Robust lossless data hiding using clustering and statistical quantity histogram

Neurocomputing 77 (2012) 1–11

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Robust lossless data hiding using clustering and statistical quantity histogram Lingling An a, Xinbo Gao a,b, Yuan Yuan c,n, Dacheng Tao d a

VIPS Lab, School of Electronic Engineering, Xidian University, Xi’an, 710071, China Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of China, Xidian University, Xi’an 710071, China c Center for Optical Imagery Analysis and Learning (OPTIMAL), State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, Shaanxi, China d Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology, Sydney, Broadway, NSW 2007, Australia b

a r t i c l e i n f o

abstract

Article history: Received 4 March 2011 Received in revised form 1 June 2011 Accepted 4 June 2011 Communicated by L. Shao Available online 18 August 2011

Lossless data hiding methods usually fail to recover the hidden messages completely when the watermarked images are attacked. Therefore, the robust lossless data hiding (RLDH), or the robust reversible watermarking technique, is urgently needed to effectively improve the recovery performance. To date a couple of methods have been developed; however, they have such drawbacks as poor visual quality and low capacity. To solve this problem, we develop a novel statistical quantity histogram shifting and clustering-based RLDH method or SQH-SC for short. The benefits of SQH-SC in comparison with existing typical methods include: (1) strong robustness against lossy compression and random noise due to the usage of k-means clustering; (2) good imperceptibility and reasonable performance tradeoff due to the consideration of the just noticeable distortion of images; (3) high capacity due to the flexible adjustment of the threshold; and (4) wide adaptability and good stability to different kinds of images. Extensive experimental studies based on natural images, medical images, and synthetic aperture radar (SAR) images demonstrate the effectiveness of the proposed SQH-SC. & 2011 Published by Elsevier B.V.

Keywords: Just noticeable distortion k-Means clustering Robust lossless data hiding Statistical quantity histogram

1. Introduction Currently, a large number of lossless data hiding (LDH) methods [6,14] have been developed for copyright protection and content authentication in the multimedia security field. Most of the methods are designed for ‘‘lossless channel’’ scenarios, e.g., Tian’s difference expansion [23], and Ni et al.’s histogram shifting [20]. In using these methods to recover the hidden data correctly, the watermarked images should be free from any attack, degradation, or even a little noise. Although these methods have shown their effectiveness, they are problematic in practical applications. For example, the hidden data will be recovered wrongly if medical images transmitted to the family doctor are attacked by lossy compression [10]. As a consequence, LDH methods are expected to be robust against the unintentional alterations, such as lossy compression and random noise. Robust lossless data hiding (RLDH) has been identified to be an effective tool to address this problem by incorporating the robust mechanism into LDH. The past ten years have witnessed the significance of RLDH and a dozen of RLDH methods have been proposed. From the viewpoint of the embedding model, we can

n

Corresponding author. E-mail address: [email protected] (Y. Yuan).

0925-2312/$ - see front matter & 2011 Published by Elsevier B.V. doi:10.1016/j.neucom.2011.06.012

classify them into two categories [3]: histogram rotation (HR)-based schemes and histogram distribution constrained (HDC) schemes. HR-based schemes, which embed watermarks into images by drawing the inspiration from the patchwork theory [5], was proposed by De Vleeschouwer et al. [9,10] and has been deemed as the start of RLDH. In [10], a host image is first divided into the non-overlapping blocks, and two zones, denoted as A and B respectively, are chosen randomly from each block and their histograms are mapped into a circle. Then the vectors pointing from the center of the circle to the centers of the mass of zones A and B are rotated clockwise and anticlockwise, respectively. By controlling the direction of the rotation, a bit of watermarks, ‘‘0’’ or ‘‘1’’, can be embedded into the host image. To prevent the overflow and underflow of pixels, the modulo-256 operation is utilized, which leads to ‘‘salt-and-pepper’’ noise in the watermarked images, especially for medical images. It is universally agreed that this drawback is a big problem of HR-based schemes, so HDC schemes are developed. HDC schemes embed the watermarks by modifying the statistical characteristics of images according to the histogram distribution of the host images and to-be-embedded watermark bits [21,22,27,28]. To be specific, the absolute value of the statistical characteristics, denoted by e, will be increased by l 40 for a bit ‘‘1’’ to be embedded and remains unchanged for ‘‘0’’. To handle overflow and underflow, some watermark bits are changed from

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L. An et al. / Neurocomputing 77 (2012) 1–11

‘‘1’’ to ‘‘0’’. The intentional errors have to be corrected by the error correction coding (ECC) in the watermark extraction. Because of this, the capacity of HDC schemes is decreased a lot, and its reversibility is challenged under ‘‘lossless channel’’ circumstances, letting alone the robustness when the watermarked images are attacked intentionally. Although the method in [15] reduces this problem to some extent, the question of the robustness against attacks remains largely unexplored. The aforementioned two kinds of RLDH methods function impressively in both lossless environments and practical applications with the help of the gray-scale histogram distributions of the host images. However, they fail to achieve good and stable comprehensive performance, e.g., poor visual quality for HRbased schemes, and low capacity for HDC ones. Therefore, it is necessary to reconsider RLDH methods by taking a more efficient and stable histogram as well as a novel embedding and extraction model into account. To solve the aforementioned problems, we propose a novel embedding scheme by incorporating the merits of the statistical quantity histogram (SQH) and bidirectional histogram shifting based on our recent work [16]. We design this scheme carefully so that it (a) picks up some blocks as candidates for embedding by determining the embedding level to make performance tradeoff and to avoid overflow and underflow problems; (b) is scalable for embedding from the perspectives of both capacity and image quality due to the sparsity of statistical quantity. Under the robustness analysis, we investigate the effects of lossy compression on the SQH of the watermarked images. Based on this, k-means clustering is studied and used to extract hidden watermarks. To further improve the adaptability and stability, we propose an adaptive extraction strategy, which handles the initial clustering centers by considering the distribution characteristics of the SQH. Thorough experiments based on natural images, medical images, and synthetic aperture radar (SAR) images show that the proposed scheme achieves much better comprehensive performance including capacity, visual quality, and robustness than the first two kinds of RLDH schemes. Because the shifting and clustering of SQH are used for lossless data embedding and extraction, we term the proposed scheme as the statistical quantity histogram shifting and clustering-based RLDH schemes, or SQH-SC for short. The rest of the paper is organized as follows: In Section 2, SQH is presented. Section 3 introduces the proposed scheme, which describes the block selection and SQH construction, briefs the SQH-based embedding model, and details the adaptive watermark extraction strategy using k-means clustering. Extensive experimental results and analysis are given in Section 4 to demonstrate the advantages of SQH-SC in comparison with the state-of-the-art, and Section 5 concludes the paper.

