guarding against degradation, due to cropping, tampering, as well as print-and-scan process in error-diffused halftone images. & 2010 Elsevier B.V. All rights reserved.

Keywords: Halftone Ordered dithering Error diffusion Least-squares Parity-matched error diffusion

1. Introduction The objective of digital halftoning [1] is to produce two-tone texture patterns as approximations of the original multi-tone images. Through the lowpass nature of the human visual system, which filters out the highfrequency artifacts, halftone images preserve a significant level of an original information content. The technique is widely used in computer printouts, printed books, newspapers, and magazines, because these printing processes operate largely in the black-and-white format. There exist various halftone methods and the most common ones are the methods based on ordered dithering [1], error diffusion [2], and least-square [3]. Among these, error diffusion is known for good visual quality with an adequate computational complexity.

n Corresponding author. Tel.: + 1 886 2 27303241; fax: + 1 886 2 27376699. E-mail addresses: [email protected] (J.-M. Guo), [email protected] (S.-C. Pei), [email protected] (H. Lee).

0165-1684/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.sigpro.2010.06.017

Watermarking and data hiding have many interesting applications, including protecting ownership rights of an image, protecting against the use of an image without permission, and authenticating an image to prove that it has not been altered. Numerous methods, applying halftones to embed watermarks, have been studied for printing security documents such as ID card, currencies, and confidential documents, to guard against illegal duplication and forgery. The challenging problem of watermarking in halftone images is to produce a robust scheme, capable of withstanding distortions, due to cropping, tampering, and print-and-scan, while increasing the embedding capacity, maintaining the embedding image quality, and reducing the computational complexity. In general, these methods can be divided into two categories. Techniques of the first category embed invisible digital data into halftone images, which can be retrieved by using extraction algorithms on the scanned images. Comparing to the methods in the other category, the main advantages of this type of methods are that the embedded information can be extracted from one single embedded image. And, since the decoding is executed

J.-M. Guo et al. / Signal Processing 91 (2011) 126–135

with only one embedded image, the robustness is generally higher than the methods in category two, where the two embedded images must have good alignments in order to avoid unsynchronized problems. The proposed parity-matched error diffusion (PMEDF) is in this category. Here we will first provide a general overview of the work in this category. Rosen and Javidi [4] employ an iteration-trained approach to embed watermark into a dithered halftone image. However, the iteration process and Fourier transformations are required to produce the temporary phase and correction function, which result in high computational complexity and makes it difficult for real-time implementation. In [5], the concept of vector quantization (VQ) is employed to embed watermarks into multilevel error-diffused images. However, the watermark is limited to the low bit-depth halftone version of the original host image. In [6], a Modified Data Hiding Error Diffusion (MDHED) method is proposed to embed data into error diffusion images. Yet, the robustness was lacking for practical print-and-scan applications. In [7], data hiding and authentication schemes are proposed based on halftoning and coordinate projection. The technique is capable of embedding images of the same size and similar bit depth into the cover image against compression. It can also detect, localize, as well as repair the tampered area of an image. However, there is no discussion regarding robustness in this work. Kim and Afif [8] presented a cryptographically secure authentication–watermarking technique for halftone and binary images. The method selects a set of pseudo-random pixels in the image, clears them, and calculates the digital signature of the resulting image, then inserts the resulting code into the selected random pixels. The method can detect the alteration of one single pixel in an embedded image, but cannot locate an alteration exactly. Chen and Pan [9] proposed a tamper-detection method to locate the tampered areas. The method divides the host image into blocks, and each block is then scrambled into codestreams. Then the MD5 and RSA algorithms are applied to the code-streams to generate encrypted signed messages. The messages are hidden in the blocks, and in the decoder, the decrypted information is compared with the tampered image to locate the attacked area. Because the detected tampered areas are not precise, when more pixels are tampered along vertical or horizontal lines, this method is capable of addressing only ‘‘part of the tampered areas’’. Hsu and Lu [10] proposed a high-resolution halftoning process, in which watermarking can be performed directly on grayscale images by exploiting existing robust watermarking methods. An embedded grayscale image is expanded into a high-resolution image, and is then subjected to an AM halftoning. The watermark can be detected by high-resolution inverse halftoning. The main application is to protect ‘‘expanded high-resolution’’ halftone images. Yet, in some cases, the original grayscale image itself is already of high resolution, which does not need to be expanded further. The method fails to perform well in these cases. Our research team has also made several contributions to this area. The bit-interleaving pre-processing is developed to ordered dither image to obtain pairs of sub-blocks

