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Joint Compression/Watermarking Scheme Using Majority-Parity Guidance and Halftoning-Based Block Truncation Coding Jing-Ming Guo, Member, IEEE, and Yun-Fu Liu, Student Member, IEEE

Abstract—In this paper, a watermarking scheme, called majority-parity-guided error-diffused block truncation coding (MPG-EDBTC), is proposed to achieve high image quality and embedding capacity. EDBTC exploits the error diffusion to effectively reduce blocking effect and false contour which inherently exhibit in traditional BTC. In addition, the coding efficiency is significantly improved by replacing high and low means evaluation with extreme values substitution. The proposed MPG-EDBTC embeds a watermark simultaneously during compression by evaluating the parity value in a predefined parity-check region (PCR). As documented in the experimental results, the proposed scheme can provide good robustness, image quality, and processing efficiency. Finally, the proposed MPG-EDBTC is extended to embed multiple watermarks and achieves excellent image quality, robustness, and capacity. Nowadays, most multimedia is compressed before it is stored. It is more appropriate to embed information such as watermarks during compression. The proposed method has been proved to solve effectively the inherent problems in traditional BTC, and provide excellent performance in watermark embedding. Index Terms—Block truncation coding, digital halftoning, digital watermarking, error diffusion.

I. INTRODUCTION LOCK truncation coding (BTC), which was proposed by Delp and Mitchell in 1979 [1], is a technique for image compression. The basic concept of this technique is to divide the original image into many nonoverlapped blocks, each of which is represented by two distinct values. In traditional BTC, the two values also preserve the first- and second-moment characteristics of the original block. When a BTC image is transmitted, each pair of values (2 8 bits/block) and the bitmap which stores the arrangement of the two values in each block (1 bit/pixel) are required. Although BTC cannot provide comparable coding gain as other modern compression techniques, such as JPEG or JPEG2000, the complexity of BTC is much lower than that of these modern techniques, which makes it feasible for less powerful processing kernel, such as Arm-based applications.

B

Manuscript received April 09, 2009; revised November 02, 2009. First published March 15, 2010; current version published July 16, 2010. This work was supported by the National Science Council of Taiwan, R.O.C., under Contract NSC 96-2221-E-011-172-MY3. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Lina J. Karam. The authors are with the Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan, R.O.C. (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TIP.2010.2045709

In the literature, many approaches have been proposed to improve BTC. One category involves preserving the moment characteristic of the original image. Halverson et al. [2] generalized a family of moment-preserving quantizers, by employing moments higher than three. Udpikar and Raina [3] proposed a modified BTC algorithm, which preserves only the first-order moment. The algorithm is optimum in the mean-square sense, and it is also convenient for hardware implementation. Another category involves improving the image quality and reducing the blocking effect. Kanafani et al. [4] decomposed the image into homogeneous and nonhomogeneous blocks and then compressed them using BTC or vector quantization (VQ). This block classification is achieved by image segmentation using the expectation-maximization (EM) algorithm. The new EM-BTC-VQ algorithm can significantly improve the quality and fidelity of compressed images when compared with BTC or VQ. A new video codec algorithm combined with discrete cosine transform (DCT) is proposed by Horbelt and Crowcroft [5]. The basic concept of this algorithm is that the traditional BTC provides excellent performance in high-contrast and detailed regions, while the DCT works better for smooth regions. A problem of BTC is its poor image quality under low bit rate condition, and some studies have attempted to address this issue. Kamel et al. [6] proposed two modifications on BTC. The first one allows the partitioning of the image into variable block sizes rather than a fixed size. The second modification involves the use of an optimal threshold to quantize the blocks by minimizing the mean square error. Chen and Liu [7] proposed a visual pattern block truncation coding (VPBTC), in which the bitmap is employed to compute the block gradient orientation and match the block pattern. Another refinement is the classification of blocks according to the properties of human visual perception. However, most of the improvements described previously increase the complexity substantially. Nowadays, an emerged method, called halftoning-based BTC [21], [22], is developed to effectively solve the annoying false contour and blocking effect inherently exits in a BTC image while further reducing its complexity. Digital halftoning [8] is a technique which converts a grayscale image into a binary image or called a halftone image, which can resemble the original image when viewed from a distance with the lowpass characteristic of human visual system (HVS). Many halftoning schemes have been proposed in the literature, including ordered dithering (OD) [8], error diffusion (ED) [9]–[15], dot diffusion (DD) [16], [17], and direct binary search (DBS) [18]–[20]. To