2. Statistical quantity histogram Owing to low computational complexity and good invariance, the histogram has gained a considerable interest in the LDH field. As mentioned, the two kinds of RLDH schemes have employed the gray-scale histogram distribution of images to model the embedding and extraction processes. Unfortunately, different gray-scale histograms of images will result in an unstable performance, as reported in [1]. In this paper, the SQH is therefore introduced, which virtually has a zero-mean and Laplacian-like distribution. Eq. (1) shows the probability density function of Laplace(m, s) as   9xm9 1 exp  , ð1Þ f ðx9m, sÞ ¼ 2s s in which m and s 40 are the location and scale parameters, respectively. To further illustrate this distribution, Fig. 1 compares

Lena

Host Images

Grayscale Histogram

Histogram Generation

q = g( A ) − g(B

Airplane

)

SQH

Fig. 1. Comparisons between gray-scale histograms and SQHs of the example images: Lena and Airplane.

the gray-scale histograms and SQHs of two example images: Lena and Airplane. Obviously, the SQH can efficiently reduce the diversity of images. Therefore, it has been shown to be well suitable for LDH and provide a stable performance. To better present the technical details of the proposed scheme, we describe the generation process of SQH used in the rest of this paper. Given a t-bit host image I0 with n non-overlapping blocks, consider the k-th block Xk with the size of h  w, with w being an even integer. For Xk ¼ fXkði,jÞ 9Xkði,jÞ A f0, 1, . . ., 2t 1g, i¼ 1,y,h, j ¼1,y,w}, the statistical quantity is defined as qk ¼ gðAk ÞgðBk Þ,

ð2Þ

where g(U) is the arithmetic average function, and Ak and Bk comprise a partition of Xk, which is to say, Ak[Bk ¼Xk, Ak\Bk ¼| and 9Ak9¼9Bk9. Here, 9 U 9 is the cardinality of a set, i.e., the number of elements of a set. In order to make qk as close to zero as possible [1], Ak is obtained by n o ð3Þ Ak ¼ Xkði,jÞ 9Xkði,jÞ A Xk ,modðiþ j,2Þ ¼ 0 : With Eq. (2), the statistical quantities of n blocks can be calculated, described as Q¼[q1,q2,y,qn], and thus the SQH of the host image is built. By adopting the SQH as the embedding carrier, a novel RLDH scheme is proposed in the next section.

3. The proposed scheme In this section, we introduce a novel RLDH scheme, i.e., SQHSC, which finds a stable and effective histogram, i.e., SQH, as the embedding carrier, and combines the histogram shifting with clustering techniques to model the watermarking embedding and extraction processes. The proposed SQH-SC can be divided into four main components (as shown in Fig. 2): the block selection, which picks up the candidates for embedding, SQH construction, SQH-based watermark embedding, and the watermark extraction by utilizing the k-means clustering. 3.1. Block selection Given the k-th block Xk in the host image I0, there is a mapping fe:Xk-Yk after watermark embedding, where Yk represents the watermarked block and Yk ¼ fYkði,jÞ 9i ¼ 1,K ,h, j ¼ 1,K ,wg. Usually, Ykði,jÞ A f0, 1, . . ., 2t 1g is needed to prevent the overflow and underflow of pixels. Therefore, we discard the unavailable blocks, i.e., those blocks resulting in overflow and underflow, and take those left as the candidates for embedding. For convenience, we denote the set of the unavailable blocks as Xu and that of

L. An et al. / Neurocomputing 77 (2012) 1–11

3

Fig. 2. The proposed robust lossless data hiding scheme using clustering and SQH.

0 0

candidates as Xc. Let ðXkði,jÞ , Xkði ,j Þ Þ be an arbitrary pixel pair in Xk, 0 0 wherein Xkði,jÞ A Ak , Xkði ,j Þ A Bk , 1 ri,i0 r h, 1r j,j0 rw, and (i,j)a(i0 ,j0 ), the Xu can be obtained by Xu ¼ [ XuðrÞ , in which r

XuðrÞ ¼

8 > > > Xk , < > > > : +,

0 0

if Xkði,jÞ o de , Xkði ,j Þ 4 l, or 0 0

Xkði,jÞ 4 l, Xkði ,j Þ o de

,

ð4Þ

otherwise

l ¼2t  de  1, de 40 is the embedding level, and r ¼9Xu9. In this way, the Xc will be selected successfully. It should be noted that the embedding level de plays an important role in block selection, as shown in Eq. (4). In practical scenarios, it is desired to adaptively determine de for different images. In this paper, luminance masking, which measures the just noticeable distortion (JND) inherent in an image [7], is employed for this purpose. To be specific, the embedding level de of the host image I0 is de ¼ maxfgðJNDXk Þgnk ¼ 1 ,

