A Unified Min-Max Transition-Based Data Hiding Algorithm for ...

JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 24, 1159-1173 (2008)

Short Paper__________________________________________________ A Unified Min-Max Transition-Based Data Hiding Algorithm for Mixed Text/Halftone Images* SHIH-TUNG WU, KUO-LIANG CHUNG, YONG-HUAI HUANG AND JUNG-GEN WU+ Department of Computer Science and Information Engineering National Taiwan University of Science and Technology Taipei, 106 Taiwan E-mail: [email protected] + Department of Computer Science and Information Engineering National Taiwan Normal University Taipei, 106 Taiwan Recently, several algorithms have been developed to hide data in either text images or halftone images. According to an observation that the number of transitions between black pixel and white pixel in the halftone image is much larger than that in the text image, this paper presents a unified min-max transition (MMT) scheme to embed data into the above two types of images without visual degradation. For text (halftone) images, data hiding can be performed by modifying the values of pixels to minimize (maximize) the number of the transitions. Based on our proposed MMT scheme, a unified block- and MMT-based data hiding (BMMTDH) algorithm is developed for text images, halftone images, and mixed text/halftone (MTH) images. Experimental results demonstrate that for MTH images, our proposed BMMTDH algorithm outperforms the previous relevant algorithms. Keywords: data hiding, flippable pixel hafltone image, maximum transition, minimal transition, mixed text/halftone image, text image

1. INTRODUCTION Due to the growth of internet and digital media, the issue of data hiding [2] becomes more and more important since hiding data into digitized images has many applications, such as authentication, identification, annotation, and copyright protection, etc. Among these digitized images, halftone images [13], text images, and mixed text/halftone (MTH) images are three widely used binary document images. Previously, several algorithms have been presented to hide data in either text images or halftone images [4-9, 11, 12, 14]. For text images, Zhao and Koch [16] embed one’s (or zero’s) into each selected block by enforcing the ratio of the number of black pixels over that of white pixels to be larger (or smaller) than 1. In [5, 7], the concept of modifying word spaces or line spaces Received October 11, 2006; revised January 2 & March 30, 2007; accepted April 26, 2007. Communicated by Tzong-Chen Wu. * This research was supported by the National Council of Science of Taiwan, R.O.C. under contract No. NSC 95-2221-E-011-153.

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is used to embed data into text images. Tseng et al. [11] utilize a secret key and a weight matrix to embed data into the input text image. Tzeng and Tsai [12] proposed a pixelbased data hiding algorithm to minimize the image distortion. Wu and Liu [14] presented a block-based algorithm to embed data by flipping pixels according to the consideration of connectivity and smoothness in each block. For halftone images, Fu and Au [4] embed data into those randomly selected pixels by modifying the values of pixels to minimize the connection in a 3 × 3 subimage. By using two different error diffusion kernels, Pei and Guo [8] presented a kernel-alternated error diffusion scheme to combine halftoning and data hiding. Pei and Guo [9] further proposed an improved data hiding algorithm with higher capacity to embed data into a set of halftone images. Kacker and Allebach [6] adopt the direct binary search halftoning algorithm to transform a grey image into a halftone image, and then a block-based spread spectrum scheme is used to hide data in the halftone image. According to an observation that the number of transitions between black pixel and white pixel in the halftone image is much larger than that in the text image, this paper presents a unified min-max transition (MMT) scheme to embed data into the above two types of images without visual degradation. For text (halftone) images, data hiding can be performed by modifying the values of pixels to minimize (maximize) the number of the transitions. Based on our proposed MMT scheme, a unified block- and MMT-based data hiding (BMMTDH) algorithm is developed for text images, halftone images, and MTH images. Experimental results demonstrate that for MTH images, our proposed BMMTDH algorithm outperforms the previous relevant algorithms.

