2014 7th International Symposium on Telecommunications (IST'2014)
Improving Reversible Image Watermarking using Additive Interpolation Technique Majid Khorramdin, Milad Amini, Nasser Torabi, Mojtaba Mahdavi Department of Information Technology Faculty of Computer Engineering University of Isfahan, Isfahan, Iran
[email protected],
[email protected],
[email protected],
[email protected] Abstract— Embedding an identifying data into digitized music, video or image is known as digital watermarking. Reversible image watermarking is used to embed and extract hidden data to and from the watermarked image without any distortion to the original. In this paper, we propose an improved reversible watermarking scheme using an additive interpolation technique, which increases embedding capacity with inconspicuous degradation of image quality. Unlike former watermarking schemes, a new interpolation-error is exploited to embed bit "1" or "0" using additive expansion or leaving it unchanged. Consequently, original image is remained at a high level of quality. Moreover, a cryptographic scheme is utilized to prevent an adversary from accessing embedded data. Therefore, achieving watermarked data will not be straightforward. The experimental results show that the proposed method in addition to greater embedding capacity, has higher image fidelity compared to previous schemes. Keywords— Digital Watermarking; Reversible Watermarking; Additive Interpolation-Error Expansion.
I.
Image
INTRODUCTION
Literary and artistic works, referred to Intellectual Property (IP) are protected in law by copyright [1]. However, it is not always an applicable way to trace ownership of a digital production. Digital watermarking is a method to provide protection against illegitimate use of digital media such as digital audio, video or image. The key idea is to embed a piece of covert data into a digital media to pursue proprietorship or protect privacy. Traditional watermarking methods usually make modifications, even slight in the original media that is irreversible. In the literature, there are watermarking schemes which impose degradations in original media, leads to incompetence of traditional watermarking schemes for most of the military, medical and artistic applications. However, removing the watermark after decoding may enhance tolerability of these applications to additional noise arisen from the watermarking. Watermarking methods which offer such an ability are called reversible watermarking schemes. Reversible watermarking shall eliminate the noise after decoding and extract the original media without any relic left from the watermark. Its capability to recover the original cover media through the watermark extracting operation makes it very useful, particularly in applications which entail high conformity of multimedia content.
978-1-4799-5359-2/14/$31.00 ©2014 IEEE
Because of its ability to restore the original media, reversible watermarking has drawn more attentions. Plenty of reversible watermarking methods have been proposed in the literature. Among them, schemes which adopt Difference Expansion (DE) approaches are accepted widely because of low computational complexity and high capacity. After Tian's [2] DE-based scheme introduction, Alattar [3] developed a DE scheme which is based on the difference expansion of vectors of arbitrary size to embed reversible watermarks. Despite Tian, Alattar used spatial triplets and quads instead of spatial pairs. However Alattar's algorithm do not always outperform Tian's algorithm. Several reversible watermarking schemes based on interpolation-error expansion proposed in the literature [3] – [7]. An interpolation-error expansion technique differs from other DE methods in two ways: First, it employs interpolation error to embed data instead of adjacent pixels difference or prediction error. Two, it expands the error by addition rather than bit shifting [8]. The approach is efficient since interpolation-errors exploits correlation between pixels more extensively and additive expansion is free of expensive overhead information. Lou et al. [4] proposed a reversible image watermarking scheme based on additive interpolation-error. Interpolationerror is used to embed data, instead of interpixel difference, and the interpolation-error is expanded through addition, instead of bit-shifting. Exploiting additive expansion eventuates to a highly efficient reversible watermarking scheme. However, experimental results of re-implementation of the algorithm showed that the scheme is not 100% reversible. Moreover, the number of computations in the algorithm is fairly high. In this paper, we extend the Lou's scheme to improve reversibility and decrease complexity of the algorithm. On the other hand, high embedding capacity and low noise is preserved. Furthermore, a cryptographic scheme is applied to protect privacy and strengthen ownership protection. In addition, a weakness of the Lou's algorithm is reported. Accordingly, section II will provide an introduction to the interpolation-error method and additive interpolation-error expansion. Then in section III, algorithm of the proposed scheme is explained. In section IV, we present the experimental results. Finally, in section V, we give a summary and conclusion.
II.