ð5Þ

3.2. SQH construction Based on the above results, a natural concern is the possibility of utilizing all candidates to construct the SQH. In view of the distribution of the SQH, the peaks and its neighbors in it are more useful than others for watermark embedding. As a consequence, the additional sparsity constraint is applied to the candidates to retain only areas of interests. To implement this objective, we first introduce the following definition. Definition 1. (Statistical Quantity Frequency or SQF): Let Qc ¼ [q1,q2,y,q9Xc9] be the statistical quantity vector of all candidates, and O ¼ {x1,x2,y,xZ} be the value range of Qc, the SQF of the i-th value xi is defined by   Pðxi Þ ¼ 9 qj 9qj ¼ xi , j ¼ 1,2,. . .,9Xc 9 9, ð7Þ in which Z is the number of different values of Qc. According to Eq. (7), the two peaks of SQH are defined by qmr ¼ arg max Pðxi Þ,

n JNDXk ¼ JNDðXi,jk Þ 9i ¼ 1,. . .,h,

ð8Þ

xi A O

and o j ¼ 1,. . .,w :

and ð6Þ

Here JNDði,jÞ Xk ¼ maxffs ðlbg ði,jÞÞ,fv ðlbg ði,jÞ,lmg ði,jÞÞg represents the JND value of the pixel at (i,j) in block Xk, which is dependent on the spatial masking function fs(U) and visibility threshold fv(U), wherein, lbg(U) and lmg(U) are the average background luminance and maximum weighted average of luminance differences, respectively. Due to space limitation, refer to [7] for their definitions.

qml ¼ arg max Pðxi Þ:

ð9Þ

xi A O, xi a qmr

Without the loss of generality, we suppose qml rqmr. Based on this, the blocks of interest can be retained, each of which satisfies the following condition: dðq,qk Þ r dz ,

k ¼ 1, . . ., 9Xc 9,

ð10Þ

where qA{qml, qmr}, qk is the statistical quantity of the k-th candidate, d(U) computes the Euclidean distance between q and

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L. An et al. / Neurocomputing 77 (2012) 1–11

qk, and dz is a predefined constant for threshold control. We denote the set of the blocks of interest as Xe in the rest of this paper. In summary, this sparsity operation preserves the expected blocks to generate the SQH for watermark embedding. Meanwhile, it is also helpful to the flexible adjustment of capacity by controlling the threshold dz, which will be demonstrated through experiments later. It should be noted that the necessary side information, as a key, will be transmitted to the receiver side for SQH construction.

Table 1 Partition process of Z1L, Z1R and Z0. Input: The vector Qc ¼ [q1,q2,y,q9Xe9], and the number of clusters k. Output: The set of clusters S¼ {S1, S2,y, Sk}. ð1Þ ð1Þ 1. Initialize the cluster centers mð1Þ 1 , m2 ,. . .,mk , and the iteration time r. 2. Repeat 3. Assign each of Qc to one of the clusters according to the distance between it ðrÞ

ðrÞ

and the cluster centers: qiASj, if dðqi ,mj Þr dðqi ,ml Þ for all l ¼1,2,y,k. P ðr þ 1Þ 4. Update the cluster centers with mj ¼ qi =9Sj 9. qi A Sj

3.3. SQH-based embedding

5. Until argmin S

In this section, we will utilize the SQH constructed by the blocks of interest as the embedding carrier for watermark embedding. Given the k-th watermark bit wkA{0,1} and block XkAXe, 1rkr9Xe9, the embedding model can be described as a generalized form of the spread spectrum watermarking [8] by q0k ¼ qk þ ade wk :

ð11Þ

q0k

Here qk and are the statistical quantity of Xk and Yk, respectively, and a is a factor defined as

a ¼ ðqk qm Þ=9qk qm 9,

ð12Þ

where qm ¼ argmin fdðqk ,qml Þ,dðqk ,qmr Þg:

ð13Þ

q A fqml ,qmr g

By applying Eq. (11) to all of the blocks belonging to Xe, the watermark WM¼[w1,y,w9Xe9] can be embedded into the host image I0 and thus the corresponding watermarked image Iw is generated. 3.4. k-Means clustering based extraction Usually, it is almost impossible to transmit the watermarked images through the lossless channel; therefore, a robust watermark extraction model is designed in this section by investigating the effects of the attacks, e.g., lossy compression, on the SQH of the watermarked image. According to the aforementioned embedding model, the SQH of the host image is shifted towards right and left to embed the watermarks. In this way, the SQH of the watermarked image will consist of three embedding zones, i.e., Z1L, Z1R and Z0, in which Z1L and Z1R correspond to the watermark bit ‘‘1’’ and Z0 to bit ‘‘0’’, as shown in Fig. 3. In order to extract the watermarks, the most important task is to partition these embedding zones dynamically. In lossless environments, we can use the embedding level for this purpose; however, it cannot

Fig. 3. Examples of SQHs of (a) watermarked images, and (b) watermarked images attacked by JPEG2000 compression.

k P P j ¼ 1 qi A Sj

ðr þ 1Þ 2 :qi mj : .

work well when the watermarked image is destroyed by the attacks because some elements belonging to Z1L and Z1R may ‘‘drift’’ to Z0. Therefore, it is essential to find a better solution to the partition of the embedding zones. In view of the distribution characteristics of SQH after the distortion, this problem can be modeled as a clustering problem with a certain number of clusters. For the sake of simplicity, we adopt k-means clustering [24] to target this problem. Let Qc ¼[q1, q2,y,q9Xe9] be the statistical quantity vector of all of blocks of interest in the watermarked image Iw, and M¼ {m1,m2,y,mk} be the cluster centers, the partition process of Z1L, Z1R and Z0 can be summarized as Table 1. In particular, considering the distribution characteristics of the embedding zones, we adaptively set the initial centers of clusters, e.g., M ¼ fbminðQc Þ, 0, bmaxðQc Þg for k¼3. Using Table 1, we can effectively partition the embedding zones, i.e., Z1L, Z1R and Z0, even when the watermarked images are degraded a little. Based on this, the hidden watermarks will be extracted and then the statistical quantities of all of the blocks of interest in the watermarked image Iw can be recovered with the inverse operation of Eq. (11). To be specific, the statistical quantity of the k-th block of interest, qk00 , is obtained by q00k ¼ q0k ade w00k ,

ð14Þ

in which w00k is the k-th bit of the recovered watermarks. Finally, the images can be recovered, which will be identical to the host one when there are no attacks.