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with different numbers of black pixels [11]. The watermark is then embedded into the dithered image by considering switching the positions of the sub-blocks according to the bit distribution of the watermark. The advantages of the method include good quality result and flexible watermark rate. The shortcoming is the dependence of a prior knowledge of an original watermark in decoding. In [12], the high watermark rate data hiding using minimal error bit searching technique is also developed. The main advantage is the capability of achieving 33–50% watermark rate. Yet, when it comes to robust applications, the watermark rate decreases considerably. The method employs the secret sharing concept to embed watermark to a set of images in order to improve the security. The print-and-scan distortion leads to severe geometric distortions to the embedded images. Hence, an alignment in decoding can be problematic, which also translates into lower correctdecoded rates. Another watermarking scheme is developed by exploiting the superior efficiency of ordered dithering and performance of error diffusion [13]. The method produces quality images with reasonable computation complexity and robustness. The disadvantage is the lack of flexibility of watermark rate, which is highly dependent on the size of the halftone screen in the ordered dithering. Methods in the second category embed hidden visual patterns into two or more halftone images. The hidden visual patterns can be perceived directly when the halftone images are overlaid. Since the hidden information is distributed into several images, the security level is generally higher than the methods in the first category. Using visual decoding, this type of method is also advantageous of rapid decoding by human perception. These techniques include the use of stochastic screen patterns [14], stochastic error diffusion [15], conjugate error diffusion [16], conjugate error diffusion in color halftone images [17], noise-balanced error diffusion [18], and hybrid pixel-based data hiding and block-based watermarking [19]. In [19], a noise-balanced error diffusion (NBEDF) method is proposed for data hiding, and a robust watermarking decoder is also proposed using 2-D FFT and lookup table (LUT). In another paper [20], the weighted LUT (WLUT) is used to improve the decoded rate of LUT. However, the 2-D FFT is time-consuming and LUT (WLUT) involves added memory requirement. In addition, the watermarking and data hiding are two separate and unrelated techniques. This often results in added hardware complexity. The methods described above, in the second category, all have a general problem that the watermark itself is binary and does not contain detailed features. The extracted watermark contains residual patterns from the two overlaid images, and hence reduces the fidelity of the extracted watermark image. For this, Wu et al., [21] proposed the iterative isotropic algorithm via halftoning and coordinate projection to reduce the artifact caused by one-pass error diffusion. The technique is able to extract watermark with greater details and achieve multiplewatermark embedding. But the contrast of the embedded halftone images is lower. Then, Sharma and Wang

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benefit to control the embedding capacity and image quality. Moreover the low complexity parity-matched method can significantly reduce the overall computational complexity. In addition to the preliminary result [24], this paper describes the significance, analysis, and overall performance of the proposed method from the perspective of error diffusion using the eight test images as shown in Fig. 1.

proposed an interesting watermarking approach that involves controlling the phase shift in clustered dot halftones, and then printing on duplex printed documents [22]. The embedded watermark pattern is revealed when the sheet is viewed with a light source placed behind it. Their method is useful in some applications. But its watermark can only be decoded with duplex printed documents. An overall performance comparisons are summarized as in Table 1. Recently, a watermarking for a block truncation coding (BTC) compressed image is developed by cooperating ordered dithering [23]. Since the format of the bitmap in a BTC compressed result is similar to a binary halftone image, the bitmap can be used for halftone-based watermarking. For applications, where the content accuracy of the original halftone image is critical, a look-up table based reversible data hiding for error-diffused halftone images was introduced [37]. A visible watermarking scheme was also proposed by exploiting human visual system (HVS) to transform the image in binary domain into continuous-tone domain for watermark embedding. The scheme can be used in applications, where original continuous-tone images may not be available and the halftoning method is unknown [38]. In this paper, we present the parity-matched error diffusion (PMEDF) watermarking method using the block-wised majority voting strategy to improve the robustness against cropping, tampering, and print-andscan degradation processes. The additive noise used in a noise-balanced scheme can provide a user-adjustable

2. Watermarking with parity-matched error diffusion To provide an overview on error diffusion (EDF), the basic structure of an EDF is introduced in this section [25–32]. The variable bi,j is denoted as the binary output in position (i,j), and the Floyd error diffusion kernel is 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. The relationship among bi,j, vi,j and ei,j is given as vi,j ¼ xi,j þ xui,j ,

where

xui,j ¼

1 1 X X

ei þ m,j þ n  hm,n

m ¼ 0 n ¼ 1

ð1Þ ( ei,j ¼ vi,j bi,j ,

where

bi,j ¼

0

if

vi,j o128

255

if

vi,j Z128

ð2Þ

We numerically define 0 as a black pixel and 255 as a white pixel. Fig. 2(a) and (b) shows the original gray-level

Table 1 Comparisons of various methods (advantages (+ ), moderate (  ), and shortcomings (  )).

