Improving the Security of Spatial Domain Based Digital Image Watermarking using Chaotic Map and Cellular Automation

Published Online January 2016 in MECS

Due to the development of information and communication technology, the security of information has attracted the interest of the researchers over the last decade [1]. Digital image watermarking is one of the effective schemes for providing such a security and it is a technique of embedding information called watermark into original image by ensuring the imperceptibility. There are two domains on which image watermarking is performed- spatial domain and transformed domain. The embedding procedure of spatial domain based watermarking is to embed the bits of watermark into bit planes of cover image directly. So in spatial domain, the computational complexity is low; normally it is used for fragile watermarking as well as the capacity is also high depending on the size of image. On the other-hand, in transformed domain, watermarks are embedded into the frequency coefficients; so the computational complexity is high as well as the capacity is low. The main feature of transformed domain based watermarking is that it shows the robustness against different image processing attacks. Different transforms such as Discrete Cosine Transform (DCT) [2], Discrete Wavelet Transform (DWT) [3] are used in watermarking techniques.

The security of digital image watermarking is improved by involving different chaotic maps such as Arnold’s cat map, logistic map. Cellular automata show the complex characteristic which is used in different types of applications such as- random number generation, pattern recognition, games [4]. Wu et al. [5] proposed a chaos based robust spatial domain watermarking algorithm where for encrypting watermark 1-D logistic map is used and for encrypting embedding position of cover image 2-D Arnold’s Cat map is used. Rawat et al. [6] proposed a chaotic system based fragile watermarking scheme for image tamper detection. In this scheme the authors proposed a chaos based watermarking technique for image authentication, tamper detection and localization where two chaotic maps- Arnold’s Cat map and logistic map are used. Liu et al. [7] proposed an image fragile watermark scheme based on chaotic image pattern and pixel pattern. In this scheme the authors used the chaotic map for generating chaotic pattern image and watermark embedding procedure results from calculating the difference between host image and its chaotic pattern. Wenyin et al. [8] proposed semi fragile spatial watermarking based on local binary pattern operators where LBP is used for embedding and extracting watermark. Chaotic based watermarking is also performed on transformed domain. Dawei et al. [9] proposed a chaos based robust wavelet domain watermarking algorithm where DWT is used and chaotic watermark is embedded into the part of sub-band coefficients. Yantao et al. [10] proposed a robust chaos based DCT domain watermarking algorithm. In this scheme the author scrambled the watermark using chaotic map and then the chaotic watermark is embedded into LSB of the DCT coefficients which are determined by another chaotic map with another secret keys. Rosline et al. [11] proposed normalized image  watermarking scheme using chaotic system. Chrysochos et al. [12] proposed robust watermarking of digital images based on chaotic mapping and DCT. Song et al. [13] proposed a blind digital watermark method based on SVD and chaos. In this scheme the author encrypted the watermark using Tent chaotic map and embedded encrypted watermark into singular values of cover image. Image can be scrambled by using cellular automata. Dalhoum et al. [14] proposed Digital Image Scrambling Using 2D Cellular Automata where rules of game of life are used for scrambling image.

(a)                       (b)                        (c)

Fig.1. (a) Random Configurations Generated by Logistic Map Using Secret key (µ=3.9745 and x (1) =0.1245); (b) Jet-Plane Image; (c) Chaotic Jet-Plane Image using Logistic Map

Birth

Death by overcrowding

Death by exposure

Survival

= Alive           = Death

Fig.2. Rules of Game of Life

In this proposed scheme Game of life cellular automation [14] is used to scramble the cover image and the binary watermark is X-ORed with the logistic map in order to form the chaotic watermark. In this scheme watermarking is performed in spatial domain. For embedding chaotic watermark bits in spatial domain, one bit of chaotic watermark is embedded into 3×3 block of scrambled cover image by considering and modifying only one of the eight neighbors of 3×3 block [8].

The remainder of the paper is arranged as follows. The background of the proposed scheme including logistic map, game of cellular automation is described in Section II. The proposed scheme including scrambling, embedding, descrambling and extraction is described in Section III. The experimental results and comparison with the existing methods are described in Section IV.

Finally the paper is concluded is Section V.