4. Experimental results and analysis This section presents an experimental study to evaluate the performance of the proposed scheme. Comprehensive results demonstrate the superiority of this scheme from the aspects of capacity, imperceptibility and robustness. For all the experiments, we utilize the same experimental setup, i.e., database and evaluation metrics. We first briefly describe our experimental setup. In this study, we used three kinds of images to support our experimental investigation: i.e., 100 natural images, 100 medical images and 100 SAR images. Natural images are selected from CVGUGR image database [29], including figures, landscape, animals, and flowers and so on. Medical images consist of 30 MR and MRI images from DICOM sample image sets [30], 35 CT and 35 PET CT images from OsiriX website [31]. As for SAR images, we choose them from some open image database through the Internet. Fig. 4 shows six example images and we term them as: (a) Lena, (b) Cabin, (c) MR, (d) CT, (e) Coast, and (f) City. To facilitate experimental comparison, all images have a fixed size, i.e., 512  512  8 for natural and medical images and 256  256  8 for SAR images. In our experiments, the peak signal-to-noise ratio (PSNR), which is universally employed to evaluate imperceptibility, i.e., the distortion of the watermarked images versus host ones, is

L. An et al. / Neurocomputing 77 (2012) 1–11

5

BS

BS

2δ

BS 2δ

Q

2δ

Q

Fig. 5. Effects of block size and threshold on capacity: (a) block size BS, and BS1 4 BS2; (b) threshold dz, and dz1 o dz2. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

4.1. Capacity

Fig. 4. Example images of the experimental database. Natural images: (a) Lena, (b) Cabin; Medical images: (c) MR, (d) CT; SAR images: (e) Coast, (f) City.

C ¼ 9Xe 9 ¼ 9fqk 9dðq,qk Þ r dz ,

Table 2 Parameter settings for different attacks. Parameters

JPEG

JPEG2000

AGN

g

1 100

1 2.0

0.1 0.001

L

adopted as follows: PSNR ¼ 10 logð2552 =MSEÞ,

ð15Þ

and MSE ¼

H X W X 1 ðI0 ði,jÞIw ði,jÞÞ2 , H  W i¼1j¼1

ð16Þ

wherein I0(i,j) and Iw(i,j) are the pixel values at row i and column j of the host and watermarked images, and H and W are the height and width of the images, respectively. Apart from imperceptibility, the robustness against attacks is also an essential criterion for evaluating the performance. In this paper, we applied lossy compression including JPEG and JPEG2000 compression, and additive Gaussian noise (AGN) to the watermarked images to test the robustness of the proposed scheme. In our experiments, the strength of JPEG compression expressed by the quality factor is from 100 to 20 with a step of 10. As for JPEG2000 compression, the Kakadu command line tool is adopted, wherein the rate changes from 2.0 to 0.2 with a step of 0.2. Also, a series of AGNs with zero mean and variances from 0.001 to 0.01 with a step of 0.001 are employed. Because of different units for different attacks, we define a novel unified metric named the surviving level to evaluate the robustness, denoted as L¼g

absðLcÞ

L

,

In this section, we will investigate the capacity of the proposed scheme, which measures the number of bits conveyed by the watermark. Let IS and BS be the sizes of the host image and block, the capacity C can be computed with Eqs. (4) and (10) as

ð17Þ

and 0 rLo1, where g is the normalization factor, L represents the benchmark of the attack strength, and c is the tolerated attack strength, i.e., when the attack strength is smaller than c, the hidden watermarks can be recovered correctly. According to Eq. (17), the greater L is, the better the robustness; and vice versa. Table 2 illustrates the parameter settings for different attacks in our experiments.

k ¼ 1, 2, . . ., 9Xc 9g9,

ð18Þ

in which qA{qmr,qml}, and 9Xc9¼ IS/BS 9Xu9 represents the number of the candidates for embedding. Because 9Xu9 is usually small, C is dependent mainly on two factors, the block size BS and threshold dz. To make a qualitative analysis of the effects of BS and dz on the capacity, we offer an example of the SQHs for different cases in Fig. 5. With Eq. (18), the capacity can be approximately determined by the area of the region enveloped with SQH, dz, and the horizontal axis, shown in the shadow region in Fig. 5(a). On the one hand, given dz, the smaller the block size is, e.g., BS1-BS2, the larger the area is, or, the greater the capacity is. On the other hand, suppose BS¼BS2, the capacity is improved with the increase of the threshold from dz1 to dz2. It should be noted that the increase of the capacity will slow down with dz becoming ever larger, which can be verified by the decrease of the slope of the histogram, as illustrated by the blue hollow arrow in Fig. 5(b). For empirical justification, the experiments are conducted on the three kinds of test images for the block size BS from 2  2 to 8  8, and the threshold dz from 0 to 7, wherein the embedding level is 8. Fig. 6 shows the experimental results of three example images, i.e., Lena, MR, and Coast, and the statistical averages for different kinds of images. It is found that the capacity can be controlled flexibly by adjusting the block size and threshold, and thus either high or low capacities, e.g., up to 50 Kbits for natural images, can be obtained according to the practical requirements. In addition, it can be seen that the capacity of medical images is the highest at the same threshold; this is because the adjacent pixels in medical images are more closely correlated than those in others. Here, we have to mention that the effect of dz on capacity will be weakened with the block becoming ever larger.