DISCRIPTION OF ADDITIVE INTERPOLATION-ERROR EXPANSION
A. Interpolation Method We exploit interpolation-error, the difference between pixel value and its interpolation value, to embed data. An algorithm is proposed to calculate interpolation values. Fig. 1(a) presents some sample and non-sample pixels in an original image, with black and white dots, respectively. According to Fig. 1(a), black dots will stay unchanged after watermarking. These pixels are used in interpolation of white dots. White dots are pixels of the image which will be interpolated. These pixels are grouped into three categories: 1. Pixels which are located in x ( 2i, 2j ) 2. 3.
(a)
(b)
Pixels which are located in x ( 2i, 2j-1 )
Pixels which are located in x ( 2i-1, 2j )
where 1 ≤ i ≤ N , 1 ≤ j ≤ M original image.
which N×M is the size of
(c)
(d)
For pixels of first category, interpolation values, x ′ are calculated via
Fig 1. (a) Sample and non-sample pixels in original image are depicted by black and white dots respectively. (b) Interpolation of first category pixels. (c) Interpolation of second category pixels. (d) Interpolation of third category pixels.
⎢ x ( 2i-1, 2j-1 )+ x ( 2i+1, 2j+1 ) ⎥ +⎥ ⎢ 4 ⎥ x ′ ( 2i, 2j ) = ⎢ ⎢ x ( 2i-1, 2j+1 )+ x ( 2i+1, 2j-1 ) ⎥ ⎢ ⎥ ⎣ 4 ⎦
Simplicity and low number of computations are two advantages of the described interpolation method compared with interpolation method introduced in [4]. Moreover, using floor in the equations has a great effect on embedding capacity. More details are explained in Section II-B.
(1)
Fig. 1(b) illustrates the interpolation of first category pixels. Interpolated pixel is labeled with x ′ ( 2i, 2j ) . After interpolation of all pixels of first category, interpolation values for pixels of second category are obtained using
⎢ x ( 2i-1, 2j-1 )+ x ( 2i+1, 2j-1 ) ⎥ +⎥ ⎢ 4 ⎥ x' ( 2i, 2j-1 ) = ⎢ ⎢ x' ( 2i, 2j-2 )+ x' ( 2i, 2j ) ⎥ ⎢ ⎥ ⎣ 4 ⎦
(2)
Fig. 1(c) shows interpolation process of second category pixels. It should be noted that red dots are pixels interpolated in the previous step. Finally x ′ values for third category pixels are computed using ⎢ x ( 2i-1, 2j-1 )+x ( 2i-1, 2j+1 ) ⎥ +⎥ ⎢ 4 ⎥ x ′ ( 2i-1, 2j ) = ⎢ ⎢ x ′ ( 2i-2, 2j )+ x ′ ( 2i, 2j ) ⎥ ⎥ ⎢ ⎣ ⎦ 4
(3)
B. Additive Interpolation-Error Expansion Additive interpolation-error expansion is the embedding approach used in the proposed reversible image watermarking scheme. This method has two key features makes it different from other Difference Expansion (DE) approaches. First, interpolation-error is used instead of interpixel difference to embed data. And secondly, difference is expanded through addition instead of bit-shifting. To begin, a pixel value is estimated from its neighboring pixels which is called an interpolation value. In section II-A, the method used to obtain interpolation values has been described. Then interpolation-error is calculated using e =x - x ′
(4)
where x are pixels of cover media, x' are the interpolation values of pixels x, and e are interpolation-error values. Suppose that LM and RM are error values corresponding to two highest points of interpolation-error histogram. Referring to Fig. 2, assuming LM < RM, then interpolation-errors can be divided into two parts: 1.
Left interpolation-errors (LE): s.t e satisfies e ≤ LM .
2.
Right interpolation-errors (RE): s.t e satisfies e ≥ RM .
With the same interpolation algorithm, it is possible to obtain same interpolation values x' and the corresponding interpolation-errors through e ′ = x ′′ - x ′
(11)
Eq. (11) is employed to extract the embedded data, once the same LM, RM, LN and RN are known.
Fig 2. Error frequency vs. interpolation-error values. Error values between RM and LM do not change.
