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IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 21, NO. 12, DECEMBER 2012

High Capacity Data Hiding for Error-Diffused Block Truncation Coding Jing-Ming Guo, Senior Member, IEEE, and Yun-Fu Liu, Student Member, IEEE

Abstract— Block truncation coding (BTC) is an efficient compression technique with extremely low computational complexity. However, the blocking and false contour effects are two major deficiencies in BTC which cause severe perceptual artifacts. The former scheme, error-diffused BTC (EDBTC), can significantly improve the above issues through the visual low-pass compensation on the bitmap, which thus widens its possible application market, yet the corresponding security issue may limit its value. In this paper, a method namely complementary hiding EDBTC is developed to cope the above issue. This paper is managed by firstly discussing when a single watermark is embedded, and then multiple watermarks are employed to test the limitation of the proposed scheme. Herein, an adaptive external bias factor is employed to control the watermark embedding, and this factor also affects the image quality and robustness simultaneously. Experimental results demonstrate that the proposed method only requires an extremely small external bias factor to carry watermarks, which enables a high capacity scenario without significantly damaging image quality. Index Terms— Block truncation coding (BTC), data hiding, error diffusion, secret sharing, spread spectrum.

I. I NTRODUCTION

B

LOCK TRUNCATION CODING (BTC) was firstly introduced by Delp and Mitchell in 1979 [1]. The standard procedure is to divide an image into non-overlapped blocks, and every pixel in a block is represented by either high- or low-mean of the block according to the corresponding binary bitmap. The principal advantage of this method is its very low computational complexity compared to some modern compression techniques, such as JPEG or JPEG2000. However, the image quality obtained by the traditional BTC degrades rapidly with the increase of coding gain. For this, several investigations have addressed this issue by further improving the image quality or the coding gain of the BTC [2]–[6], which include using Vector Quantization (VQ) to further compress the overhead information of the BTC outputs [2]; applying a hybrid coding model by using the Look-Up-Table (LUT)-based VQ to fast encode the bitmap while employing the Discrete Cosine Transform (DCT) to encode the high- and low-mean sub-images [3]; adopting universal Hamming code and Differential Pulse Code Modulation (DPCM) to the bit-plane and

Manuscript received January 19, 2012; revised June 11, 2012; accepted July 6, 2012. Date of publication July 25, 2012; date of current version November 14, 2012. This work was supported in part by the National Science Council, Taiwan, under Contract NSC 101-2221-E-011 -136 -MY3. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Jana Dittmann. The authors are with the Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei 10607, Taiwan (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TIP.2012.2210236

the side information of BTC to reduce bit-rate and preserve a low computational complexity [4]; using moment and visual information to determine the regions for further BTC processing or just neglecting to reduce the computational overhead, which preserves quality while enabling the possibility of real-time processing [5], and employing a two-step criterion to determine whether or not a block is encoded with its neighboring coded blocks to reduce the bit rate of the BTCcompressed images [6]. Digital halftoning [7] is a technique for converting grayscale images into binary fashion (so-called halftone images). These halftone images can resemble the original grayscale images when viewed from a distance by the low-pass nature of Human Visual System (HVS). Many important halftoning schemes have been developed, such as Ordered Dithering (OD) [7], Error Diffusion (ED) [8], [9], and Dot Diffusion (DD) [10], [11]. Among these, OD provides the highest processing efficiency, ED offers good image quality, and DD presents a balance performance between the above two schemes. In our observation, the form of a halftone image is similar to the bitmap of a BTC image. Thus, many former methods have been proposed by catering halftoning to improve the quality or coding efficiency of the BTC, including the Error-Diffused BTC (EDBTC) [12], Ordered Dithering BTC (ODBTC) [13], and Dot-Diffused BTC (DDBTC) [14]. The main contributions of these halftoning-based BTC methods are that they can significantly reduce the blocking effect and the false contour while using fewer computations. Data hiding is a science of transmitting message in a hidden manner, whereas the message should be imperceptible. BTC is generally used for compression, and then transmits the compressed data to the receiver. Thus, it is also a good carrier to deliver extra information between two parties. Until now, few BTC-based data hiding/watermarking studies have been proposed, including the methods which exploit the characteristic of the BTC to hide continue-tone watermarks [15], [16]. The methods embed compressed watermarks into host images, and thus less data are required to be hidden, meaning that the marked image quality is relatively better than embedding those uncompressed continue-tone watermarks (in a typical BTC, a block can be compressed into M × N × 1 + 2 × 8 bits, where M × N denotes the block size, and 2×8 denotes the two grayscale quantized levels (high and low means). Conversely, another group of methods regards the BTC image as the carrier of watermarks. For example, based upon the premise that without changing the structure of BTC image, Chang et al. [17] selected some available blocks before hiding data, and employed the corresponding quantization levels and the