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exploit the advantage of halftoning, Guo [21] adopts ED to improve the bitmap arrangement, called error-diffused block truncation coding (EDBTC), in which the energy-preserving property of EDF is exploited to improve image quality. Later, Guo and Wu [22] presented another halftoning-based approach to improve its performance, called ordered dithering block truncation coding (ODBTC), which has innate parallel processing characteristic, while the image quality in inferior to that of the EDBTC. Digital watermarking is a value-added technique for providing copyright protection or authentication features [23]. Nowadays, it is impossible to store or transmit an image or a video sequence without prior compression. As mentioned previously, BTC is a good solution for image/video compression with an extremely low complexity. Subsequently, the possibility of embedding watermarks in BTC-compressed images has been investigated. For example, Tu and Hsu [24] proposed an ownership share approach, which combines the image and its watermark by generating a secret key, while leaving the original image unmodified. The ownership share is then required in the process of decoding. Lin and Chang [25] proposed a data hiding scheme for a image compressed by BTC. They information is embedded into both high and low means by alternating one bit value, according to the value of the messages, as well as into the bitmap using the minimum distortion algorithm (MDA). In this paper, a watermarking, namely majority-parity-guided error-diffused block truncation coding (MPG-EDBTC), is proposed, in which the energy-preserving property of EDF is exploited to improve image quality. Experimental results prove that the proposed MPG-EDBTC provides excellent image quality, robustness, and embedded capacity. The rest of this paper is organized as follows. Section II introduces the performance evaluation approaches employed in this study. Section III describes the EDBTC. The proposed MPGEDBTC for single and multiple watermarks embedding are presented in Sections IV and V, respectively. Finally, the conclusions are drawn in Section VI.

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denotes a Gaussian filter (GF) for simulating the where lowpass characteristic of HVS, and denotes the support region. The support region size is affected by the viewing distance and resolution (dpi), and the support region is defined as the number of pixels in one visual degree as where

(2)

where denotes one viewing degree; denotes the viewing distance (cm); denotes the viewed width, and . Suppose and , , which means 31 pixels are involved for one then perceived degree calculation. In 2-D case, this will consume of the many time. Thus, in this work the standard deviation GF is set at 1.3, and is fixed at 9 9, since the size of GF is along 1-D for maintaining sufficient information, this setting can yield efficient processing and reliable evaluating accuracy. The other performance evaluation is the BER, which deterand mines the difference between the original watermark . Suppose a waterthe corresponding decoded watermark mark is of size and in binary fashion, the BER is defined as (3) denotes exclusive OR (XOR) operation. In general, where the BER is inversely proportional to the accuracy of a decoded result. III. ERROR-DIFFUSED BLOCK TRUNCATION CODING The motivation of adopting EDBTC [21] for the proposed MPG-EDBTC is introduced in this section. The main advantage of EDBTC is to solve the annoying false contour and blocking effect of traditional BTC. Fig. 1 shows the flowchart of BTC and is divided EDBTC. Suppose the original image of size and into nonoverlapped blocks, each of which is of size processed independently. For traditional BTC, the first-moment, second-moment, and the corresponding variance are obtained as

II. PERFORMANCE EVALUATION (4) In this section, two performance evaluation approaches are introduced, which include human visual system peak signal-tonoise ratio (HVS-PSNR) and bit error rate (BER). HVS-PSNR is different from traditional PSNR, since the HVS is involved in the former measurement to provide more objective quality and its corassessment. Let’s denote the original image as . Suppose an image is of size responding altered image as , the quality evaluation is defined as

(1)

(5) (6) where denotes the grayscale value of the original image. The concept of traditional BTC is to preserve the first- and second- moments of a block when original value is substituted by its high- or low-means. Thus, the following two equations should be maintained: (7) (8)

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Fig. 2. Processed result with the left eye of Lena image. (a) Original image. (b) BTC reulst. (c) BTC result with bitmap generated by Pseudo-Noise (PN). (d) EDBTC. (all printed at 150 dpi).

Fig. 3. Error-diffused block truncation coding.

Fig. 1. Algorithms of traditional BTC and EDBTC.

where , and is the number of pixels greater than . The high- and low-means can be evaluated as follows: (9)

Fig. 4. Three well-known error kernels. (a) Floyd [9]. (b) Jarvis et al. [10], (c) Stucki [11].

(10) where and denote low-mean and high-mean, respectively. Since BTC is a one-bit quantizer, the mean is employed to threshold the block. The binarized result is called bitmap, which is used for recording the arrangement of the two represented values, low-mean and high-mean if if

