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A semi-blind watermarking algorithm for color images using chaotic maps
Somayyeh Mohammadi
Department of Engineering, Payame Noor University (PNU), Kerman, Iran
*Corresponding Author's E-mail: [email protected]
Abstract
n this paper a semi-blind watermarking method for color images is introduced based on chaotic maps. To achieve a secure design, the method generates a pseudo-random binary watermark by a chaotic map and embeds the watermark bits in Red, Green, and Blue pixels of the color image. In the detection stage, the watermark bits are extracted without requirement to the original image, of course the embedding positions’ addresses are needed. The simulation results show that the proposed method has good performance in terms of the peak signal to noise ratio and the bit error rate quality measures.
Keywords: robustness; chaotic maps; watermarking
1. Introduction
Digital transmission networks like internet allow any user to easily exchange and copy digital information. Though these aforesaid avails present huge chances for authors the facility to create great copies but also assist fraud and illegal copying. Therefore owners are worried about the outcome of illegal copying. This problem is solved by some techniques such as digital watermarking.
Digital watermarking is a solution to protect data and preserve copyright owners. It is the insertion of a signal, identified as the watermark, into original data in an invisible mode. The watermark depicts information that detects the owner of the original data. Since some application like saving, transmission over a network or deliberate processing by a hostile, may remove or damage the watermark signal, processing the watermarked signal is known as an attack, whether the aim of such processing is malicious or not. A watermarking system should detect the watermark, even the signal has been subjected to attack. It means the watermark should be securely embedded and difficult to remove. Security can be reached by utilizing some keys during the watermark generation or watermark insertion. Keys consist of information which only owners know them and their existence are necessary in the extraction stage. Many watermarking systems create the watermark signal using a pseudo-random number generator (PRNG) which the key is typically the seed to the PRNG.
Recently chaotic maps for enjoying particular characteristics have been interested to researches in many fields such as secure communication and watermarking systems. Intense sensitivity to seeds is an advantage that makes these sequences more importance among others. Indeed chaotic parameters and seeds are considered as keys in a watermarking system. We can put watermarking schemes in three groups from detection viewpoint which are known as blind, semi-blind, and non- blind watermarking methods. Actually methods which detect the watermark without requiring to the host signal are put in the blind class. Algorithms that need to know some information about the original signal or require the original signal to extract the watermark are recognized as semi-blind and non-blind methods, respectively. Since our proposed method in this study does not need the original signal, only the embedding positions' addresses are required, so it is semi-blind and we evaluate our algorithm for color images in Red, Green, and Blue (RGB) mode. Of course it can be
I
extended to both kinds of images (color and gray scale). We select pixels from R, G, and B channels based on a principle which detailed more in the proposed method section. The rest of this paper is organized as follows. Section 2 describes some new related works in the watermarking field. The watermarking scheme based on chaotic maps is presented in section 3. Simulation results are discussed in section 4. Section 5 is the conclusion.
2. Relevant Studies
There are many watermarking systems which proposed in the pixel [1, 2] or transform [3-5]
domain. By exploration of chaotic maps, most researchers have motivated to use these sequences in their schemes [6, 7]. The presented method in [3] is a watermarking system based on Sparse Coding (SC), Discrete Wavelet Transform (DWT) and Singular Value Decomposition (SVD). The reason for incorporating SC in their system is to encode the watermark before embedding it in the host image and their system is oblivious.
The study in [4] represents a watermarking scheme based on Double Random Phase Encoding (DRPE)in quaternion gyrator transform domain. In their proposed method, an RGB-scale watermark together with gray scale watermark or not as encoded into quaternion matrix and encrypted through the DRPE, the encrypted data is then fused into the middle coefficients of the quaternion gyrator- transformed host image.
The proposed algorithm in [8] is a scheme developed in the wavelet domain based on the SVD and artificial bee colony (ABC) algorithm. The host image is transformed into an invariant wavelet domain by applying redistributed invariant the wavelet transform, subsequently the low frequency sub-band of wavelet transformed image is segmented into non-overlapping blocks. The most suitable embedding blocks are selected using the human visual system for the watermark embedding.
The algorithm in [6] constructs a binary watermark by taking advantage of a chaotic map known as Tent map. To embed this binary sequence in the host image they apply a three level decomposition DWT to the host image. Then by modifying some wavelet coefficients from some sub- bands that are obtained from the decomposition process, the watermarked image is constructed.
In [9], a reversible watermarking algorithm based on chaotic system is proposed; chaotic system is not only used to search space of reversibility of the scheme, but also used to randomly select the position of watermarking embedding.
