International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT) - 2016
DWT-SVD based Digital Image Watermarking using Swarm Intelligence Vibha Verma
Vinay Kumar Srivastava
Falgun Thakkar
Department of ECE MNNIT, Allahabad Allahabad, India
[email protected]
Department of ECE MNNIT, Allahabad Allahabad, India
[email protected]
Department of ECE MNNIT, Allahabad Allahabad, India
[email protected]
Abstract In this paper, a digital image watermarking technique based on Discrete Wavelet Transform (DWT) and Singular Value Decomposition (SVD) is proposed. For embedding the watermark, cover image is decomposed into different subbands using 2-level DWT. SVD is applied on both medium frequency subbands after 2level decomposition of cover image. A watermark image is splitted into two equal images on column basis. These images are again resized to the size of original watermark image by zero padding. The singular value matrices of medium frequency subbands of cover image are modified by splitted watermark images using suitable scale factor obtained by Particle Swarm Optimization (PSO). Again SVD is applied on these modified singular value matrices. Inverse SVD is applied on these singular value matrices along with respective orthogonal matrices of subbands to recover the modified wavelet subbands. The Inverse DWT on these modified subbands along with remaining subbands of cover image makes the watermarked image. Extracted spitted watermark images are added together to reconstruct the original watermark. The Analysis and experimental results show that the proposed technique is more robust against common image manipulation attacks. Keywords: particle swarm optimization; singular value decomposition; discrete wavelet transform; peak signal to noise ratio; mean square error; normalized correlation coefficient
I.
INTRODUCTION
Watermarking basically refers to hide some information in digital media (digital music, digital video and Photographs) such that it is imperceptible to common users [1]. Nowadays copyright protection has become a very important part of multimedia data because, it can be easily downloaded from internet and several copies can be generated without the permission of content owner [16][17] [18]. Transparency and robustness are two important factors. A tradeoff between transparency and robustness is maintained while applying watermark to the image.
Aslantas [1] proposed a watermarking technique based on SVD using Differential Evolution (DE) algorithm. In this paper singular values of host image are modified by different scale factors for embedding a watermark. The modifications are optimized using DE algorithm to achieve highest transparency and robustness. Mohammad et al. [2] presented a SVD based watermarking method to solve the false positive problem. They have used a text message as watermark. Tsai et al. [3] proposed a DSS scheme based on DWT-SVD in which LL band of DWT of host image is decomposed by SVD to get three components U, S and V in SVD domain. A watermark bit is embed in LL band by modifying the coefficient at U. Scale factor is computed by PSO to optimize the DSS scheme. Bhatnagar and Raman [4] proposed a DWT and SVD based semi blind watermarking technique. They used a gray scale logo image as watermark. Watermarking is done by modifying the singular value of cover image with the singular value of watermark. Run et al. [5] proposed two watermarking methods. In the first method principal components of the watermark are embed into the cover image in DCT domain. In the second method those are embed into the host image in DWT domain. PSO is used to find the suitable scale factors. Guo and Prasetyo [6] presented a SVD based image watermarking technique in which principal components of a watermark are embed into the cover image of block based manner using spread spectrum concept. So it becomes free from false positive problem. Jane et al. [7] proposed a hybrid approach based on DWT-SVD. After 1-level decomposition of cover image, SVD is applied on LL band then modification of singular value is done with a watermark by a suitable scale factor. Ganic and Eskicioglu [8] presented a DWT-SVD based scheme in which watermark is embed in all frequency components. SVD is applied on each band after decomposing the cover image into four bands, then embed the same watermark by modifying the singular values. Seema and Sharma [9] proposed a DWTSVD based watermarking technique. The singular
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value of HL band (after third level decomposition of host image) is modified with the singular value of the watermark after application of SVD on it. Kumar et al. [14] presented a DWT-SVD based watermarking algorithm. They divide the watermark image in two parts then modified the medium frequency bands of third level decomposition of DWT with two parts of watermark and different scale factors. Again singular value of each modified component after SVD is embed into two bands. Bhandari et al. [15] proposed a cuckoo search algorithm and DWT-SVD based contrast enhancement approach to improve the performance of low contrast satellite images. II.
