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Integer transform based reversible watermarking incorporating block selection
Accepted Manuscript Integer Transform based Reversible Watermarking Incorporating Block Selection Shaowei Weng, Jeng-Shyang Pan PII: DOI: Reference:
S1047-3203(15)00221-7 http://dx.doi.org/10.1016/j.jvcir.2015.11.005 YJVCI 1634
To appear in:
J. Vis. Commun. Image R.
Received Date: Accepted Date:
11 May 2015 12 November 2015
Please cite this article as: S. Weng, J-S. Pan, Integer Transform based Reversible Watermarking Incorporating Block Selection, J. Vis. Commun. Image R. (2015), doi: http://dx.doi.org/10.1016/j.jvcir.2015.11.005
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Integer Transform based Reversible Watermarking Incorporating Block Selection Shaowei Weng1 , and Jeng-Shyang Pan2,3 ,
Abstract We propose a new scheme based on integer Haar wavelet transform (IHWT), which utilizes block selection and difference expansion (DE) (or histogram shifting (HS)). IHWT has the characteristic that the average of a block remains unchanged before and after watermark embedding. Hence, this invariability can be used for determining whether a block is located in a smooth region or not. Specifically, for a block, its mean value and the neighborhood surrounding it are used for estimating the correlation between it and its neighborhood. In this way, only a reduced size location map is needed, and the block size can also be set to a small value. Since small blocks have stronger intra-block correlation than large ones, the embedding distortion caused by modifying small blocks is lower. Otherwise, if the difference between any two neighboring pixels in a block is large, then the distortion produced by directly expanding it is also high. To decrease the class of distortions, DE (or HS) is introduced into the proposed method.
Index Terms Reversible watermark, Invariability of Mean value, Histogram Shifting
I. I NTRODUCTION
I
N some applications, such as the fields of law enforcement, medical and military image system, any permanent distortion induced to the host images by data watermarking techniques is intolerable. In such cases, the original image is required
to be recovered without any distortion after extraction of the embedded watermark. The watermarking techniques satisfying these requirements are referred to as reversible (or lossless) watermarking. A considerable amount of research on RW has been carried out over the last several years since the concept of RW firstly appeared in the patent owned by Eastman Kodak [1]. Among the various categories of RW schemes, three most influential 1 School 2 College 3 Harbin
of Information Engineering, Guangdong University of Technology, P. R. China: [email protected]. of Information Science and Engineering, Fujian University of Technology, P. R. China. Institute of Technology, Shenzhen Graduate School, P. R. China.
2
ones are RW based on lossless compression [2], RW using DE and RW using HS (short for histogram shifting) in [3], [4]. RW using DE has been firstly presented by Tian [5]. DE is the process that difference (between a pair of neighboring pixels) is shifted left by one unit to create a vacant least significant bit (LSB), and 1-bit watermark is appended to this LSB. There are different extensions of DE. Among them, three main types of extensions are: RW based on integer transform, RW with the improvement in compressibility of location map and RW using the prediction-error expansion (PEE). DE has been extended to the pixel blocks of arbitrary length by Alattar in [6], Wang et al. in [7], [8], and Peng et al. in [9]. Based on integer Haar wavelet transform in [5], the new integer transforms have been proposed in papers [10]–[13]. Kamstra et al. in [14] and Kim et al. in [15] adopt different embedding strategies so that the location map can be remarkably compressed, respectively. Thodi et al. have proposed the first PEE scheme, wherein the prediction-errors instead of the difference values are expanded [16]. HS is incorporated into Thodi et al.’s method so as to efficiently compress the location map. Afterwards, PEE has also been developed by some recent studies in [17]–[30]. Among them, Qin et al. have proposed a prediction-based reversible steganographic scheme based on image inpainting. By the use of the adaptive strategy for choosing reference pixels and the inpainting predictor, Qin et al. provide a greater embedding rate and better visual quality compared with recently reported methods. In addition, a lot of RDH algorithms (e.g., [31]–[34]) have been proposed in the encrypted domain. Alattar’s transform (short for the integer transform proposed by Alattar) can be deemed to contain an additional term and a prediction process, which uses the mean value of a block to predict each pixel in this block [6]. This additional term has its advantage and disadvantage. The advantage is that its existence can guarantee the mean value of a block remains unchanged even after watermark embedding. The disadvantage is that its existence will result in the decrease of PSNR (peak signal to noise ratio) in Alattar’s method. This is also the reason that the performance of Alattar’s method is incapable of exceeding that of Wang et al.’s (see paper [7] for details). Wang’s transform (short for the transform proposed by Wang et al.) can also be considered as a prediction process, in which the mean value of a block is used to predict each pixel in this block [7]. In their method, a location map is generated to record the locations of the modified blocks in the embedding process. In order to ensure reversibility, after this map is losslessly compressed, it is embedded into the original image together with the payload. Hence, the low compression ratio can significantly decrease the payload. Experimental results in [7] demonstrate that when the host image is divided into 4 × 4-sized blocks, the performance is the best. Although 2 × 2-sized blocks can provide higher intra-block correlations than 4 × 4-sized ones, they cannot perform the best. This is due to that when the block size is 2×2, the compression ratio is very low. As a result, the performance is weak. To this end, Wang have to select 4 × 4 blocks so as to increase embedding performance. However, the performance is not increased largely owing to low intra-block correlation. In this light, it is necessary to investigate high
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performance RW methods. Besides, Wang calculate the variance of a block so as to determine the length of the watermark bits embedded into this block. As long as the calculated variance is smaller than a predefined threshold, even if the difference between some pixel and the mean value is large, Wang still embed the corresponding watermark bit into this pixel. In another word, to ensure reversibility, Wang’s transform has to modify all the pixels in a block uniformly even if the distortions introduced by modification are high for some pixels. Considering that a block can embed at most (n − 1) data bits in Wang’s transform, Peng (short for Peng et al.) have introduced adaptive embedding into Wang’s transform, in which a block can embed (n − 1) log2 k bits, where n is used to denote the size of an image block, and k(k ∈ {1, 2, 4, 8, 16}) is determined adaptively by the pre-estimated distortion. By the basic idea that embeds more bits into smooth blocks while avoids large distortion generated by noisy ones, Peng’s method enables very high capacity with good image quality. However, Peng can not solve the problems existed in Wang’s transform. With the above consideration, we argue that Peng’s method can be further improved. In order to solve two problems above, a novel RW scheme based on block selection is proposed in this paper. We employ the correlation between a block and its total adjacent pixels to determine if this block is located in a smooth or a complex region. These neighboring pixels along with the mean value of this block constitute a set. The correlation is defined as the local variance of this set. As long as the mean value is invariant, the local variance remains unchanged after watermark embedding. This is the reason that the integer transform having the invariant mean value (i.e., Alattar’s transform) is selected in this paper. Since the variance is invariant, only a reduced size location map is needed, and the map can be efficiently compressed. Besides, by means of the invariant variance, the locations of all the already-modified blocks in watermark embedding process can be correctly determined on the decoding side. Hence, in the proposed method, even if the block size is set to 2 × 2, we still can achieve the low ERs with high PSNR values. For the second problem existing in Wang’s method, DE (or HS) is incorporated into the proposed method so as to further decrease the embedding distortions.
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II. T HE RELATED METHODS A. Wang’s method The integer transform defined in Eq. (3) of the paper [7] is listed in Eq. (1). y1 = 2x1 − a(x) y2 = 2x2 − 2f (a(x)) + w1 = 2x2 − (a(x) + LSB(a(x))) + w1
(1)
··· yn = 2xn − 2f (a(x)) + wn−1 = 2xn − (a(x) + LSB(a(x))) + wn−1 where x = (x1 , · · · , xn ) ∈ Zn and y = (y1 , · · · , yn ) ∈ Zn respectively represent a n-sized pixel array and its corresponding ⌊¯ ¯ − ⌊¯ x⌋ if x x⌋ < 0.5 ∑n 1 ¯ = n i=1 xi , a(x) = watermarked one, x , f (x) = ⌈ x2 ⌉, and wi (i ∈ {0, 1, · · · , n − 1}) denotes ⌈¯ x⌉ otherwise 1-bit watermark and wi ∈ {0, 1}, and LSB(·) represents the least significant bit (LSB). a(x) is actually the rounded value of ¯. x As can be seen from Eq. (1), Wang’s transform can be considered as a prediction process, in which a(x) is used to predict each pixel in this block. The experimental results in [7] show that when the original image is divided into 4 × 4-sized blocks, the performance is the best. However, refer to Figs. 2 and 3 of the paper [7], Wang are incapable of achieving high PSNR values at the given ERs. This is due to that the larger the block size, the weaker the intra-block correlation. This is to say, 4 × 4-sized blocks are unable to provide the same intra-block correlations as 2 × 2-sized blocks. However, when the block size is set to 2 × 2, the location map can not be high-efficiently compressed, and thus all the available capacity is almost consumed by the compressed location map. So, Wang can only select 4 × 4 block so as to increase the compression ratio and achieve the required ERs. However, Wang can not obtain high PSNR due to low intra-block correlation. Besides, to ensure reversibility, Wang’s transform can not modify flexibly each pixel in a block according to the different difference value between each pixel and the mean value of a block.
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B. Alattar’s transform Alattar’s transform in [6] can be summarized in Eq. (3). ⌊ ⌋ n −x1 )+wn−1 y1 = ⌊¯ x⌋ − 2(x2 −x1 )+w1 +···+2(x n ∑ ∑ 2 n x +n−1 i=1 i i=1 wi −2nx1 = ⌊¯ x⌋ − n
(2)
y2 = y1 + 2 (x2 − x1 ) + w1 ··· yn = y1 + 2 (xn − x1 ) + wn−1 Suppose k2 =
∑n i=1
xi − n⌊¯ x⌋, and then k2 ∈ {0, · · · , n − 1}. Substitute y1 = ⌊¯ x⌋ + 2(x1 − ⌊¯ x⌋) − ⌊
2k2 +
∑n−1 i=1
wi
2k2 +
i=1
xi = k2 + n⌊¯ x⌋ into Eq. (2), we have
⌋
n
y2 = ⌊¯ x⌋ + 2(x2 − ⌊¯ x⌋) + w1 − ⌊
∑n
∑n−1 i=1
n
wi
⌋
(3)
··· yn = ⌊¯ x⌋ + 2(xn − ⌊¯ x⌋) + wn−1 − ⌊ where ⌊a⌋ rounds a to the nearest integers less than or equal to a,
∑ 2k2 + n−1 i=1 wi ⌋ n
∑n−1 i=1
wi ∈ {0, · · · , n − 1}.
As is illustrated in Eq. (3), Alattar’s transform can be deemed to contain an additional term and a process which uses ⌊¯ x⌋ to predict each pixel in the block. Specially, for each yi (i ∈ {0, 1, · · · , n}) in Eq. (3), it has a term, i.e., ⌊ k2 ∈ {0, 1, · · · , n − 1} and wi ∈ {0, 1}, 0 ≤ ⌊
2k2 +
∑n−1 i=1
n
wi
⌋ ≤ ⌊ 3(n−1) ⌋ = ⌊3(1 − n1 )⌋ = 2, i.e., n
2k2 +
∑n−1 i=1
n
∑ 2k + n−1 w ⌊ 2 ni=1 i ⌋
wi
⌋. Since
∈ {0, 1, 2}.
For instance, when k2 reaches its maximum value (i.e., n − 1), if all to-be-embedded bits are 1, then this term will reach its maximum value (namely 2). Similarly, Wang’s method contains a term, i.e., LSB(a(x)) ∈ {0, 1} except the process which uses a(x) to predict each pixel in the block (Refer to Eq. (3) in paper [7]). Alattar’s transform has its own disadvantage: it introduces higher distortion than Wang’s transform due to this additional term. Abundant experiments in the paper [7] also demonstrate that Wang’s method has superior performance to Alattar’s. In this paper, we will make full use of the property of the unchanged mean value in Alattar’s transform. The mean value of a n-sized block and the 2 × n + 1 neighbors surrounding this block can be used to evaluate whether this block is located in a smooth region or not. Based on the unchanged mean value, the value of n can be set to a small value, e.g. 2 × 2, 1 × 3. Small block size means strong intra-block correlation. By means of increasing the intra-block correlation and introducing DE (or HS), we compensate for the shortage existing in paper [7]. By multi-layer embedding, we can achieve high ERs (about 1.0 bpp (bit per pixel)). Experimental results also demonstrate the proposed method outperforms Wang’s at almost all ERs.