1057–7149/$31.00 © 2012 IEEE

GUO AND LIU: HIGH CAPACITY DATA HIDING FOR ERROR-DIFFUSED BTC

bitmap to hide data. This method can well preserve the image quality. Yet, the embedding capacity is unstable caused by the diverse properties of natural images. Recently, the halftoningbased methods were employed to embed watermarks while generating BTC-compressed images simultaneously [18], [19]. To exploiting the inherent advantage of the halftoning, the marked images can better cope with the human vision, and thus a better image quality can be yielded. Based upon the nature advantages of the halftoning-based BTC method, a high capacity data hiding scheme, called Complementary Hiding Error-Diffused Block Truncation Coding (CHEDBTC), is proposed in this study. The algorithm is designed based on the former EDBTC [12] scheme, and it is able to embed one or multiple watermarks. Former related works were hardly to achieve good balance between image quality and embedding capacity. Yet, as documented in the experimental results, the proposed method can achieve this goal by applying the concept of the spread spectrum [20]. The rest of this paper is organized as follows. Section II introduces the former EDBTC. Section III describes the proposed CHEDBTC, and this section is separated into two parts in terms of single and multiple watermarks embedding. The corresponding experimental results are presented in Section IV, and finally the conclusions are drawn in Section V. II. E RROR -D IFFUSED B LOCK T RUNCATION C ODING In this study, an EDBTC-based data hiding with a high image quality and data payload is proposed, in which the infrastructure of the former EDBTC [12] is briefly introduced in this section for providing a better comprehension of the proposed method. The traditional BTC [1] divides an original image into many non-overlapped blocks of size M × N, and each block can be processed independently. A corresponding flowchart is illustrated in Fig. 1. In this process, the firstmoment (x), ¯ second-moment (x 2 ), and variance (σ 2 ) of the input block are calculated to yield the mean, high-mean, and low-mean for further BTC processing. The corresponding calculations are organized below 1  M  N x i, j , x¯ = (1) M × N i=1 j =1 1 M N x2 , x2 = (2) M × N i=1 j =1 i, j ¯ 2, (3) σ 2 = x 2 − (x) where x i, j denotes the grayscale value of the original image (X). The concept of the BTC is to preserve the first- and second-moment characteristics of a block when the original block is substituted by its quantization levels. Thus, the following two conditions are maintained: m x¯ = (m − q) a + qb, mx 2

2

(4) 2

= (m − q) a + qb ,

(5)

where m = M × N, and q denotes the number of pixels with values greater than x. ¯ The high- and low-mean used to represent a block can be evaluated as follows  q , (6) a = x¯ − σ m−q

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Original block

Compressed block Obtain mean and two quantization levels

N

N

BTC M Fig. 1.

M Conceptual flow chart of the traditional BTC [1].

 b = x¯ + σ

m−q , q

(7)

where the two variables a and b denote the low-mean and high-mean, respectively. Since BTC is a one-bit quantizer, x¯ is employed for binarizing the block. The result is called bitmap which is used to record the distributions of the two quantization levels, low-mean and high-mean,   b, if h i, j = 1 1, if x i, j ≥ x¯ yi, j = where h i, j = ¯ a, if h i, j = 0, 0, if x i, j < x, (8) where h i, j denotes the element of the bitmap (H ), and yi, j denotes the element of the compressed BTC image (Y ). Since a BTC image normally accompanies with annoying false contour and blocking effect, an improved scheme, namely EDBTC [12], was developed to cope with these two issues. Figure 2 shows an example processed by the two methods, BTC and EDBTC, using the Elaine image [21]. The EDBTC exploits the inherent dithering property of the error diffusion to overcome false contour problem. Moreover, the blocking effect can also be eased by its error kernel, since both sides of a boundary between any pair of resulting image blocks being correlation. In a block process, the raster scan path (from left to right and top to bottom) is applied to process each pixel. The corresponding flowchart is shown in Fig. 3, and the related variables are defined below, v i, j = x i, j + x  i, j , where

ei, j = v i, j

x  i, j = (m,n) ei+m, j +n ×ekm,n, (9)  x max , if h i, j = 1 − yi, j , where yi, j = x min , if h i, j = 0,  1, if v i, j ≥ x¯ and h i, j = (10) ¯ 0, if v i, j < x.

The variables x i, j ∈ X and yi, j ∈ Y denote the input grayscale value and the EDBTC output, respectively. The output yi, j is substituted by either maximum (x max ) or minimum (x min ) of the block according to the bitmap h i, j ∈ H . The reason of choosing the extreme values to represent a block is to generate a dithered result to destroy the annoying blocking effect or false contour inherently existing in BTC images. The variable ekm,n, denotes the employed error kernel, which is used to diffuse the error ei, j to its neighboring pixels. Herein, the Floyd-Steinberg’s error kernel [8] as shown in Fig. 4 was employed, where the notation x denotes the current processing position. Notably, the error at the boundary of a block should

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X1 X2 W

Pseudorandom permutation

DW

De pseudorandom permutation

encoder

Y2 Y1

Secret key

(a) Fig. 5.

(b)

(c)

Fig. 2. Compressed results of different BTC methods. (a) Original Elaine image [21]. (b) Traditional BTC [1]. (c) EDBTC [12]. (All printed at 150 dpi.)

Thresholding hi,j xi,j

vi,j

+ x'i,j

+

Fill quantization levels + ei,j

Diffuse errors with error kernel

Fig. 3.

yi,j

Pixelwise processing flow chart of the EDBTC [12].

3/16 Fig. 4.

x 5/16

7/16 1/16

Floyd-Steinberg’s error kernel [8].

be diffused to its neighboring blocks, thus the blocking effect can be significantly eased. III. C OMPLEMENTARY H IDING EDBTC In this study, the concept of the secret sharing is employed to boost the security of the embedded data. Given a scenario that one watermark (W ) is embedded into two host images (X 1 and X 2 ) by the secret sharing scheme, the receiver requires to have the two marked images (Y 1 and Y 2 ) simultaneously for decoding the corresponding watermark (DW , if it does not suffer from any attack, it should resemble W ). Some of the methods utilizing this concept also employ an additional secret key to further improve the security of the watermark. By doing this, even if the embedding scheme is disclosed, the watermark is still encrypted safely. Thus, this strategy is also catered in the proposed scheme as illustrated in Fig. 5. The infrastructure of the proposed encoder and decoder is introduced in detail in this section. Moreover, the proposed method is extended to multiple watermarks embedding to increase the capacity of transmitted information, which is introduced at the end of this section. A. Encoder When an image is divided into blocks for EDBTC processing, each block is undergone identical processing procedure,

decoder

Conceptual diagram of the proposed data hiding.