2. THE PROPOSED UNIFIED MMT SCHEME FOR TEXT IMAGES AND HALFTONE IMAGES In this section, by adopting the concept of flippable pixels [14], our proposed unified MMT scheme is presented to determine theses flippable pixels in both text images and halftone images. As shown in Figs. 1 (a) and (b), it is observed that in text images, usually black pixels or white pixels are connected together; in halftone images, usually black pixels and white pixels are appeared alternately. The following property is given to distinguish the text image from the halftone image. Property 1 The number of transitions between black pixel and white pixel in the halftone image is much larger than that in the text image. By Property 1, a unified MMT scheme is proposed to select pixels for hiding data in text images and halftone images without visual degradation. In our proposed MMT scheme, the input text image is first partitioned into equal-sized blocks. For each text block, our proposed MMT scheme flips each pixel and counts the number of transitions between black pixel and white pixel; the pixel results in minimal number of transitions is the flippable pixel in the block. In the text block X, the pixel X(i', j') is a flippable pixel if it satisfies the following equality: (i ′, j ′) = arg min

( i ′, j ′ )

∑

(i , j )∈ X

t f (i, j , i ′, j ′).

(1)

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(a) Text image.

(b) Halftone image. Fig. 1. Two examples.

In Eq. (1), the function tf is defined by

⎧ X (i, ⎪ ⎪⎪ X (i, t f (i, j , i ′, j ′) = ⎨ ⎪ X (i, ⎪ ⎪⎩ X (i,

j ) − X (i − 1, j ) + X (i, j ) − X (i, j − 1) ,

if i = i ′ and j = j ′

j ) − X (i − 1, j ) + X (i, j ) − X (i, j − 1) ,

if i = i ′ + 1 and j = j ′

j ) − X (i − 1, j ) + X (i, j ) − X (i, j − 1) ,

if i = i ′ and j = j ′ + 1

j ) − X (i − 1, j ) + X (i, j ) − X (i, j − 1) ,

otherwise

(2)

where X (i, j ) denotes the complement of X(i, j) and |x| denotes the absolute value of x. The transition between X(i, j) and X(i + 1, j) (X(i, j) and X(i, j + 1)) is not considered in Eqs. (1) and (2) because it will be checked when (i, j) = (i + 1, j) ((i, j) = (i, j + 1)). By the same argument, our proposed MMT scheme partitions the input halftone image into equal-sized blocks and for each halftone block X, Eq. (3) is used to select the flippable pixel X(i', j') which results in maximum number of transitions.

(i ′, j ′) = arg max ( i ′, j ′ )

∑

(i , j )∈ X

t f (i, j , i ′, j ′)

(3)

After the flippable pixel in each block has been determined, we embed data into the blocks according to the following way. In the data embedding process, each block can be embedded at most one bit. If the current embedding bit is one, the number of black pixels in the current block is enforced to even, i.e. the flippable pixel must be flipped if the number of black pixels is odd; otherwise, the number of black pixels in the current block is enforced to odd. In the data extracting process, we can check the number of black pixels in each block to determine the embedded bit is one or zero. Figs. 2 and 3 are used to illustrate the effectiveness of our proposed MMT scheme. Fig. 2 (a) shows a text image used to embed six-bit hiding data. We partition the text image into 64 equal-sized blocks and among them, we randomly select six blocks to be embedded by using the minimal transition scheme. After the six-bit hiding data has been embedded into the text image, we have a marked text image as shown in Fig. 2 (b). Instead of using the minimal transition scheme, Fig. 2 (c) is a marked text image by embedding the six bits into the randomly selected six blocks. In Figs. 2 (b) and (c), the gray pixels denote the original image pixels and the black pixels denote the six hiding data. From the small example in Fig. 2, the proposed minimal transition scheme works well for embedding data into the text image without visual degradation. By the same argument,

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(a) (b) (c) Fig. 2. Example for illustrating the effectiveness of our proposed minimal transition scheme. (a) Input text image; (b) The marked text image using the proposed minimal transition scheme; (c) The market text image without using the proposed minimal transition scheme.