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C. Peng’s method As illustrated in Eq. (4), unlike Wang’s transform which embeds data uniformly, Peng’s method can embed (n − 1) log2 k (k ∈ {1, 2, 4, 8, 16}) bits into a block according to the block type determined by the local complexity, where k is the capacity parameter. y1 = kx1 − an,k (x) y2 = kx2 − an,k (x) + w1
(4)
··· yn = kxn − an,k (x) + wn−1 where an,k (x) = arg min E(∥y − x∥)2l2 , and E(·) is the expected value of l2 -error ∥y − x∥2l2 . By tuning k according to the an,k
local complexity, Peng’s method enables very high capacity with good image quality. However, Peng cannot still resolve the problems existed in Wang’s method.
III. T HE PROPOSED METHOD Given an 8-bit graylevel I with size R × C, the image I is partitioned into n-sized non-overlapping image blocks:
B1 , · · · , B⌊ R ⌋×⌊ C ⌋ r
c
x1,1 , · · · , x1,c in by working each r rows from left to right, where n = r × c. All the pixels · · · xr,1 , · · · , xr,c
some block Bi (i ∈ {1, · · · , ⌊ Rr ⌋ × ⌊ Cc ⌋}) are arranged into a one-dimensional pixel array x according to a predefined order, i.e., x = {x1 , · · · , xn }. Specifically, we work the first row from left to right, the second row from right to left, then continue alternating row direction in this manner, so that a one-dimensional pixel array x is created. Alattar’s transform is defined as follows ¯= x
⌊ x1 +x2 +···+xn ⌋ n
d1 = x2 − x1 d2 = x3 − x2 ··· dn−1 = xn − xn−1
(5)
7
where dk (k ∈ {1, · · · , n − 1}) represents the difference value between two neighboring pixels. The inverse integer transform is defined as ¯− x1 = x
⌊
⌋
(n−1)×d1 +(n−2)×d2 +···+dn−1 n
x2 = x1 + d1 (6)
x3 = x2 + d2 ··· xn = xn−1 + dn−1
For some difference value dk (k ∈ {1, · · · , n − 1}), if it belongs to the inner region [−pTh , pTh ), then 1- bit watermark is ′
embedded into dk to get the watermarked value dk via Eq. (7). If dk belongs to the outer region (−∞, −pTh )
∪
[pTh , ∞),
dk will be shifted by pTh according to Eq. (7). 2 × dk + b, dk ∈ [−pTh , pTh ) ′ dk = dk − pTh , dk ≤ −pTh − 1 dk + pTh , dk ≥ pTh
(7)
where pTh is used for estimating the correlation between two adjacent pixels, b represents 1-bit watermark, i.e., b ∈ {0, 1}. ′
′
After the modifications given by Eq. (7) are done to dk (k ∈ {1, · · · , n−1}) to produce dk , substitute dk (k ∈ {1, · · · , n−1}) into Eq. (6) to get the watermarked pixel list y = {y1 , · · · , yn } (refer to Eq. (8)). ⌊ ¯− y1 = x
′
′
′
(n−1)×d1 +(n−2)×d2 +···+dn−1 n
⌋
′
y2 = y1 + d1 ′
(8)
y3 = y2 + d2 ··· ′
yn = yn−1 + dn−1 A. Smoothness Classification by Pixel Neighborhood and Mean Value For some block Bi (i ∈ {1, · · · , ⌊ Rr ⌋×⌊ Cc ⌋}), there are the total (r +c+1) neighbors surrounding it, i.e., x1,c+1 , · · · , xr,c+1 , ¯ b of block Bi constitute a pixel set named by IEN P . xr+1,c+1 , xr+1,1 , · · · , xr+1,c . All these neighbors and the mean value x The standard deviation, denoted by ∆, of set IEN P is used to estimate if this block is located in a smooth or complex region.
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∆ is obtained via
v u ∑ r 2 u u k=1(xk,c+1 −uEN P ) u n u u (x −u )2 +(¯ xb −uEN P )2 ∆=u u + r+1,c+1 EN Pn u c ∑ u (xr+1,k −uEN P )2 t k=1 + n
(9)
where µEN P is the mean value of set IEN P . When ∆ < vTh , the block Bi is regarded as having a strong relation with its total neighbors, and therefore, it is classified to be within a smooth region, where vTh is a predefined threshold which is used for distinguishing which classification Bi belongs to. Otherwise, Bi is estimated in a complex region. Note that if R has no remainder when divided by r, then the blocks obtained by partitioning the last r rows of the image I have not (2 × n + 1) neighbors. So, in order to ensure reversibility, they only can be kept unchanged during watermark embedding process. This is similar to C and c.
B. Algorithm Description For each layer embedding, the corresponding overhead information is composed of three parts: the 8-bit representation of each of vTh and pTh ; the compressed location map which is utilized to solve potential overflow/underflow problem. A unique EOS symbol is added at the end of the overhead information. To prevent the overflow/underflow, each watermarked pixel value should be contained in [0, 255]. We define { D=
} x ∈ A : 0 ≤ yi ≤ 255(1 ≤ i ≤ n, yi ∈ Z)
where A = {x = (x1 , · · · , xn ) ∈ Z : 0 ≤ xi ≤ 255(1 ≤ i ≤ n)}. For a pixel-value array x ∈ A, it is classified into one of three sets: •
Es = {x ∈ D : ∆ < vTh };
•
Os1 = {x ∈ / D : ∆ < vTh };
•
Os2 = {x ∈ A − Es ∪ Os1 : ∆ ≥ vTh }.
where Es and Os = Os1 ∪ Os2 are used to denote the sets of pixels which are altered according to Eq. (7) or kept unaltered, respectively. A location map is generated in which the locations of the image blocks belonging to Es are marked by ‘1’ while the ones of the blocks in Os1 are marked by ‘0’. Note that it’s not necessary to record the locations of the blocks in Os2 . This is due to that their locations can be correctly determined only by evaluating their variances. If the variance is larger than or equal to vTh , the block belong to Os2 . Here, suppose that the size of the location map is LS , The location map is compressed
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Original Image I
The next embedding layer
Divide I into non-overlapped 2 ´ 2-sized blocks N x Î Os 2
Satisfy the condition s < vTh ?
y=x
Y xÎ D?
x Î Os1
x Î Es Y
y=x
ì2 ´ d k + b, d k Î [- pTh , pTh ) ï d k ' = í d k - pTh , d k £ - pTh - 1 ï d + pT , d k ³ pTh h î k
Embed auxiliary information
N
Paylaod complete? Y Watermarked Image IW
Fig. 1.
Embedding mechanism
Bitstream L
pTh
vTh
# EOS
(a)
Bitstream L
pTh
vTh
EC
# EOS
(b) Fig. 2.
Auxiliary information formats in an embedding layer: (a) the other embedding layers; (b) last embedding layer.
losslessly by an arithmetic encoder and the resulting bitstream is denoted by L. LSC is the bit length of L. Fig. 1 shows the block diagram of watermark embedding mechanism. Fig. 2 shows the two overhead information formats for the last embedding layer and the other embedding layers. Because only the last layer may not be fully embedded, an extra information EC is appended after the vTh of the last layer. The EC consists of 18 bits (representing embedding capacity in the last layer, specially, 218 = 512 × 512) and 6 bits (the number of layers). Both of the last layer and the other ones consist of the compressed location map (LSC bits), vTh (8 bits), pTh (8 bits) and EOS (8 bits). The difference in format is that the EC is added in the type B format. Therefore, for the other layers, the overhead information occupies LSC plus 16 bits, i.e., L∑ = LSC + 16. While for the last layer, L∑ consumes LSC + 42 bits in total, where the size of the overhead information is denoted by L∑ .
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Determination of ve for Lena 18000 16000
The number of vT
h
14000 12000 10000 8000 6000 4000 2000 0
0
10
20
30
40 vT
50
60
70
80
h
Fig. 3.
The number of vTh in the unit interval, and the unit on horizontal axis is 1, e.g., the number of vTh is 18,000 when 1 < vTh ≤ 2 .
1) Determination of the values of pTh and vTh : vTh has an initial value, denoted by vs , which is capable to embed the payload. In the experiments, vs is set to 1 for six images. vTh runs from this initial value to ve (i.e., the upper limit of vTh ). Take Lena for example, Fig. 3 provides an intuitive illustration of determining ve . From Fig. 3, one can know the number of the variances smaller than or equal to 10 (i.e., ∆ ≤ 10) accounts for over 90% of the total variances. Therefore, ve is set to 10 for Lena in our method. Similarly, pTh also has an initial value, denoted by ps , which is set to a value capable of ensuring the embedding rate larger than 0. In this paper, ps is set to 1 for Lena. From Fig. 4, it can be seen that the upper limit of pTh , denoted by pe , is selected as 15. It is not necessary to continue to increase this upper limit (namely exceeding 15), since the increase of
Nd Nt
can almost
be ignored. 2) Optimal-threshold-determination for combined embedding: For a one-layer embedding process, when vTh is fixed, we increase pTh gradually from the initial value ps = 1 to its maximum with a step size of 1. For each value of pTh , when the required capacity is just accommodated, stop the embedding process. Meanwhile, calculate the corresponding PSNR, and record the value of pTh . The optimal pTh∗ is the one which can yields the highest PSNR. It is clear that (vT1∗ , pTh∗ ) yields the highest PSNR whatever the block size and the image are. ∗ ∗ For a two-layer embedding process, we utilize the similar method to determine optimal threshold combination, i.e., (vTh1 , pTh1 ∗ ∗ ∗ ∗ ∗ ∗ , vTh2 , pTh2 ), where (vTh1 , pTh1 ) and (vTh2 , pTh2 ) represent optimal threshold combination used in the first-layer and second∗ ∗ ∗ ∗ layer embedding process, respectively. From Fig. 5, one can also see that the values of vTh1 , pTh1 , vTh2 and pTh2 obtained ∗ ∗ ∗ ∗ ∗ ∗ by experiments is small. Take Fig. 5(a) for example, (vTh1 , pTh1 , vTh2 , pTh2 ) = (2, 1, 0, 0). Note that, (vTh2 , pTh2 ) = (0, 0)
means that the highest PSNR is achieved only by the first layer embedding.
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Determination of pe for Lena 1 vT =1 h
0.9
vT =2 h
vTh=3
0.8
vTh=4 vTh=5
0.7
Nd/Nt
vTh=6 vTh=7
0.6
vTh=8
0.5
vTh=9 vTh=10
0.4 0.3 0.2 0.1
Fig. 4.
0
5
10 pTh
15
20
Determination of the value of pe , and the vertical axis denotes the ratio of Nd to Nt ,(i.e.,
Nd ), Nt
where the total number of the difference values is
denoted by Nt for given vTh and pTh , and the number of the difference values capable of carrying 1 bit is denoted by Nd . Barbara 60 (vT*h1,pT*h1, vT*h2,pT*h2)=(2,1,0,0)
54 Quality Measurement PSNR (dB)
58 Quality Measurement PSNR (dB)
Barbara (vT*h1,pT*h1, vT*h2,pT*h2)=(4,1,0,0)
55
56
54
52
50
53 52 51 50 49 48 47
48 46 46
0
2
4
6 vTh1
8
10
(a) ER=0.0381 bpp (or 10,000 bits) Fig. 5.
12
45
1
2
3
4
5 vTh1
6
7
8
9
(b) ER=0.0763 bpp (or 20,000 bits)
Performance comparison for a given capacity on Barbara by using different (vTh1 , pTh1 , vTh2 , pTh2 ).