[4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18,19] [20] [21] [22] PMEDF

Quality

Robustness

Complexity

Capacity

Additional special feature (s)

 + + +   +  + +   + + + +   +

+   +   + +  + +    + +  + +

  +  + +  + + + + + + +  + + + +

+ + + + + +   +   + + + +  +  +

– Progressive Transmission – Can recover the original host image Sensitive in detecting a single pixel alteration Can detect and locate part of the tampered areas For high-resolution halftone applications – Can be applied for secret sharing application – Effective to overcome print-and-scan distortion Can be applied for secret sharing application Can be applied for secret sharing application Focus on color halftone images Can apply for data hiding and watermarking simultaneously – Multiple watermarks embedding For duplex printed documents Effective to overcome print-and-scan distortion

Fig. 1. Thumbnail of eight test images. Left to right: Lena, Mandrill, Yosemite, Paris, Airplane, Peppers, Milk, and Lake.

J.-M. Guo et al. / Signal Processing 91 (2011) 126–135

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strategy, even at high NA values, it is still capable of producing good embedded halftone images. In the same manner, when the following two conditions are met, Eqs. (1) and (2) are replaced with Eqs. (5) and (6), respectively.

Fig. 2. (a) Original 512  512 gray-level Lena image. (b) Floyd errordiffused Lena image (PSNR =35.29 dB).

image and the corresponding Floyd error-diffused halftone image with PSNR of 35.29 dB, respectively. The proposed PMEDF is introduced in detail as below. Suppose the original gray-level image xi,j of size P  Q is divided into cell blocks of size M  N. The size of a P watermark wi,j is then M  QN . An initial binary output bi,j and its surrounding pixels are set to be black. Since the error diffusion is a causal process, a pre-defined region in bi,j can be defined to include the pre-processed points (i–x,j–y). Hence, the intervals of x and y are set to 0 rxo11 and 0 ryo11, respectively. Then the parity sum as defined below is applied to this region. " !, # X Pi,j ¼ bix,jy 255 mod 2 x,y2PDR

where PDR stands for the pre-defined region. We note that, before the process reaches to the binary output at the location (i,j), bi,j remains a black pixel. The variable wW denotes the set of locations corresponding to all the white pixels in the watermark and wB denotes the black pixels. When the following two conditions are satisfied, Eqs. (1) and (2) are replaced with Eqs. (3) and (4), respectively. xi,j þ xui,j Z128: 1.       i j 2. , 2 wB AND ðPi,j ¼ 0Þ M N      i j , 2 wW AND ðPi,j ¼ 1Þ : OR M N vi,j ¼ xi,j þ xui,j NA ,

ð3Þ

ei,j ¼ vi,j bi,j þ NA ,

ð4Þ

xi,j þ xui,j o128: 1.       i j 2. , 2 wB AND ðPi,j ¼ 1Þ M N      i j , 2 wW AND ðPi,j ¼ 0Þ : OR M N vi,j ¼ xi,j þ xui,j þ NA

ð5Þ

ei,j ¼ vi,j bi,j NA

ð6Þ

To illustrate the process, the flow chart of the paritymatched error diffusion (PMEDF) method is shown in Fig. 3. To summarize, the proposed PMEDF method inherently is a one-pass processing, with extra parity evaluation and around 50% additive noise subtraction or an addition (in an average) more than ordinary error diffusion. In general, only four multiplications (when Floyd error kernel is applied) and two additions are required for a pixel processed with an error diffusion. Subsequently, it has a low computation complexity and can operate in real-time format. The PMEDF method can be illustrated as: 1. Given a host image xi,j of size P  Q and a permutated watermark wi,j with a pseudo-random key of size Q P M  N. 2. Divide the host image into blocks of size M  N.     