(a) (b) (c) Fig. 3. Example for illustrating the effectiveness of our proposed minimal transition scheme. (a) Input halftone image; (b) The marked halftone image using the proposed minimal transition scheme; (c) The marked halftone image without using the proposed minimal transition scheme.

we can embed six-bit into a halftone image, where Fig. 3 (a), Fig. 3 (b) and Fig. 3 (c) denote the original halftone image and two relevant marked halftone images with and without using our proposed maximum transition scheme, respectively. Fig. 3 (b) shows that our proposed maximum transition scheme can embed data into the halftone image without visual degradation. In summary, the above two transition scheme can be combined to constitute the proposed min-max transition scheme for embedding the text image and the halftone image.

3. THE PROPOSED UNIFIED BLOCK-AND MMT-BASED DATA HIDING ALGORITHM In this section, based on our proposed MMT scheme, we propose a unified blockand MMT-based data hiding (BMMTDH) algorithm to embed data into MTH images. 3.1 Classify Blocks

The input MTH image is of size M × N and the hiding data is an m × n binary image. In order to embed the hiding binary image into the input image evenly, the proposed N BMMTDH algorithm partitions the input image into mn blocks, each with size M m× n. For ease of exposition, the size of input MTH image and hiding binary image are set to 1024 × 1280 and 32 × 40, respectively, and thus the input MTH image is partitioned into 32 × 40 blocks, each block with size 32 × 32. In order to apply our proposed MMT scheme to embed data into each block, all partitioned blocks must be classified according to the major content of each block. In the proposed BMMTDH algorithm, each 32 × 32 block is further partitioned into 16 equal-sized subblocks, each subblock with size 8 × 8 since each small subblock might contain simple content. Thus, the major content of each block can be determined by the majority of text subblocks or halftone subblocks.

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From Property 1, it is known that the number of transitions between black pixel and white pixel in the input image is an important characteristic to distinguish the text image from the halftone image. The number of transitions Ntr in a subblock X is defined as follows.

N tr =

∑

X (i, j ) − X (i − 1, j ) + X (i, j ) − X (i, j − 1)

(4)

(i , j )∈ X

From a large set of training subblocks, we find that the value of Ntr in text and halftone subblocks are ranged from 12 to 41 and ranged from 18 to 102, respectively. To alleviate the classification error caused by the case when both text and halftone contents appear in that subblock, a second feature is required. In section 2, it has been indicated that in text images, black pixels or white pixels are often connected together; in halftone images, black pixels and white pixels often appeared alternately. Thus, we have the following property. Property 2 The number of isolated pixels in the halftone image is much larger than that in the text image.

From Property 2, the number of isolated pixels Ni in a subblock X is defined by Ni =

⎛ ⎞ ⎜ ⎟ ⊕ X ( i , j ) X ( k , l ) ∑ ∏ ⎟ (i , j )∈X ⎜ ⎝ ( k ,l )∈Yi , j ⎠

(5)

where the symbol ⊕ denotes the exclusive OR operation and Yi,j denotes eight neighboring pixels of pixel X(i, j). Besides the text content and halftone content, the sparse/blank content are further considered in our proposed algorithm since embedding data into this kind of content will result in visual degradation. To distinguish sparse/blank content from text content and halftone content, the number of black pixels Nb in the subblock X is defined by Nb =

∑

X (i, j ),

(i , j )∈X

⎧1, if X (i, j ) is a black pixel X (i, j ) = ⎨ . ⎩0, otherwise

(6)

After Ntr, Ni, and Nb in each subblock have been calculated by Eqs. (4)-(6), the following four rules are used to classify each sub-block to be a text subblock, a halftone subblock, or a sparse/blank subblock. Rule 1: A subblock is a sparse/blank subblock if the number of black pixels, Nb, is smaller than the threshold TNb. Rule 2: A subblock is a halftone subblock if the number of transitions, Ntr, is larger than the threshold TNt . r

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Rule 3: A subblock is a halftone subblock if Ntr is not larger than TNt , but the number of r isolated pixels, Ni, is larger than the threshold TNi. Rule 4: A subblock is a text subblock if it is neither a sparse/blank subblock nor a halftone subblock.

Among the above four rules, halftone subblocks can be recognized by Rule 2 or Rule 3. Fig. 4 shows three kinds of sub-blocks classified by Rules 1-4. The three thresholds TNb, TNt , and TNi are obtained by using a large set of training images and the training r process will be described in section 4.