OVERVIEW OF DWT AND SVD
A. Discrete Wavelet Transform (DWT) Discrete Wavelet Transform is a frequency transformation that provides time frequency representation of an image [10]. DWT decomposes the image into four subbands in a first level decomposition- LL (low-low), LH (low-high), HL (high-low), HH (high-high).They give approximate, horizontal, vertical and diagonal details of an image respectively. For second level decomposition LL band is further decomposed into four different subbands. These subbands are LL2, HL2, LH2, HH2 corresponding to 2-level decomposition of DWT. B. Singular Value Decomposition (SVD) Singular Value Decomposition is a mathematical technique, used to extract the geometrical features of an image. SVD decomposes a rectangular matrix into three matrices- U, S and V, U and V satisfy unitary property. S is known as rectangular diagonal matrix with diagonal entries in descending order known as singular values [11]. These singular values have high stability so, when they are modified with watermark image don’t affect the perceptual quality of an image. Let A is a rectangular matrix of order M X M A = U S VT U and V are unitary matrices such that U*UT = I V*VT = I where, I is an Identity matrix The column vectors of U and V are called left and right singular vectors respectively and S is a diagonal matrix. The diagonal coefficients of matrix A represent singular values of A and they are in decreasing order.
C.
Particle Swarm Optimization (PSO)
PSO is a stochastically global optimization algorithm used to improve candidate solutions. Its applications areas are classifications, association rule mining and reactive power dispatch. Scale factor plays a very important role in watermark embedding, because it controls robustness and imperceptibility of watermark image. Different watermarks require different scale factors although they are embed in the same cover image. Run et al. [5] used matrix scale factor and Jain et al. [12] proposed scalar scale factor for watermark embedding. In this paper, a PSO algorithm is used to find the suitable scalar scale factor for embedding the watermark in the cover image. In PSO algorithm, different particles movement is in discrete steps along a high dimensional parameter space searching for the optimal solution. On the basis of the iterations, every particle search for the optimal goal by taking reference of previous movement directions and the optimal position. [3] Each particle is regarded as a point in D- dimensional space. Let ith particle in D-dimensional space is defined as: ܺ ൌ ሺݔଵǡ ݔଶǡ ǥ ǥ ǥ ǥ ǥ Ǥ ݔ ሻ The ith particle of swarm population has the knowledge of its personal best position (the best position, particle has visited that produces the highest fitness value): ܲ ൌ ሺଵǡ ଶǡǥǥǥǥǥǥǥǥǥǥǤǤ ሻ, the global best position (the best particle position that gives the best fitness value in the whole population): ܲ ൌ ሺଵǡ ଶǡǥǥǥǥǥǥǥǥǥǥǤǤ ሻ and its current velocity (denotes its position change for determining the new modified velocity for each particle in the fourth upcoming iteration steps): ܸ ൌ ሺݒଵǡ ݒଶǡ ǥ ǥ ǥ ǥ ǥ Ǥ ݒ ሻ The particles modify their velocity and position according to the following equations. ݒௗ ൌ ݒ כ ݓௗ ܿଵ ݀݊ܽݎ כଵ כሺௗ െ ݔௗ ሻ ܿଶ כ ݀݊ܽݎଶ *(ௗ െ ݔௗ ) ݔௗ ൌ ݔௗା ݒௗ
(1) (2)
where, ݓis an inertia weight of value 0.9, ݀݊ܽݎଵ & ݀݊ܽݎଶ are two random functions in range [0 1] for an ith particle, ܿଵ and ܿଶ are positive acceleration constants having value 2, the initial velocity is set at 0.5, velocity limit is -0.5 and +0.5, number of particles is 50 and maximum iteration is 400. The following fitness function is used in this proposed algorithm to calculate the performance of each generation:
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f(x) = (corr2(A, ܣ௪ )+corr2(W,ܹ ) / 2) where, A and ܣ௪ are cover and watermarked image respectively and W and ܹ are original and extracted watermark respectively. Fitness function value range is from 0 to1. Previous velocity of particles affects the new velocity and the distance of its current position from its own best position, known as experience and the swarm best position is calculated by above velocity equation (1) and modified position is given by above position equation (2). Now particles fly according to this new modified velocity. Inertia weight w has a very important place. It controls the effect of previous velocity on the current velocity. A large w search for new areas, gives global exploration and a small w confined to current search area, gives local exploration. [20] III.