3) Computational Complexity: The time cost of the proposed method is determined by the image size M × N , thus the computational complexity is O(M ×N ). The required processing mainly lies on obtaining the difference values and the average value of a 2 × 2-sized block, smoothness classification, generating location map, compressing location map, and modifying difference values by DE (or HS). Here, for the sake of simplicity, Alattar and Luo are used as an abbreviation of Alattar et al. and Luo et al., respectively. In Table I, we calculate the average time cost of Alattar’s, Luo’s, Wang’s and Peng’s methods for one-layer embedding on six test images, respectively. For the proposed method, in Table I, we provide the average time cost of performing one-layer embedding and two-layer embedding, respectively. The one-layer embedding refers to a single watermark embedding process having the fixed thresholds (or embedding capacity) for the proposed, Luo’s, Alatter’s, Wang’s and Peng’s methods. The source codes of Luo’s and Alattar’s methods are provided by the authors of paper [35]. The source code of Peng’s and Wang’s methods
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TABLE I C OMPARISON OF TIME COST, WHERE THE UNIT OF RUNTIME IS SECOND . Images
Lena
Baboon
Airplane
Barbara
Goldhill
Sailboat
Alattar
18.9060
18.3364
18.9925
19.7876
18.4751
18.5884
Luo
0.6832
0.6434
0.6614
0.6646
0.6618
0.6642
Wang
4.8961
3.9306
6.5665
4.6592
4.5164
4.4952
Peng
3.5381
3.5608
4.1835
3.5261
3.5894
3.5190
Proposed(one-layer embedding)
1.2627
1.2052
2.002
1.2178
1.2429
1.2009
Proposed(two-layer embedding)
2.7976
2.2240
3.6692
2.3857
2.3887
2.3290
are provided by the authors of paper [36]. The proposed and the compared algorithms are implemented on Matlab R2013a, and the experiments are run on a personal PC. It can be seen that the runtime of the proposed method varies with images. Although our time cost is much larger than the prior arts (e.g., Luo’s), it is still acceptable in this age as it can be reduced by a high-performance PC or an effective programming language such as C++. For a one-layer embedding process using DE, our method has comparable or lower computational complexity than those of Alattar’s, Wang’s and Peng’s. Otherwise, we have to determine the number of iterations so as to obtain the desired embedding capacity. The process of determining the number of iterations will add the time cost. Decreasing computational complexity is beyond the scope of this paper, and we will investigate this issue in our future work. 4) Comparison with Alattar’s method: The basic idea of our method is to make best use of the advantage of Alattar’s scheme (i.e., the unaltered mean value ⌊¯ x⌋) while avoid its disadvantage. Specifically, by utilizing ⌊¯ x⌋ to estimate whether a block is located in a smooth region or not, the block size n can be set to a small value, e.g., 1 × 3 or 2 × 2, and more importantly, the location map can still be high-efficiently compressed. It is well known that small blocks have stronger intrablock correlation than large ones. Therefore, ⌊¯ x⌋ is highly related to all pixels in a block, and finally, the distortion introduced by pixel modification is lower. In this way, our method efficiently avoids the disadvantage of Alattar’s one. Depending on the above improvements, our method achieves higher embedding performance compared with Alattar’s one. 5) Comparison with Wang’s and Peng’s methods: Compared with Wang’s and Peng’s methods, ours utilizes the invariant ⌊¯ x⌋ to estimate whether a block is located in a smooth region or not. Thus, the block size can be set to a smaller value, e.g., 2 × 2 or 1 × 3 and more importantly, the location map can be high-efficiently compressed. From Tables II and III, one can observe that our compression ratio (i.e.,
LS −LSC ) LS
is higher compared with that of Wang’s
method. Take Table II for example, when PSNR is 47.7982 (dB), the obtained embedding capacity is 58253 (bits) and the compression ratio equals 99.92%. While in Wang’s method with n = 4 × 4, when PSNR is 47.7570 (dB), the embedding
13
TABLE II C OMPARISONS OF LSC ( BITS )
AND
LS ( BITS )
The proposed method (n = 2 × 2)
BETWEEN THE PROPOSED METHOD AND
WANG ’ S METHOD FOR L ENA .
Wang’s method (n = 2 × 2)
Wang’s method (n = 4 × 4)
LS
LSC
Payload size
PSNR(dB)
LS
LSC
Payload size
PSNR(dB)
LS
LSC
Payload size
PSNR(dB)
2704
32
2686
64.5405
36540
34968
8331
52.1491
7968
6080
23295
52.1296
30566
40
23069
54.0675
45100
43477
26634
48.7127
9496
8464
51435
47.7570
30566
40
42757
49.9629
49852
45096
46932
46.4100
9998
8768
64965
46.3622
47771
40
58253
47.7982
53235
42448
69309
44.5593
10481
8824
77160
45.2526
TABLE III C OMPARISONS OF LSC ( BITS ) AND LS ( BITS ) BETWEEN THE PROPOSED METHOD AND WANG ’ S METHOD FOR BARBARA . The proposed method (n = 2 × 2)
Wang’s method (n = 2 × 2)
Wang’s method (n = 4 × 4)
LS
LSC
Payload size
PSNR(dB)
LS
LSC
Payload size
PSNR(dB)
LS
LSC
Payload size
PSNR(dB)
14120
40
11546
57.5657
28765
28040
7587
52.9696
5352
3552
10470
55.9220
23868
40
18034
55.2656
34287
33096
24357
49.5767
6066
5032
20925
52.5364
29204
40
39602
50.2157
37405
32400
41736
47.4129
6637
5936
32220
50.2757
32386
40
58887
47.3181
39881
30040
57390
45.7986
7069
6384
43050
48.6410
capacity is 51435 (bits) and the compression ratio is 10.87%. Therefore, our method achieves higher embedding capacity than Wang’s at almost the same PSNR. However, when the block size is changed from 4 × 4 to 2 × 2 in Wang’s method, the performance becomes weaker due to the lower compression ratio. For example, when PSNR is 46.4100 (dB), the embedding capacity is 46932 (bits) and the compression ratio is 9.54% (refer to Table II for details). Besides, our method can achieve high embedding performance even at low embedding capacity. For instance, when PSNR is 64.5405 (dB), the embedding capacity is 2686 (bits). The experimental results illustrated in Tables. IV and V prove that our method outperforms Peng’s method due to higher compression ratio. TABLE IV C OMPARISONS OF LSC ( BITS )
AND
LS ( BITS )
The proposed method (n = 2 × 2)
BETWEEN THE PROPOSED METHOD AND
P ENG ’ S METHOD FOR L ENA .
Peng’s method (n = 2 × 2)
Peng’s method (n = 4 × 4)
LS
LSC
Payload size
PSNR(dB)
LS
LSC
Payload size
PSNR(dB)
LS
LSC
Payload size
PSNR(dB)
2704
32
2686
64.5405
90860
64968
11685
47.7482
16959
3680
4960
58.8807
30566
40
23069
54.0675
101703
79360
29822
44.9345
17548
5368
12107
54.9793
30566
40
42757
49.9629
106383
80072
51214
43.3613
18429
7632
23058
51.7755
47771
40
58253
47.7982
107561
89440
69347
41.4729
19460
9584
36571
49.3347
14
TABLE V C OMPARISONS OF LSC ( BITS ) AND LS ( BITS ) BETWEEN THE PROPOSED METHOD AND P ENG ’ S METHOD The proposed method (n = 2 × 2)
Peng’s method (n = 2 × 2)
FOR
BARBARA .
Peng’s method (n = 4 × 4)
LS
LSC
Payload size
PSNR(dB)
LS
LSC
Payload size
PSNR(dB)
LS
LSC
Payload size
PSNR(dB)
14120
40
11546
57.5657
85967
53904
7692
48.7100
17369
4872
9903
55.5029
23868
40
18034
55.2656
94382
62728
24113
45.9891
18179
7000
19925
52.2130
29204
40
39602
50.2157
99458
63680
38389
44.5888
18975
8432
30433
50.0366
32386
40
58887
47.3181
104928
71248
50768
42.7966
19729
10288
39887
48.4191
C. Data Embedding Now, the embedding procedure is described as follows step by step. Step 1 Watermark embedding in a single layer The overhead information is formed. Suppose that the payload to be embedded in the current layer is PC . We know |PC | ≤ PM , where PM = N PM , we must perform multiple-layer so as to obtain the payload P. First, for this layer, perform Step 1 for the payload of length PM and the corresponding overhead information. Note that the size of the residual payload is PL − PM . Set |PC | = |PC | − PM . Next, go to Step 1 for next layer embedding.
D. Data Extraction and Image Restoration The LSBs of the pixels in Iw are collected into a bitstream B according to the same order as in embedding. B is decompressed by an arithmetic decoder to retrieve the location map. Once LSC is known, pTh , vTh will be extracted one by one according to their fixed lengths. If the current layer is the last one, we will easily know the number of embedding layers, the embedded bits for the last layer by extracting EC, respectively.
15
The watermarked image Iw is partitioned into n-sized image blocks: B1w , · · · , B⌊wR ⌋×⌊ C ⌋ according to the same order as in r
c
embedding. In order to ensure reversibility, the watermark extraction is executed according to the inverse order as in embedding, i.e., B⌊wR ⌋×⌊ C ⌋ , · · · , B1w . r
c
One watermarked image block Biw (i ∈ {⌊ Rr ⌋ × ⌊ Cc ⌋, ⌊ Rr ⌋ × ⌊ Cc ⌋ − 1, · · · , 1}), is scanned in the same way as in embedding to produce its corresponding array ym = (y1 , · · · , yn ) (m ∈ {⌊ Rr ⌋ × ⌊ Cc ⌋, ⌊ Rr ⌋ × ⌊ Cc ⌋ − 1, · · · , 1}). For each of ym , if it has not the total (r + c + 1) neighbors surrounding it, then it is kept unchanged, namely, ym = xm . Otherwise, the total neighbors ¯ b,m of block ym constitute the same set IEN P as in x1,c+1 , · · · , xr,c+1 , xr+1,c+1 , xr+1,1 , · · · , xr+1,c and the mean value x embedding. Note that the total neighbors x1,c+1 , · · · , xr,c+1 , xr+1,c+1 , xr+1,1 , · · · , xr+1,c must be correctly retrieved prior to the ym . If ∆ via Eq. (9) of ym is larger than or equal to vTh , then it is kept unaltered. If ∆ is smaller than vTh , and its location is associated with ‘0’ in the location map, then it is ignored. Otherwise, the watermark can be extracted using the ′
following formula: b = mod(dk , 2) if dk ∈ [−2pTh , 2pTh − 1] . And meanwhile, the original difference value is retrieved by Eq. (10).
′ ′ ⌊dk ⌋ dk ∈ [−2pTh , 2pTh − 1] ′ ′ dk = dk + pTh dk ≤ −2pTh − 1 d′k − pTh , d′k ≥ 2pTh
(10)
If the number of extracted watermark bits is equal to the capacity calculated by EC, stop extraction and form P; else go the next layer extraction and repeat steps above. When the current layer is fully extracted, classify the extracted bitstream into watermark bits and restore the pixels by simple LSB replacement.
IV. E XPERIMENTAL RESULTS The proposed RW scheme is carried out in MATLAB environment. The Lena, Baboon, Barbara, Airplane, Goldhill and Sailboat images with size 512 × 512 are provided by the authors of paper [9]. For convenience of description, Weng and Coatrieux are used as an abbreviation of Weng et al. and Coatrieux et al., respectively. In the experiments, the block size is set to 2 × 2. Fig. 6 shows performance comparisons between the proposed method and following six methods: Peng [9], Wang [7] Alattar [6], Luo [22], Weng [29] and Coatrieux [37]. It also can be seen from Fig. 6 that our method performs well, and significantly outperforms Peng’s, Wang’s, Alattar’s and Luo’s whatever the ER is. Especially when ER is low, the proposed method can achieve better performance than Peng’s. When you take a careful look at the curve of Peng’s method, you will find the points on this curve are very sparse when ER is lower than 0.5 bpp. With the ER increased, the points becomes denser. While our method can achieve better performance even when ER is lower than 0.5 bpp. This is mainly because our method
16
Capacity vs. Distortion Comparison on Airplane (F−16)
50 48 46 44 42 40 38 36 34 32 30
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Payload Size (bpp)
Quality Measurement PSNR (dB)
Quality Measurement PSNR (dB)
55
25
Capacity vs. Distortion Comparison on Barbara
Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg. Weng et al.’s Alg.
55 50 48 46 44 42 40 38 36 34 32 30 25
1.1 1.2 1.3 1.4 1.5
Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg. Weng et al.’s Alg.
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Payload Size (bpp)
(a)
1
1.1 1.2 1.3 1.4
(b)
Capacity vs. Distortion Comparison on Sailboat
Capacity vs. Distortion Comparison on Goldhill 55
Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg. Weng et al.’s Alg.
50 48 46 44 42 40 38 36 34 32 30
25
Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg. Weng et al.’s Alg.
50 Quality Measurement PSNR (dB)
Quality Measurement PSNR (dB)
55
48 46 44 42 40 38 36 34 32 30
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Payload Size (bpp)
1
25
1.1 1.2 1.3 1.4
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Payload Size (bpp)
(c)
1
1.1 1.2
(d)
Capacity vs. Distortion Comparison on Baboon
Capacity vs. Distortion Comparison on Lena
55 50 48 46 44 42 40 38 36 34 32 30
60 55 50 45 40 35
25
0
0.1
0.2
0.3 0.4 0.5 Payload Size (bpp)
(e) Fig. 6.
Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg. Weng et al.’s Alg. Coatrieux et al.’s Alg.
65 Quality Measurement PSNR (dB)
Quality Measurement PSNR (dB)
70 Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg. Weng et al.’s Alg. Coatrieux et al.’s Alg.
0.6
0.7
0.8
30
0
0.2
0.4
0.6 0.8 Payload Size (bpp)
1
1.2
1.4
(f)
Performance comparisons between the proposed method and following six methods: Peng [9], Wang [7], Alattar [6], Luo [22], Coatrieux [37] and
Weng [29] for the test images: (a) Airplane, (b) Barbara, (c) Sailboat, (d) Goldhill, (e) Baboon, and (f) Lena.