4.2. Imperceptibility Imperceptibility, which evaluates the distortion of the watermarked images versus host ones, is investigated in this section. As mentioned, PSNR is used to evaluate this performance, which is dependent on three factors, the block size BS, the embedding level de and the threshold dz, in the proposed scheme. Based on this, two groups of experiments are conducted on the test database to examine the effects of these factors on imperceptibility. Given the block size BS, the PSNRs of the k-th watermarked ðkÞ image Iw for different thresholds and embedding levels can be

L. An et al. / Neurocomputing 77 (2012) 1–11

70

60

60 Capacity (Kbit)

Capacity (Kbit)

Lena 70

50 40 30 20

12

50 40 30 20

1

2

3

4

5

6

0

7

1

2

3

Threshold (δz)

5

6

30 20 10 3

1

2

3

4

5

6

7

4

5

6

7

5

6

7

SAR Image

8

50 40 30 20

6 4 2

0 2

0

10

10 1

4

Threshold (δz)

Capacity (Kbit)

40

0

6

0

7

60 Capacity (Kbit)

Capacity (Kbit)

4

Medical Image

70

50

0

8

Threshold (δz)

Natural Image

60

10

2

0 0

Coast

14

10

10 0

MR

Capacity (Kbit)

6

0

1

2

3

Threshold (δz)

4

5

6

0

7

0

1

2

3

Threshold (δz)

4

Threshold (δz)

Fig. 6. Capacities of example images, i.e., Lena, MR, and Coast, and statistical averages of three kinds of images, i.e., natural, medical, and SAR images. Lena

60

45 40

PSNR (dB)

50

50 45 40

35 1

2

3

4

5

6

7

35

8

50 45 40

2

3

4

5

6

7

30

8

1

2

3

Embedding Level (δe)

4

5

6

7

8

6

7

8

Embedding Level (δe)

Medical Image

Natural Image

SAR Image

55

60

65 60

55 50 45

PSNR (dB)

50 PSNR (dB)

PSNR (dB)

55

35 1

Embedding Level (δe)

45

55 50 45

40

40 35

Coast

65

55 PSNR (dB)

PSNR (dB)

55

30

MR

60

60

40 1

2

3

4

5

Embedding Level (δe)

6

7

8

35

1

2

3

4

5

6

7

Embedding Level (δe)

8

35

1

2

3

4

5

Embedding Level (δe)

Fig. 7. Effects of the embedding level de and threshold dz on imperceptibility. Here, the error bars are used, in which the maximum, average, and minimum of PSNR are plotted one by one for a given embedding level.

represented by 0

xð1,1Þ B k B 0 B B B ^ @ 0

xð1,2Þ k



xð2,2Þ k

 &

0



xð1,jÞ k

1

C C xð2,jÞ C k C, ^ C A ði,jÞ xk

ð19Þ

is the PSNR at threshold iZ1 and embedding level in which xði,jÞ k j Zi. Because the embedding level is greater than the threshold, Eq. (19) is an upper triangular matrix. By computing the average, maximum, and minimum of PSNRs for different i’s at a fixed j, we can investigate the effect of de and dz on imperceptibility. Fig. 7 shows the experimental results of the three example images, in which BS¼2  2, 1 ri,j r8 and j Zi. Meanwhile, the statistical results for each kind of test images can be obtained by setting xði,jÞ k with the average PSNR of N(e.g., N ¼100) images at i and j, i.e., PN ð1=NÞ k ¼ 1 xði,jÞ , also shown in Fig. 7. It can be seen that the PSNR k is decreased with the increase of the embedding level de. In particular, when de ¼8, the average PSNRs of the three kinds of images are higher than 35 dB, which means the watermarked images are accepted in practical applications. It should also be noted that the PSNR at the same de will fluctuate narrowly with

the change of dz, especially for medical images. This means the capacity can be adjusted by dz when a fixed embedding level de is given. Next, we consider the effect of the block size BS on imperceptibility. To be specific, let ne ¼9Xe9 be the number of the blocks of interest and n be that of all blocks, MSE can be equivalently rewritten as 1 2 ne ð20Þ d U : 2 e n By substituting Eq. (20) into Eq. (15), it can be deduced that with the decrease of block size, the PSNR is up slightly because n increases at a faster rate than ne. The experimental results of the three example images and statistical averages of each kind of test images are plotted in Fig. 8, where BS is changed from 2  2 to 8  8 with a step of 2. In particular, the PSNR of medical images remains approximately unchanged due to the small change of ne/n for different block sizes. MSE ¼

4.3. Robustness In this section, we investigate the watermarked images attacked by JPEG, JPEG2000 compressions, and AGN, respectively,

L. An et al. / Neurocomputing 77 (2012) 1–11

Lena

60

60

45

50 45

40

40

35

35

1

2

3

4

5

6

7

8

PSNR (dB)

50

55 50 45 40

1

2

3

Embedding Level (δe)

4

5

6

7

35

8

1

2

3

Embedding Level (δe)

4

5

6

7

8

6

7

8

Embedding Level (δe) SAR Image

Medical Image

Natural Image 55

60

65 60

55 50 45

PSNR (dB)

50 PSNR (dB)

PSNR (dB)

Coast

65

55 PSNR (dB)

PSNR (dB)

MR

60

55

45

55 50 45

40

40 35

7

40 1

2

3

4

5

6

7

35

8

Embedding Level (δe)

1

2

3

4

5

6

7

35

8

1

2

Embedding Level (δe)

3

4

5

Embedding Level (δe)

Fig. 8. Effect of block size BS on imperceptibility. For each block size, the average PSNR is used for comparison.