,

where

if if

(11) denotes bitmap, and denotes the resulted BTC where image. Fig. 2(b) shows the processed result by traditional BTC using the left eye of Lena image. It is clear that BTC has serious blocking effect and false contour which significantly reduce image quality. To reduce these effects, the pseudo-noised (PN) is employed to randomly generate bitmap as shown in Fig. 2(c). Apparently, the false contour is reduced, yet the blocking effect is still prominent. The image information is also significantly reduced as the eye is barely recognizable. The EDBTC enjoys the benefit of local image average preserving by diffusing the quantization error and, thus, significantly reduces the blocking effect and false contour effects as proved in Fig. 2(d). Fig. 3 shows the flow chart of EDBTC. The processing order is in raster scan path in a block, which means from left to right and top to bottom. The corresponding variables are defined as

where

(12)

where

if if

(13)

where , and are defined as in (11). The variable denotes the diffused error sum added up from neighboring processed pixels. The binary result is replaced by either or minimum value of a block. The maximum reason of choosing extreme values is to generate dithered result to destroy the annoying false contour inherently existed in denotes the employed error a BTC image. The variable kernel to diffuse the quantized error to its neighboring pixels. Three well-known error kernels, Floyd [9], Jarvis et al., [10], and Stucki [11], are shown in Fig. 4, where the notation x denotes the current processing position. Notably, the error in the boundary pixels of a block should also diffuse to its neighboring blocks to eliminate the blocking effect. IV. MAJORITY-PARITY-GUIDED ERROR-DIFFUSED BLOCK TRUNCATION CODING A. MPG-EDBTC Encoder The proposed watermarking encoder is shown in Fig. 5, which is developed based upon the framework of EDBTC. Notably, the only different part is that the functional block is replaced by “MPG error diffusion,” which controls the watermark embedding. In addition, one watermark bit associates to one block of the original image. In MPG error diffusion algorithm, watermark is embedded by modifying the bitmap of

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BTC image, as shown in Fig. 6. The corresponding equations are formulated as follows, which is modified from (12) and (13)

where

(14)

if if

where if the request of otherwise if the request of

(15) is 1 and is 0 and (16)

denotes noise increment. A positive increases the where , and conversely, a negative inprobability of . The rest variables are creases the probability of defined the same as that in (4), (12), and (13). In fact, the request of (16) depends upon the watermark and the diffused grayscale image. Fig. 7 shows an example to demonstrate this idea. In this example, the binary patterns represent bitmaps, and black and white associate to values 0 and 1, respectively. Fig. 7(a) shows a black watermark bit is attempted to be embedded to the current processing position, which has not been binarized yet. First, a parity-check region (PCR) with a predefine region of size 4 4 is employed in this example for calculating the parity, which is used for representing the embedded watermark bit. The PCR always covers the top-left processed region relative to the cur. The parity calculation is defined as rently position if otherwise

(17)

denotes the bitmap. At this time, the PCR exwhere . According to this example, the cludes the position is derived. This result is not consistent to the expected black watermark bit. Thus, the calculated parity has to be modified to 0 for representing correct watermark information. For this, if the diffused grayscale value is greater than mean, an additive noise “-Noise” is added on the current processing position to make the bitmap has higher probability becoming 0. Conversely, if the diffused grayscale is less than mean, the current bitmap will value become 0 without any noise adding. In the decoder, when the parity of the current processing position of the bitmap on the right hand side of Fig. 7(a) is calculated, the correct watermark . Notably, the PCR can be yielded since includes the currently processed position for watermark extracting. Fig. 7(b) shows another case by embedding a white watermark bit with a different PCR of size 5. In this case, the is equal to the white calculated parity watermark bit 1. Consequently, if the diffused grayscale value is lower than mean, an additive noise “+Noise” is added on the current processing position to make the bitmap has higher probability becoming 1. Conversely, if the diffused grayscale

Fig. 5. Encoder of the MPG-EDBTC watermarking scheme.

Fig. 6. Majority-parity-guided (MPG) error diffusion algorithm.

value is higher than mean, the current bitmap will become 1 without any noise adding. B. MPG-EDBTC Decoder Fig. 8 shows the general concept of decoding. First, the bitmap of the received watermarked EDBTC image is extracted since it stores the information of watermarks. In practical application, attacks may exist, which would alter the bitmap arrangement. Hence, instead of finding the positions of the local minimum and maximum directly, a simple thresholding method is employed for producing a robust temporary bitmap as (18) if if

(19)

where and denote the watermarked BTC image and denotes the the extracted bitmap, respectively. block size as introduced in Fig. 5. Notably, this processing is

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Fig. 9. Example of watermark extracting.

Fig. 7. Two distinct watermark bits embedding examples. (a) Black watermark embedding. (with PCR size = 4) (b) White watermark embedding. (with PCR size = 5).