THE PROPOSED TECHNIQUE
A. Watermark embedding procedure In the proposed algorithm, the cover image is decomposed using 2-level DWT. SVD is applied on both medium frequency subbands after decomposition. A watermark image is splitted into two equal images on column basis and again resized to the size of original watermark image by zero padding. The singular values of medium frequency bands are modified by splitted watermark images using suitable scale factor obtained by PSO. Again SVD is applied on these modified singular value matrices. Inverse SVD is applied on these singular value matrices along with respective orthogonal matrices of subbands to recover the modified wavelet subbands. SVD
2.Apply SVD on both medium frequency subbandsሺܪܮଶ ,ܮܪଶ ) of 2-level decomposition. ܣ = ܷ ܵ ்ܸ , where ܣ ൌ ܪܮଶ ǡ ܮܪଶ 3. Divide watermark image into two parts on column basis and resize to the size of watermark image by zero padding. W=ܹଵ + ܹଶ
ܵ௪ ൌ ܵ ܳ ൈ ݎݐ݂݈ܿܽ݁ܽܿݏ where, ܵ௪ is the modified singular value of ܣ and ܳ represents two resized parts of watermark image 5.Apply SVD on modified singular matrix of medium frequency subbands of cover image. ் ܵ௪ ൌ ܷ௦௪ ܵ௦௪ ܸ௦௪
6.Obtain the modified DWT coefficients corresponding to both medium frequency subbands. ܣ௪ ൌ ܷ ܵ௦௪ ்ܸ
7.Obtain the watermarked image ܣ௪ by applying 2level inverse DWT
ܷଵ ܵଵ ܸଵ்
ْ
ܮܮଶ
1.Apply 2- level DWT to decompose the host image into four subbands. (i.e.ܮܮଶ ǡ ܪܮଶ ǡ ܮܪଶ ܽ݊݀ܪܪଶ )
4. Modify singular values of both medium frequency scale factor obtained by PSO.
The proposed technique is discussed in this section. It has two procedures: watermark embedding and extraction, shown in figure 1(a) and 1(b) respectively
ܪܮଶ
The Inverse DWT on these modified subbands along with remaining subbands of cover image makes the watermarked image. Steps of the watermarking embedding are discussed as follows: Let the size of cover and watermark image is N×N
Singular value modification
ܵଵଵ
SVD
் ܷ௨ଵ ܵ௦ଵ ܸ௩ଵ
ISVD
Cover image
2- level DWT
ܹଵ
Watermark image
Modified DWT coefficients
ܹଶ ܪܪଶ
ܮܪଶ
ْ SVD
2-level IDWT
Watermarked image
ISVD Singular value modification
ܷଶ ܵଶ ܸଶ்
ܵଶଶ
SVD
் ܷ௨ଶ ܵ௦ଶ ܸ௩ଶ
Fig. 1(a) Watermark embedding process.
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B.