• II.    B ACKGROUND

The proposed watermarking scheme involved logistic map and game of life cellular automation techniques. These techniques are described in this section as follows:

• A.    Loistic Map

For improving  the  security of digital image watermarking, different types of chaotic maps have been proposed. Among them logistic map is the simplest chaotic map. This map is described by

Хк* i = №(1-X_k)           ⁽¹⁾

where, 0 <  ц < 4 . The values of ц and x (1) are the initial conditions which can be used as the secret keys. This map is sensitive to initial conditions. Sensitive to initial condition means that the relationship between two logistic sequences with different initial conditions is statistically uncorrelated. Fig.1 (a) shows the random configurations generated by logistic map using secret key (µ=3.9745 and x(1)=0.1245). Fig.1 (b) shows the jetplane image and Fig.1 (c) shows the chaotic jet-plane image using logistic map.

• B.    Game of Life Cellular Automation

  Cellular Automata show the complex characteristics which are proposed by Stani-slaw Ulam and John Von Neumann in the 1940s [14]. The applications of cellular automata are in the fields of random number generation, pattern recognition, games etc. Game of life is a well-known example of cellular automation which is normally used in order to scramble the pixel positions of digital images.

The rules of game of life are applied to the initial matrix (GL) of size M×N which is formed in this paper by using logistic map. Either of two states such as death

• (0) or alive (1) is represented by each cell of M×N cells. The initial matrix GL is run for K times (called generations- used as secret key in this paper). Here Moore neighborhood is considered, so each cell updates its state (dead or alive) by considering the states of eight neighbors according to the rules of game of life. Fig. 1 shows the rules of game of life for scrambling digital images.

In case of rule of birth, where center cell is death and exactly three neighbor cells are alive at time t shown Fig. 2 (a) so the center cell will be alive at time t+1 shown in Fig. 2 (b). In case of rule of death by overcrowding, where center cell is alive and four (or more) neighbor cells are alive at time t shown Fig. 2 (c) so the center cell dies at time t+1 shown Fig. 2 (d). In case of rule of death by exposure, where center cell is alive and one (or none) neighbor cell is alive at time t shown Fig. 2 (e) so the center cell dies at time t+1 shown Fig. 2 (f). In case of rule of survival, where center cell is alive and two (or three) neighbor cells are alive at time t shown Fig. 2 (g) so the center cell survives at time t+1 shown Fig. 2 (h).

Fig.3. Block Diagram of Cover Image Scrambling and Chaotic Watermark Embedding Procedure

Fig.4. Block Diagram of Watermark Extracting Procedure

(a)                (b)                 (c)

Fig.5. (a) Gray Values of 3×3 Mask; (b) Gray Difference Matrix; (c) Sign Matrix

• III.    P ROPOSED M ETHOD

The proposed watermark embedding algorithm and the proposed watermark extraction algorithm are explained in this section.

• A. Embedding Algorithm

A gray-scale image of size 255×255 is considered as a cover image and a binary image of size 85×85 is considered as watermark. Cover image scrambling by using game of life cellular automation and chaotic watermark embedding procedure into scrambled cover image is shown in Fig. 3. The scrambling and embedding algorithm is described as follows:

• •    Then another logistic map G 0 of size equal to cover image is generated using key K1 for performing the rules of game of life upon it.

• •    The rules of game of life are applied to the matrix G₀ to obtain first generation G₁ , rules applied to G₁ to obtain second generation G₂ and this process is repeated for K2 (key) number of generations.

• •    For the first generation of game of life G 1 , pixels of the cover image are scrambled according to G 1 (x, y) = 1

• •    For the second generation of game of life G 2 , pixels (that are not scrambled in case of first generation) are scrambled according to G 2 (x, y) = 1 and G₁ (x, y) + 1 .

• •    Step 5 is repeated from iteration third generation to K2 generation.

• •    After completing K2 iterations, remaining of the pixels are scrambled according to G_K2 (x, y) = 0.

• •    At first, a logistic map is generated using key K3 . By performing the X-OR operation between binary watermark and generated logistic map, a binary chaotic watermark is obtained.

• •    For embedding binary chaotic watermark into the scrambled cover image, a mask of size 3×3(shown in Fig. 5 (a)) is run over the scrambled cover image of size 255×255.

• •    The gray difference matrix (shown in Fig. 5 (b)) is obtained by calculating the difference between the center pixel and neighbor 8 pixels.