(a) (b) (c) Fig. 4. Three kinds of sub-blocks classified by Rules 1-4. (a) Sparse/blank sub-blocks classified by Rule 1; (b) Halftone sub-blocks classified by Rule 2; (c) Text and halftone sub-blocks classified by Rules 3 and 4, respectively.

After all subblocks in the current block have been classified by Rules 1-4, we next count the number of text sub-blocks Nt, the number of halftone sub-blocks Nh, and number of sparse/blank subblock Ns. Finally, the current block can be classified to be either a sparse/blank block, a text block, or a halftone block by using the following three rules. Rule 5: A block is a sparse/blank block if the number of sparse/blank subblock, Ns, is larger than the threshold TNs. Rule 6: A block is a halftone block if Ns is smaller than or equal to TNs and the number of halftone subblock, Nh, is larger than the number of text subblocks Nh. Rule 7: A block is a text block if it is neither a sparse/blank block nor a halftone block. 3.2 Estimate the Embedding Capacity of Each Block

According to the seven rules mentioned in the least subsection, each block of the input image has been classified to be a sparse/blank block, a text block, or a halftone block. Since the major portion of sparse/blank blocks is empty and they are not suitable to embed data, some other text or halftone blocks in the input image can be considered to the candidates; for this case, these selected candidates may be assigned more than one bit data in the data embedding process. Thus, the embedding capacity of each text or halftone block should be estimated. In our proposed BMMTDH algorithm, the embedding capacity of a text (halftone) block is determined by the number of its own embeddable text (halftone) subblocks using the proposed min (max) transition scheme. Note that a subblock may contain more than

AN EFFICIENT DATA HIDING ALGORITHM FOR MIXED TEXT/HALFTONE DOCUMENT IMAGE 1165

one kind of contents when that subblock is lying on the boundary between two different contents. To enhance the robustness of our proposed MMT scheme, the following property is utilized to find the pure text (halftone) subblocks in each text (halftone) block. Property 3 If the majority of neighboring subblocks of the current text (halftone) subblock are text (halftone) subblocks, the current subblock has a high probability to be a pure text (halftone).

(a) (b) (c) (d) Fig. 5. Example for selecting the pure halftone subblocks. (a) A 48 × 48 subimage with a 32 × 32 block; (b) Subblock partition; (c) Type of each subblock; (d) NH for each subblock.

Figs. 5 (a)-(c) show the example to illustrate Property 3. Fig. 5 (a) illustrates a 48 × 48 subimage where a 32 × 32 block is cut off. Fig 6 (b) illustrates the magnified subimages, block, and partitioned subblocks. According to Rules 1-4 mentioned in subsection 3.1, the type of each partitioned subblock is shown in Fig. 5 (c). Based on Rules 5-7, the block in Fig. 5 (a) is classified to be a halftone block. Thus, given a text (halftone) subblock Xi, Eq. (7) is used to calculate the number of neighboring text (halftone) subblocks, says NH. NH =

∑

j∈YX i

C( Xi , X j )

⎧⎪1, if both X i and X j are text or halftone subblocks C( Xi , X j ) = ⎨ ⎪⎩0, otherwise

(7)

where YXi denotes the eight neighboring subblocks of Xi. Fig. 5 (d) shows the value of NH’s for these 16 subblocks in the current block. Suppose it is known that the current block is a text (halftone) block, we then want to identify those pure text (halftone) subblocks as the embeddable text (halftone) subblocks by Eq. (7). In order to maximize the visual quality, for each text (halftone) block, we select text (halftone) subblocks with maximal NH as the embeddable subblock for the minimal (maximal) transition scheme. Consequently, the embedding capacity of a block is equal to the number of its own embeddable subblocks. For example, the embedding capacity of the block in Fig. 5 (a) is six bits since there are six subblocks with maximum NH (= 8) and each of these subblocks can be embedded one-bit data. In our proposed BMMTDH algorithm, if a data bit wants to be assigned to a sparse/blank block, a text or