Watermark extraction procedure
For watermark extraction, noisy watermarked image is decomposed into different subbands using 2-level DWT. SVD is applied on both medium frequency subbands after 2-level decomposition. Possibly corrupted singular value is obtained by inverse SVD. Extracted spitted watermark images are added together to recover the original watermark image. Steps of the watermark extraction are discussed as follows:
2. Apply SVD on two medium frequency subbands i.eǤܪܮଶ ǡ ܮܪଶ ் ܣ௪ ൌ ܷ௪ ܵ௪ ܸ௪ ǡ ܣ௪ ൌ ܪܮଶ ǡ ܮܪଶ 3. Obtain possibly corrupted singular value. כ ் ൌ ܷ௦௪ ܵ௪ ܸ௦௪ ܵ௪ 4. Obtain two extracted parts of watermark image (possibly distorted) כ כ ൌ ሺܵ௪ െ ܵ ሻȀݎݐ݂݈ܿܽ݁ܽܿݏ ܪ௪
1. Apply 2-level DWT to decompose the noisy watermarked image into four subbands i.e. ܮܮଶ ǡ ܪܮଶ ǡ ܮܪଶ ǡ ܪܪଶ
כ represents two watermark parts whereǡ ܪ௪
5. Add two watermark parts to reconstruct the watermark image. ܪܮଶ
SVD
ܷଵ ܵଵ ܸଵ்
ISVD
Possibly distorted ܹଵ
ܮܮଶ Noisy Watermarked
i
2-level DWT
ْ ܪܪଶ ܮܪଶ
SVD
ܷଶ ܵଶ ܸଶ்
ISVD
Extracted Watermark image
Possibly distorted ܹଶ
Fig. 1(b) Watermark extraction process
IV.
RESULTS AND DISCUSSIONS
This section represents experimental setup and results for the proposed technique. Watermark and host images and their sizes are explained in section A and different results are explained is section B
a
b
d
e
c
A. Watermark and host images: A gray scale logo of size 128×128 is used as watermark image and Water, Forest, Desert, Plain, Snow and Urban area satellite images are used as host images are of size 512×512
Fig 2: MNNIT logo as watermark image
f
Fig 3: (a) Water (Image taken from Article published in The Blade newspaper of US) (b) Forest (Image courtesy NASA’s Earth Observatory) (c) Desert (Image courtesy NASA’s Earth Observatory), (d) Plain (Image taken from Arch Atlas) (e) Snow (Image taken from AGU Blogosphere –Satellite view of the ice and snow) (f) Urban (Image courtesy NASA’s Earth Observatory) Satellite images as host images
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The original and extracted watermark similarity is represented by normalized correlation coefficient. [14] NCC=
Fig 4: Splitted watermark images
σ సభ σೕసభ ௐሺǡሻכௐ ሺǡሻ మ
మ ටσ సభ σೕసభሺௐሺǡሻሻ ටσసభ σೕసభሺௐ ሺǡሻሻ
where, W and ܹ are original and extracted watermark respectively 3) Parameters for different attacks Fig 5: Resized watermark images
• •
B. Performance parameters: 1) Peak signal to noise ratio (PSNR)
•
PSNR is used to estimate the image quality and calculated between cover and watermarked image, represented by PSNR and Mean square error between the host and watermarked image is represented by MSE [5].
• • •
ܴܲܵܰ ൌ ͳͲ݈݃ሺʹͷͷሻ2Ȁܧܵܯ
•
Mܵ ܧൌ
ଵ ேൈே
Rotation angle is 2 degrees. Size and position of cropping rectangle =̴݊݅݉ݔ1ǡ =̴݊݅݉ݕ10, width= 512 and height=502 Contrast adjustment with ݈ ̴݊݅ݓൌ ͲǤ003 , ̴݄݄݅݃݅݊=0.95, ݈=ݐݑ̴ݓ0.0015 and ̴݄݄݅݃ ݐݑ0.925 Gamma correction with scale 0.95 Averaging window size 3×3 Gaussian noise, Speckle noise and Salt & pepper noise with mean 0 and variance 0.01 Gaussian, median and wiener filtering window size 3×3.
• 4) Normalized correlation coefficient between original and extracted watermark under different attacks for different host images are shown in table 1 and PSNR of watermarked image for different host images are shown in table 2.