• •    If the gray difference is positive (or zero) then one is assigned or if the gray difference is negative then zero is assigned in order to form sign matrix.

• •    X-OR is performed among the bits of sign matrix (shown in Fig. 5(c)) which is given by

ex = b 1 ⊕ b 2 ⊕ b 3 ⊕ ………… ⊕ b 8      (2)

• •    Only one bit of chaotic binary watermark is embedded in 3×3 mask of scrambled cover image. Suppose w is one of the bits of binary chaotic watermark of size 85×85. If w is equal to ex , then no change is occurred in the neighbor pixels of 3×3 mask. If w is not equal to ex , then one of the neighbor pixels is changed according to the following steps:

• a.    From the absolute values of gray differences of gray difference matrix, the minimum value d_min is determined as well as the pixel value p_min corresponding to d_min is also determined.

• b.    Gray value of that pixel is changed as follows:

  p_mo d =(p

  
  

  min

  
  

  - d min ) – α; if b min = 1

  
  
  
  

p_mo d =(p_m i _n + d_m i _n) + α; if b_m i _n= 0       (4)

where, p mod is the modified pixel, b min is the binary bit of sign matrix and a is scaling factor ranging from 1 to 5.

• •    After embedding all the bits of chaotic watermark into scrambled cover image, the modified scrambled cover image is obtained.

• •    The pixels of modified scrambled cover image return back to their original positions according to G 1 (x, y) = 1.

• •    Pixels that are not descrambled in case of first generation return back to their original positions according to G 2 (x, y) = 1 and G j (x, y) + 1 .

• •    Step 15 is repeated from iteration third generation to K2 generation.

• •    After completing K2 iterations, remaining of the pixels return back to their original positions according to G K2 (x, y) = 0.

• •    When all the pixels of modified scrambled cover are descrambled to their original positions, then watermarked image is obtained.

• B.    Extraction Algorithm

Chaotic watermark is extracted from watermarked image and binary watermark is recovered from chaotic watermark by using logistic map. The whole procedure is shown in Fig. 4.

• •    Using the secret keys K1 and K2, steps 1 to 6 (described in section) are repeated for scrambling the watermarked image.

• •    A mask of size 3×3 is run over the scrambled watermarked image.

• •    The gray difference matrix is obtained by calculating the gray the difference between the center pixel and neighbor 8 pixels of 3×3 mask.

• •    If the gray difference is positive (or zero) then one is assigned or if the gray difference is negative then zero is assigned in order to form sign matrix.

• •    Chaotic watermark is obtained from the result after performing X-OR operation among the binary bits of sign matrix.

• •    A logistic map is generated using the secret key K3. Then the binary watermark is recovered after Performing the X-OR operation between the chaotic watermark and generated logistic map.

  (a)

  
  

  (b)

  
  

  (c)

  
  

  (d)

  
  

  (e)

  
  

  (f)

  
  

l^lSf

Wnjj|

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)

(t)

(u)

Fig.6. (a)-(c) Original Cover Images; (d)-(f) Watermark Images; (g)-(i) Scrambled Cover Images using Cellular Automation for First Generation; (j)-(l) Chaotic Watermarks using Logistic Map; (m)-(o) Watermarked Images; (p)-(r) Recovered Watermarks; (s)-(u) Extracted Watermarks using Wrong Keys.

• IV.    E XPERIMENTAL R ESULTS AND C OMPARISON

We have evaluated our proposed scheme in case of different gray scale images. Three gray scale images (Cameraman, Lena, Peppers) of size 255×255 are used as the original cover images which are shown in the first row of Fig. 6. Three images (jet-plane, rice, coins) of size 85×85 are used as the watermarks which are shown in the second row of Fig. 6. The third row of Fig. 6 shows the scrambled cover images using game of life cellular automation for first generation as well as the forth row shows the chaotic watermarks using logistic map. Three watermarked images are shown in the fifth row of Fig. 6. Three recovered watermarks are shown in the sixth row of Fig. 6. Three extracted watermarks using wrong keys are shown in the seventh row of Fig. 6.

There are three performance evaluating parameters such as Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE) and Normalized Correlation (NC) are used in order to the evaluate performance of this proposed scheme. In order to implement this watermarking procedure and also evaluate the performance of this scheme, MATLAB (v. 13.0.1) is used.