thus in the following the explanation towards a single block processing is adopted for simplicity, and which can be easily extended to the whole image. Without losing generality, suppose the width and height of a block is defined as M and N, and M = N = β. In practical applications, the aspect ratio of a block is adjustable for security. Figure 5 shows that when two grayscale host images of size P × Q and one binary watermark of the same size as that of each host image are imported, the two corresponding marked images are then generated. In each marked block, two quantization levels and one bitmap are involved. According to the discussions toward Fig. 2, the EDBTC can overcome the blocking effect and false contour artifacts, thus the essential issue in this study is how to maintain a high marked image quality as similar to that of the original EDBTC image. The values in a bitmap are in 0 and 1, respectively, which can be considered as black and white two tones. Consequently, when the two different bitmap from two compressed EDBTC images processed by the exclusive NOR (XNOR) can yield an additional binary output, and which can be considered as a watermark. Considering the case when no watermark is embedded, in general around 50% of the XNOR result from the two EDBTC bitmaps is identical to a watermark. Thus, this study is to look for a strategy to force the other 50% as close as possible to the watermark while maintaining the image quality. Considering Fig. 3 and the variable h i, j defined in Eq. (10), the bitmap can be modified to embed a watermark. To that end, the input variable v i, j can be modified accordingly to adapt to the fluctuations in watermark, and then use the threshold x¯ to determine the final result. For instance, the definition of v i, j in Eq. (9) can be modified as v i, j = x i, j + x  i, j + ε,

(11)

where the parameter ε is a bias factor to force v i, j having higher or lower possibility greater or smaller than the threshold x¯ by controlling the bias factor as a positive or negative value. Yet, this additional factor also induces an additional error to the overall system. To cope with this, when ε is added to affect v i, j for embedding watermark, the error as defined in Eq. (10) should be simultaneously compensated with the following equation, ei, j = v i, j − yi, j − ε,

(12)

where the value of ε is identical to that used in Eq. (11). It is easy to imagine that a greater ε has a higher probability to obtain a correct h i, j for embedding watermark, and vice versa. Yet, a greater ε also degrades the marked image quality.

GUO AND LIU: HIGH CAPACITY DATA HIDING FOR ERROR-DIFFUSED BTC

In addition, in practice the grayscale distributions of the host blocks are unpredictable, thus making all of the host values modified with an identical ε to change the bitmap is unnecessary. For example, even though a case which simply requires a small external bias factor (suppose v i, j = 98 and x¯ = 100, and the goal is to make h i, j = 1) to change its expected state, a greater ε (= 15) is very likely to be utilized to meet most of the cases in the block. As a result, it will lead to unnecessary degradation in image quality, since it only requires a small ε (= 2 in this example). The issue can be solved with the proposed strategy as introduced below. Figure 6 illustrates the encoder of the proposed data hiding. When two grayscale host blocks are acquired, the differences between the means of the blocks and the modified host inputs si,t j are calculated as below, di,t j = x¯ t − si,t j ,

where si,t j = x i,t j + x  i, j , t

(13)

where the label t ∈ {1, 2} is used to designate the two different host images, and the mean x¯ t of the tth host image is defined in Eq. (1). Moreover, to know whether or not the output yielded by applying XNOR to si,1 j and si,2 j requires an additional external bias factor to modify the v i, j for carrying watermark, a pre-prediction index sti, j as defined below is calculated, ⎧

1 ≥ x¯ 1 ∧ s 2 < x¯ 2 ∨ ⎪ 0, if s ⎪ i, j i, j ⎪ ⎪

⎪ ⎪ ⎨ si,1 j < x¯ 1 ∧ si,2 j ≥ x¯ 2

(14) sti, j = 1 ≥ x¯ 1 ∧ s 2 ≥ x¯ 2 ∨ ⎪ 1, if s ⎪ i, j i, j ⎪ ⎪

⎪ ⎪ ⎩ si,1 j < x¯ 1 ∧ si,2 j < x¯ 2 , where the two operations ∧ and ∨ denote AND and OR, respectively; the 0 and 1 of the sti, j output represent black and white, respectively. Since the image quality is inversely proportional to the strength of the external bias factor, the label of the host image which only needs a relatively lower difference to make a different h ti, j is obtained by tc = argmint (di,t j ).

(15)

Subsequently, the position (i , j ) of the tc th host image (X tc ) is used to embed watermark with the following strategy, and X t¯c on the same position is still processed with Eqs. (9)–(10).   ⎧  tc  tc ⎪ d , if di, j  ≤ γ ∧ sti, j ⎪ ⎪ ⎪ i, j ⎪ ⎪ ⎪ = wi, j ∧ di,tc j ≥ 0 ⎪ ⎨   (16) v i,tc j = si,tc j + d tc − τ, if d tc  ≤ γ ∧ st i, j ⎪ i, j i, j ⎪ ⎪ ⎪ ⎪ = wi, j ∧ di,tc j < 0, ⎪ ⎪ ⎪ ⎩ 0, O.W, ei,tc j =

v i,tc j − yi,tc j

  ⎧  tc  tc ⎪ d , if di, j  ≤ γ ∧ sti, j ⎪ i, j ⎪ ⎪ ⎪ ⎪ ⎪ = wi, j ∧ di,tc j ≥ 0 ⎪ ⎨   − d tc − τ, if d tc  ≤ γ ∧ st (17) i, j ⎪ i, j i, j ⎪ ⎪ ⎪ ⎪ = wi, j ∧ di,tc j < 0, ⎪ ⎪ ⎪ ⎩ 0, O.W.

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Thresholding

d it,cj ≤ γ , sti , j ≠ wi , j

xi,j

+ x'i,j

si,j

Decision Otherwise -τ

+ Get di,j and sti,j

Diffuse errors with error kernel

Yes

-di,j

Yes

di,j<0

vi,j

No

hi,j Fill quantization levels +

ei,j

+τ

Fig. 6.