ே ଶ σே σ ሺ ܣെ ܣ௪ ሻ
where A and ܣ௪ are host and watermarked image respectively and N ×N is image size 2) Normalized correlation coefficient (NCC)
TABLE 1: Normalized correlation coefficient between original and extracted watermark under different attacks for different host images Sr. No. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
Attacks Rotation Cropping Contrast adjustment Gamma correction Averaging Gaussian noise Speckle noise Salt & pepper noise Gaussian filtering Median filtering Wiener filtering Rescaling (256-512-256) Rescaling (1024-512-1024) Sharpening Histogram equalization
Normalized correlation coefficient Water 0.9113 0.9788 0.9986 0.9997 0.9751 0.9229 0.9810 0.9684 0.9923 0.9859 0.9744 0.9798 0.9980 0.9551 0.9690
The experimental results discussed in table 1 show that the proposed technique is robust to almost all
Forest 0.9301 0.9247 0.9900 0.9981 0.9841 0.9602 0.9933 0.9883 0.9919 0.9805 0.9834 0.9820 0.9980 0.9618 0.9285
Desert 0.9068 0.9103 0.9848 0.9990 0.9874 0.9392 0.9566 0.9713 0.9953 0.9896 0.9891 0.9804 0.9993 0.9326 0.9168
Plain 0.9180 0.9879 0.9590 0.9999 0.9683 0.9367 0.9867 0.9840 0.9844 0. 9757 0.9778 0.9781 0.9978 0.9323 0.9159
Snow 0.9302 0.9190 0.9721 0.9842 0.9784 0.9569 0.9796 0.9829 0.9845 0.9831 0.9782 0.9822 0.9948 0.9546 0.9543
Urban 0.9326 0.9205 0.9982 0.9642 0.9734 0.9373 0.9956 0.9920 0.9845 0.9737 0.9728 0.9693 0.9974 0.9490 0.9397
attacks such as rotation, cropping, contrast adjustment, gamma correction, averaging, Gaussian,
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Speckle, salt and pepper noise, Gaussian, median, wiener filtering, rescaling, sharpening and histogram equalization. It is much robust against Gaussian, Median, Wiener filtering, Rescaling (256-512-256), Rescaling (1024-512-1024) attacks for all host images having minimum NCC 0.9844, 0.9737, 0.9728, 0.9693 and 0.9948 respectively. TABLE 2: Peak signal to noise ratio (PSNR) of watermarked image for different host images Sr. no. 1. 2. 3. 4. 5. 6.
Host images Water Forest Desert Plain Snow Urban
PSNR 62.0047 64.4008 65.9686 68.4165 67.6096 62.4829
Table 2 shows higher PSNR for all host images because watermark embedding is done into both medium frequency subbands of 2-level decomposition of DWT and two parts of watermark are embed into both medium frequency subbands of 2- level decomposition. The proposed technique shows the highest PSNR value of 68.4165 for Plain host image. V.
CONCLUSIONS
In this paper a DWT-SVD based watermarking technique using PSO is proposed. Watermark image is splitted in two equal parts and resized to the size of original watermark then embedded into both medium frequency subbands of 2-level DWT. At the extraction end, both spitted watermark images are added together to reconstruct the original watermark. The proposed technique is tested for various host images under various attacks. Performance of the proposed technique is estimated by peak signal to noise ratio (PSNR) and normalized correlation coefficient (NCC). Experimental results show that proposed technique is more robust and imperceptible in terms of normalized correlation coefficient and peak signal to noise ratio. For obtaining a suitable scale factor in this proposed algorithm a Particle swarm optimization (PSO) technique is used. REFERENCES 1. Veysel Aslantas, “An optimal robust digital image watermarking based on SVD using differential evolution algorithm,” in journal of Optics Communications 282 (2009) 769–777 2. Ahmad A. Mohammad, Ali Alhaj, Sameer Shaltaf, “An improved SVD-based watermarking scheme for protecting rightful ownership,” in Signal Processing 88 (2008) 2158– 2180
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