 i j , 2 wB 3. If xi,j þ xui,j Z 128 AND M N      i j , 2 wW AND ðPi,j ¼ 0Þ OR M N AND ðPi,j ¼ 1Þ , then vi,j ¼ xi,j þ xui,j NA and ei,j ¼ vi,j bi,j þ NA :     

 i j , 2 wB If xi,j þ xui,j o 128 AND 4. M N      i j , 2 wW AND ðPi,j ¼ 1Þ OR M N AND ðPi,j ¼ 0Þ , then vi,j ¼ xi,j þ xui,j þ NA and ei,j ¼ vi,j bi,j NA :

where the notations AND and OR stand for the logic operations, and the variable NA denotes the additive noise we apply to force the current binary output to the parity sum desired. The objective is to match the parity sum to the corresponding watermark value. The value of an additive noise NA determines the image quality, robustness, as well as correct-decoding rate. Improvement of robustness and correct-decoding rate can be achieved with a greater level of an NA. On the other hand, a greater value in NA also degrades the image quality. An objective criterion is thus introduced to determine the trade-off value of an additive noise NA. With the noise-balanced

The original watermark or the halftone image is not required during decoding. The watermark can be decoded with the equation given below. wum,n ¼

8 255, > < > :

0,

P    ½ðP x,y2PDR bix,jy =255Þmod 2=ðM  NÞ Z 0:5 i j ¼ m, ¼n M N otherwise: if

In simple terms, this can be described as the majorityvoting procedure. When most of the parity-sum values are 1, it suggests that a white pixel in the watermark was embedded into its corresponding cell of the halftone image, and vice versa. Two criteria are employed for determining whether a watermark was embedded in the

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Noise Adding (NW)

+ x i, j x 'i , j

+

v i, j

128

Noise Subtrating (NW)

wm , n

+

EDF kernel hm , n e i, j

b i, j

Threshold

-

Noise Subtrating ( NW )

Buffer

Pseudo random permutation

Parity check Noise Adding ( NW )

w *m , n

Fig. 3. Flow chart of parity-matched error diffusion.

halftone image. The first is the correct-decoding rate (DR), which is given as P 0 r i r M1 ðwi,j =255ÞYðwui,j =255Þ 0 r j r N1 DR ¼  100%, ð7Þ MN where wi,j and wui,j stand for the original watermark and the decoded watermark, and the notation Y stands for the Not exclusive OR (NXOR) operation. A higher DR value translates into higher certainty of the decoded watermark. For an image of size P  Q, the quality evaluation of halftone images is defined as PSNR ¼

P P

Q P

i¼1j¼1

P  Q  2552

2 P P xi,j  m,n2R wm,n bi þ m,j þ n

ð8Þ

where wm,n denotes the human visual system coefficient at position (m,n), and R denotes the support region of the human visual system coefficients. In this paper, we fix R at the size of 15  15. The human visual system w can be obtained by psychophysical experiments [33]. Another way to derive w is to use a training set of both pairs of gray-level images with good halftone results. The images can be produced by using an error diffusion or ordered dithering. Herein, the least-mean-square (LMS) value is utilized to formulate w in the form of X X _ x i,j ¼ ð9Þ wm,n bi þ m,j þ n , m,n2R _

e2i,j ¼ ðxi,j x i,j Þ2 , @e2i,j @wm,n (

¼ 2ei,j bi þ m,j þ n ,

if wm,n 4 wm,n,opt , slope 40, wm,n be decreased if wm,n owm,n,opt , slope o 0, wm,n be increased,

þ 1Þ ¼ wkm,n þ mei,j bi þ m,j þ n , wðk m,n

ð10Þ

ð11Þ

ð12Þ

ð13Þ

where wi,j,opt denotes an optimum LMS coefficient; e2i,j is _ an MSE between xi,j and x i,j ; and m denotes an adjusting

parameter used to control the convergent speed of an LMS optimum procedure, which is set at 10  5 in the experiments. Eight test images are employed in the training process, including Lena, Mandrill, Yosemite, Paris, Airplane, Peppers, Milk, and Lake images, as shown in Fig. 1. The Floyd error diffusion [2] and Bayer-5 dispersed-dot halftone screen [1] are used to produce the corresponding halftone training results. The filter contains basic human visual system characteristics, which includes (1) the diagonal has less sensitivity than the vertical and horizontal directions and (2) the center portion has the highest sensitivity and the sensitivity decreases as it is farther away from the center. The parameter of watermark rate is defined below as an index of the performance of watermarking Watermark rate ¼