In this paper a novel watermarking based on chaotic maps is proposed. As the extraction will be done with the knowledge of addresses of embedding locations, it is semi-blind and we consider our algorithm for RGB color images. It is noticeable to say that our scheme also can be applied on gray scale images. Indeed to contrast the performance of our design against a new novel watermarking method, to have the same data in comparison we use a gray scale image as a host image. The embedding positions in our algorithm are chosen as a principle that explained more in section III.
3. Algorithm Theory
This section is dedicated to the explanation of watermark embedding and watermark extraction.
Of course in order to enjoy the particularity of chaotic maps, we generate the binary watermark signal by using a chaotic map called Logistic map [10]. This generation is done by (1).
(
1)
,1 xn xn
xn+ =ρ − ) ,binery round(xn
xn =
(1)
Where 0<ρ<4and nis the iteration number that it is as same as watermark’s length. Here the chaotic parameter (
ρ
) and the seed are considered as watermarking keys.A. Watermark Embedding
A functional block diagram of the watermark embedding is demonstrated in Fig. 1. Referring to Fig. 1, the embedding procedure comprises the following steps.
Step 1. Consider the host color image in RGB mode, so there are three kind regions: R, G, and B.
Step 2. Find the maximum and minimum values in R and name them as “ma_R” and “mi_R”, respectively.
Do step 2 also for G and B. So we have 6 numbers as “ma_R, ma_G, ma_B, mi_R, mi_G, mi_B”.
Step 3. Construct a collection (named A1) which its elements are pixels of R which valued ma_R . Extend this collection by using G and B. (put pixels of G which valued ma_G and pixels of B which valued ma_B in the collection A1).
And also construct a collection (named A2) which its elements are pixels of R which valued mi_R.
Extend this collection by using G and B. (put pixels of G which valued mi_G and pixels of B which valued mi_B in the collection A2).
Note 1: The total numbers in set A1 should be as same as the “1” numbers in the watermark signal.
Note 2: The total numbers in set A2 should be as same as the “0” numbers in the watermark signal.
Note 3: It may be observed that you do not reach the Note 1 or Note 2, then you should complete elements for Note 1 by finding extra pixels from R (or G or B) which their values are closed to ma_R (or ma_G or ma_B) and also complete elements for Note 2 by finding extra pixels from R (or G or B) which their values are closed to mi_R (or mi_G or mi_B).
Step 4. Apply the embedding relation by (2):
l i wi i if
w LSB i A
wi i if
w LSB i A
,..., 1 1 )
( 2
0 )
(
1 =
=
=
=
=
(2)
Here A1 and A2 are collections which described in step 3, w is the binary watermark, l is the watermark’s length and LSB is the Least Significant Bit.
Note 4: Save the embedding locations’ addresses, because their existence is a necessity in the extraction stage. Obviously these addresses are considered as watermarking system keys.
Now we obtain to the watermarked image and to confirm the copyright ownership, it is sufficient to extract the watermark as explained in the next sub-section.
Fig. 1: Embedding Procedure.
B. Watermark Extraction
To detect the binary watermark, complete the following steps on watermarked color image.
1) Find the maximum and minimum values among all pixels of three modes (R, G, and B) and call them as B1 and B2, respectively.
2) Apply the extraction formula to extract w’ (the extracted watermark) by (3).
l
i others
B B B
n m I if
wi , 1,...,
1
2 1 1 2
) , ( '
' 0 =
− −
=
(3) Where I’ (m, n) are addresses (embedding positions) which saved in the embedding stage and l is the watermark's length. (B1 and B2 have been gained from previous step.
4. Experimental Results
This section is divided to two sub-sections. First the resistance of our proposed scheme against some usual attacks is evaluated, next we comprise the efficiency of the proposed algorithm in this study against [3].
A. Evaluation Results
MATLAB simulations are performed by using 512 × 512 pixel RGB color ‘‘Baboon, Lena, and House” images and a 1000 bits’ length binary watermark. Parameters which we use, are: X0=0.036,
72 .
=3
ρ
. Fig. 2 (a–c) and (d – f) show the original watermarked images, respectively. To quantitatively calculate the performance of the proposed idea, the Peak Signal to Noise Ratio (PSNR) is assumed to determine the image quality of the watermarked image which is given by (4).∑= ∑
= −
=
= M i
N j
j i X j i X MSE
MSE PSNR
1 1
) , '( ) , (
) / ) 2
^ 255 log((
10
(4)
Where X( ji, )is the original signal, X'(i,j)is the watermarked one.
As it can be seen from Fig. 2, there is no understandable perceptual alteration between the watermarked image and the original one.