0.7

δe=8 δe=12 δe=16 δe=20

Surviving Level

0.6 0.5 0.4 0.3 0.2 0.1 0 Lena

MR

Coast

0.7 δe=8 δe=12 δe=16 δe=20

Surviving Level

0.6 0.5 0.4 0.3 0.2 0.1 0 Natural Image

Medical Image

SAR Image

Fig. 9. Illustration of robustness against JPEG compression for different embedding levels.

to show the robustness of the proposed SQH-SC. The procedure for evaluation is as follows: (1) similar to other schemes, e.g., [10], we repeatedly embed a message generated randomly with a fixed length (e.g., 100 bits) into the host images, and utilize the major voting at the receiver side to count the correctly extracted watermark bits; (2) based on the counted results, we obtain the tolerated attack strength c, and then compute the surviving level with Eq. (17) as the evaluation result. Because the robustness is influenced by two factors, the block size and embedding level, the experimental results under different attacks are discussed from the two aspects in the following parts. (1) Robustness against JPEG compression As mentioned above, the JPEG compression of the quality factor from 100 to 20 with a step of 10 is utilized here. To examine the effects of the embedding level de on robustness, we conducted statistical experiments 86,400 times over 300 test images, where the block size is 8  8, the

embedding level de changes from 8 to 20 with a step of 4, and the threshold dz from 1 to 8 with a step of 1. Given de, the average of the surviving levels at different thresholds are shown in Fig. 9, where the top figure shows the results of the three example images, and the bottom one is the statistical average for each kind of test images. As shown, the robustness is improved greatly with the increase of de from 8 to 20. Moreover, on the average, the similar results are obtained for different kinds of images. For example, when de ¼20, the surviving levels of the three kinds of images are up to 0.6. With Eq. (17) and Table 2, we can obtain the tolerated attack strength, i.e., c ¼40, which is to say, when the quality factor of JPEG compression is greater than or equal to 40, all of the hidden watermark bits can be extracted correctly from the destroyed watermarked images. These observations not only show the strong robustness of SQH-SC against JPEG compression, but also reveal its wide adaptability for different images.

8

L. An et al. / Neurocomputing 77 (2012) 1–11

Besides the embedding level, the effect of block size on robustness is also investigated. Table 3 reports the experimental results for different block sizes from 4  4 to 16  16 (by column), and different images from natural images to SAR images (by row), wherein the embedding level is 16. It can be seen that the surviving levels are the same, i.e., 0.5, for test images when the block is larger than 4  4. That is to say, the robustness against JPEG compression of SQH-SC is basically insensitive to the changes of block size. (2) Robustness against JPEG2000 compression In this section, the same experiments were carried out to evaluate the robustness of the proposed watermarking scheme against JPEG2000 compression in terms of the effects of the embedding level and block size, respectively. From the experimental results illustrated in Fig. 10, we can see that the robustness shows differences for different kinds of images. For the natural and SAR images, the robustness is gradually becoming stronger with the increase of the embedding level, similar to the tendency for JPEG compression. As for medical images, the increase of the embedding level does not contribute much to robustness. This is because strong robustness has already been achieved for smaller embedding levels, e.g., the average surviving level is up to 0.8 when de ¼8; in such a case, there is no big room to further improve the robustness. Consequently, considered as a whole, medical images have

the strongest robustness than others, and natural images come second. Table 4 shows the results when the block size changes. For the same block size, higher robustness against JPEG2000 compression is achieved in comparison with that shown in Table 3; at the same time, the robustness is also basically unchanged when the block size ranges from 8  8 to 16  16. (3) Robustness against AGN Apart from lossy compression, the channel random noise is valuable to consider. In our experiments, the AGN frequently encountered in the communication system was added to the watermarked images. The experimental results for different embedding levels from 8 to 20 with a step of 4 are plotted in Fig. 11. Different from the first two kinds of images, SAR images have better performance when the embedding level is small, e.g., de ¼8. Similar results are shown in Table 5, in which the insensitivity of robustness to the change of block size is also demonstrated.

Table 3 Effects of block size on robustness against JPEG compression.

Table 4 Effects of block size on robustness against JPEG2000 compression.

Image

Block size

4.4. Parameter analysis As discussed, there are three free parameters affecting the performance of the proposed SQH-SC, i.e., the embedding level de, threshold dz, and block size BS. In this section, we will pay attention to their optimal selection and performance tradeoff.

Image

44

88

12  12

16  16

Lena MR Coast

0.2 0.1 0.2

0.5 0.5 0.5

0.5 0.5 0.5

0.5 0.5 0.5

Natural Medical SAR

0.2 0.2 0.3

0.5 0.5 0.5

0.5 0.5 0.5

0.5 0.5 0.5

44

88

12  12

16  16

Lena MR Coast

0.7 0.7 0.6

0.8 0.8 0.7

0.8 0.8 0.7

0.8 0.8 0.7

Natural Medical SAR

0.6 0.8 0.3

0.7 0.9 0.4

0.7 0.9 0.5

0.7 0.9 0.5

0.8

δe=8 δe=12 δe=16 δe=20

0.7 Surviving Level

Block Size

0.6 0.5 0.4 0.3 0.2 0.1 0 Lena

MR

Coast

Surviving Level

1 δe=8 δe=12 δe=16 δe=20

0.8 0.6 0.4 0.2 0 Natural Image

Medical Image

SAR Image

Fig. 10. Illustration of robustness against JPEG2000 compression for different embedding levels.