17
can set a small block size (e.g., 2 × 2 or 1 × 3), and thus strong intra-block correlation can be obtained. From Fig. 6, we can also see that Peng’s method obtains weaker performance than Luo’s when ER is low (e.g. smaller than 0.5 bpp for Lena and Airplane). While our method can achieve higher performance than Luo’s at almost all ERs. So far, among all the RW methods based on integer transform [5]–[13], Peng’s and Wang’s methods have achieved the best rate-distortion performance. Fig. 6 illustrates that our method can achieve a better or comparable visual quality than Peng’s and Wang’s methods at the same ER. The embedding-distortion curves of Lena and Baboon are provided in Coatrieuxs paper. So, we need to get the embeddingdistortion curves of the other four images. We tried all kinds of methods to look for the source code of Coatrieux’s method. Unfortunately, we did not find it. After studying deeply Coatrieux’s paper, we decide to write the code of Coatrieux’s method by ourselves. However, the obtained performance is weaker than that given in Coatrieux’s paper. We spend a lot of time in modifying our source code until we have no time. However, for Lena and Baboon, the obtained PSNR value is still smaller than that illustrated in Coatrieux’s paper at any given ER. Based on this consideration, we think our experimental results are not suitable for being used in this paper. In this paper, we illustrate the embedding performance of Coatrieux’s method only for Lena and Baboon. From Figs. 6(e) and 6(f), we can observe that our method outperforms Coatrieux’s method when the ERs are larger than 0.4 bpp. Compared with Alattar’s, Wang’s and Peng’s methods, ours increases embedding performance by using the mean value of a block to estimate a block whether it is located in a smooth region or not. Refer to Figs. 6(a), 6(b) and 6(c), our method outperforms Weng’s method at almost all ERs. For Lena, Baboon and Goldhill, Figs. 6(d), 6(e) and 6(f) show Weng’s method is superior to ours at high ERs (e.g.,> 0.1335 bpp). Fig. 7 shows performance comparisons between the proposed and Weng’s methods when the ER is low (e.g., < 0.1335 bpp for Lena). From Fig. 7, one can observe that the proposed method is superior to Weng’s method at low ERs. We will investigate to increase prediction performance in our future work. The SSIM index based on structural similarity [38] has been tested in experiments for comparison. A close to 1 SSIM index represents that two images possess a higher perceptual similarity. Fig. 8 shows SSIM comparisons between the proposed and Alattar’s, Wang’s, Peng’s, Luo’s methods. From Fig. 8, we can observe that SSIM index of the proposed method is higher than those of three methods (e.g., Alattar’s, Wang’s, Peng’s) at almost all ERs. For Sailboat, the SSIM index of our method outperforms that of Luo’s method whatever the ER is. For the other five images, when the ER exceeds 0.5 or 0.6 bpp, the SSIM index of our method outperforms that of Luo’s method. V. C ONCLUSIONS A new RW scheme is proposed in this letter. This scheme fully exploits the invariability of the mean value. The mean value is favorable to estimate accurately if a block is located in a smooth or complex region. Depending on the invariability
18
Capacity vs. Distortion Comparison on Airplane
Capacity vs. Distortion Comparison on Barbara
59
62 Prop. Alg. Weng et al.’s Alg.
Prop. Alg. Weng et al.’s Alg.
60 Quality Measurement PSNR (dB)
Quality Measurement PSNR (dB)
58 57 56 55 54 53 52
58 56 54 52 50 48 46
51 1.5
2
2.5
3
3.5 4 4.5 Payload Size (bits)
5
5.5
44
6
0
0.05
0.1
4
x 10
(a)
0.3
0.35
Capacity vs. Distortion Comparison on Goldhill
62
64 Prop. Alg. Weng et al.’s Alg.
Prop. Alg. Weng et al.’s Alg.
62 Quality Measurement PSNR (dB)
60 Quality Measurement PSNR (dB)
0.25
(b)
Capacity vs. Distortion Comparison on Sailboat
58
56
54
52
50
60 58 56 54 52 50
48 0.5
1
1.5
2 2.5 Payload Size (bits)
3
3.5
48
4
0
0.02
0.04
4
x 10
(c)
0.06 0.08 Payload Size (bits)
0.1
0.12
0.14
(d)
Capacity vs. Distortion Comparison on Baboon
Capacity vs. Distortion Comparison on Lena
62
65 Prop. Alg. Weng et al.’s Alg.
60 58
Prop. Alg. Weng et al.’s Alg. Quality Measurement PSNR (dB)
Quality Measurement PSNR (dB)
0.15 0.2 Payload Size (bits)
56 54 52 50 48
60
55
46 44
0
0.02
0.04
0.06 0.08 0.1 Payload Size (bits)
(e) Fig. 7.
0.12
0.14
0.16
50
0
0.5
1
1.5 2 2.5 Payload Size (bits)
3
3.5
4 4
x 10
(f)
Performance comparisons between the proposed and Weng’s methods [29] for the test images: (a) Airplane, (b) Barbara, (c) Sailboat, (d) Goldhill,
(e) Baboon, and (f) Lena.
19
Capacity vs. Distortion Comparison on Barbara
Capacity vs. Distortion Comparison on Lena 1
1 Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg.
0.99 0.98
Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg.
0.99 0.98 0.97
0.97 SSIM
SSIM
0.96 0.96 0.95
0.95 0.94
0.94
0.93
0.93
0.92
0.92 0.91
0.91 0
0.1
0.2
0.3 0.4 0.5 Payload Size (bpp)
0.6
0.7
0.9
0.8
0
0.1
0.2
(a)
0.3 0.4 0.5 Payload Size (bpp)
0.6
0.7
0.8
(b)
Capacity vs. Distortion Comparison on Airplane
Capacity vs. Distortion Comparison on Goldhill
1
1 Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg.
0.99 0.98
Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg.
0.98
0.96 SSIM
SSIM
0.97 0.96
0.94
0.95 0.92 0.94 0.9 0.93 0.92
0
0.1
0.2
0.3 0.4 0.5 Payload Size (bpp)
0.6
0.7
0.88
0.8
0
0.1
0.2
(c) Capacity vs. Distortion Comparison on Baboon
0.8
Capacity vs. Distortion Comparison on Sailboat Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg.
0.98
0.96 SSIM
0.96 SSIM
0.7
1 Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg.
0.98
0.94
0.94
0.92
0.92
0.9
0.9
0
0.1
0.2
0.3 0.4 0.5 Payload Size (bpp)
0.6
0.7
0.8
(e) Fig. 8.
0.6
(d)
1
0.88
0.3 0.4 0.5 Payload Size (bpp)
0.88
0
0.1
0.2
0.3 0.4 0.5 Payload Size (bpp)
0.6
0.7
0.8
(f)
SSIM comparisons between the proposed method and following four methods: Peng [9], Wang [7], Alattar [6] and Luo [22] for the test images: (a)
Lena, (b) Barbara, (c) Airplane, (d) Goldhill, (e) Baboon, and (f) Sailboat.
20
of the mean value, we can set a small block size, and meanwhile strong intra-block correlation can be obtained. Due to this invariability, we only need to record the locations of the blocks with small local complexity. Hence, the map can be compressed efficiently. Thus, our method can achieve better performance even when ER is low. Experimental results also demonstrate our method is efficient. ACKNOWLEDGMENT This work was supported in part by National NSF of China (No. 61201393, No. 61272498, No. 61571139), New Star of Pearl River on Science and Technology of Guangzhou (No. 2014J2200085). R EFERENCES [1] C. W. Honsinger, P. Jones P., M. Rabbani, and J. C. Stoffe, “Lossless recovery of an original image containing embedded data,” US patent: 6278791W, 2001. [2] J. Fridrich, M. Goljan, and R. Du, “Lossless data embedding-new paradigm in digital watermarking,” in EURASIP J. Appl. Signal Process., 2002, vol. 2002, pp. 185–196. [3] Z. Ni, Y. Q. Shi, N. Ansari, and W. Su, “Reversible data hiding,” IEEE Trans. Circuits Syst. Video Technol., vol. 16, pp. 354–362, 2006. [4] G. R. Xuan, C. Y. Yang, Y. Z. Zhen, and Y. Q. Shi, “Reversible data hiding using integer wavelet transform and companding technique,” in Proceedings of IWDW, 2004, vol. 5, pp. 23–26. [5] J. Tian, “Reversible data embedding using a difference expansion,” IEEE Trans. Circuits Syst. Video Technol., vol. 13, no. 8, pp. 890–896, 2003. [6] A. M. Alattar, “Reversible watermark using the difference expansion of a generalized integer transform,” IEEE Trans. Image Process., vol. 13, no. 8, pp. 1147–1156, 2004. [7] X. Wang, X. L. Li, B. Yang, and Z. M. Guo, “Efficient generalized integer transform for reversible watermarking,” IEEE Signal Process. Lett., vol. 17, no. 6, pp. 567–570, 2010. [8] X. Wang, X. L. Li, and B. Yang, “High capacity reversible image watermarking based on in transform,” in Proceedings of ICIP, 2010. [9] F. Peng, X. Li, and B. Yang, “Adaptive reversible data hiding scheme based on integer transform,” Signal Process., vol. 92, no. 1, pp. 54–62, 2012. [10] D. Coltuc and J. M. Chassery, “Very fast watermarking by reversible contrast mapping,” IEEE Signal Process. Lett., vol. 14, no. 4, pp. 255–258, 2007. [11] S. W. Weng, Y. Zhao, J. S. Pan, and R. R. Ni, “Reversible watermarking based on invariability and adjustment on pixel pairs,” IEEE Signal Process. Lett., vol. 45, no. 20, pp. 1022–1023, 2008. [12] S. W. Weng, Y. Zhao, R. R. Ni, and J. S. Pan, “Parity-invariability-based reversible watermarking,” IET Electronics Lett., vol. 1, no. 2, pp. 91–95, 2009. [13] D. Coltuc, “Low distortion transform for reversible watermarking,” IEEE Trans. Image Process., vol. 21, no. 1, pp. 412–417, 2012. [14] L. Kamstra and H. J. A. M. Heijmans, “Reversible data embedding into images using wavelet technique and sorting,” IEEE Trans. Image Process., vol. 14, no. 12, pp. 2082–2090, 2005. [15] H. J. Kim, V. Sachnev, Y. Q. Shi, J. Nam, and H. G. Choo, “A novel difference expansion transform for reversible data embedding,” IEEE Trans. Inf. Forensic Secur., vol. 4, no. 3, pp. 456–465, 2008. [16] D. M. Thodi and J. J. Rodrłguez, “Expansion embedding techniques for reversible watermarking,” IEEE Trans. Image Process., vol. 16, no. 3, pp. 721–730, 2007. [17] Y. Hu, H. K. Lee, and J. Li, “DE-based reversible data hiding with improved overflow location map,” IEEE Trans. Circuits Syst. Video Technol., vol. 19, no. 2, pp. 250–260, 2009.