Fig. 8. MPG-EDBTC decoding procedure.

independent for each block. Fig. 9 shows an example to demonstrate the watermark extracting. The extracted bitmap on the left-hand side as introduced previously is employed to yield a voting matrix on the right-hand side by parity determination with PCR of size 4 as if if

(20)

where denotes the pixels in the voting matrix. Since a watermark bit is embedded into a 4 4 block, the majority voting scheme, as defined in the following, is employed to produce a robust decoded watermark. if

(21)

otherwise where the denotes the decoded watermark, in which 0 and 1 represent white and black pixels, respectively. C. Parameters Three adjustable parameters, noise increment, PCR size, and watermark size, are involved in the proposed scheme. Extensive experimental results with various parameter configurations are discussed in this section. Herein, 10 different tested host

Fig. 10. Average performance with different PCR size. (a) Average HVS-PSNR of the watermarked images. (b) Average BER of the decoded watermarks. (c) Average processing time of encoding and decoding.

images of size 512 512 and 10 different watermarks of size 64 64 are employed in the simulation. Fig. 10 shows the full results in terms of marked image quality, decoded watermark quality, and processing efficiency by adjusting the PCR size. , the parity value cannot be In Fig. 10(a), when changed via the encoding algorithm (because the current processing position is excluded from the PCR). Hence, the whole block is directly affected by the embedded watermark bit (each pixel in a block is added with the same additive noise), which significantly decrease the image quality. Fig. 10(b) shows is employed, the decoded watermark quality. When the worst CDR is achieved since the watermark information cannot be embedded under this condition. When a small PCR size is employed, only few decoded votes can be utilized in

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Fig. 11. Watermarked images and the corresponding decoded watermarks ( = 21). (a) Original grayscale image and binary watermark. (b) PCR = 1. (c) PCR = 7. (Watermarked images printed at 400 dpi, decode watermarks printed at 200 dpi).

N

majority voting for yielding a watermark bit. As indicated from Fig. 10(a) and (b), a greater PCR size accompanies a better performance in image quality and decoded accuracy, yet which impedes the processing speed as shown in Fig. 10(c). By summarizing the results in Fig. 10(a)–(c), is a good choice for the proposed watermarking. In addition, the PCR size also is a secret key for watermark extracting. We suggest that the selected possibilities of PCR sizes are greater or equal to four. Fig. 11 shows some watermarked images and the corresponding decoded watermarks. Fig. 12 shows the variations in performance with different watermark sizes. In these results, the PCR size is fixed at 4. Fig. 12 indicates that the image quality is proportional to the , the watermark size, since the block size is influence of blocking effect is increased with increasing in block size. For BER, the bigger block means that the higher likelihood in obtaining the required parity value is available by a small noise, which is a positive benefit for system performance. On the other hand, the block size also affects the bit rate, which is formulated as follows:

Fig. 12. Average performance with different data capacity (PCR = 4). (a) Average HVS-PSNR. (b) Average BER. (c) Bit rate.

(22)

Fig. 13. Practical embedded images and the corresponding decoded watermarks with different sizes of watermarks (PCR = 4 and = 14). (a) Watermark of size 8 8. (b) Watermark of size 256 256. (all printed at 400 dpi).

in denominator denotes block size; and where 2 8 in numerator denote the bitmap and the two represented maximum and minimum values, respectively. In practical application, when data capacity is adjusted, the bit rate issue has to be taken into consideration. Fig. 13 shows the practical watermarked images and the corresponding decoded watermarks with different watermark sizes. According to the experiments of Figs. 10 and 13, the noise increment is inversely proportional to image quality and BER. The optimal noise increment can be determined from these results to yield acceptable image quality (around 40 dB) and BER (around , 0.005). Under this condition,

, and . So far, few former approaches address the issue of embedding watermarks in BTC images. In Tu-Hsu’s method [24], the watermark embedding is independent of BTC image compression. Hence, the image quality of the obtained watermarked image is identical to that of the original BTC image, while an overhead of the same size as the watermark should be transmitted. For practical usage, Tu-Hsu’s method is different from the proposed MPG-EDBTC, and the comparison is, thus, made with Lin-Chang’s method [25] only. Lin-Chang’s method employs different embedding targets to increase data capacity, such as different bit-planes of

2

2

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Fig. 14. Performance comparisons in terms of HVS-PSNR and BER.

IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 19, NO. 8, AUGUST 2010

to concatenate with another high complexity compression scheme. Figs. 16, 17 show the corresponding experimental results, where the dashed-line represents theoretical results which will be discussed in Section IV-D-2. As can be seen, the robustness of the proposed method is superior to that of Lin-Chang’s method for five types of attacks, including darkening, pulse noising, Gaussian noising, Gaussian smoothing, and jittering. On cropping attack comparison, these methods have similar performance, and the proposed method inferior to their method with the lightening attack. These results demonstrate that the proposed MPG-EDBTC is more robust than Lin-Chang’s method, since the proposed decoding manner can resist some unstable pixel values and the majority-vote strategy compensates the influences of decoding errors. 2) Theoretical Analyses: In the theoretical analyses, a grayscale EDBTC image is assumed as uniform distribution without losing generality. To begin with, the MPG-EDBTC is analyzed first. In encoder, the probability that a pixel in a bitmap can correctly embed watermark is formulated (23) if if otherwise

Fig. 15. Embedded results with Lin-Chang’s methods [25]. (a) Minimum Distortion Algorithm (MDA). (b) Low-mean. (c) High-mean. (all printed at 200dpi).