L. An et al. / Neurocomputing 77 (2012) 1–11

9

Surviving Level

1 0.8

δe=8 δe=12 δe=16 δe=20

0.6 0.4 0.2 0 Lena

MR

Coast

Surviving Level

1 δe=8 δe=12 δe=16 δe=20

0.8 0.6 0.4 0.2 0 Natural Image

Medical Image

SAR Image

Fig. 11. Illustration of robustness against AGN for different embedding levels.

Table 5 Effects of block size on robustness against AGN. Image

Table 7 Tradeoff between robustness and capacity.

Block Size

Image

44

88

12  12

16  16

Lena MR Coast

0.3 0.1 0.6

0.9 0.7 0.9

0.9 0.9 0.9

0.9 0.9 0.9

Natural Medical SAR

0.3 0.2 0.8

0.9 0.8 0.9

0.9 0.9 0.9

0.9 0.9 0.9

Table 6 Tradeoff between capacity, imperceptibility and robustness. Image

Lena MR Coast Natural Medical SAR

de

11 20 17 15 19 13

Capacity (bit)

3900 3900 990 3892 3900 968

PSNR (dB)

34.72 29.21 36.95 32.60 29.45 36.85

Robustness JPEG

JPEG2000

AGN

0.3 0.6 0.5 0.5 0.6 0.4

0.7 0.9 0.7 0.7 0.9 0.3

0.5 0.9 0.9 0.9 0.9 0.9

(1) Embedding level de and threshold dz: The embedding level de plays an important role in block selection and embedding strength adjustment, and affects imperceptibility, robustness and capacity. In this paper, the luminance masking discussed in Section 2 is utilized to optimize this parameter, which can adaptively determine de for different images due to the consideration of the just noticeable distortion (JND) of images, as shown in Eq. (5). Because de Z dz, we can flexibly select dz according to this relationship as well as the requirements of capacity and imperceptibility. Based on this, an adaptive embedding and performance tradeoff can be achieved. Table 6 illustrates the optimal results of the three example images and statistical average of each kind of test

Robustness/Capacity (bit) 44

88

12  12

16  16

Lena MR Coast

0.2/16300 0.1/16300 0.2/3850

0.5/3900 0.5/3900 0.5/990

0.5/1700 0.5/1700 0.5/410

0.5/900 0.5/900 0.5/230

Natural Medical SAR

0.2/15846 0.2/16300 0.3/3543

0.5/3892 0.5/3900 0.5/965

0.5/1692 0.5/1700 0.5/403

0.5/898 0.5/900 0.5/227

images, in which the block size is 8  8. It can be seen that this optimization can work well for natural, medical and SAR images, which is to say, strong robustness, high capacity and accepted imperceptibility are obtained. An exception appears when the JPEG2000 is imposed on SAR images. At this time, the robustness is much lower than that of other images. If stronger robustness is required, we can slightly adjust the embedding level in practical applications. (2) Block size BS: According to Fig. 8, the block size has a slight effect on imperceptibility. Therefore, we only discuss how to optimize the block size to balance the capacity and robustness. Given a fixed de of 16, Table 7 shows the experimental results for different block sizes from 4  4 to 16  16. With the increase of the block size, the capacity drops greatly while the robustness remains unchanged when BSZ 8  8. In view of this, we take 8  8 as an optimal solution to the block size, wherein the high robustness and moderate capacity can be obtained.

4.5. Comprehensive comparison In this part, we compare the proposed SQH-SC with the typical RLDH schemes including HR-based and HDC ones in terms of capacity, imperceptibility, and robustness to further demonstrate its superiority. To simplify the notation, we term two HDC

10

L. An et al. / Neurocomputing 77 (2012) 1–11

Table 8 Comprehensive performance comparison of test database under attacks of JPEG compression. Image

Natural Medical SAR

HR

HDC (1)

HDC (2)

SQH-SC

C

P

R

CR

C

P

R

CR

C

P

R

CR

C

P

R

CR

3891 3900 990

22.67 8.92 21.35

0.5 0.6 0.7

1 1 1

3003 3003 748

30.04 30.09 30.34

0.5 0.5 0.5

0.97 1 0.92

748 748 187

37.03 47.94 39.20

0 0 0.2

0.81 0.54 0.67

3892 3900 966

32.04 30.98 34.42

0.5 0.5 0.5

1 1 1

Table 9 Comprehensive performance comparison of test database under attacks of JPEG2000 compression. Image

Natural Medical SAR

HR

HDC (1)

HDC (2)

SQH-SC

C

P

R

CR

C

P

R

CR

C

P

R

CR

C

P

R

CR

3891 3900 990

22.67 8.92 21.33

0.7 0.6 0.6

1 1 1

3003 3003 748

30.10 30.07 30.22

0.7 0.9 0.4

0.96 1 0.84

748 748 187

36.94 47.92 39.35

0.3 0.4 0.2

0.53 0.41 0.37

3892 3900 966

31.98 30.93 34.67

0.7 0.9 0.4

1 1 1

Table 10 Comprehensive performance comparison of test database under attacks of AGN. Image

Natural Medical SAR

HR

HDC (1)

HDC (2)

C

P

R

CR

C

P

R

CR

C

P

R

CR

C

P

R

CR

3891 3900 990

22.67 8.92 21.33

0.9 0.9 0.9

1 1 1

3003 3003 748

30.01 30.12 30.39

0.4 0.5 0.8

0.89 0.98 0.9

748 748 187

37.06 47.97 39.16

0 – 0.6

0.07 0 0.58

3892 3900 966

32.04 30.95 34.97

0.9 0.8 0.9

1 1 1

schemes, i.e., [22,28], as HDC (1) and HDC (2). For fair comparison, we apply these compared schemes to the aforementioned 300 test images, and the same block size and embedding strength are adopted here. To be specific, the block size is 8  8, and the embedding strength is 16, i.e., (1) the embedding level is 8 in HR, (2) bn defined in HDC (1) is 16, and (3) de ¼16 in SQH-SC. In addition, the embedding strength in HDC (2) is adaptive to the images based on [28], and BCH(15,11,1) is used in HDC (1) and (2). Furthermore, to evaluate the confidence degree of robustness, we use the confidence rate defined as CR ¼