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[18] V. Sachnev, H. J. Kim, J. Nam, S. Suresh, and Y. Q. Shi, “Reversible watermarking algorithm using sorting and prediction,” IEEE Trans. Circuits Syst. Video Technol., vol. 19, no. 7, pp. 989–999, 2009. [19] P. Y. Tsai, Y. C. Hu, and H. L. Yeh, “Reversible image hiding scheme using predictive coding and histogram shifting,” Signal Process., vol. 89, no. 6, pp. 1129–1143, 2009. [20] W. L. Tai, C. M. Yeh, and C. C. Chang, “Reversible data hiding based on histogram modification of pixel differences,” IEEE Trans. Circuits Syst. Video Technol., vol. 19, no. 6, pp. 906–910, 2009. [21] W. Hong, T. S. Chen, and C. W. Shiu, “Reversible data hiding for high quality images using modification of prediction errors,” J. Syst. Softw., vol. 82, no. 11, pp. 1833–1842, 2009. [22] L. Luo, Z. Chen, M. Chen, X. Zeng, and Z. Xiong, “Reversible image watermarking using interpolation technique,” IEEE Trans. Inf. Forensic Secur., vol. 5, no. 1, pp. 187–193, 2010. [23] W. Hong, “An efficient prediction-and-shifting embedding technique for high quality reversible data hiding,” EURASIP J. Adv. Signal Process., 2010. [24] D. Coltuc, “Improved embedding for prediction-based reversible watermarking,” IEEE Trans. Inf. Forensic Secur., vol. 6, no. 3, pp. 873–882, 2011. [25] X. L. Li, B. Yang, and T. Y. Zeng, “Efficient reversible watermarking based on adaptive prediction-errorexpansion and pixel selection,” IEEE Trans. Image Process., vol. 20, no. 12, pp. 3524–3533, 2011. [26] H.-T. Wu and J. W. Huang, “Reversible image watermarking on prediction errors by efficient histogram modification,” Signal Process., vol. 92, no. 12, pp. 3000–3009, 2012. [27] C. Qin, C. C. Chang, Y. H. Huang, and L. T. Liao, “An inpainting-assisted reversible steganographic scheme using a histogram shifting mechanism,” IEEE Trans. Circuits Syst. Video Technol., vol. 23, no. 7, pp. 1109–1118, 2013. [28] W. Hong, T. Chen, and M. Wu, “An improved human visual system based reversible data hiding method using adaptive histogram modification,” Opt. Commun., vol. 291, pp. 87–97, 2013. [29] S. W. Weng and J. S. Pan, “Reversible watermarking based on multiple predictionmodes and adaptive watermark embedding,” Multimedia Tools and Application, vol. 72, no. 3, pp. 3063–3083, 2014. [30] C. F. Lee, C. C. Chang, P. Y. Pai, and C. M. Liu, “An adjustable and reversible data hiding method based on multiple-base notational system without location map,” Journal of Information Hiding and Multimedia Signal Processing, vol. 6, no. 1, pp. 1–28, 2015. [31] X. P. Zhang, “Reversible data hiding in encrypted images,” IEEE Signal Process. Lett., vol. 18, no. 4, pp. 255–258, 2011. [32] X. P. Zhang, Z. X. Qian, G. R. Feng, and Y. L. Ren, “Efficient reversible data hiding in encrypted images,” J. Vis. Commun. Image R., vol. 25, pp. 322–328, 2014. [33] W. Hong, “An improved reversible data hiding in encrypted images using side match,” IEEE Signal Process. Lett., vol. 19, no. 4, pp. 199–202, 2011. [34] C. Qin and X. P. Zhang, “Effective reversible data hiding in encrypted image with privacy protection for image content,” J. Vis. Commun. Image R., vol. 31, pp. 154–164, 2015. [35] B. Ou, X. L. Li, Y. Zhao, and R. R. Ni, “Reversible data hiding based on pde predictor,” Journal of Systems and Software, vol. 86, no. 10, pp. 2700–2709, 2013. [36] X. L. Li, W. M. Zhang, X. L. Gui, and B. Yang, “A novel reversible data hiding scheme based on two-dimensional difference-histogram modification,” IEEE Trans. Inf. Forensic Secur., vol. 8, no. 7, pp. 1091–1100, 2013. [37] G. Coatrieux, W.Pan, N.Cuppens-Boulahia, F.Cuppens, and C.Roux, “Reversible watermarking based on invariant image classification and dynamic histogram shifting,” IEEE Trans. Inf. Forensic Secur., vol. 8, no. 1, pp. 111–120, 2013. [38] Z. Wang, W. Pan, N. Cuppens-Boulahia, F. Cuppens, and C. Roux, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Inf. Forensic Secur., vol. 13, no. 4, pp. 600–612, 2013.
Highlights
We use the invariant mean value of a block to evaluate the local complexity. The block size can be set to a small value by the invariability of the mean value. The reduced size location map is created by the invariability of the mean value. We can modify flexibly each pixel in a block using DE or HS.
S1047-3203(15)00221-7 http://dx.doi.org/10.1016/j.jvcir.2015.11.005 YJVCI 1634
To appear in:
J. Vis. Commun. Image R.
Received Date: Accepted Date:
11 May 2015 12 November 2015
Please cite this article as: S. Weng, J-S. Pan, Integer Transform based Reversible Watermarking Incorporating Block Selection, J. Vis. Commun. Image R. (2015), doi: http://dx.doi.org/10.1016/j.jvcir.2015.11.005
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1
Integer Transform based Reversible Watermarking Incorporating Block Selection Shaowei Weng1 , and Jeng-Shyang Pan2,3 ,
Abstract We propose a new scheme based on integer Haar wavelet transform (IHWT), which utilizes block selection and difference expansion (DE) (or histogram shifting (HS)). IHWT has the characteristic that the average of a block remains unchanged before and after watermark embedding. Hence, this invariability can be used for determining whether a block is located in a smooth region or not. Specifically, for a block, its mean value and the neighborhood surrounding it are used for estimating the correlation between it and its neighborhood. In this way, only a reduced size location map is needed, and the block size can also be set to a small value. Since small blocks have stronger intra-block correlation than large ones, the embedding distortion caused by modifying small blocks is lower. Otherwise, if the difference between any two neighboring pixels in a block is large, then the distortion produced by directly expanding it is also high. To decrease the class of distortions, DE (or HS) is introduced into the proposed method.
Index Terms Reversible watermark, Invariability of Mean value, Histogram Shifting
I. I NTRODUCTION
I
N some applications, such as the fields of law enforcement, medical and military image system, any permanent distortion induced to the host images by data watermarking techniques is intolerable. In such cases, the original image is required
to be recovered without any distortion after extraction of the embedded watermark. The watermarking techniques satisfying these requirements are referred to as reversible (or lossless) watermarking. A considerable amount of research on RW has been carried out over the last several years since the concept of RW firstly appeared in the patent owned by Eastman Kodak [1]. Among the various categories of RW schemes, three most influential 1 School 2 College 3 Harbin
of Information Engineering, Guangdong University of Technology, P. R. China: [email protected]. of Information Science and Engineering, Fujian University of Technology, P. R. China. Institute of Technology, Shenzhen Graduate School, P. R. China.
2
ones are RW based on lossless compression [2], RW using DE and RW using HS (short for histogram shifting) in [3], [4]. RW using DE has been firstly presented by Tian [5]. DE is the process that difference (between a pair of neighboring pixels) is shifted left by one unit to create a vacant least significant bit (LSB), and 1-bit watermark is appended to this LSB. There are different extensions of DE. Among them, three main types of extensions are: RW based on integer transform, RW with the improvement in compressibility of location map and RW using the prediction-error expansion (PEE). DE has been extended to the pixel blocks of arbitrary length by Alattar in [6], Wang et al. in [7], [8], and Peng et al. in [9]. Based on integer Haar wavelet transform in [5], the new integer transforms have been proposed in papers [10]–[13]. Kamstra et al. in [14] and Kim et al. in [15] adopt different embedding strategies so that the location map can be remarkably compressed, respectively. Thodi et al. have proposed the first PEE scheme, wherein the prediction-errors instead of the difference values are expanded [16]. HS is incorporated into Thodi et al.’s method so as to efficiently compress the location map. Afterwards, PEE has also been developed by some recent studies in [17]–[30]. Among them, Qin et al. have proposed a prediction-based reversible steganographic scheme based on image inpainting. By the use of the adaptive strategy for choosing reference pixels and the inpainting predictor, Qin et al. provide a greater embedding rate and better visual quality compared with recently reported methods. In addition, a lot of RDH algorithms (e.g., [31]–[34]) have been proposed in the encrypted domain. Alattar’s transform (short for the integer transform proposed by Alattar) can be deemed to contain an additional term and a prediction process, which uses the mean value of a block to predict each pixel in this block [6]. This additional term has its advantage and disadvantage. The advantage is that its existence can guarantee the mean value of a block remains unchanged even after watermark embedding. The disadvantage is that its existence will result in the decrease of PSNR (peak signal to noise ratio) in Alattar’s method. This is also the reason that the performance of Alattar’s method is incapable of exceeding that of Wang et al.’s (see paper [7] for details). Wang’s transform (short for the transform proposed by Wang et al.) can also be considered as a prediction process, in which the mean value of a block is used to predict each pixel in this block [7]. In their method, a location map is generated to record the locations of the modified blocks in the embedding process. In order to ensure reversibility, after this map is losslessly compressed, it is embedded into the original image together with the payload. Hence, the low compression ratio can significantly decrease the payload. Experimental results in [7] demonstrate that when the host image is divided into 4 × 4-sized blocks, the performance is the best. Although 2 × 2-sized blocks can provide higher intra-block correlations than 4 × 4-sized ones, they cannot perform the best. This is due to that when the block size is 2×2, the compression ratio is very low. As a result, the performance is weak. To this end, Wang have to select 4 × 4 blocks so as to increase embedding performance. However, the performance is not increased largely owing to low intra-block correlation. In this light, it is necessary to investigate high
3
performance RW methods. Besides, Wang calculate the variance of a block so as to determine the length of the watermark bits embedded into this block. As long as the calculated variance is smaller than a predefined threshold, even if the difference between some pixel and the mean value is large, Wang still embed the corresponding watermark bit into this pixel. In another word, to ensure reversibility, Wang’s transform has to modify all the pixels in a block uniformly even if the distortions introduced by modification are high for some pixels. Considering that a block can embed at most (n − 1) data bits in Wang’s transform, Peng (short for Peng et al.) have introduced adaptive embedding into Wang’s transform, in which a block can embed (n − 1) log2 k bits, where n is used to denote the size of an image block, and k(k ∈ {1, 2, 4, 8, 16}) is determined adaptively by the pre-estimated distortion. By the basic idea that embeds more bits into smooth blocks while avoids large distortion generated by noisy ones, Peng’s method enables very high capacity with good image quality. However, Peng can not solve the problems existed in Wang’s transform. With the above consideration, we argue that Peng’s method can be further improved. In order to solve two problems above, a novel RW scheme based on block selection is proposed in this paper. We employ the correlation between a block and its total adjacent pixels to determine if this block is located in a smooth or a complex region. These neighboring pixels along with the mean value of this block constitute a set. The correlation is defined as the local variance of this set. As long as the mean value is invariant, the local variance remains unchanged after watermark embedding. This is the reason that the integer transform having the invariant mean value (i.e., Alattar’s transform) is selected in this paper. Since the variance is invariant, only a reduced size location map is needed, and the map can be efficiently compressed. Besides, by means of the invariant variance, the locations of all the already-modified blocks in watermark embedding process can be correctly determined on the decoding side. Hence, in the proposed method, even if the block size is set to 2 × 2, we still can achieve the low ERs with high PSNR values. For the second problem existing in Wang’s method, DE (or HS) is incorporated into the proposed method so as to further decrease the embedding distortions.
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II. T HE RELATED METHODS A. Wang’s method The integer transform defined in Eq. (3) of the paper [7] is listed in Eq. (1). y1 = 2x1 − a(x) y2 = 2x2 − 2f (a(x)) + w1 = 2x2 − (a(x) + LSB(a(x))) + w1
(1)
··· yn = 2xn − 2f (a(x)) + wn−1 = 2xn − (a(x) + LSB(a(x))) + wn−1 where x = (x1 , · · · , xn ) ∈ Zn and y = (y1 , · · · , yn ) ∈ Zn respectively represent a n-sized pixel array and its corresponding ⌊¯ ¯ − ⌊¯ x⌋ if x x⌋ < 0.5 ∑n 1 ¯ = n i=1 xi , a(x) = watermarked one, x , f (x) = ⌈ x2 ⌉, and wi (i ∈ {0, 1, · · · , n − 1}) denotes ⌈¯ x⌉ otherwise 1-bit watermark and wi ∈ {0, 1}, and LSB(·) represents the least significant bit (LSB). a(x) is actually the rounded value of ¯. x As can be seen from Eq. (1), Wang’s transform can be considered as a prediction process, in which a(x) is used to predict each pixel in this block. The experimental results in [7] show that when the original image is divided into 4 × 4-sized blocks, the performance is the best. However, refer to Figs. 2 and 3 of the paper [7], Wang are incapable of achieving high PSNR values at the given ERs. This is due to that the larger the block size, the weaker the intra-block correlation. This is to say, 4 × 4-sized blocks are unable to provide the same intra-block correlations as 2 × 2-sized blocks. However, when the block size is set to 2 × 2, the location map can not be high-efficiently compressed, and thus all the available capacity is almost consumed by the compressed location map. So, Wang can only select 4 × 4 block so as to increase the compression ratio and achieve the required ERs. However, Wang can not obtain high PSNR due to low intra-block correlation. Besides, to ensure reversibility, Wang’s transform can not modify flexibly each pixel in a block according to the different difference value between each pixel and the mean value of a block.
5
B. Alattar’s transform Alattar’s transform in [6] can be summarized in Eq. (3). ⌊ ⌋ n −x1 )+wn−1 y1 = ⌊¯ x⌋ − 2(x2 −x1 )+w1 +···+2(x n ∑ ∑ 2 n x +n−1 i=1 i i=1 wi −2nx1 = ⌊¯ x⌋ − n
(2)
y2 = y1 + 2 (x2 − x1 ) + w1 ··· yn = y1 + 2 (xn − x1 ) + wn−1 Suppose k2 =
∑n i=1
xi − n⌊¯ x⌋, and then k2 ∈ {0, · · · , n − 1}. Substitute y1 = ⌊¯ x⌋ + 2(x1 − ⌊¯ x⌋) − ⌊
2k2 +
∑n−1 i=1
wi
2k2 +
i=1
xi = k2 + n⌊¯ x⌋ into Eq. (2), we have
⌋
n
y2 = ⌊¯ x⌋ + 2(x2 − ⌊¯ x⌋) + w1 − ⌊
∑n
∑n−1 i=1
n
wi
⌋
(3)
··· yn = ⌊¯ x⌋ + 2(xn − ⌊¯ x⌋) + wn−1 − ⌊ where ⌊a⌋ rounds a to the nearest integers less than or equal to a,
∑ 2k2 + n−1 i=1 wi ⌋ n
∑n−1 i=1
wi ∈ {0, · · · , n − 1}.