low mean and high mean (the definition of these is the same as that of traditional BTC), and bitmap. Fig. 14 shows the performance comparisons of Lin-Chang’s three approaches and the proposed MPG-EDBTC. The results obtained with Lin-Chang’s method are shown in Fig. 15. Although the image quality of proposed method is inferior to that of Lin-Chang’s method, the robustness of the decoded watermark and quality of decoded multiple watermarks are all superior to that of Lin-Chang’s method as will be elaborated in the following sections. D. Attacks This section is separated into experimental results and theoretical analyses to provide persuadable and predictable results with the proposed MPG-EDBTC scheme. 1) Experimental Results: In this section, the proposed MPG-EDBTC is compared with Lin-Chang’s three different embedding schemes with various types of attacks, including lightening, darkening, pulse noising, Gaussian noising, Gaussian smoothing, jittering, and cropping. Two common attacks, JPEG and JPEG2000, are not taken into consideration in our simulation, since BTC is a compression scheme for efficient coding application, and, thus, it is rarely employed

(24)

denotes the noise increment; denotes a unit step where function; d denotes the difference between the maximum and denotes the probminimum values of one BTC block, and is shown in ability of d occurrence. The distribution of Fig. 18. The is proportional to the noise increment which can also be proved by the experimental results. In a BTC image, each block is represented its maximum and minimum values. If an additional noise increment is higher than the half difference between the two represented values, the noise has sufficient strength to make the diffused grayscale value ( , see in Fig. 6) match the expected bitmap output . Otherwise, the correct embedding is determined by whether the diffused grayscale value higher than the mean of . its block When receive an EDBTC image at decoder, the bitmap is extracted to detect the embedded watermark. This bitmap can be modeled as a Binomial distribution since which only has two types of values, black and white. To calculate the parity with the received PCR, the voting matrix can be obtained. This voting matrix also can be represented by a Binomial distribution, since it has two possibilities, correct and incorrect embedding. Finally, the extracted watermark is determined by majority voting from the voting matrix. The error probability (BER) of the extracted watermark is formulated as

(25)

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Fig. 16. Robustness comparisons between Lin-Chang’s watermarking [25] and the proposed MPG-EDBTC under seven different types of attacks. (a) Lightening. (b) Darkening. (c) Pulse noising. (d) Gaussian noising. (e) Gaussian smoothing. (f) Jittering. (g) Cropping.

(26)

(27)

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Fig. 17. Practical results with seven various types of attacks. (Watermarked images printed at 400 dpi, decode watermarks printed at 200 dpi). (a) Without attack: 43.09 dB, 0; (b) Lighting: 10 and 50 grayscale value; (c) Darkening: 10 and 50 grayscale value; (d) Pulse noising: 0.02 and 0.16 ratio of noisy area; (e) Gaussian noising: 1 and 21 standard deviation; (f) Gaussian smoothing: 0.1 and 0.5 standard deviation; (g) Jittering: 1/512 and 1/16 jitter scale; (h) Cropping: 10% and 50% cropped area.

+

+

0

(28) where and denote the block size of a BTC image and the number of correct extracting results from the voting matrix, denotes the correct extracting respectively. The probability of each result from voting matrix using the PCR is constructed by four different size (PCRS). The combinations which can obtain one watermark result from the denotes the probability that voting matrix. Among these,

0

a bit in bitmap is different from the original transmitted bit and denote the caused by attack. number of error bits is even or odd, respectively, which are also caused by attack in PCR excepting the currently processing position. Two components, and , are employed for constructing the equation . The first compoindicates that when nent the current position is not suffered by attack and other bits of bitmap in PCR have even number error, the calculated parity will be the same as the correct parity and, thus, the bitmap is considered as without being attack. The second component indicates that when the

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Fig. 19. Probability distribution of p (d; s) with three different additional grayscale value strengths.

Fig. 18. Probability distribution of p (d).

current bit in bitmap is wrong caused by attack, and odd number of others bits in PCR are incorrect, this condition will make the calculated parity in this PCR as the original parity without attack as well. According to this analysis, if a received EDBTC image and is not suffered any attack, then (it includes the case when none of the bit in bitmap is suffered . attack), in which The seven types of attacks considered in Section IV-D-1 are discussed in the following. These attacks can be separated into two groups according to their attack types. The first type demonstrates that each pixel in an EDBTC image has identical attack, can be modeled directly for evaluating the BER. in which This type of attacks includes lighting, darkening, pulse noising, Gaussian noising, and Gaussian smoothing. The second type of attacks associates that different area has different attack extent, in which the whole mathematical analysis of decoder has to be taken into account. This type of attacks includes jittering and cropping. The previously mentioned seven attacks are analyzed in order as below. The theoretically derived results are represented by the dashed-lines in Fig. 16. The probability distribution of an EDBTC image is assumed as uniform, which still provide very close prediction ability to practical situation. Notably, in our theoretical derivation, we found that if the distribution of an EDBTC image is known, the predicted result is almost identical to the practical one. The analyzed results demonstrate that the proposed method can widely be employed on different kinds of images and still achieves satisfactory robustness under different distortions. is affected a) Lighting and darkening: The variable by the strength of the added value (from lighting or darkening), and the decoded error occurs when the mean of a block cannot correctly separate the maximum and minimum values of a block. Since the dynamic range of a digital image is from 0 to 255, the error occurs when the added value causes the maximum and minimum values to be an identical value. This type of attack can be formulated as

where if and if and otherwise

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(29)