Total bit number of the watermark : Total pixel number of the host image

ð14Þ A higher watermark rate represents more information can be embedded in host image. 3. Experimental results In this section, the proposed watermarking scheme is applied for quantitative performance evaluation. Fig. 4 shows the image quality and the correct-decoding rates under nine different levels of an additive noise. These data represent the average values of the eight tested images as shown in Fig. 1. The watermark rate of this experiment is 1.5%, corresponding to a watermark of size 64  64 embedded into a 512  512 halftone image. The additive noise at the level of 25 is an adequate experimental value, because the curve shown in Fig. 4(b) rises rapidly before 25. Beyond the value of 25, we benefit little in decoded watermark correction, and the quality decreases significantly as the noise level increases from that point on. With the additive noise of value 25, a good image quality with PSNR at 32.5 dB and high correct-decoding rate of 99.43% can be achieved simultaneously. An

J.-M. Guo et al. / Signal Processing 91 (2011) 126–135

131

120 100

Correct DR

80 60 40 Watermark noise 40

20

Watermark noise 30 Watermark noise 20

0

Watermark noise 10

0.39

1.5

6.25

25

Watermark rate

Fig. 5. Correct-decoding rates under different watermark rates and additive noises.

36 35 34 PSNR(dB)

33 32 31 30 29 28 27 Fig. 4. (a) PSNR of embedded halftone image and (b) correct-decoding rates under different additive noises.

26

Watermark noise 40 Watermark noise 30 Watermark noise 20 Watermark noise 10

0.39

1.5

6.25

25

Watermark rate Fig. 6. PSNR of embedded halftone images under different watermark rates and additive noises.

encoding method described in Section 2 employs the noise-balanced strategy. Consequently, when an additive noise is added to force the parity-matching watermark bit, additive noise of the opposite polarity is applied to compensate the neighborhood unprocessed pixels with the predefined error kernel. Thus, the average gray level of an embedded image is identical to the original host image, which is the key to the superior perceptual quality of this method. Fig. 5 shows the correct-decoding rates under four different watermark rates of 10, 20, 30, and 40. For the most critical case of an NA at 10 with 25% watermark rate, the algorithm produces correct-decoding rate of 66.16%. Fig. 6 shows the image quality under the four different watermark rates. In addition, four various additive noises are also applied for the tests. The image quality is generally degraded with an increasing watermark rate. Nonetheless, it is clear that with the proposed technique, at the same noise level the image quality does not degrade significantly even when the watermark rate is increased. This implies, with the proposed watermarking, the quality of the embedded image is mainly governed by the level of an additive noise. The kernels-alternated error diffusion method can offer a PSNR of 32.26 dB and the watermark rate of

0.39%, when a watermark of size 32  32 is embedded into a 512  512 halftone image [19]. At the same watermark rate level, the PMEDF method can achieve better quality of 33.69 dB with the Lena image. The computational complexity is also significantly lower than the conventional approaches [19], where 2-D FFT or LUT is involved. Under the same watermark rate, the PMEDF method can achieve the correct-decoding rate of 100%, comparing to 95.77% in [19]. Fig. 7 shows the image quality comparisons under various additive noise configurations. Fig. 7(a)–(c) are the embedded images with noise level of 10, 20, and 30, respectively, and the corresponding PSNR at 36.29, 34.79, and 32.78 dB, respectively. Fig. 7(d)–(f) are the corresponding decoded watermarks corresponding to the noise level of 10, 20, and 30, and the corresponding CDR at 88.87%, 98.63%, and 100%, respectively. As it can be seen that the image quality degrades and the decoded rate is improved as the noise level is increased. Fig. 8(a)–(b) shows the original watermark of sizes 64  64 and 256  256, printed at 150 dpi. Fig. 8(c)–(d) shows the embedded halftone images of PSNR at 32.6 dB and 32.08 dB, with the watermarks shown in Fig. 8(a)–(b),

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Fig. 7. Image quality comparisons under various additive noise configurations. (a)–(c) Embedded images with noise =10, 20, and 30, respectively, and the corresponding PSNR= 36.29, 34.79 dB, and 32.78, respectively. (d)–(f) Decoded watermarks with noise= 10, 20, and 30, respectively, and the corresponding CDR= 88.87%, 98.63%, and 100%, respectively.