As is illustrated in Eq. (3), Alattar’s transform can be deemed to contain an additional term and a process which uses ⌊¯ x⌋ to predict each pixel in the block. Specially, for each yi (i ∈ {0, 1, · · · , n}) in Eq. (3), it has a term, i.e., ⌊ k2 ∈ {0, 1, · · · , n − 1} and wi ∈ {0, 1}, 0 ≤ ⌊
2k2 +
∑n−1 i=1
n
wi
⌋ ≤ ⌊ 3(n−1) ⌋ = ⌊3(1 − n1 )⌋ = 2, i.e., n
2k2 +
∑n−1 i=1
n
∑ 2k + n−1 w ⌊ 2 ni=1 i ⌋
wi
⌋. Since
∈ {0, 1, 2}.
For instance, when k2 reaches its maximum value (i.e., n − 1), if all to-be-embedded bits are 1, then this term will reach its maximum value (namely 2). Similarly, Wang’s method contains a term, i.e., LSB(a(x)) ∈ {0, 1} except the process which uses a(x) to predict each pixel in the block (Refer to Eq. (3) in paper [7]). Alattar’s transform has its own disadvantage: it introduces higher distortion than Wang’s transform due to this additional term. Abundant experiments in the paper [7] also demonstrate that Wang’s method has superior performance to Alattar’s. In this paper, we will make full use of the property of the unchanged mean value in Alattar’s transform. The mean value of a n-sized block and the 2 × n + 1 neighbors surrounding this block can be used to evaluate whether this block is located in a smooth region or not. Based on the unchanged mean value, the value of n can be set to a small value, e.g. 2 × 2, 1 × 3. Small block size means strong intra-block correlation. By means of increasing the intra-block correlation and introducing DE (or HS), we compensate for the shortage existing in paper [7]. By multi-layer embedding, we can achieve high ERs (about 1.0 bpp (bit per pixel)). Experimental results also demonstrate the proposed method outperforms Wang’s at almost all ERs.
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C. Peng’s method As illustrated in Eq. (4), unlike Wang’s transform which embeds data uniformly, Peng’s method can embed (n − 1) log2 k (k ∈ {1, 2, 4, 8, 16}) bits into a block according to the block type determined by the local complexity, where k is the capacity parameter. y1 = kx1 − an,k (x) y2 = kx2 − an,k (x) + w1
(4)
··· yn = kxn − an,k (x) + wn−1 where an,k (x) = arg min E(∥y − x∥)2l2 , and E(·) is the expected value of l2 -error ∥y − x∥2l2 . By tuning k according to the an,k
local complexity, Peng’s method enables very high capacity with good image quality. However, Peng cannot still resolve the problems existed in Wang’s method.
III. T HE PROPOSED METHOD Given an 8-bit graylevel I with size R × C, the image I is partitioned into n-sized non-overlapping image blocks:
B1 , · · · , B⌊ R ⌋×⌊ C ⌋ r
c
x1,1 , · · · , x1,c in by working each r rows from left to right, where n = r × c. All the pixels · · · xr,1 , · · · , xr,c
some block Bi (i ∈ {1, · · · , ⌊ Rr ⌋ × ⌊ Cc ⌋}) are arranged into a one-dimensional pixel array x according to a predefined order, i.e., x = {x1 , · · · , xn }. Specifically, we work the first row from left to right, the second row from right to left, then continue alternating row direction in this manner, so that a one-dimensional pixel array x is created. Alattar’s transform is defined as follows ¯= x
⌊ x1 +x2 +···+xn ⌋ n
d1 = x2 − x1 d2 = x3 − x2 ··· dn−1 = xn − xn−1
(5)
7
where dk (k ∈ {1, · · · , n − 1}) represents the difference value between two neighboring pixels. The inverse integer transform is defined as ¯− x1 = x
⌊
⌋
(n−1)×d1 +(n−2)×d2 +···+dn−1 n
x2 = x1 + d1 (6)
x3 = x2 + d2 ··· xn = xn−1 + dn−1
For some difference value dk (k ∈ {1, · · · , n − 1}), if it belongs to the inner region [−pTh , pTh ), then 1- bit watermark is ′
embedded into dk to get the watermarked value dk via Eq. (7). If dk belongs to the outer region (−∞, −pTh )
∪
[pTh , ∞),
dk will be shifted by pTh according to Eq. (7). 2 × dk + b, dk ∈ [−pTh , pTh ) ′ dk = dk − pTh , dk ≤ −pTh − 1 dk + pTh , dk ≥ pTh
(7)
where pTh is used for estimating the correlation between two adjacent pixels, b represents 1-bit watermark, i.e., b ∈ {0, 1}. ′
′
After the modifications given by Eq. (7) are done to dk (k ∈ {1, · · · , n−1}) to produce dk , substitute dk (k ∈ {1, · · · , n−1}) into Eq. (6) to get the watermarked pixel list y = {y1 , · · · , yn } (refer to Eq. (8)). ⌊ ¯− y1 = x
′
′
′
(n−1)×d1 +(n−2)×d2 +···+dn−1 n
⌋
′
y2 = y1 + d1 ′
(8)
y3 = y2 + d2 ··· ′
yn = yn−1 + dn−1 A. Smoothness Classification by Pixel Neighborhood and Mean Value For some block Bi (i ∈ {1, · · · , ⌊ Rr ⌋×⌊ Cc ⌋}), there are the total (r +c+1) neighbors surrounding it, i.e., x1,c+1 , · · · , xr,c+1 , ¯ b of block Bi constitute a pixel set named by IEN P . xr+1,c+1 , xr+1,1 , · · · , xr+1,c . All these neighbors and the mean value x The standard deviation, denoted by ∆, of set IEN P is used to estimate if this block is located in a smooth or complex region.
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∆ is obtained via
v u ∑ r 2 u u k=1(xk,c+1 −uEN P ) u n u u (x −u )2 +(¯ xb −uEN P )2 ∆=u u + r+1,c+1 EN Pn u c ∑ u (xr+1,k −uEN P )2 t k=1 + n
(9)
where µEN P is the mean value of set IEN P . When ∆ < vTh , the block Bi is regarded as having a strong relation with its total neighbors, and therefore, it is classified to be within a smooth region, where vTh is a predefined threshold which is used for distinguishing which classification Bi belongs to. Otherwise, Bi is estimated in a complex region. Note that if R has no remainder when divided by r, then the blocks obtained by partitioning the last r rows of the image I have not (2 × n + 1) neighbors. So, in order to ensure reversibility, they only can be kept unchanged during watermark embedding process. This is similar to C and c.
B. Algorithm Description For each layer embedding, the corresponding overhead information is composed of three parts: the 8-bit representation of each of vTh and pTh ; the compressed location map which is utilized to solve potential overflow/underflow problem. A unique EOS symbol is added at the end of the overhead information. To prevent the overflow/underflow, each watermarked pixel value should be contained in [0, 255]. We define { D=
} x ∈ A : 0 ≤ yi ≤ 255(1 ≤ i ≤ n, yi ∈ Z)
where A = {x = (x1 , · · · , xn ) ∈ Z : 0 ≤ xi ≤ 255(1 ≤ i ≤ n)}. For a pixel-value array x ∈ A, it is classified into one of three sets: •
Es = {x ∈ D : ∆ < vTh };
•
Os1 = {x ∈ / D : ∆ < vTh };
•
Os2 = {x ∈ A − Es ∪ Os1 : ∆ ≥ vTh }.
where Es and Os = Os1 ∪ Os2 are used to denote the sets of pixels which are altered according to Eq. (7) or kept unaltered, respectively. A location map is generated in which the locations of the image blocks belonging to Es are marked by ‘1’ while the ones of the blocks in Os1 are marked by ‘0’. Note that it’s not necessary to record the locations of the blocks in Os2 . This is due to that their locations can be correctly determined only by evaluating their variances. If the variance is larger than or equal to vTh , the block belong to Os2 . Here, suppose that the size of the location map is LS , The location map is compressed
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Original Image I
The next embedding layer
Divide I into non-overlapped 2 ´ 2-sized blocks N x Î Os 2
Satisfy the condition s < vTh ?
y=x
Y xÎ D?
x Î Os1
x Î Es Y
y=x
ì2 ´ d k + b, d k Î [- pTh , pTh ) ï d k ' = í d k - pTh , d k £ - pTh - 1 ï d + pT , d k ³ pTh h î k
Embed auxiliary information
N
Paylaod complete? Y Watermarked Image IW
Fig. 1.
Embedding mechanism
Bitstream L
pTh
vTh
# EOS
(a)
Bitstream L
pTh
vTh
EC
# EOS
(b) Fig. 2.
Auxiliary information formats in an embedding layer: (a) the other embedding layers; (b) last embedding layer.
losslessly by an arithmetic encoder and the resulting bitstream is denoted by L. LSC is the bit length of L. Fig. 1 shows the block diagram of watermark embedding mechanism. Fig. 2 shows the two overhead information formats for the last embedding layer and the other embedding layers. Because only the last layer may not be fully embedded, an extra information EC is appended after the vTh of the last layer. The EC consists of 18 bits (representing embedding capacity in the last layer, specially, 218 = 512 × 512) and 6 bits (the number of layers). Both of the last layer and the other ones consist of the compressed location map (LSC bits), vTh (8 bits), pTh (8 bits) and EOS (8 bits). The difference in format is that the EC is added in the type B format. Therefore, for the other layers, the overhead information occupies LSC plus 16 bits, i.e., L∑ = LSC + 16. While for the last layer, L∑ consumes LSC + 42 bits in total, where the size of the overhead information is denoted by L∑ .
10
Determination of ve for Lena 18000 16000
The number of vT
h
14000 12000 10000 8000 6000 4000 2000 0
0
10
20
30
40 vT
50
60
70
80
h
Fig. 3.
The number of vTh in the unit interval, and the unit on horizontal axis is 1, e.g., the number of vTh is 18,000 when 1 < vTh ≤ 2 .
1) Determination of the values of pTh and vTh : vTh has an initial value, denoted by vs , which is capable to embed the payload. In the experiments, vs is set to 1 for six images. vTh runs from this initial value to ve (i.e., the upper limit of vTh ). Take Lena for example, Fig. 3 provides an intuitive illustration of determining ve . From Fig. 3, one can know the number of the variances smaller than or equal to 10 (i.e., ∆ ≤ 10) accounts for over 90% of the total variances. Therefore, ve is set to 10 for Lena in our method. Similarly, pTh also has an initial value, denoted by ps , which is set to a value capable of ensuring the embedding rate larger than 0. In this paper, ps is set to 1 for Lena. From Fig. 4, it can be seen that the upper limit of pTh , denoted by pe , is selected as 15. It is not necessary to continue to increase this upper limit (namely exceeding 15), since the increase of
Nd Nt
can almost
be ignored. 2) Optimal-threshold-determination for combined embedding: For a one-layer embedding process, when vTh is fixed, we increase pTh gradually from the initial value ps = 1 to its maximum with a step size of 1. For each value of pTh , when the required capacity is just accommodated, stop the embedding process. Meanwhile, calculate the corresponding PSNR, and record the value of pTh . The optimal pTh∗ is the one which can yields the highest PSNR. It is clear that (vT1∗ , pTh∗ ) yields the highest PSNR whatever the block size and the image are. ∗ ∗ For a two-layer embedding process, we utilize the similar method to determine optimal threshold combination, i.e., (vTh1 , pTh1 ∗ ∗ ∗ ∗ ∗ ∗ , vTh2 , pTh2 ), where (vTh1 , pTh1 ) and (vTh2 , pTh2 ) represent optimal threshold combination used in the first-layer and second∗ ∗ ∗ ∗ layer embedding process, respectively. From Fig. 5, one can also see that the values of vTh1 , pTh1 , vTh2 and pTh2 obtained ∗ ∗ ∗ ∗ ∗ ∗ by experiments is small. Take Fig. 5(a) for example, (vTh1 , pTh1 , vTh2 , pTh2 ) = (2, 1, 0, 0). Note that, (vTh2 , pTh2 ) = (0, 0)
means that the highest PSNR is achieved only by the first layer embedding.
11
Determination of pe for Lena 1 vT =1 h
0.9
vT =2 h
vTh=3
0.8
vTh=4 vTh=5
0.7
Nd/Nt
vTh=6 vTh=7
0.6
vTh=8
0.5
vTh=9 vTh=10
0.4 0.3 0.2 0.1
Fig. 4.