(30)

where is defined in (24); s denotes the strength of the added value; denotes the error probability when conditions d and s occur. Fig. 19 shows the probability distributions

of with three different added value strengths ( , 128, and 224). b) Pulse noising: The well-known salt-and-pepper noise is considered in this type of attack. When a pixel in a bitmap is undergone this type of attack, there are 50% possibility that a can be formulated as pixel will change its polarity. Thus, where

(31)

where nr denotes the ratio of noisy area. c) Gaussian noising: In this type of attack, the decoded error occurs when the distortion caused by the Gaussian noise is higher than a half of the difference between maximum and minimum values in a block. Thus, this attack can be modeled as

(32)

where is defined in (24), and denotes a 1-D Gaussian distribution with standard deviation . d) Gaussian smoothing: The bit error caused by this attack occurs when the altered value of an EDBTC image is higher than a half of the difference between maximum and minimum values. The attack is modeled as

(33) where and denote the difference and grayscale value, respecdenotes a 2-D Gaussian distribution with standard tively. deviation . In this analysis, the probability distribution of all grayscale values in smoothed region except the currently processing position is assumed as uniform. Consequently, the mean of this distribution is 128, and the decision on each grayscale value shares the same probability 1/256. e) Jitter: This attack is caused by packet transmission delay. Fig. 20 shows an example to demonstrate this phenomenon, in which a 1-D BTC image of size 10 is transmitted and affected by jitter attack with scale 1/3. The squares in this figure denote the received values. The dashed circle denotes

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Fig. 20. Example of jitter attack on 1-D BTC image with jitter scale 1/3.

the case changes to a new value from the same block. Based upon this observation, the amount of error bits is varied with different jitter scale as well as the position and width of the corresponding block. Hence, when an image of size as that in Fig. 1 is transmitted, and supposes a 1-D jitter attack happens on the image, the error probability of the extracted watermark can be derived by the following equation, Fig. 21. Multiple watermarks embedding mechanism.

V. MULTIPLE WATERMARKS EMBEDDING

(34)

if if

(35)

where

denotes the jitter scale which ranges from 0 to 1, and denotes the probability of on rth region. For example, block one and three are denoted as and 3, respectively. The number of the extracted results from the voting matrix only has correct and incorrect two possibilities and, thus, the error rate is defined as 0.5. f) Cropping: Without losing generality, the cropped region is set as black, while the rest parts are remained the same in this study. Consequently, the error rate of a pixel caused by cropping is varied according to its position (attack region or nonattack region). The error rate caused by cropping is formulated as

where where

denotes the ratio of the cropped area.

(36)

The proposed MPG-EDBTC can be extended for multiple watermarks embedding. Fig. 21 shows the embedding mechanism where watermark bits are embedded to the current processing position simultaneously. Each watermark embedding employs a different PCR size to ensure that the calculated parities are independent with each other. Notably, if the PCR exceeds the boundary of the host image, such as the case of watermark embedding as shown in the bottom of Fig. 21, all the exceeding areas are set as 0 for parity calculating. In addition, each watermark embedding has identical request for bitmap output as that in (16). All the requests from the watermarks are collected, and the two values, and , are employed to make the final decision by selecting “+Noise,” “-Noise,” or no action as if otherwise if

and (37) and

.

With this embedding manner and the proposed majority voting strategy, the decoded results still maintain excellent quality. Moreover, for multiple watermarks decoding, each watermark decoding shares the same method, as shown in Fig. 8. Notably, the PCR size of each watermark extracting has to be synchronized in encoder and decoder and, thus, the PCR size is carried as side information. Fig. 22 shows the performance of multiple watermarks embedding. The same test image set, including host images and watermarks, as that employed in Section IV-C is involved in this experiment. The parameters are set at and

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TABLE I RECOMMENDED NOISE STRENGTHS AND THE CORRESPONDING PERFORMANCE FOR EACH NUMBER OF WATERMARKS (PCR size = 4)

Fig. 22. Average performance with different number of watermarks. (PCR

4 and N = 14).

=

Fig. 23. Average performance with different number of watermarks and noise increments. (PCR = 4) (a) Average HVS-PSNR. (b) Average BER.