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halftone block whose embedding capacity is large than one bit indeed can provide an embeddable subblock to embed this bit. After embeddable subblocks of each block are determined, we now consider the embedding order of those embeddable subblocks. From the consideration of visual quality, the number of transitions Ntr (see Eq. (4)) is utilized to determine the priority of each embeddable subblock. Thus, for each text block, we sort embeddable subblocks by the values of Nt′r s in descending order. Based on the order of sorted embeddable subblocks, the first embeddable subblock is the subblock with highest priority, the second one is the subblock with second priority, and so on. By the same argument, the priority of each embeddable subblock in the halftone block can also be determined by sorting these subblocks by the values of Nt′r s in increasing order. Afterwards, when we want to embed more than one bit into a block, the first bit is embedded into the subblock with highest priority, the second bit is embedded into the subblock with second priority, and so on. 3.3 Embedding Data

To embed data into the input image, each bit in the data is assigned to a block of the input image. No matter what the assigned text or halftone block is, we embed this bit into the subblock with highest priority. If the assigned block is a sparse/blank block, the other block whose embedding capacity is larger than one can loan an unused embeddable subblock to support the embedding work. In our proposed BMMTDH algorithm, the shuffling method proposed by Wu and Liu [14, 15] is adopted to deal with this job. Adopting the shuffling method, embedding bits distributed to text/halftone blocks are assigned to the subblocks with highest priority and the subblocks with second priority are used to hide embedding bits which are assigned to sparse/blank blocks. If the total number of subblocks with second priority is less than the number of sparse/blank blocks, the subblocks with third priority will be utilized to hide data. The above shuffling process is performed until each bit in the hiding image have been assigned to an embeddable subblock. Each pair of sparse/blank blocks and the selected embeddable subblocks must be recorded in the shuffling table. To save the space of the context, the detail of the shuffling method is omitted here and it can be referred in [14, 15]. After embedding hiding image into the input image, we next explain how to extract the embedded data. 3.4 Data Extracting Process

To extract the hiding image from the marked image, we partition the marked image into 32 × 40 blocks, each block with size 32 × 32. For each block, the subblock partition is performed to obtain 16 subblocks, each subblock with size 8 × 8. The embeddable subblocks which have been used to embedded data can be extracted by using the shuffling method. In the embedding process, the number of black pixels in each embedded subblock is enforced to even (odd) when current embedding bit is one (zero). Thus, the embedded bit in each extracted subblock is one (zero) exactly when the number of black pixels is even (odd). Finally, the whole hiding image can be extracted from the marked image.

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4. EXPERIMENTAL RESULTS 4.1 Threshold Training

Before implementing our proposed BMMTDH algorithm, a training process is performed to obtain the four thresholds TNb, TNt , TNi, and TNs mentioned in section 3.1. From r a large set of MTH training images, the block partition and subblock partition are performed to each MTH training image to generate a large set of training subblocks. Each training subblock is classified to be the text or halftone artificially. To obtain the three thresholds TNb, TNt , and TNi, we test different cases and use Rules 1-4 to classify the trainr ing subblocks. In our training process, TNb = 10, TNr = 45, and TNi = 2 can minimize the error rate of subblcok classification. By the same argument, the threshold TNs used in Rules 5-7 is set to 8. 4.2 Performance Comparison

In our experiments, two relevant data hiding algorithms, one proposed by Wu and Liu [14] for text images and the other proposed by Fu and Au [4] for halftone images, are implemented to evaluate the performance of our proposed BMMTDH algorithm. The data hiding algorithms proposed by Pei and Guo [6] and Kacker and Allebach [6] are not included in our experiments since the input images used in these algorithms are gray level images. As shown in Fig. 6, two 1024 × 1280 MTH images, one with the majority of text contents and the other with the majority of halftone contents, are used to evaluate the

(a) The MTH image with the majority of text (b) The MTH image with the majority of halfcontents. tone contents. Fig. 6. Two testing MTH images.

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Fig. 7. Binary hiding image.