+di,j

di,j<0

d it,cj

yi,j

-

Otherwise Decision ≤ γ , sti , j ≠ wi , j

No

Flowchart of the proposed CHEDBTC encoder.

where the variable wi, j denotes the binary watermark information. Comparing with Eqs. (11)–(12), the bias factor ε is replaced by the self-adjustable parameter di,tc j . This manner can obtain a perfect matched external bias factor to yield the expected h ti,c j without redundant extra force to degrade image quality. Moreover, in this study an adjustable parameter γ, called bias limitation, is used to constrain the maximum external force. Consequently, a di,tc j higher than the predefined γ is rejected to be used. The external force di,tc j is disabled when sti, j = wi, j . Given the case when |di,tc j | ≤ γ and sti, j = wi, j are simultaneously met, an inside exploration on the operation of the “thresholding” block shown in Fig. 6 as defined in Eq. (10) is discussed. When sti, j = 0 and, wi, j = 1 the di,tc j is positive, and v i,tc j constructed by adding si,tc j with the positive di,tc j will be equal to x¯ tc , which makes the recalculated sti, j = wi, j . Conversely, when sti, j = 1 and wi, j = 0, a negative di,tc j is obtained, the v i,tc j constructed by adding si,tc j with the negative di,tc j will also equal to x¯ tc , which makes this modification cannot affect the recalculated sti, j since it is still equal to 1. To deal with this, a smallest value is designed to add with the di,tc j when di,tc j < 0, thus the recalculated sti, j can yield an expected alteration. B. Decoder Focusing on the decoder shown in Fig. 5, when two marked images Y 1 and Y 2 are received, each divided block of size M × N (where both M and N are identical to the β used in encoder) is decrypted independently. First, the mean of a received block is calculated as below, 1  M  N yt , y¯ t = (18) M × N i=1 j =1 i,t where t denotes the label of the marked image. The bitmap which used to embed watermark can be obtained by  1, if yi,t j ≥ y¯ t t bi, j = (19) 0, if yi,t j < y¯ t . The hidden information (DW ) can be extracted by applying the XNOR operation over the bitmaps of the marked images as below,  1, if bi,1 j = bi,2 j (20) dwi, j = 0, if bi,1 j = bi,2 j , where 0 and 1 represent black and white, respectively.

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C. Multiple Watermarks Embedding Extension In this sub-section, the extended multiple watermark embedding with two host images is introduced. Supposing a watermark pool {W P 1 , W P 2 , . . . , W P s } of size S has been established, and T watermarks {W 1 , W 2 , . . . , W T } are selected from the watermark pool (T ≤ S) to be encrypted. The encoding mechanism is similar to that introduced in subsection III.A, yet the variable wi, j as used in Eqs. (16)–(17) are redefined as below, ⎧ t ⎪ ⎨1, if wi, j = 1 (21) ri, j = tT=1 −1, if wi,t j = 0 ⎪ ⎩ 0, O.W,  1, if ri, j ≥ 0 wi, j = (22) 0, if ri, j < 0, where wi,t j ∈ W t denotes a binary watermark value. The concept of the decoding is to consider all of the embedded watermarks contribute something to the final watermark, thus the decoding introduced in sub-section III.B is impractical. For further exploring the exact embedded watermarks from the single decoded watermark, the correlation analysis is utilized and formulated as below, W P s · DW

(23) , where |C s | ≤ P × Q, cs = √ DW · DW

where s is in between 1 to S, denoting the label of watermark in the watermark pool, and the operation · denotes inner product. Notably, the values of W P s and DW should be modified from (0, 1) to (−1, 1) for this correlation calculation. The embedded watermarks are determined by the following thresholding operation, DW = {W P s |cs ≥ λγ ,T },

(24)

where the DW denotes the set of the watermarks in the pool which are embedded into the host images, and the threshold λγ ,T is used to determine whether the sth WP associates to the decoded watermark. This threshold is affected by the number of the embedded watermarks (T ), and the used bias limitation (γ ). The corresponding parameter values are further discussed in the following section. IV. E XPERIMENTAL R ESULTS In this section, the performance of the proposed CHEDBTC is examined with various aspects. In terms of image quality assessment, the traditional Peak Signal-to-Noise Ratio (PSNR) is avoided since it does not consider the nature of HVS. Instead, the substitution, namely Human visual system PSNR (HPSNR) [22], is exploited and formulated as below, HPSNR = 10log10 P × Q × 2552 2 ,

P Q i=1 W (x −Y )  m,n i+m,j+n i+m,j+n (m,n)∈R j =1 (25) where P × Q denotes the image size; the two variables x i, j and yi, j denote the values of the original grayscale image

and the estimated image, respectively; variable wm,n denotes the HVS-like 2-D filter with a support region R, in which the Gaussian filter with standard deviation 1.3 is utilized to simulate the HVS. Another index, named Correct Decode Rate (CDR), is employed to estimate the similarity between two binary watermarks as defined below, Q

P  i=1 j =1 wi, j ⊗ dwi, j

, (26) P×Q where the two variables wi, j and dwi, j denote the original watermark and the estimated watermark, respectively, and the notation ⊗ denotes the exclusive NOR (XNOR) operation. When one watermark is embedded, the marked image quality and CDR are affected by two factors, i.e., the size of the divided block (β) and the bias limitation (γ). Figure 7 shows the corresponding results, in which each of the HPSNRs or CDRs is averaged from 100 decoded results obtained with the dataset. The dataset involves 100 different pairs (each pair for the two host images) of natural images of size 512 × 512 [23], and 100 random-generated binary watermarks of size 512 × 512. In this experiment, the case β = 1 is not considered, since the quantization levels of any block (a pixel) are identical. As it can be seen from Fig. 7(a), the image quality is inversely proportional to the block size. This trend is caused by the number of quantization levels used to render a block. For instance, the image quality of an image of size 8 × 8 represented by the 32 grayscale values (β = 2) is higher than that represented by eight grayscale values (β = 4). In addition, the CDR results indicated in Fig. 7(b) reveal the optimal block size, the phenomenon can be explained by the two reasons: 1) The average difference between the bitmap and the corresponding original grayscale values is directly proportional to the block size, thus a bigger block requires a greater γ , in which |di,t j | ≤ γ to allow a greater di,t j to control the pixel greater or smaller than x¯ t for correctly embedding the watermark information. 2) A small block, for instance, β = 2, has a relatively higher probability that the four pixels of a block have identical bitmap results, e.g., all highmean or all low-mean, which is caused by the digital image quantization and the characteristic of natural images. Thus, this property makes that the smallest block tend to yield a decoded watermarks with low decoding rate. As a result, four is considered as the best block size through the above analysis for yielding good image quality and CDR simultaneously. Figure 8 shows some practical results, in which each of the images is of size 512 × 512. Subsequently, two more aspects, processing time and bit rate, are discussed. Herein, the platform gears with Intel Core i7-950, 6 GB RAM, Win7 OS, Microsoft Visual Studio 2008. Figure 9 shows corresponding experimental results. In which, the processing time is inversely proportional to the block size since in average the bigger blocks diffuse errors to fewer pixels than the smaller ones, thus a block of bigger size is favored in terms of processing efficiency. Yet, a lower bit rate favors a bigger block size. Considering the practical use of the data hiding, watermarking, or steganography, CDR is more important than processing efficiency or bit rate, thus β = 4 is recommended in this study. CDR =