Fig. 24. Practical embedded images and the corresponding decoded watermarks with different sizes of watermarks (PCR = 4). (a) 10 original water= 32). (c) 10 watermarks embedmarks. (b) Two watermarks embedding ( = 24). (Watermarked images printed at 400 dpi, decode watermarks ding ( printed at 200 dpi).

N

. It is interesting to note that even number of watermarks embedding is superior to odd number of watermarks embedding. The reason behind this observation is that when even watermarks are embedded, there is possible that no is required to add to achieve the desired parity, which contributes to its image quality. However, the benefit decreases as the number of watermarks is increased, as shown in Fig. 22. As expected, the BER increases as the number of embedded watermarks is increased. In multiple watermarks embedding, noise increment can be further optimized for different numbers of watermark embedding. Fig. 23 shows the performance under different number of watermarks and noise increments. The objective of this experiment is to determine a recommended for the corresponding

N

number of watermarks to achieve acceptable image quality ) and BER (when HVS-PSNR (around is fixed, different number of watermarks embedding has different BER, as shown in Table I). According to Fig. 23, the recommended for each number of watermarks is organized in Table I which also includes the optimized (20) discussed in Section IV-C. For the extremely high-capacity case of embedding 10 watermarks, it still achieves . Fig. 24 shows the watermarked images and the corresponding decoded watermarks using the recommended from Table I when even numbers of watermarks are embedded. Fig. 24(a) shows

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IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 19, NO. 8, AUGUST 2010

thus, proves that the proposed watermarking is effective in addressing the security issues in compressed images.

REFERENCES

Fig. 25. Image quality comparison between Lin-Chang’s watermarking [25] and the proposed MPG-EDBTC.

the 10 employed watermarks. The results demonstrate that the proposed method can achieve good image quality and decoded rate under huge embedding capacity. Fig. 25 shows the image quality comparisons between LinChang’s watermarking and the proposed MPG-EDBTC under the condition of multiple watermarks embedding. Lin-Chang employs different embedding manners simultaneously for increasing data capacity and, thus, the image quality is decreased rapidly when more watermarks are embedded. The parameters addressed in Table I are employed for the proposed method, which is the reason why the HVS-PSNRs of the proposed MPGEDBTC are always around 40 dB. VI. CONCLUSION Nowadays, most images are compressed before they are transmitted or stored, and, thus, watermarking is highly suggested to be catered into compressed domain of an image. In this work, a high-capacity watermarking technique for block truncation coding (BTC) images is proposed. This technique improves image quality of traditional BTC for configurations of high coding gain, where the energy-preserving property of EDF is exploited to effectively remove the false contour and blocking effect inherently exist in BTC images. Moreover, the efficiency can also be improved by replacing the high and low means with the maximum and minimum values in a block. When watermarks are embedded, the proposed majority-parity-guided error-diffused BTC (MPG-EDBTC) can achieve good image quality and decoded rates under a huge embedded capacity. Two parameters, parity-check region (PCR) size and noise increment, are employed in this study for controlling the performance. The PCR size controls the quality of an embedded image, decoded watermark, and processing efficiency; the amount of noise increment provides the tradeoff between embedded image quality and decoded watermark quality. This study provides extensive experimental results with various parameter settings. The prospective reader can choose any configurations they need to meet practical applications. The robustness of the proposed method is superior to that of Lin-Chang’s method for many types of attacks, and,