Table 1. Quality comparison for Figs. 11 (a)-(c) in terms of PSNR. Algorithm BMMTDH Algorithm [14]

Fig. 11 (a) 43.91 44.02

Fig. 11 (b) 44.06 44.17

Fig. 11 (c) 43.15 43.21

Table 2. Quality comparison for Figs. 12 (a)-(c) in terms of PSNR. Algorithm BMMTDH Algorithm [4]

Fig. 12 (a) 44.66 43.88

Fig. 12 (b) 44.05 43.14

Fig. 12 (c) 42.61 41.92

Table 3. Quality comparison for Figs. 13 (a)-(c) in terms of PSNR. Algorithm BMMTDH Algorithm [14] Algorithm [4]

Fig. 13 (a) 43.77 43.25 43.02

Fig. 13 (b) 42.87 42.19 42.01

Fig. 13 (c) 44.85 43.24 43.66

Fig. 13 (d) 44.75 43.78 43.85

Table 4. Execution-time comparison for Figs. 11-13 in terms of second. Algorithm BMMTDH Algorithm [14] Algorithm [4]

(a) 4.45 4.39 0.41

Fig. 11 (b) (c) 5.78 5.91 5.12 5.20 0.45 0.44

(a) 5.98 5.70 0.51

Fig. 12 (b) (c) 6.07 6.12 5.68 5.69 0.41 0.49

(a) 5.25 5.12 0.50

Fig. 13 (b) (c) 5.45 5.68 5.07 5.38 0.45 0.53

(d) 5.52 5.25 0.50

effectness of our proposed algorithm. Fig. 7 denotes a 32 × 40 binary hiding image to be embedded into Figs. 6 (a) and (b). Figs. 8 (a) and (b) show two marked MTH images obtained by performing our proposed BMMTDH algorithm to embed Fig. 7 into Figs. 6 (a) and (b), respectively. From Figs. 6 and 8, it observed that it is difficult to distinguish original MTH images from marked MTH images by human visual system. Figs. 9 (a) and (b) are two magnified text subimages of Figs. 6 (a) and 8 (a), respectively. The data hiding algorithm for text image [14] is performed to embed Fig. 7 into Fig. 6 (a) and the magnified text subimages of the marked image is shown in Fig. 9 (c). In Figs. 9 (b) and (c), the gray pixels denote the original image pixels and the black pixels denote the hiding data. From the magnified text subimages in Fig. 9, the visual quality of the proposed BMMTDH algorithm is quite competitive to that of [14] for text contents. By the same argument, Figs. 10 (a)-(c) show the magnified halftone subimages of Fig. 6 (b), Fig. 8 (b), and the marked image by running the data hiding algorithm for halftone image [4], respectively. It can be observed that for halftone content, the visual quality of the proposed BMMTDH algorithm is also quite competitive to that of [4]. Further, more testing images are used to demonstrate the visual quality of our proposed BMMTDH algorithm. Fig. 11 shows three text images and we first run the data

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(a) The marked MTH image of Fig. 6 (a). (b) The marked MTH image of Fig. 6 (b). Fig. 8. Two marked MTH images.

(a) (b) (c) Fig. 9. Magnified text subimages for visual quality comparison. (a) The magnified text subimage of Fig. 6 (a); (b) The magnified text subimage of Fig. 8 (a); (c) The magnified text subimage of the marked image using the data hiding algorithm for text image [14].

(a) (b) (c) Fig. 10. Magnified halftone subimages for visual quality comparison. (a) The magnified halftone subimage of Fig. 6 (b); (b) The magnified halftone subimage of Fig. 8 (b); (c) The magnified halftone subimage of the marked image using the data hiding algorithm for halftone image [4].

hiding algorithm for text image [14] and our proposed BMMTDH algorithm to embed Fig. 7 into Fig. 11. The edge- and LUT-based inverse halftoning algorithm [1] is applied to reconstruct original and marked text images to gray original and marked text images, respectively, for evaluating the quality performance in terms of peak signal-to-noise ratio (PSNR). Table 1 shows the PSNR comparison between the data hiding algorithm [14] and our proposed BMMTDH algorithm for text image. From Table 1, it is demonstrated

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(a)

(b) Fig. 11. Three testing text images.