(a) (b) (c)
(d) PSNR= 80.91 dB (e) PSNR= 80.72 dB (f) PSNR= 80.07 dB
Fig. 2: (a)-(c): Original Images. (d)-(f): Wteramrked Images
In order to measure the reliability, the bit error rate (BER) of the extracted watermark, is calculated by using (5).
l BER= B
(5)
Where B is the amount of erroneously discovered bits and l is the watermark‘s length. We evaluate the robustness of our algorithm versus the attacks that are given in Table I. The quality of the extracted watermark is revealed by analyzing the BER value using (5) and the corresponding results put into Table I. A lower BER value shows that the algorithm is more competent in extracting watermark bits, correctly. All written results in Table I indicate that our proposed method enjoys an acceptable rank of resistance against attacks.
TABLE I. BER Results
Baboon Lena House
No Attack 0.000 0.000 0.000
Salt & Pepper (0.001) 0.001 0.000 0.001
Gaussian Noise (0.001) 0.000 0.000 0.000
Rotation (5o) 0.000 0.060 0.125
Rotation (15o) 0.005 0.177 0.150
Rotation (25o) 0.004 0.367 0.163
JPEG (QF=85) 0.000 0.000 0.024
JPEG (QF=70) 0.000 0.000 0.045
JPEG (QF=55) 0.000 0.000 0.059
Median [3 3] 0.000 0.000 0.027
Median [5 5] 0.000 0.000 0.039
Averaging Filter 0.000 0.000 0.055
B. Comparison Results
To assess the proposed design in this paper, we make a comparison between our proposed scheme and a new watermarking model [3].To make a fair comparison with [3], we use the parameters as those indicated in that paper and consider its performance against our method based on NC (Normalized cross-correlation) criteria (Formula (6)).
∑ ∑
= ∑
'2 2*
'
*
W W
W NC W
(6)
Where w is the original watermark and w’ is the extracted watermark. The ideal value of the NC is 1 which means the original and the extracted watermarks are exactly the same.
As validated by Fig. 3, the scheme has been depicted in this study displays superior performance in contrasted to the approach suggested by [3].
Fig. 3: Comparison Results.
Conclusion
In this study we introduced a novel watermarking algorithm for color images, although it can be applied on gray scale images as well. The most significant contribution of the work is utilizing a chaotic map to generate the watermark signal and its ability for preserving the watermark.
Simulation and comparison results confirmed the efficiency of our proposed method.
References
[1] S. Behnia, M. Teshnelab, P. Ayubi, “Multiple-watermarking scheme based on improved chaotic maps,” Commun Nonlinear Sci Numer Simulat 15, pp. 2469-2478, 2010.
[2] M. Keyvanpour, F. Merrikh-Bayat, “An effective chaos-based image watermarking scheme using fractal coding,”
Procedia Computer Science 3, pp. 89-95, 2011.
[3] A. Tareef and A. Al-Ani, “A highly secure oblivious sparse coding-based watermarking system for ownership verification,” Expert Systems with Applications 42, pp. 2224-2233, 2015.
[4] Z. Shao, Y. Duan, G. Coatrieux, J. Wu, J. Meng, and H. Shu, “Combining double random phase encoding for color image watermarking in quaternion gyrator domain,” Optics Communications 343, pp. 56-65, 2015.
[5] M. Ali, and C. Wook Ahn, “Comments on ‘‘Optimized gray-scale image watermarking using DWT-SVD and Firefly Algorithm’’ Expert Systems with Applications 42, pp. 2392-2394, 2015.
[6] S. Mohammadi and S. Talebi, “An Image watermarking Algorithm Based on Chaotic Maps and Wavelet Transform,’’
9th International ISC Conference on Information Security and Cryptology , 2012.
[7] S. Mohammadi, S. Talebi, and A. Hakimi, “Two Novel Chaos-Based Algorithms for Image and Video Watermarking,’’ Iranian Journal of Electrical & Electronic Engineering, Vol. 8, No. 2, pp. 97-107, 2012.
[8] M. Ali, C. Wook Ahn, M. Pant, P. Siarry, “An image watermarking scheme in wavelet domain with optimized compensation of singular value decomposition via artificial bee colony,’’ Information Sciences 301, pp. 44-60, 2015.
[9] Q. Gu, T. Gao, “A novel reversible robust watermarking algorithm based on chaotic system,’’ Digital Signal Processing 23, pp. 213-217, 2013.
[10] K. T. Alligood, Tim D. Sauer and James A. Yorke, Chaos: An Introduction to Dynamical systems. Springer, New York, 2001.
0.9 1
Proposed Method in[3]