[1] E. J. Delp and O. R. Mitchell, “Image compression using block truncation coding,” IEEE Trans. Commun., vol. 27, no. 9, pp. 1335–1342, Sep. 1979. [2] D. R. Halverson, N. C. Griswold, and G. L. Wise, “A generalized block truncation coding algorithm for image compression,” IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP–32, no. 3, pp. 664–668, Jun. 1984. [3] V. Udpikar and J. P. Raina, “Modified algorithm for block truncation coding of monochrome images,” Electron. Lett., vol. 21, no. 20, pp. 900–902, Sep. 1985. [4] Q. Kanafani, A. Beghdadi, and C. Fookes, “Segmentation-based image compression using BTC-VQ technique,” in Proc. IEEE Int. Conf. Information Science Signal Processing and their Applications, Paris, Jul. 1–4, 2003, vol. 1, pp. 113–116. [5] S. Horbelt and J. Crowcroft, “A hybrid BTC/ADCT video codec simulation bench,” presented at the Proc. 7th Int. Workshop on Packet Video, Mar. 18–19, 1996. [6] M. Kamel, C. T. Sun, and G. Lian, “Image compression by variable block truncation coding with optimal threshold,” IEEE Trans. Signal Process., vol. 39, no. 1, pp. 208–212, Jan. 1991. [7] L. G. Chen and Y. C. Liu, “A high quality MC-BTC codec for video signal processing,” IEEE Trans. Circuits Syst. Video Technol., vol. 4, no. 1, pp. 92–98, Feb. 1994. [8] R. Ulichney, Digital Halftoning. Cambridge, MA: MIT Press, 1987. [9] R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial gray scale,” in Proc. SID 75 Dig. Soc. Information Display, 1975, pp. 36–37. [10] J. F. Jarvis, C. N. Judice, and W. H. Ninke, “A survey of techniques for the display of continuous-tone pictures on bilevel displays,” Comput. Graph. Image Process., vol. 5, pp. 13–40, 1976. [11] P. Stucki, MECCA-A Multiple-Error Correcting Computation Algorithm for Bilevel Image Hardcopy Reproduction IBM Res. Lab., Zurich, Switzerland, Res. Rep. RZ1060, 1981. [12] V. Ostromoukhov, “A simple and efficient error-diffusion algorithm,” in Proc. SIGGRAPH, 2001, pp. 567–572. [13] J. N. Shiau and Z. Fan, “A set of easily implementable coefficients in error diffusion with reduced worm artifacts,” Proc. SPIE-Int. Soc. Opt. Eng., vol. 2658, pp. 222–225, 1996. [14] P. Li and J. P. Allebach, “Tone-dependent error diffusion,” IEEE Trans. Image Process., vol. 13, no. 2, pp. 201–215, Feb. 2004. [15] P. Li and J. P. Allebach, “Block interlaced pinwheel error diffusion,” J. Electron. Imag., vol. 14, no. 2, Apr.–Jun. 2005. [16] D. E. Knuth, “Digital halftones by dot diffusion,” ACM Trans. Graph., vol. 6, no. 4, Oct. 1987. [17] M. Mese and P. P. Vaidyanathan, “Optimized halftoning using dot diffusion and methods for inverse halftoning,” IEEE Trans. Image Process., vol. 9, no. 4, pp. 691–709, Apr. 2000. [18] M. Analoui and J. P. Allebach, “Model based halftoning using direct binary search,” in Proc. SPIE, Human Vision, Visual Proc., Digital Display III, San Jose, CA, Feb. 1992, vol. 1666, pp. 96–108. [19] Q. Lin and J. P. Allebach, “Color FM screen design using DBS algorithm,” Proc. SPIE-Int. Soc. Opt. Eng., vol. 3300, pp. 353–361, 1998. [20] A. U. Agar and J. P. Allebach, “Model-based color halftoning using direct binary search,” IEEE Trans. Image Process., vol. 14, no. 12, pp. 1945–1959, Dec. 2005. [21] J. M. Guo, “Improved block truncation coding using modified error diffusion,” IET Electron. Lett., vol. 44, no. 7, pp. 462–464, Mar. 2008. [22] J. M. Guo and M. F. Wu, “Improved block truncation coding based on the void-and-cluster dithering approach,” IEEE Trans. Image Process., vol. 18, no. 1, pp. 211–213, Jan. 2009. [23] I. J. Cox, J. Kilian, F. T. Leighton, and T. Shamoon, “Secure spread spectrum watermarking for multimedia,” IEEE Trans. Image Process., vol. 6, no. 12, pp. 1673–1687, Dec. 1997. [24] S. F. Tu and C. S. Hsu, “A BTC-based watermarking scheme for digital images,” Int. J. Inf. Security, vol. 15, no. 2, pp. 216–228, 2004. [25] M. H. Lin and C. C. Chang, “A novel information hiding scheme based on BTC,” in Proc. Int. Conf. Computer and Information Technology, 2004, vol. 14–16, pp. 66–71.

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Jing-Ming Guo (M’06) was born in Kaohsiung, Taiwan, R.O.C., on November 19, 1972. He received the B.S.E.E. and M.S.E.E. degrees from National Central University, Taoyuan, Taiwan, in 1995 and 1997, respectively, and the Ph.D. degree from the Institute of Communication Engineering, National Taiwan University, Taipei, Taiwan, in 2004. From 1998 to 1999, he was an Information Technique Officer with the Chinese Army. From 2003 to 2004, he was granted the National Science Council scholarship for advanced research from the Department of Electrical and Computer Engineering, University of California, Santa Barbara. He is currently an Associate Professor with the Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei. His research interests include multimedia signal processing, multimedia security, digital halftoning, and digital watermarking. Dr. Guo is a member of the IEEE Signal Processing Society. He received the Excellence Teaching Award in 2009, the Research Excellence Award in 2008, the Acer Dragon Thesis Award in 2005, the Outstanding Paper Awards from IPPR, Computer Vision and Graphic Image Processing in 2005 and 2006, and the Outstanding Faculty Award in 2002 and 2003.

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Yun-Fu Liu (S’09) was born in Hualien, Taiwan, R.O.C., on October 30, 1984. He received the M.S.E.E. degree from the department of Electrical Engineering, Chang Gung University, Taoyuan, Taiwan, in 2009, and is currently a doctorate student in the Department of Electronic Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan. His research interests include intelligent transportation system, digital halftoning, and digital watermarking.

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