In multilayer embedding, it could happen a situation that LM > RM. Therefore, overlap between LE and RE will be unavoidable. To prevent this condition, we apply the following ⎧ LM = max {T1 ,T 2 } ⎪ ⎨ ⎪ RM = {T ,T } - {LM } 1 2 ⎩
(5)
where T1 and T2 equal to
(12)
To recover the original interpolation-errors, the inverse function of additive interpolation-error expansion is used ⎧e ′ − sign (e ′ )* b , ⎪ e = ⎨e ′ − sign (e ′ )* b , ⎪ ⎩e ′ ,
(13) e ′ ∈ [ LM − 1, LM ] ∪ [ RM , RM + 1]⎫ ⎪ e ′ ∈ [ LM − 1, LM ] ∪ [ RM , RM + 1]⎬ ⎪ otherwise . ⎭
At the last stage, it is simple to obtain the original pixels via
⎧T1 = arg max hist (e ) ⎪ e ∈E ⎨ hist (e ) ⎪⎩T 2 = arg emax ∈E- {T1 }
(6)
where the number of times that the interpolation-error equals to e is denoted by hist(e) and E is the set of total interpolationerrors. In accordance with the above, additive interpolation-error expansion can be formulated as
⎧e+ sign (e ) × b, e = LM or RM ⎪ e' = ⎨e+ sign (e ) ×1, e ∈ [ LN, LM ) U ( RM, RN ⎪e , otherwise ⎩
⎧ 0, e ' = LM or RM b=⎨ ' ⎩1, e = LM- 1 or RM+1
⎫ ⎪ ]⎬ ⎪ ⎭
(7)
x = x ′+ e
(14)
According to Section II-A, during calculation of interpolation values, floor function is used to determine interpolation values. Such a consideration, results in improved embedding capacity. Referring to Fig. 3, the histogram of error values in an original image has a Gaussian distribution and errors with higher frequency (LM and RM) are used to embed watermark. On the other hand, floor function increases the frequency of RM and LM error values. As a result, higher embedding capacity is achieved. Experimental results, described in section IV, show that the increased capacity will not compromise the image quality.
where the expanded interpolation-error is denoted by e', b is the embedded bit, and sign(e) is a sign function defined as ⎧ 1, sign (e ) = ⎨ ⎩-1,
e ∈ RE e ∈ LE
(8)
It should be noted that LN and RN in (7) are defined as ⎧⎪ LN = min {LE } ⎨ ⎪⎩ RN = max {RE }
(9)
After expansion of interpolation-error, the watermarked pixels x ′′ are calculated as below x ′′ = x ′ + e ′
(10)
Fig 3. Gaussian distribution of error values for an arbitrary original image.
III.
ALGORITHM OF THE PROPOSED SCHEME
A. Embedding Procedure After calculation of interpolation values and interpolationerrors, additive expansion is applied to embed watermark data. The following procedure explains the embedding process with details.
1. 2. 3. 4. 5. 6.
Take LSBs of the pixels in the bordered area and put them to the end of watermark. Obtain interpolation values x' and interpolation-errors e of non-sample pixels. Calculate LM, RM, LN, and RN values. Record the length of the array B denoted by L. Compute expanded interpolation-error e' values. Find out watermarked pixels x ′′ . Embed encrypted B, L, LM, LN, RM, and RN into bordered area of the cover image using LSB replacement.
⎛ MAX 2 ⎞ I ⎟ PSNR = 10Log10 ⎜ ⎜ MSE ⎟ ⎝ ⎠
(15)
where Mean Squared Error (MSE) is obtained via
MSE =
2 1 m-1 n-1 ∑ ∑ ⎡⎣ I(i, j) - K(i, j) ⎤⎦ m×n i=0 j=0
(16)
where the size of original cover image I and watermarked image K is m×n. In (15), MAX equals to maximum possible value for each pixel which is 255 for tested images used in this paper. Fig. 5 illustrates the comparison between our proposed scheme and previous methods in case of PSNR vs. embedding capacity for tested images. It can be seen from Fig. 5(a) through Fig. 5(c) that with the same capacity, the proposed scheme has better PSNR compared to preceding schemes in all cases.
B. Extraction Procedure
The process described below is the procedure of extracting watermark form the watermarked image. 1. 2. 3. 4. 5.
Extract and decrypt LSBs of the pixels of bordered area to obtain B, L, LM, LN, RM, and RN. Calculate interpolation values x'. Obtain e' values of non-sample pixels. Achieve e values and obtain embedded information b. Obtain original LSBs of bordered area of image from the end of watermark and replace with existing LSBs of the bordered area.