and printed at 300 dpi. Fig. 8(e)–(f) shows the decoded watermarks from Fig. 8(c)–(d) with the correct-decoding rate of 99.29% and 80.03%, respectively. The additive noise NA of value 25 is applied in this experiment. Subsequently, we perform experiments to demonstrate the robustness of this proposed technique. Fig. 9(a) shows one quarter cropping of Fig. 8(d). The corresponding decoded watermark is shown in Fig. 9(b) with correct-decoding rate of 74.71%. Fig. 9(c) shows the tampered of Fig. 8(d), and the decoded watermark is shown in Fig. 9(d). For this case, the correct-decoding rate is 64.64%. The experiments indicate that this watermarking technique can perform well under cropping and tampering, for the watermark rate is as high as 25%. In the most common applications of halftoning in printed books, newspapers, and magazines, the original embedded watermarked image is often damaged by the print-and-scan process, e.g., zooming, rotation and dot gain. Extracting the original watermarks perfectly has been challenging. There has been recent research work on the print-and-scan problems. Investigation includes using the registration marks to extract hidden data accurately [34], and Walsh transform to embed marks in the frequency domain to identify the alignment positions of the embedded shares [35]. Transform coefficient polarity based watermarking algorithm are also studied for an insertion of owner ID into photographs [36]. In this study, during the extraction process, we place auxiliary synchronized black pixels in four corners of the embedded halftone image. The print-and-scan embedded image is first re-rotated by Adobe Photoshop 7.0. Because the size of print-and-scan image is generally larger than the expected when the same DPI of printing and scanning are applied, the print-and-scan embedded image should be geometrically transformed into size of 512  512 before the decoding process. To overcome this problem, the print-and-scan image is divided into 262,144 square blocks, under the assumption that the original image is

Fig. 8. (a)–(b) Original watermarks with 64  64 and 256  256, respectively. (Printed at 150 dpi) (c)–(d) Embedded halftone images with PSNR= 32.6 and 32.08 dB, respectively. (Printed at 300 dpi) (c) embedded with (a), and (d) embedded with (b). (e)–(f) Decoded watermarks from (c) and (d), respectively with decoded rate of 99.29% and 80.03%, respectively.

J.-M. Guo et al. / Signal Processing 91 (2011) 126–135

values. Also, we need an additional buffer for the storage of the diffused errors. Suppose the host image is of size P  Q, where P and Q denote its height and width, respectively. Then, we need 4  Q bytes to store the diffused errors. In fact, an optimal PDR is exactly 11  11 according to our experiments. Fig. 11(a) and (b) shows the average relationships of PSNR vs. PDR and CDR vs. PDR, respectively, using the eight test images. Without losing generality, an additive noise is set at 20 for both Figs. 11(a) and (b), and the embedded images are undergone 50% cropping for Fig. 11(b). As it can be seen in Fig. 11, as the PDR increases from 1 to 11, the PSNR increases as well. Although a slight improvement in an image quality can be obtained as PDR is higher than 11, as shown in Fig. 11(a), the computational complexity is increased also. Although PDR at 11 is a good setting, the value of PDR can be considered as a secret key to provide a higher security. Any decoder should be informed with the

PSNR

512  512. The average of the pixels within each block is threshold to recover the original halftone image pixel. Since the laser printer often introduces dot gain, the threshold was reduced from 128–100 to prevent the dotgain darkening effect. For these experiments, the HP LaserJet 4050 printer and HP OfficeJet 7100 scanner were utilized. Before the embedded halftone image is printed, the format is saved in bitmap and sent directly to the printer. For that, the printer driver does not involve any further halftone process with the image. The overall preprocesses of the decoder are illustrated in Fig. 10. For a host image of size 512  512 and a watermark of size 64  64, an average encoding and decoding time (using eight test images) of the proposed method is 38 and 22 ms, respectively. The memory consumption of the proposed PMEDF method is very limited. Suppose the PDR is 11  11. When a pixel is processed, we need a buffer of the size 121 bits to store the previous halftone pixel

133

PSNR vs. PDR

34.5 34.4 34.3 34.2 34.1 34 33.9 33.8 1

3

5

7

9 11 PDR

13

15

17

19

CDR vs. PDR 85

CDR

80 75 70 65 60 Fig. 9. Robustness testing under cropping and tampering attacks. (a) One quarter cropping with Fig. 8(d). (b) The decoded watermark in Fig. 9(a). The correct-decoding rate is 74.71. (c) Tampering with Fig. 8(d). (d) The decoded watermark in Fig. 9(c). The correct-decoding rate is 64.64.