(a)

(b) Fig. 12. Three testing halftone images.

(c)

(c)

that the PNSR performance of our proposed BMMTDH algorithm is quite competitive to that of [14]. We also perform the data hiding algorithm [4] and our proposed BMMTDH algorithm image to embed Fig. 7 into three halftone images as shown in Fig. 12. By using the inverse halftoning algorithm [1], the PSNR comparison is shown in Table 2. Since the inverse halftoning algorithm utilizes the neighboring pixels to reconstruct the gray value of the current pixel, it may result in larger reconstruction errors around the neighbors of each isolated pixel. Because the number of isolated pixels created in our proposed algorithm is less than that in [4], the quality of the reconstructed gray image can be improved significantly by using the proposed algorithm. From Table 2, it is demonstrated that our proposed BMMTDH algorithm has better PNSR performance when compared to [4]. Finally, we perform the above three algorithms to four MTH images in Fig. 13. As shown in Table 3, the PSNR comparison among these three algorithms demonstrate that our proposed BMMTDH algorithm outperforms the previous two relevant algorithms. Table 4 shows the execution-time comparison for Figs. 11-13. From Table 4, it is observed that the execution-time of our proposed BMMTDH algorithm is slightly slower than that of [14] since our proposed BMMTDH algorithm requires additional time in the block classi-

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(a)

(b) (c) Fig. 13. Four testing MTH images.

(d)

(a) (b) (c) (d) Fig. 14. Marked images under different attacks. (a) Drawing attack to Fig. 8 (a); (b) Noising attack to Fig. 8 (a); (c) Cropping attack to Fig. 8 (b); (d) Tempering attack to Fig. 8 (b).

(a) (b) (c) (d) (e) (f) Fig. 15. Extracted hiding images. (a) and (b) are the hiding images extracted from Figs. 8 (a) and (b), respectively; (c)-(f) are the hiding images extracted from Figs. 14 (a)-(d), respectively.

Table 5. Error rates of extracted hiding images. Error rate

Fig. 15 (a) 0%

Fig. 15 (b) 0%

Fig. 15 (c) 8.7%

Fig. 15 (d) 3.8%

Fig. 15 (e) 27.9%

Fig. 15 (f) 3.5%

fication process. In addition, Table 4 also shows that [14] and our proposed BMMTDH algorithm spend much more execution-time when compared to [4]; the reason is that [14] and our proposed BMMTDH algorithm need to consider the whole image to determine the flippable pixels, but in [4], only the selected pixels are required to perform the connection minimization for data embedding. The robustness of our proposed BMMTDH algorithm is verified by applying different attacks to marked images. Fig. 14 shows four attacked marked images where Figs. 14 (a) and (b) are the results by using the drawing attack and the cropping attack to Fig. 8 (a), respectively; Figs. 14 (c) and (d) are the results by using the noising attack and the tempering attack to Fig. 8 (b), respectively. Fig. 15 shows the hiding image extracted from

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SHIH-TUNG WU, KUO-LIANG CHUNG, YONG-HUAI HUANG AND JUNG-GEN WU

marked images with or without attack. Figs. 15 (a) and (b) are hiding images extracted from Figs. 8 (a) and (b), respectively. The hiding images extracted from Figs. 14(a)-(d) are shown in Figs. 15 (c)-(f), respectively, and Table 5 shows the error rates of these extracted hiding images. Fig. 15 and Table 5 demonstrate that our proposed BMMTDH algorithm is rather robust to different attacks.

5. CONCLUSION In this paper, we have proposed a unified MMT scheme to embed data into text and halftone images without visual degradation. Based on our proposed MMT scheme, a unified BMMTDH algorithm is developed for text images, halftone images, and MTH images. For evaluating the quality performance in terms of PSNR, the edge- and LUT-based inverse halftoning algorithm [1] is applied to reconstruct gray images from binary images. Experimental results show that our proposed BMMTDH algorithm is rather robust to different attacks.

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