Fig 4. Gray scale sample images tested in the proposed algorithm.
During embedding process, pixels with 0 and 255 values are not embeddable. These pixels are called boundary pixels. It is also possible that the value of pixels with 1 and 254 values, pseudo-boundary pixels change to 0 and 255, respectively. In this case, during extraction process, there is an ambiguity with distinguishing between boundary and pseudo-boundary pixels. As a matter of fact, a bitwise array B is exploited to determine boundary and pseudo-boundary pixels. Also it should be noticed that we encrypt the overhead information, B, L, LM, LN, RM, and RN using a simple XOR encryption method to protect watermarked data against illegitimate manipulations.
IV.
EXPERIMENTAL RESULTS
We use MATLAB to implement the proposed scheme and test the algorithm with three various 512×512 gray-scale test images: Baboon, Lena, and Sailboat. Fig. 4 shows the utilized test images. To demonstrate the efficiency of the proposed scheme, Peak Signal to Noise Ratio (PSNR) is calculated for each test image through
Fig 5. (a) Lena image: PSNR vs Capacity in the proposed scheme compared with previous methods.
REFERENCES [1] [2]
Fig 5. (b) Baboon image: PSNR vs Capacity in the proposed scheme compared with previous methods.
Fig 5. (c) Sailboat image: PSNR vs Capacity in the proposed scheme compared with previous methods.
V.
CONCLUSION
In this research, an improved reversible image watermarking method has been proposed which offers high embedding capacity, low computational complexity and improved security aspects. The proposed scheme uses additive interpolation-error expansion to embed watermarks leads to a high PSNR, in addition to high embedding capacity. Experimental results demonstrate the advantage of the proposed method to the previous works in case of image quality and embedding capacity. Also, it can be shown that number of computations of the algorithm is fairly low compared with Lou's algorithm.
Http://www.wipo.int/about-ip/en/ J. Tian, “Reversible watermarking by difference expansion,” in Proc. of Workshop on Multimedia and Security: Authentication, Secrecy, and Steganalysis, J. Dittmann, J. Fridrich, and P. Wohlmacher, Eds., Dec. 2002, pp. 19-22. [3] Alattar, A.M., "Reversible watermark using the difference expansion of a generalized integer transform," Image Processing, IEEE Transactions on , vol.13, no.8, pp.1147,1156, Aug. 2004. [4] Lixin Luo; Zhenyong Chen; Ming Chen; Xiao Zeng; Zhang Xiong, "Reversible Image Watermarking Using Interpolation Technique," Information Forensics and Security, IEEE Transactions on , vol.5, no.1, pp.187,193, March 2010. [5] Zhang, D.; Xiaolin Wu, "An edge-guided image interpolation algorithm via directional filtering and data fusion," Image Processing, IEEE Transactions on , vol.15, no.8, pp.2226,2238, Aug. 2006. [6] Abadi, M.A.M.; Danyali, H.; Helfroush, M.S., "Reversible watermarking based on interpolation error histogram shifting," Telecommunications (IST), 2010 5th International Symposium on , vol., no., pp.840,845, 4-6 Dec. 2010. [7] Wien Hong , Tung-Shou Chen, "Reversible data embedding for high quality images using interpolation and reference pixel distribution mechanism," Journal of Visual Communication and Image Representation, v.22 n.2, p.131-140, February, 2011. [8] A Khan, A Siddiqa, S Munib, SA Malik, "A recent survey of reversible watermarking techniques," Information Sciences, 2014 – Elsevier, in press. [9] L. Luo, Z. Chen, M. Chen, X. Zeng, and Z. Xiong, "Reversible image watermarking using interpolation technique," Information Forensics and Security, IEEE Transactions on, vol. 5, pp. 187-193, 2010. [10] P. Tsai, Y.-C. Hu, and H.-L. Yeh, "Reversible image hiding scheme using predictive coding and histogram shifting," Signal Processing, vol. 89, pp. 1129-1143, 2009. [11] K.-S. Kim, M.-J. Lee, H.-Y. Lee, and H.-K. Lee, "Reversible data hiding exploiting spatial correlation between sub-sampled images," Pattern Recognition, vol. 42, pp. 3083-3096, 2009.