Processing time vs. Various block sizes

HPSNR vs. Various block sizes

60 40

Processing time (millisecond)

Bias limitation=5 Bias limitation=10 Bias limitation=15

20 2

110 CDR (%)

4813

4

8 16 Various block sizes

32

92

85.25

Bias limitation=5 Bias limitation=15

78.82

Bias limitation=10

60 4

8 16 Various block sizes

8 6 4 2 0

5 2

Fig. 9.

4

1.25

1.0625

1.015625

8 16 Various block sizes

32

Embedded watermark

(a) Processing time and (b) bit rate of CHEDBTC.

HPSNR vs. Various bias limitations

50 48 46 44 42

10

CDR (%)

= 2

30 40 50 60 70 Various bias limitations

80

90

100

Practical result Simulated result (with practical difference) Simulated result (with simulated difference)

75 50 0

CDR=91.99%

20

(a) CDR vs. Various bias limitations

100

HPSNR=53.04 dB

32

(a) Bit rate vs. Various block sizes

0

HPSNR=49.75 dB

8 16 Various block sizes

(b)

HPSNR (dB)

Marked image 2

4

2

Original images

Marked image 1

74.49

68

32

(b) Fig. 7. Performance of the proposed CHEDBTC method under various block sizes and bias limitations when only one watermark is embedded. (a) Image quality. (b) CDR.

76.29

76 2

85

2

82.92

84

(a) CDR vs. Various block sizes Bit rate

HPSNR (dB)

GUO AND LIU: HIGH CAPACITY DATA HIDING FOR ERROR-DIFFUSED BTC

10

20

30 40 50 60 70 Various bias limitations

80

90

100

(b) = 4

Fig. 10. (β = 4).

HPSNR=46.49 dB

Prob. vs. Grayscales

0.06

CDR=96.55%

Simulated result Practical result

0.03

= 8

Prob.

HPSNR=43.94 dB

(a) Image quality and (b) CDR under various bias limitations.

0 0

HPSNR=36.78 dB

189

252

(a)

CDR=89.32%

= 16 HPSNR=34.37 dB

126 Grayscales

Prob. vs. Absolute difference

0.009 0.006 0.003

CDR=80.74%

Simulated result Practical result

0 0

63 126 189 Absolute difference

0.18 0.15 0.12 0.09 0.06 0.03 0

Prob. of practical result

HPSNR=41.55 dB

Prob. of simulated result

HPSNR=39.12 dB

63

252

= 32

(b) Fig. 11.

HPSNR=30.4 dB

HPSNR=32.46 dB

CDR=73.09%

Fig. 8. Results of the CHEDBTC when only one watermark is embedded, where γ = 10. (All printed at 600 dpi.)

Focusing on the case when β = 4, the influences caused by various bias limitations are examined. Figure 10 shows

Statistics of (a) Px¯ (·) and (b) P|d| (·). (β = 4).

the corresponding experimental results, in which each of the values (‘practical result’ for CDR) is averaged from the samples in the dataset as that used in Fig. 7. According to these results, the image quality is inversely proportional to the bias limitations, while the CDR is directly proportional to the bias limitations. To give a simulated result of the CDR

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IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 21, NO. 12, DECEMBER 2012

Embedded watermark

Marked image 2

= 5

Marked image 1

HPSNR=48.44 dB

CDR=89.27%

500 400 300 200 100 0 -100

= 10

Correlation

HPSNR=44.6 dB

HPSNR=43.99 dB HPSNR=46.7 dB Correlation vs. Watermark numbers

HPSNR=46.49 dB

CDR=96.55%

HPSNR=43.48 dB

HPSNR=45.49 dB

CDR=98.62%

46

91 136 181 226 271 316 361 406 451 496 Watermark numbers

(a)

HPSNR=43.15 dB

HPSNR=44.86 dB

CDR=99.33%

Correlation

= 20

= 15

HPSNR=43.94 dB

1

200 150 100 50 0

HPSNR=44.01 dB HPSNR=46.74 dB Correlation vs. Watermark numbers

-50 1

Fig. 12. Results of the CHEDBTC when only one watermark is embedded, where β = 4. (All printed at 600 dpi.)