0
5
10 pTh
15
20
Determination of the value of pe , and the vertical axis denotes the ratio of Nd to Nt ,(i.e.,
Nd ), Nt
where the total number of the difference values is
denoted by Nt for given vTh and pTh , and the number of the difference values capable of carrying 1 bit is denoted by Nd . Barbara 60 (vT*h1,pT*h1, vT*h2,pT*h2)=(2,1,0,0)
54 Quality Measurement PSNR (dB)
58 Quality Measurement PSNR (dB)
Barbara (vT*h1,pT*h1, vT*h2,pT*h2)=(4,1,0,0)
55
56
54
52
50
53 52 51 50 49 48 47
48 46 46
0
2
4
6 vTh1
8
10
(a) ER=0.0381 bpp (or 10,000 bits) Fig. 5.
12
45
1
2
3
4
5 vTh1
6
7
8
9
(b) ER=0.0763 bpp (or 20,000 bits)
Performance comparison for a given capacity on Barbara by using different (vTh1 , pTh1 , vTh2 , pTh2 ).
3) Computational Complexity: The time cost of the proposed method is determined by the image size M × N , thus the computational complexity is O(M ×N ). The required processing mainly lies on obtaining the difference values and the average value of a 2 × 2-sized block, smoothness classification, generating location map, compressing location map, and modifying difference values by DE (or HS). Here, for the sake of simplicity, Alattar and Luo are used as an abbreviation of Alattar et al. and Luo et al., respectively. In Table I, we calculate the average time cost of Alattar’s, Luo’s, Wang’s and Peng’s methods for one-layer embedding on six test images, respectively. For the proposed method, in Table I, we provide the average time cost of performing one-layer embedding and two-layer embedding, respectively. The one-layer embedding refers to a single watermark embedding process having the fixed thresholds (or embedding capacity) for the proposed, Luo’s, Alatter’s, Wang’s and Peng’s methods. The source codes of Luo’s and Alattar’s methods are provided by the authors of paper [35]. The source code of Peng’s and Wang’s methods
12
TABLE I C OMPARISON OF TIME COST, WHERE THE UNIT OF RUNTIME IS SECOND . Images
Lena
Baboon
Airplane
Barbara
Goldhill
Sailboat
Alattar
18.9060
18.3364
18.9925
19.7876
18.4751
18.5884
Luo
0.6832
0.6434
0.6614
0.6646
0.6618
0.6642
Wang
4.8961
3.9306
6.5665
4.6592
4.5164
4.4952
Peng
3.5381
3.5608
4.1835
3.5261
3.5894
3.5190
Proposed(one-layer embedding)
1.2627
1.2052
2.002
1.2178
1.2429
1.2009
Proposed(two-layer embedding)
2.7976
2.2240
3.6692
2.3857
2.3887
2.3290
are provided by the authors of paper [36]. The proposed and the compared algorithms are implemented on Matlab R2013a, and the experiments are run on a personal PC. It can be seen that the runtime of the proposed method varies with images. Although our time cost is much larger than the prior arts (e.g., Luo’s), it is still acceptable in this age as it can be reduced by a high-performance PC or an effective programming language such as C++. For a one-layer embedding process using DE, our method has comparable or lower computational complexity than those of Alattar’s, Wang’s and Peng’s. Otherwise, we have to determine the number of iterations so as to obtain the desired embedding capacity. The process of determining the number of iterations will add the time cost. Decreasing computational complexity is beyond the scope of this paper, and we will investigate this issue in our future work. 4) Comparison with Alattar’s method: The basic idea of our method is to make best use of the advantage of Alattar’s scheme (i.e., the unaltered mean value ⌊¯ x⌋) while avoid its disadvantage. Specifically, by utilizing ⌊¯ x⌋ to estimate whether a block is located in a smooth region or not, the block size n can be set to a small value, e.g., 1 × 3 or 2 × 2, and more importantly, the location map can still be high-efficiently compressed. It is well known that small blocks have stronger intrablock correlation than large ones. Therefore, ⌊¯ x⌋ is highly related to all pixels in a block, and finally, the distortion introduced by pixel modification is lower. In this way, our method efficiently avoids the disadvantage of Alattar’s one. Depending on the above improvements, our method achieves higher embedding performance compared with Alattar’s one. 5) Comparison with Wang’s and Peng’s methods: Compared with Wang’s and Peng’s methods, ours utilizes the invariant ⌊¯ x⌋ to estimate whether a block is located in a smooth region or not. Thus, the block size can be set to a smaller value, e.g., 2 × 2 or 1 × 3 and more importantly, the location map can be high-efficiently compressed. From Tables II and III, one can observe that our compression ratio (i.e.,
LS −LSC ) LS
is higher compared with that of Wang’s
method. Take Table II for example, when PSNR is 47.7982 (dB), the obtained embedding capacity is 58253 (bits) and the compression ratio equals 99.92%. While in Wang’s method with n = 4 × 4, when PSNR is 47.7570 (dB), the embedding
13
TABLE II C OMPARISONS OF LSC ( BITS )
AND
LS ( BITS )
The proposed method (n = 2 × 2)
BETWEEN THE PROPOSED METHOD AND
WANG ’ S METHOD FOR L ENA .
Wang’s method (n = 2 × 2)
Wang’s method (n = 4 × 4)
LS
LSC
Payload size
PSNR(dB)
LS
LSC
Payload size
PSNR(dB)
LS
LSC
Payload size
PSNR(dB)
2704
32
2686
64.5405
36540
34968
8331
52.1491
7968
6080
23295
52.1296
30566
40
23069
54.0675
45100
43477
26634
48.7127
9496
8464
51435
47.7570
30566
40
42757
49.9629
49852
45096
46932
46.4100
9998
8768
64965
46.3622
47771
40
58253
47.7982
53235
42448
69309
44.5593
10481
8824
77160
45.2526
TABLE III C OMPARISONS OF LSC ( BITS ) AND LS ( BITS ) BETWEEN THE PROPOSED METHOD AND WANG ’ S METHOD FOR BARBARA . The proposed method (n = 2 × 2)
Wang’s method (n = 2 × 2)
Wang’s method (n = 4 × 4)
LS
LSC
Payload size
PSNR(dB)
LS
LSC
Payload size
PSNR(dB)
LS
LSC
Payload size
PSNR(dB)
14120
40
11546
57.5657
28765
28040
7587
52.9696
5352
3552
10470
55.9220
23868
40
18034
55.2656
34287
33096
24357
49.5767
6066
5032
20925
52.5364
29204
40
39602
50.2157
37405
32400
41736
47.4129
6637
5936
32220
50.2757
32386
40
58887
47.3181
39881
30040
57390
45.7986
7069
6384
43050
48.6410
capacity is 51435 (bits) and the compression ratio is 10.87%. Therefore, our method achieves higher embedding capacity than Wang’s at almost the same PSNR. However, when the block size is changed from 4 × 4 to 2 × 2 in Wang’s method, the performance becomes weaker due to the lower compression ratio. For example, when PSNR is 46.4100 (dB), the embedding capacity is 46932 (bits) and the compression ratio is 9.54% (refer to Table II for details). Besides, our method can achieve high embedding performance even at low embedding capacity. For instance, when PSNR is 64.5405 (dB), the embedding capacity is 2686 (bits). The experimental results illustrated in Tables. IV and V prove that our method outperforms Peng’s method due to higher compression ratio. TABLE IV C OMPARISONS OF LSC ( BITS )
AND
LS ( BITS )
The proposed method (n = 2 × 2)
BETWEEN THE PROPOSED METHOD AND
P ENG ’ S METHOD FOR L ENA .
Peng’s method (n = 2 × 2)
Peng’s method (n = 4 × 4)
LS
LSC
Payload size
PSNR(dB)
LS
LSC
Payload size
PSNR(dB)
LS
LSC
Payload size
PSNR(dB)
2704
32
2686
64.5405
90860
64968
11685
47.7482
16959
3680
4960
58.8807
30566
40
23069
54.0675
101703
79360
29822
44.9345
17548
5368
12107
54.9793
30566
40
42757
49.9629
106383
80072
51214
43.3613
18429
7632
23058
51.7755
47771
40
58253
47.7982
107561
89440
69347
41.4729
19460
9584
36571
49.3347
14
TABLE V C OMPARISONS OF LSC ( BITS ) AND LS ( BITS ) BETWEEN THE PROPOSED METHOD AND P ENG ’ S METHOD The proposed method (n = 2 × 2)
Peng’s method (n = 2 × 2)
FOR
BARBARA .
Peng’s method (n = 4 × 4)
LS
LSC
Payload size
PSNR(dB)
LS
LSC
Payload size
PSNR(dB)
LS
LSC
Payload size
PSNR(dB)
14120
40
11546
57.5657
85967
53904
7692
48.7100
17369
4872
9903
55.5029
23868
40
18034
55.2656
94382
62728
24113
45.9891
18179
7000
19925
52.2130
29204
40
39602
50.2157
99458
63680
38389
44.5888
18975
8432
30433
50.0366
32386
40
58887
47.3181
104928
71248
50768
42.7966
19729
10288
39887
48.4191
C. Data Embedding Now, the embedding procedure is described as follows step by step. Step 1 Watermark embedding in a single layer The overhead information is formed. Suppose that the payload to be embedded in the current layer is PC . We know |PC | ≤ PM , where PM = N
D. Data Extraction and Image Restoration The LSBs of the pixels in Iw are collected into a bitstream B according to the same order as in embedding. B is decompressed by an arithmetic decoder to retrieve the location map. Once LSC is known, pTh , vTh will be extracted one by one according to their fixed lengths. If the current layer is the last one, we will easily know the number of embedding layers, the embedded bits for the last layer by extracting EC, respectively.
15
The watermarked image Iw is partitioned into n-sized image blocks: B1w , · · · , B⌊wR ⌋×⌊ C ⌋ according to the same order as in r
c
embedding. In order to ensure reversibility, the watermark extraction is executed according to the inverse order as in embedding, i.e., B⌊wR ⌋×⌊ C ⌋ , · · · , B1w . r
c
One watermarked image block Biw (i ∈ {⌊ Rr ⌋ × ⌊ Cc ⌋, ⌊ Rr ⌋ × ⌊ Cc ⌋ − 1, · · · , 1}), is scanned in the same way as in embedding to produce its corresponding array ym = (y1 , · · · , yn ) (m ∈ {⌊ Rr ⌋ × ⌊ Cc ⌋, ⌊ Rr ⌋ × ⌊ Cc ⌋ − 1, · · · , 1}). For each of ym , if it has not the total (r + c + 1) neighbors surrounding it, then it is kept unchanged, namely, ym = xm . Otherwise, the total neighbors ¯ b,m of block ym constitute the same set IEN P as in x1,c+1 , · · · , xr,c+1 , xr+1,c+1 , xr+1,1 , · · · , xr+1,c and the mean value x embedding. Note that the total neighbors x1,c+1 , · · · , xr,c+1 , xr+1,c+1 , xr+1,1 , · · · , xr+1,c must be correctly retrieved prior to the ym . If ∆ via Eq. (9) of ym is larger than or equal to vTh , then it is kept unaltered. If ∆ is smaller than vTh , and its location is associated with ‘0’ in the location map, then it is ignored. Otherwise, the watermark can be extracted using the ′
following formula: b = mod(dk , 2) if dk ∈ [−2pTh , 2pTh − 1] . And meanwhile, the original difference value is retrieved by Eq. (10).
′ ′ ⌊dk ⌋ dk ∈ [−2pTh , 2pTh − 1] ′ ′ dk = dk + pTh dk ≤ −2pTh − 1 d′k − pTh , d′k ≥ 2pTh
(10)
If the number of extracted watermark bits is equal to the capacity calculated by EC, stop extraction and form P; else go the next layer extraction and repeat steps above. When the current layer is fully extracted, classify the extracted bitstream into watermark bits and restore the pixels by simple LSB replacement.
IV. E XPERIMENTAL RESULTS The proposed RW scheme is carried out in MATLAB environment. The Lena, Baboon, Barbara, Airplane, Goldhill and Sailboat images with size 512 × 512 are provided by the authors of paper [9]. For convenience of description, Weng and Coatrieux are used as an abbreviation of Weng et al. and Coatrieux et al., respectively. In the experiments, the block size is set to 2 × 2. Fig. 6 shows performance comparisons between the proposed method and following six methods: Peng [9], Wang [7] Alattar [6], Luo [22], Weng [29] and Coatrieux [37]. It also can be seen from Fig. 6 that our method performs well, and significantly outperforms Peng’s, Wang’s, Alattar’s and Luo’s whatever the ER is. Especially when ER is low, the proposed method can achieve better performance than Peng’s. When you take a careful look at the curve of Peng’s method, you will find the points on this curve are very sparse when ER is lower than 0.5 bpp. With the ER increased, the points becomes denser. While our method can achieve better performance even when ER is lower than 0.5 bpp. This is mainly because our method
16
Capacity vs. Distortion Comparison on Airplane (F−16)
50 48 46 44 42 40 38 36 34 32 30
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Payload Size (bpp)
Quality Measurement PSNR (dB)
Quality Measurement PSNR (dB)
55
25
Capacity vs. Distortion Comparison on Barbara
Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg. Weng et al.’s Alg.