MSE is used to measure the error between host image X and watermarked image Y which is defined as follows:

PSNR is an important performance evaluating parameter in order to find out similarity between host image and watermarked image and basically it is used for estimating the imperceptibility. PSNR is calculated from MSE which is defined as follows:

PSNR = 10 log, ₀ gf]           (6)

where, max = M×N

NC is another performance evaluating parameter in order to find out the similarity between the original watermark and extracted watermark NC is used which is defined as follows:

i,M^mijw'(W)

l£    j W( ,) 2                    ⁽ )

where, M and N are rows and columns of image. W and W' are the original watermark and extracted watermark respectively.

Table 1. MSE and PSNR Values of Watermarked Images (Cameraman, Lena and Peppers) for Different Values of Scaling Factor

Scaling Factor α	Cameraman		Lena		Peppers
	MSE	PSNR	MSE	PSNR	MSE	PSNR
1	1.7036	45.8510	0.4439	51.6922	0.3219	53.0872
1.5	1.8852	45.4112	0.5410	50.8325	0.4274	51.8568
2.0	2.0962	44.9505	0.6615	49.9594	0.5591	50.6898
2.5	2.3365	44.4791	0.8053	49.1053	0.7172	49.6086
3	2.6062	44.0047	0.9724	48.2864	0.9015	48.6150
3.5	2.9053	43.5329	1.1628	47.5098	1.1122	47.7030
4	3.2338	43.0677	1.3765	46.7771	1.3492	46.8642
4.5	3.5916	42.6119	1.6135	46.0871	1.6124	46.0900
5	3.9788	42.1673	1.8738	45.4375	1.9020	45.3727

(a)

(b)

(c)

(d)

(e)

Fig.7. (a) Watermarked Image Attacked by Salt & Pepper Noise; (b) Its Corresponding Recovered Watermark Image; (c) Watermarked Image Cropped by 10%; (d) Its Corresponding Recovered Watermark Image; (i)-(e) Rotated by 2 Degree; (f) Recovered Watermark Image.

(f)

The scaling factor α is very important for this proposed scheme in order to embed and extract watermark. Table 1 represents the PSNR and MSE values of three watermarked images (Cameraman, Lena and Peppers) for scaling factor ranging from 1 to 5. The PSNR values are decreasing as well as MSE values are increasing with the increasing of scaling factor. From the results it is shown that the PSNR and MSE values attain satisfactory values for scaling factor 1 to 5.

Table 2. Performance against Different Attacks

Attack Type	Cameraman	Lena	Peppers
	NC	NC	NC
No attack	1.0000	1.0000	1.0000
Salt & pepper (0.005)	0.9724	0.9732	0.9782
Cropping (10%)	0.9523	0.9627	0.9724
Image rotation (angle 5)	0.9045	0.9196	0.9256

Table 3. Comparison Results of PSNR

Images	Method [12]	Method [11]	Method [6]	Proposed Method
	PSNR	PSNR	PSNR	PSNR
Cameraman	35.16	45.42	50.14	51.51
Lena	35.15	45.35	50.49	51.76
Peppers	36.50	43.13	51.71	53.08

Fig.8. Comparison Results with other Methods

Table 2 shows the performance of the proposed scheme in terms of Normalized Correlation (NC) against three attacks. The values of NC are satisfactory in case of three attacks.

Table 3 shows the comparison results of PSNR with three existing methods in [12], [11] and [6]. Graphical representation of comparison with other three existing chaotic methods is shown in Fig. 8. From the comparison results, it can be seen that our proposed method outperforms than other three methods in terms of PSNR.

• V.    Conclusions

Improving the security of spatial domain based digital image watermarking has been proposed in this paper. In this proposed spatial domain based watermarking scheme, three secret keys are used in order to improve the security of watermarking. From logistic map one secret key is obtained and from game of life cellular automation other two secret keys are obtained. The watermark is made chaotic using logistic map and the cover image is scrambled using game of life cellular automation. So, three secret keys must be required to recover the watermark. In addition only one bit of chaotic watermark is embedded in 3×3 block of scrambled cover image which ensures the imperceptibility and robustness. Then the scrambled modified cover image is descrambled using game of life cellular automation for obtaining watermarked image. This proposed scheme is evaluated in terms of PSR, MSE and NC.