HPSNR (dB)

53 49

46

91 136 181 226 271 316 361 406 451 496 Watermark numbers

(b)

HPSNR vs. Number of embedded watermarks Bias limitation=2 Bias limitation=14

Bias limitation=8

45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Number of embedded watermarks

for theoretical analysis, the probabilities of various are modeled firstly as below,

        p|d| di,tc j  | di,tc j  > 0     = p x¯ tc − sti,tcj = di,tc j ∨ x¯ tc − sti,tcj = −di,tc j        t  255−di,cj  1 1 255  + i=0 =   tc  px¯ (i ) × px¯ (i ) × i=di, j  256 256   1 ×  255 tc  px¯ (i ) , and = i=di, j  128

1 255 × i=0 p|d| (0) = px¯ (i ) , (27) 256 where sti,tcj is reasonably assumed as a uniform distribution; the range of x¯ tc is 0 to 255; px¯ (·) denotes the x¯ tc ’s probability at a specific grayscale, and it can be modeled as a Gaussian function when the probability distribution of each x i, j is

70 40 10

-20

1 26 51 76 101 126 151 176 201 226 251 276 301 326 351 376 401 426 451 476 501

|di,tc j |s

100

Correlation

Fig. 13. Image quality of the proposed CHEDBTC when various numbers of watermarks are embedded (β = 4).

HPSNR=44.03 dB HPSNR=46.73 dB Correlation vs. Watermark numbers

Watermark numbers

(c) Fig. 14. Results of the CHEDBTC when multiple watermarks are embedded, β = 4 and γ = 10. (a) 1, (b) 4, and (c) 16 watermarks are embedded. (All printed at 450 dpi.)

theoretically modeled as a uniform distribution, px¯ (i ) = N(i |μ, σ ) 255 where μ = and σ = 2



2562 − 1 . 12β 2

(28)

In which, the μ and σ equal to that of the theoretical distribution of x i, j . Figure 11 shows the simulated and the corresponding practical results. Obviously, the two results are not similar, since the theoretical uniform assumption is not suited for the considered natural image which mostly provides

GUO AND LIU: HIGH CAPACITY DATA HIDING FOR ERROR-DIFFUSED BTC

300 100

-100

Correlation vs. Bias limitations Embedded watermark (3σ=0) No embedded watermark (3σ=3.36) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Bias limitations

CDR tolerance

Correlation

500

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Prob. difference vs. Bias limitations

40 20 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Bias limitations

(a)

Correlation

190

Correlation vs. Bias limitations

Fig. 16.

CDR tolerance under various bias limitations.

110 30 -50

Embedded watermark (3σ=2.46) No embedded watermark (3σ=3.11) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Bias limitations

(b) Correlation

80 50 20

-10

Correlation vs. Bias limitations

(a)

Embedded watermark (3σ=3.46) No embedded watermark (3σ=3.55)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Bias limitations

(c) Correlation

30

Correlation vs. Bias limitations

(b) 10

-10

Embedded watermark (3σ=3.06) No embedded watermark (3σ=3.06) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(c)

Fig. 17. Examples of attacked images. (a) Cropped with 50% area. (b) Added salt and pepper on 50% area. (c) Smoothed with the Gaussian filter with standard deviation at 2. (All printed at 450 dpi.)

Bias limitations

(d)

more low frequency components as revealed in Fig. 11(b). Thus, the CDR under various γ can be modeled as below,

CER vs. Ratio of cropped area

CER (%)

Fig. 15. Results of the correlations under various bias limitations, when (a) 1, (b) 4, (c) 32, and (d) 256 watermarks are embedded (β = 4).

100 80 60 40 20 0

4 watermarks (100% ends at 82) 32 watermarks (100% ends at 76) 256 watermarks (100% ends at 52) 40 50 60 70 80 Ratio of cropped area (%)

30

CER vs. Ratio of noisy area 4 watermarks (100% ends at 16) 32 watermarks (100% ends at 10) 256 watermarks (100% ends at 4)

CER (%)

100 80 60 40 20 0

0

10

20

30 40 50 60 70 Ratio of noisy area (%)

80

90

100

(b) CER vs. Standard deviations 90 75 60 45 30

4 watermarks (100% ends at 2.6) 32 watermarks (100% ends at 1.2) 256 watermarks (100% ends at 0.6) 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4

CER (%)

where the probability of wi, j is assumed as a uniform distribution, and due to |di,tc j | = 0 does not embed anything to the marked image, this situation should be excluded. The corresponding simulated CDRs of the two distributions in Fig. 11(b) are also drawn in Fig. 10(b). Results demonstrate that the characteristic of a natural image contributes the correctness. According to these results, when 6 ≤ γ ≤ 16, the corresponding HPSNR and the simulated CDR are higher than 45 dB and 90%, respectively. Thus, this range of the bias limitation is considered as good setting candidates in this study for one watermark embedding case. To illustrate the corresponding performance, Fig. 12 shows some corresponding practical results.

100

(a)

pc (γ )

 

  = p(sti, j = wi, j ) + p(sti, j = wi, j ) p 0 < di,tc j  ≤ γ        

    = 0.5 + 0.5 × p 0 < di,1 j  ≤ γ ∨ 0 < di,2 j  ≤ γ          1     1  = 0.5 + 0.5 × 1 − p di, j  = 0 ∨ di, j  > γ p di,2 j      2  = 0 ∨ di, j  > γ  2   ∞ , (29) p (i ) = 0.5 × 2 − p|d|(0) + i=γ +1 |d|

90

Standard deviations

(b) Fig. 18. Practical attack simulations. (a) Cropping attack. (b) Salt-and-pepper noise attack. (c) Gaussian smoothing. (β = 4 and γ = 16).

Here below, the influence on image quality when multiple watermarks are embedded is discussed. According to the introduction about the corresponding encoder described in sub-

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IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 21, NO. 12, DECEMBER 2012

TABLE I C OMPARISONS A MONG VARIOUS WATERMARKING /DATA H IDING M ETHODS

Methods

Watermark embedding manner

Embedding capacity

Decoded quality

Marked image quality

Robustness

Method descriptions

Chang et al. [17]

Bitmap and quantization levels

Low

Lossless

Low

Weak

This method was developed for color images, and each of the divided blocks of size 4 × 4 is able to hide three bits in average. Yet, the traditional BTC was employed, thus blocking effect and false contour are prominent.