SQH-SC

#F , N

ð21Þ

where N denotes the number of each kind of test images, i.e., 100, #F denotes the number of successful extractions, and an extraction is considered successful if the hidden watermark bits are extracted correctly at an attack strength. In our experiments, this criterion together with the surviving level was also used to evaluate the adaptability of the schemes. Tables 8–10 report the comparison results under three types of attacks, respectively. From this experiment, we observe that (1) the PSNR of the proposed SQH-SC is much higher than that in HR, especially for medical images, when close capacity and robustness are achieved; (2) SQH-SC gives much better performance in comparison with HDC (1), i.e., higher capacity, better PSNR, stronger robustness, and slightly wider adaptability; and (3) as for HDC (2), lower capacity and poor robustness and adaptability are its main disadvantages over SQH-SC. In summary, these experimental results demonstrate that the proposed SQH-SC achieves better comprehensive performance and is significantly superior to the typical RLDH schemes. 5. Conclusion In this paper, we have presented a novel robust lossless data hiding (RLDH) method, which combines bidirectional statistical

quantity histogram shifting with k-means clustering to achieve effective and efficient embedding and recovery of the watermarks (e.g., copyright information). Compared with the existing typical methods, the proposed one has better comprehensive performance in terms of robustness, imperceptibility, and capacity, and shows wide adaptability and good stability. However, there are still some issues to be further investigated in the future. Since robustness is essential to the expansion of practical applications of RLDH, we plan to further enhance the robustness of SQH-SC by introducing new schemes and techniques [2,4,13], e.g., feature point [11,12,17,18], bag-of-visual words [26], and sparse representation [19], [25].

Acknowledgements The authors would like to thank the editors and anonymous reviewers for their helpful comments and suggestions. This work was supported by the National Basic Research Program of China (973 Program) under Grant 2011CB707100, by the National Natural Science Foundation of China under Grants 61172143, 61072093, 61101250, 61172146 and U0835004, by the Natural Science Basic Research Plan in Shaanxi Province of China under Grants 2009JM8004, 2010JQ8026, and 2011JM8008, and by the Fundamental Research Funds for the Central Universities under Grant K50511030005. References [1] L. An, X. Gao, C. Deng, F. Ji, Reversible watermarking based on statistical quantity histogram, in: Proceedings of the Advances in Multimedia Information Processessing, LNCS 5879, 2009, pp. 1300–1305. [2] L. An, X. Gao, C. Deng, Reliable embedding for robust reversible watermarking, in: Proceedings of the ACM International Conference on Internet Multimedia Computing and Service, 2010, pp. 57–60. [3] L. An, X. Gao, C. Deng, F. Ji, Robust lossless data hiding: analysis and evaluation, in: Proceedings of the Internatioanl Conference on High Performance Computing and Simulation, 2010, pp. 512–516.

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11 Lingling An received the B.S. and M.S. degrees in computer science and technology from Xidian University, Xi’an, Shaanxi, China, in 2002 and 2005, respectively. She is currently pursuing her Ph.D. degree in intelligent information processing from the School of Electronic Engineering, Xidian University. Her current research interests include lossless data hiding and digital watermarking.

Xinbo Gao (M’02-SM’07) received the B.S., M.S., and Ph.D. degrees in signal and information processing from Xidian University, Xi’an, Shaanxi, China, in 1994, 1997 and 1999, respectively. From 1997 to 1998, he was a Research Fellow with the Department of Computer Science, Shizuoka University, Shizuoka, Japan. From 2000 to 2001, he was a Post-Doctoral Research Fellow with the Department of Information Engineering, Chinese University of Hong Kong, Shatin, Hong Kong. Since 2001, he has been with the School of Electronic Engineering, Xidian University. Currently, he is a Professor of pattern recognition and intelligent system and the Director of the VIPS Laboratory, Xidian University. His current research interests include computational intelligence, machine learning, computer vision, pattern recognition and wireless communications. In these areas, he has published 4 books and around 100 technical articles in refereed journals and proceedings including IEEE T-IP, T-CSVT, T-NN, T-SMC, Pattern Recognition, and so on. Dr. Gao is on the editorial boards of several journals, including EURASIP Signal Processing (Elsevier), and Neurocomputing (Elsevier). He served as the general chair/co-chair or program committee chair/co-chair or a PC member for around 30 major international conferences.

Yuan Yuan is a professor at Chinese Academy of Sciences. Her research interests include visual information processing and content analysis.

Dacheng Tao (M’07) received the B.Eng. degree from the University of Science and Technology of China (USTC), Hefei, Anhui, China, the M.Phil. degree from the Chinese University of Hong Kong (CUHK), Shatin, Hong Kong, and the Ph.D. degree from the University of London, London, U.K. Currently, he is a Professor with the Centre for Quantum Computation and Information Systems (QCIS) and the Faculty of Engineering and Information Technology in the University of Technology, Sydney, Australia. He mainly applies statistics and mathematics for data analysis problems in data mining, computer vision, machine learning, multimedia, and video surveillance. He has authored and co-authored more than 100 scientific articles at top venues including IEEE T-PAMI, T-KDE, T-IP, NIPS, AISTATS, AAAI, CVPR, ECCV, ICDM; ACM T-KDD, and KDD, with best paper awards. Dr. Tao serves as an Associate Editor of IEEE Transactions on Knowledge and Data Engineering (T-KDE) and the Official Journal of the International Association for Statistical Computing—Computational Statistics & Data Analysis (Elsevier).