55 50 48 46 44 42 40 38 36 34 32 30 25
1.1 1.2 1.3 1.4 1.5
Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg. Weng et al.’s Alg.
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Payload Size (bpp)
(a)
1
1.1 1.2 1.3 1.4
(b)
Capacity vs. Distortion Comparison on Sailboat
Capacity vs. Distortion Comparison on Goldhill 55
Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg. Weng et al.’s Alg.
50 48 46 44 42 40 38 36 34 32 30
25
Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg. Weng et al.’s Alg.
50 Quality Measurement PSNR (dB)
Quality Measurement PSNR (dB)
55
48 46 44 42 40 38 36 34 32 30
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Payload Size (bpp)
1
25
1.1 1.2 1.3 1.4
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Payload Size (bpp)
(c)
1
1.1 1.2
(d)
Capacity vs. Distortion Comparison on Baboon
Capacity vs. Distortion Comparison on Lena
55 50 48 46 44 42 40 38 36 34 32 30
60 55 50 45 40 35
25
0
0.1
0.2
0.3 0.4 0.5 Payload Size (bpp)
(e) Fig. 6.
Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg. Weng et al.’s Alg. Coatrieux et al.’s Alg.
65 Quality Measurement PSNR (dB)
Quality Measurement PSNR (dB)
70 Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg. Weng et al.’s Alg. Coatrieux et al.’s Alg.
0.6
0.7
0.8
30
0
0.2
0.4
0.6 0.8 Payload Size (bpp)
1
1.2
1.4
(f)
Performance comparisons between the proposed method and following six methods: Peng [9], Wang [7], Alattar [6], Luo [22], Coatrieux [37] and
Weng [29] for the test images: (a) Airplane, (b) Barbara, (c) Sailboat, (d) Goldhill, (e) Baboon, and (f) Lena.
17
can set a small block size (e.g., 2 × 2 or 1 × 3), and thus strong intra-block correlation can be obtained. From Fig. 6, we can also see that Peng’s method obtains weaker performance than Luo’s when ER is low (e.g. smaller than 0.5 bpp for Lena and Airplane). While our method can achieve higher performance than Luo’s at almost all ERs. So far, among all the RW methods based on integer transform [5]–[13], Peng’s and Wang’s methods have achieved the best rate-distortion performance. Fig. 6 illustrates that our method can achieve a better or comparable visual quality than Peng’s and Wang’s methods at the same ER. The embedding-distortion curves of Lena and Baboon are provided in Coatrieuxs paper. So, we need to get the embeddingdistortion curves of the other four images. We tried all kinds of methods to look for the source code of Coatrieux’s method. Unfortunately, we did not find it. After studying deeply Coatrieux’s paper, we decide to write the code of Coatrieux’s method by ourselves. However, the obtained performance is weaker than that given in Coatrieux’s paper. We spend a lot of time in modifying our source code until we have no time. However, for Lena and Baboon, the obtained PSNR value is still smaller than that illustrated in Coatrieux’s paper at any given ER. Based on this consideration, we think our experimental results are not suitable for being used in this paper. In this paper, we illustrate the embedding performance of Coatrieux’s method only for Lena and Baboon. From Figs. 6(e) and 6(f), we can observe that our method outperforms Coatrieux’s method when the ERs are larger than 0.4 bpp. Compared with Alattar’s, Wang’s and Peng’s methods, ours increases embedding performance by using the mean value of a block to estimate a block whether it is located in a smooth region or not. Refer to Figs. 6(a), 6(b) and 6(c), our method outperforms Weng’s method at almost all ERs. For Lena, Baboon and Goldhill, Figs. 6(d), 6(e) and 6(f) show Weng’s method is superior to ours at high ERs (e.g.,> 0.1335 bpp). Fig. 7 shows performance comparisons between the proposed and Weng’s methods when the ER is low (e.g., < 0.1335 bpp for Lena). From Fig. 7, one can observe that the proposed method is superior to Weng’s method at low ERs. We will investigate to increase prediction performance in our future work. The SSIM index based on structural similarity [38] has been tested in experiments for comparison. A close to 1 SSIM index represents that two images possess a higher perceptual similarity. Fig. 8 shows SSIM comparisons between the proposed and Alattar’s, Wang’s, Peng’s, Luo’s methods. From Fig. 8, we can observe that SSIM index of the proposed method is higher than those of three methods (e.g., Alattar’s, Wang’s, Peng’s) at almost all ERs. For Sailboat, the SSIM index of our method outperforms that of Luo’s method whatever the ER is. For the other five images, when the ER exceeds 0.5 or 0.6 bpp, the SSIM index of our method outperforms that of Luo’s method. V. C ONCLUSIONS A new RW scheme is proposed in this letter. This scheme fully exploits the invariability of the mean value. The mean value is favorable to estimate accurately if a block is located in a smooth or complex region. Depending on the invariability
18
Capacity vs. Distortion Comparison on Airplane
Capacity vs. Distortion Comparison on Barbara
59
62 Prop. Alg. Weng et al.’s Alg.
Prop. Alg. Weng et al.’s Alg.
60 Quality Measurement PSNR (dB)
Quality Measurement PSNR (dB)
58 57 56 55 54 53 52
58 56 54 52 50 48 46
51 1.5
2
2.5
3
3.5 4 4.5 Payload Size (bits)
5
5.5
44
6
0
0.05
0.1
4
x 10
(a)
0.3
0.35
Capacity vs. Distortion Comparison on Goldhill
62
64 Prop. Alg. Weng et al.’s Alg.
Prop. Alg. Weng et al.’s Alg.
62 Quality Measurement PSNR (dB)
60 Quality Measurement PSNR (dB)
0.25
(b)
Capacity vs. Distortion Comparison on Sailboat
58
56
54
52
50
60 58 56 54 52 50
48 0.5
1
1.5
2 2.5 Payload Size (bits)
3
3.5
48
4
0
0.02
0.04
4
x 10
(c)
0.06 0.08 Payload Size (bits)
0.1
0.12
0.14
(d)
Capacity vs. Distortion Comparison on Baboon
Capacity vs. Distortion Comparison on Lena
62
65 Prop. Alg. Weng et al.’s Alg.
60 58
Prop. Alg. Weng et al.’s Alg. Quality Measurement PSNR (dB)
Quality Measurement PSNR (dB)
0.15 0.2 Payload Size (bits)
56 54 52 50 48
60
55
46 44
0
0.02
0.04
0.06 0.08 0.1 Payload Size (bits)
(e) Fig. 7.
0.12
0.14
0.16
50
0
0.5
1
1.5 2 2.5 Payload Size (bits)
3
3.5
4 4
x 10
(f)
Performance comparisons between the proposed and Weng’s methods [29] for the test images: (a) Airplane, (b) Barbara, (c) Sailboat, (d) Goldhill,
(e) Baboon, and (f) Lena.
19
Capacity vs. Distortion Comparison on Barbara
Capacity vs. Distortion Comparison on Lena 1
1 Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg.
0.99 0.98
Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg.
0.99 0.98 0.97
0.97 SSIM
SSIM
0.96 0.96 0.95
0.95 0.94
0.94
0.93
0.93
0.92
0.92 0.91
0.91 0
0.1
0.2
0.3 0.4 0.5 Payload Size (bpp)
0.6
0.7
0.9
0.8
0
0.1
0.2
(a)
0.3 0.4 0.5 Payload Size (bpp)
0.6
0.7
0.8
(b)
Capacity vs. Distortion Comparison on Airplane
Capacity vs. Distortion Comparison on Goldhill
1
1 Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg.
0.99 0.98
Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg.
0.98
0.96 SSIM
SSIM
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(c) Capacity vs. Distortion Comparison on Baboon
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Capacity vs. Distortion Comparison on Sailboat Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg.
0.98
0.96 SSIM
0.96 SSIM
0.7
1 Prop. Alg. Peng et al.’s Alg. Wang et al.’s Alg. Alattar et al.’s Alg. Luo et al.’s Alg.
0.98
0.94
0.94
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0
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0.3 0.4 0.5 Payload Size (bpp)
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(e) Fig. 8.
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(d)
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(f)
SSIM comparisons between the proposed method and following four methods: Peng [9], Wang [7], Alattar [6] and Luo [22] for the test images: (a)
Lena, (b) Barbara, (c) Airplane, (d) Goldhill, (e) Baboon, and (f) Sailboat.
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of the mean value, we can set a small block size, and meanwhile strong intra-block correlation can be obtained. Due to this invariability, we only need to record the locations of the blocks with small local complexity. Hence, the map can be compressed efficiently. Thus, our method can achieve better performance even when ER is low. Experimental results also demonstrate our method is efficient. ACKNOWLEDGMENT This work was supported in part by National NSF of China (No. 61201393, No. 61272498, No. 61571139), New Star of Pearl River on Science and Technology of Guangzhou (No. 2014J2200085). R EFERENCES [1] C. W. Honsinger, P. Jones P., M. Rabbani, and J. C. Stoffe, “Lossless recovery of an original image containing embedded data,” US patent: 6278791W, 2001. [2] J. Fridrich, M. Goljan, and R. Du, “Lossless data embedding-new paradigm in digital watermarking,” in EURASIP J. Appl. Signal Process., 2002, vol. 2002, pp. 185–196. [3] Z. Ni, Y. Q. Shi, N. Ansari, and W. Su, “Reversible data hiding,” IEEE Trans. Circuits Syst. Video Technol., vol. 16, pp. 354–362, 2006. [4] G. R. Xuan, C. Y. Yang, Y. Z. Zhen, and Y. Q. Shi, “Reversible data hiding using integer wavelet transform and companding technique,” in Proceedings of IWDW, 2004, vol. 5, pp. 23–26. [5] J. Tian, “Reversible data embedding using a difference expansion,” IEEE Trans. Circuits Syst. Video Technol., vol. 13, no. 8, pp. 890–896, 2003. [6] A. M. Alattar, “Reversible watermark using the difference expansion of a generalized integer transform,” IEEE Trans. Image Process., vol. 13, no. 8, pp. 1147–1156, 2004. [7] X. Wang, X. L. Li, B. Yang, and Z. M. Guo, “Efficient generalized integer transform for reversible watermarking,” IEEE Signal Process. Lett., vol. 17, no. 6, pp. 567–570, 2010. [8] X. Wang, X. L. Li, and B. Yang, “High capacity reversible image watermarking based on in transform,” in Proceedings of ICIP, 2010. [9] F. Peng, X. Li, and B. Yang, “Adaptive reversible data hiding scheme based on integer transform,” Signal Process., vol. 92, no. 1, pp. 54–62, 2012. [10] D. Coltuc and J. M. Chassery, “Very fast watermarking by reversible contrast mapping,” IEEE Signal Process. Lett., vol. 14, no. 4, pp. 255–258, 2007. [11] S. W. Weng, Y. Zhao, J. S. Pan, and R. R. Ni, “Reversible watermarking based on invariability and adjustment on pixel pairs,” IEEE Signal Process. Lett., vol. 45, no. 20, pp. 1022–1023, 2008. [12] S. W. Weng, Y. Zhao, R. R. Ni, and J. S. Pan, “Parity-invariability-based reversible watermarking,” IET Electronics Lett., vol. 1, no. 2, pp. 91–95, 2009. [13] D. Coltuc, “Low distortion transform for reversible watermarking,” IEEE Trans. Image Process., vol. 21, no. 1, pp. 412–417, 2012. [14] L. Kamstra and H. J. A. M. Heijmans, “Reversible data embedding into images using wavelet technique and sorting,” IEEE Trans. Image Process., vol. 14, no. 12, pp. 2082–2090, 2005. [15] H. J. Kim, V. Sachnev, Y. Q. Shi, J. Nam, and H. G. Choo, “A novel difference expansion transform for reversible data embedding,” IEEE Trans. Inf. Forensic Secur., vol. 4, no. 3, pp. 456–465, 2008. [16] D. M. Thodi and J. J. Rodrłguez, “Expansion embedding techniques for reversible watermarking,” IEEE Trans. Image Process., vol. 16, no. 3, pp. 721–730, 2007. [17] Y. Hu, H. K. Lee, and J. Li, “DE-based reversible data hiding with improved overflow location map,” IEEE Trans. Circuits Syst. Video Technol., vol. 19, no. 2, pp. 250–260, 2009.
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Highlights
We use the invariant mean value of a block to evaluate the local complexity. The block size can be set to a small value by the invariability of the mean value. The reduced size location map is created by the invariability of the mean value. We can modify flexibly each pixel in a block using DE or HS.