Guo et al. [18]

Bitmap only

Low

Lossless

Median

Strong

This method used the bitmaps generated by the two conjugate dither arrays to represent different watermark bits. One block was able to embed one bit, and then decoded through the majority-voting strategy.

Weak

The bitmap outputs from the ODBTC were directly altered by the EMD method. Since the alteration was not frequently occurred, the image quality is similar to that of the original ODBTC image. In addition, this method is available to embed two bits in one block. Yet, since the quantized error cannot be diffused, the image quality of ODBTC is inferior to that of the EDBTC.

Kim [19]

Bitmap only

Proposed method

Bitmap only

Low

Lossless

Median (better than [18])

Strong High

Quantization description

Lossless

High

(when γ = 16 is adopted)

Huge number of binary watermarks of the same size of the host image can be embedded into two EDBTC images. The proposed method alters the host images with an extremely low probability (γ = 1), while the correct watermark can also be decoded.

Embedding capacity: Whether more than one watermark of size P × Q can be embedded while maintaining nearly invisible distortion on the marked images. Marked image quality (HPSNR): (Low) < 35 dB; (Median) 35 to 43 dB; (High) > 43 dB. Robustness: When 40% marked image contents are changed, whether the CDR/CER is still higher than 90%.

section III.C, the obtained HPSNR should not be affected by the variation of the numbers of embedded watermarks, and which is proved by the results organized in Fig. 13. In addition, some practical results generated with β = 4 and γ = 10 are shown in Fig. 14. In this experiment, the size of the watermark pool is set at 512, and the embedded watermarks are randomly selected from this watermark pool. Herein, each of correlation is calculated by Eq. (23). It is clear that the correlations of the embedded watermarks are much higher than rest of the watermarks in the pool. Figure 15 shows the correlations affected by various bias limitations, where each index of the horizontal axis (different bias limitation) can be considered as an independent experiment. For instance, when γ = 10, the correlation results shown in Fig. 14(b) can be separated into two correlation means, including 179.87 to “embedded watermark” and 0.075 to “no embedded watermark”. Moreover, each average correlation shown in Fig. 15 employs a T bar to indicate the top and bottom boundaries, and the length between the boundaries denotes three times standard deviation (3σ ) of the correlation mean. According to these results, it is reasonable that only the correlation means of “embedded watermark” are affected by various bias limitations. Yet, the 3σ s of the correlation means are not affected by various bias limitations or the numbers of embedded watermarks. An interesting phenomenon is observed, when 256 watermarks are embedded, even though only the smallest bias limitation is used, the “embedded watermark” can be distinguished from “no embedded watermark” since the two regions construed by the 3σ T bars are not intersected (excluding the case when γ = 0). Based upon

this observation, even when γ = 1 is utilized, the embedded watermark has at least 99.7% (caused by the 3σ , suppose the distribution is Gaussian) can be correctly decoded (the λγ ,T used in Eq. (24) is the average of the correlation mean of “embedded watermark” minus its 3σ , while the correlation mean of “no embedded watermark” plus its 3σ ). This induces an advantage that the number of the embedded watermarks is independent to image quality as proved in Fig. 13. In addition, since the upper-bound of the γ is 16 as theoretically proved above, the tolerance of the damage on pc (γ ) for correctly decoding can be represented as pc (γ |1 ≤ γ ≤ 16) − pc (1) as illustrated in Fig. 16. Thus, the additional CDR tolerance can be conducted to resist the uncertainty of the transmitting channel for higher security of the hidden data. To practically demonstrate the robust tolerance when multiple watermarks are embedded, three common attacks, including cropping, salt-and-pepper noise, and Gaussian smoothing as shown in Fig. 17 are considered. In this experiment, the parameters are set at β = 4 and γ = 16, and the size of the watermark pool is also set at 512 for consistency. In addition, the metric Correct Extract Rate (CER) defined as the ratio of the corrected extracted watermarks is adopted for estimation. In addition, since the two marked images are generated by the proposed scheme, the intensity indicated in each attack is applied on each marked image, i.e., both of marked images are cropped with the same percentage of the area. Figure 18 shows the corresponding results. According to observation, when the modified areas are aggregated and the rest area is not suffered from serious attack, the embedded watermarks can be extracted correctly. Thus, when even 52% of both marked

GUO AND LIU: HIGH CAPACITY DATA HIDING FOR ERROR-DIFFUSED BTC

images are cropped, 256 embedded watermarks still can be completely decrypted. A comparison is provided to analyze the performance amongst other recent data hiding/watermarking related works and the proposed CHEDBTC method. Herein, three former works are considered, including Chang et al.’s study [17], Guo et al.’s study [18], and Kim’s study [19]. The results are organized in Table I, in which the embedding capacity, image quality, and robustness are quantized for easier comparison, and the results with circles denote the best performance under each assessment. According to this analysis, the embedding capacity of the proposed method is greater than the other schemes, since the proposed method can embed a huge number of watermarks of the same size as that of the host image simultaneously, while other methods can simply embed one to three bits in a block. Moreover, the used low γ (even γ = 1) in the proposed CHEDBTC can yield good image quality as it can be seen in Fig. 10(a). In addition, even less watermark information survives over attacks (low CDR), normally it is still sufficient for decoding correct watermarks (consider the cases when γ = 1 in the results of Fig. 10(b) and Fig. 15(a), even the CDR is low, the correlations associate to “embedded watermark” and “no embedded watermark” are still distinguishable). This phenomenon along with the previous three types of attack simulations proves that the robustness of the proposed method is superior to other former methods. V. C ONCLUSION In this paper, a data hiding scheme namely CHEDBTC is proposed to embed a huge amount of watermarks without obviously damaging image quality. Meanwhile, the advantages of the former EDBTC are still be maintained, thus the blocking effect and the false contour as shown in the traditional BTC are eliminated. These distinctions are useful for data hiding by providing a higher embedding security, because it is difficult to aware any unnatural features of the marked images. In addition, the proposed encoder spreads watermarks into two marked images, although the transmission conditions for the two carrier images should be similar, which thus constrains the possible application scenarios, the corresponding data security is also improved with the security sharing concept. To further increase the security, five parameters/variables employed in the proposed method can be modified for different encryptions: 1) Pseudo-random key: a key which is not synchronized in between encoder and decoder leads to wrong extraction, thus an identical key is required. 2) Block size (β): various β can yield different bitmaps through the proposed decoder as described in subsection III.B, thus a β which is identical to that used in encoder is required. 3) Bias limitation (γ ) and the number of embedded watermarks (T ): the threshold λγ ,T is affected by these two parameters, and various combinations of these two parameters yield various correlations as shown in Fig. 14. Thus, these two parameters can be considered as keys to protect the embedded data. 4) Watermark pool: the transmitter and receiver have to share the same pool for their communication. Conversely, correct watermarks cannot be obtained.