1

3

5

7

11 9 PDR

13

15

17

19

Fig. 11. Optimal PDR value determination in terms of PSNR and CDR. (a) PSNR vs. PDR and (b) CDR vs. PDR.

Fig. 10. The overall pre-processes of the decoder.

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PDR value to generate the correct watermark. Actually, PDR = 1 means that each time when an information bit is embedded into an image, one pixel in host image is used to carry the information. Under this circumstance, each pixel in a divided block has to be processed with Eqs. (3) and (5) for future majority voting in the decoder, and thus an image quality is deteriorated. The extent of the ‘‘pollution’’ caused by the watermarking embedding as mentioned above can be eased as the PDR is increased. The proposed method divides the host image into cell blocks, and embeds the pseudo-permuted information bits into the blocks. Each block represents one information bit. The pixels in the decoded watermark are then re-permuted to the original positions with the pseudorandom key. Hence, an embedded image is able to withstand cropping and tampering from a cluster of decoding error. On the other hand, each pixel in the block contributes to the decoded result due to the majority voting approach, which is good for withstanding local or global geometric distortions, such as print-and-scan distortion. The size of the divided block used to embed watermark is flexible. The block size can be enlarged to improve the robustness when the communication channel is more vulnerable. We can reduce the block to increase the watermark rate when a security transmission channel is available. As documented in the Section V, the block of size 2  2 (with watermark rate of 25%) is sufficient for resisting normal cropping and tampering. However, the block size needs to be increased to 4  4 (corresponding to the watermark rate of 6.25%), in order to withstand the print-and-scan distortion. Fig. 12 shows robustness comparisons between the PMEDF and results from previous works with print-andscan distortion, using the eight test images. The watermark of size 64  64 as shown in Fig. 8(a) is embedded into 512  512 halftone images with an additive noise of value 25. Subsequently, the watermark rate is fixed at 1/64. The embedded images are printed at 150 dpi and scanned at 150, 300, and 600 dpi for variation in resolution. It can be seen that the PMEDF achieves good correct-decoding rate, and is second to the method proposed in [11]. This is because the method used in [11] flips the binary pixel value, from black to white or white to black, to meet the value of watermark bit. Instead the PMEDF employs the additive noise to force the

embedded pixel value to match the watermark bit. Hence, some pixel values may not change, and the decoded rate decreased as a result. Quality comparisons are also performed as in Fig. 13. Since the embedded image in [11] is processed with an ordered dithering, the image quality is the worst among various methods. The performance of the PMEDF method is inferior to [13], where the method compares the errordiffused embedded image with its ‘‘hidden ordered dither image,’’ and then further decodes the watermark. Because both the error-diffused result and ordered dither result can render the local fluctuation of an image, the additive noise used in [13] can be lower than PMEDF to embed the watermark. Therefore, a high quality result can be obtained. In [6], the MDHED scheme is proposed that the format of the embedded image is identical to the proposed method. However, the application of MDHED is mainly for data hiding, while the main goal of the proposed PMEDF is watermarking. Consequently, the proposed is more robust, while the MDHED can yield better image quality. Notably, the method in [12] is not included in the comparison. This is due to the fact that the algorithm in [12] is designed mainly for a high watermark-rate application with secret sharing concept, which makes it difficult to be fixed at the same watermark rate for comparison. For example, when the watermark rate is fixed at 1/64, the watermark should be distributed into 64 different halftone images. However, the quality varies responding to different images combinations in secret sharing. Another way to achieve the watermark rate of 1/64 is to employ the dot diffusion for watermark embedding. Then again, the dot diffusion approach is inherently inferior to error diffusion in quality. In [4], the format of the halftone image is dot-area modulation (DAM), which is different from the error diffusion discussed in this work. Although both formats are used for printing, the objectives are different. DAM is generally more efficient while error diffusion is quality-oriented. In [5], the main contribution of this work is to embed a watermark into a multilevel error-diffused image. Thus, the embedded image is a multilevel image, which is also different from the binary error-diffused halftone image discussed in this work. Hence, it is not adequate to compare the performance of these two approaches, since the target applications are not the same.

Fig. 12. Robustness comparisons between our previous works with print-and-scan distortion, using the eight tested images (NA =25).

Fig. 13. Quality comparisons between our previous works with the eight tested images (NA = 25).

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