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5) Watermark embedding strategy: the XNOR is employed in this study, and any variation can be use as well such as XOR. As documented in the experimental results, the proposed scheme can provide excellent image quality, huge embedding capacity, and high robustness to meet the practical data hiding scenarios. R EFERENCES [1] E. J. Delp and O. R. Mitchell, “Image compression using block truncation coding,” IEEE Trans. Commun. Syst., vol. 27, no. 9, pp. 1335–1342, Sep. 1979. [2] V. R. Udpikar and J. P. Raina, “BTC image coding using vector quantization,” IEEE Trans. Commun., vol. 35, no. 3, pp. 352–356, Mar. 1987. [3] Y. Wu and D. C. Coll, “BTC-VQ-DCT hybrid coding of digital images,” IEEE Trans. Commun., vol. 39, no. 9, pp. 1283–1287, Sep. 1991. [4] C. S. Huang and Y. Lin, “Hybrid block truncation coding,” IEEE Signal Process. Lett., vol. 4, no. 12, pp. 328–330, Dec. 1997. [5] Y.-G. Wu and S.-C. Tai, “An efficient BTC image compression technique,” IEEE Trans. Consumer Electron., vol. 44, no. 2, pp. 317–325, May 1998. [6] Y. C. Hu, “Improved moment preserving block truncation coding for image compression,” Electron. Lett., vol. 39, no. 19, pp. 1377–1379, Sep. 2003. [7] R. Ulichney, Digital Halftoning. Cambridge, MA: MIT Press, 1987. [8] R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial gray scale,” in Proc. SID Dig. Soc. Inform. Display, 1975, pp. 36–37. [9] 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, no. 1, pp. 13–40, 1976. [10] D. E. Knuth, “Digital halftones by dot diffusion,” ACM Trans. Graph., vol. 6, no. 4, pp. 245–273, Oct. 1987. [11] 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. [12] J. M. Guo, “Improved block truncation coding using modified error diffusion,” IET Electron. Lett., vol. 44, no. 7, pp. 462–464, Mar. 2008. [13] 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. [14] J. M. Guo and Y. F. Liu, “Improved block truncation coding using optimized dot diffusion,” in Proc. IEEE Int. Symp. Circuits Syst. NanoBio Circuit Fabrics Syst., May–Jun. 2010, pp. 2634–2637. [15] Y. C. Hu, M. H. Lin, and J. H. Jiang, “A novel color image hiding scheme using block truncation coding,” Fundamenta Inform., vol. 70, no. 4, pp. 317–331, 2006. [16] Y. C. Hu, “Multiple images embedding scheme based on moment preserving block truncation coding,” Fundamenta Inform., vol. 73, no. 3, pp. 373–387, 2006. [17] C. C. Chang, C. Y. Lin, and Y. H. Fan, “Lossless data hiding for color images based on block truncation coding,” Pattern Recogn., vol. 41, no. 7, pp. 2347–2357, 2008. [18] J. M. Guo, M. F. Wu, and Y. C. Kang, “Watermarking in conjugate ordered dither block truncation coding images,” Signal Process., vol. 89, no. 10, pp. 1864–1882, 2009. [19] C. Kim, “Data hiding based on compressed dithering images,” Studies Comput. Intell., vol. 283, pp. 89–98, 2010. [20] 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. [21] The USC-SIPI Image Database. (1977) [Online]. Available: http://sipi.usc.edu/database/ [22] Y. F. Liu, J. M. Guo, and J. D. Lee, “Inverse halftoning based on the Bayesian theorem,” IEEE Trans. Image Process., vol. 20, no. 4, pp. 1077–1084, Apr. 2011. [23] The Test Image Database. (2012) [Online]. Available: http://msp.ee.ntust. edu.tw/public file/ImageSet.rar

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Jing-Ming Guo (M’06–SM’10) was born in Kaohsiung, Taiwan, 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. He was an Information Technique Officer with the Chinese Army from 1998 to 1999. 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 a Professor with the Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei. His current research interests include multimedia signal processing, biometrics, computer vision, and digital halftoning. Dr. Guo is a Senior Member of the IEEE Signal Processing Society. He was a recipient of the Outstanding Youth Electrical Engineer Award from the Chinese Institute of Electrical Engineering in 2011, the Outstanding Young Investigator Award from the Institute of System Engineering in 2011, the Best Paper Award from the IEEE International Conference on System Science and

Engineering in 2011, the Excellence Teaching Award in 2009, the Research Excellence Award in 2008, the Acer Dragon Thesis Award in 2005, the Outstanding Paper Award from IPPR, the Computer Vision and Graphic Image Processing Award in 2005 and 2006, and the Outstanding Faculty Award in 2002 and 2003.

Yun-Fu Liu (S’09) was born in Hualien, Taiwan, 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. He is currently pursuing the Ph.D. degree with the Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan. He is a Visiting Scholar with the Department of Electrical Computer Engineering, University of California, Santa Barbara. His current research interests include digital halftoning, steganography, image compression, object tracking, and pattern recognition.