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New image blind watermarking method based on two-dimensional discrete cosine transform
Journal Pre-proof New image blind watermarking method based on two-dimensional Discrete Cosine Transform Zihan Yuan, Decheng Liu, Xueting Zhang, Qingtang Su
PII:
S0030-4026(19)32051-0
DOI:
https://doi.org/10.1016/j.ijleo.2019.164152
Reference:
IJLEO 164152
To appear in:
Optik
Received Date:
25 October 2019
Revised Date:
18 December 2019
Accepted Date:
28 December 2019
Please cite this article as: Yuan Z, Liu D, Zhang X, Su Q, New image blind watermarking method based on two-dimensional Discrete Cosine Transform, Optik (2019), doi: https://doi.org/10.1016/j.ijleo.2019.164152
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New image blind watermarking method based on two-dimensional Discrete Cosine Transform
Zihan Yuan1, Decheng Liu1, Xueting Zhang1, Qingtang Su1* [email protected] 1 School
of Information and Electrical Engineering, Ludong University, Yantai 264025, China
*
Corresponding author: Tel.: +86-535-6672343 , (Qingtang Su)
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Highlights
The size relationship between the selected middle frequency coefficients of 2D-DCT is used to embed and extract watermark information;
Comparing with traditional algorithms which are based on DCT, the watermark capacity of this algorithm is larger;
The proposed algorithm is a blind watermarking algorithm, and the original data or original watermark is not needed in the process of watermark extraction;
Comparing with other relevant algorithm, the proposed algorithm has higher invisibility and stronger robustness, which is suitable for digital image copyright protection.
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Abstract: In this paper, a new image blind watermarking method based on two-dimensional Discrete
Cosine Transform (2D-DCT) is presented to realize copyright protection of color image. At first,
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2D-DCT is performed on the selected image blocks, and some fixed coefficients in the middle
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frequency are selected as embedding position of watermark. Then, the watermark embedding and extraction procedure are completed by modifying the relationship of size between the selected middle-frequency coefficients with the proposed rules. The advantages of the presented algorithm include the following two points: 1) the relationship of size between the selected middle-frequency coefficients of 2D-DCT is used to fulfill the process of watermark embedding and extraction; 2) the presented algorithm uses color digital image as carrier image and watermark image, which is not 1
same as most watermarking techniques. In recent years, most of the watermarking algorithms used gray or binary image as watermark. In this presented algorithm, all the digital carrier images are chosen from two public standard image databases, i.e. CVG-UGR and USC-SIPI. A series of simulation results prove that this presented algorithm not only satisfies the invisibility of watermarking algorithm, but also makes good performance of robustness, security and embedding capacity.
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Keywords: Blind watermarking; Color image; Discrete Cosine Transform; Frequency domain
1 Introduction
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In recent years, as the rapid advancement of the multimedia and Internet, we can obtain more
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required information accurately and efficiently, and many achievements and creations are stored and
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published on the Internet in the form of digit, but it also produced a series of serious problems, such as piracy, infringement, tampering, and so on. Therefore, the protection of intellectual property and
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copyright is extremely urgent [1]-[4], and digital watermarking technology emerges at the historic moment [5]. It is well known that digital watermarking is an important branch of information hiding
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technology [6], which uses data redundancy or visual redundancy of the digital multimedia to embed the digital watermark into the digital multimedia directly by some certain embedding methods. The
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successful embedding and extraction of digital watermarks can effectively solve the problem of protecting copyright. According to the difference of carrier image processing ways, digital watermarking algorithms are divided into the spatial-domain watermarking algorithm [7, 8] and frequency-domain watermarking algorithm [5, 9, 16]. The spatial-domain watermarking algorithm 2
refers to modify the image pixel value directly in order to embed watermark information. Spatial-domain watermarking algorithm is simple and efficient in execution, but its robustness is relatively weak. For example, Abraham et al. [7] presented a novel color image watermarking algorithm using spatial-domain technique, and generated a watermarked image with excellent quality. Furthermore, the frequency-domain watermarking algorithms embed watermark information in frequency-domain coefficients, which makes good use of the human vision,
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auditory and other characteristics. This watermarking method has good robustness, but its
calculation is more complex. The frequency-domain watermarking algorithms often use Discrete Wavelet Transform (DWT) [10, 15, 24], Discrete Cosine Transform (DCT) [9, 12, 13, 16],
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Discrete Fourier Transform (DFT) [11, 21], and matrix factorization [5, 14, 19, 20, 23] and so on.
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than the spatial watermarking method [13].
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In a word, the watermarking method in frequency domain has better invisibility and robustness
Therefore, considering the invisibility and robustness of watermark, many watermarking
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algorithms based on the frequency domain have been presented to protect the copyright over the years. For instance, Ernawan et al. [9] presented a DCT-based digital image watermarking method
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which used the best psychovisual threshold. The watermark information was not embedded to the DCT coefficients directly as other watermarking methods. In this algorithm, the watermark
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information was embedded by modifying the correlation coefficients based on specific rules. This watermarking algorithm has better robustness and invisibility. However, the used carrier image is gray-scale image [16], and the used watermark image is binary image in this method. As we all know, digital color images are more vivid, bright and informative, and its utilization rate far exceeds that of gray-scale images. 3
Pradhan et al. [10] proposed a non-blind digital watermarking algorithm using DWT and cross chaos. This method belongs to non-blind watermarking algorithm since the original data is needed in watermark extraction process. Nevertheless, in practice, obtaining the primary data is not easy when detecting watermark in most cases. Therefore, non-blind watermarking method has certain defects, and blind watermarking method has more practical value and application prospect. Hence, Roy et al. [12] proposed a blind DCT-based watermarking scheme which can embed
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multiple watermark images. This watermarking scheme can extract the watermark information without the need of original data, so it belongs to blind watermarking scheme. In addition, the watermarking scheme embedded multiple watermark information into middle-frequency
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coefficients based on zig-zag order, and it has high robustness. This method can against common
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image processing attacks mainly include image enhancement such as low-pass filtering, median
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filtering, image sharpening, adding noise; geometric processing such as rotation, cropping, scaling; and compression attacks such as JPEG compression, JPEG2000 compression. But, it is needed to
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modify 22 coefficients of middle-frequency of DCT in [12] so each image block can embed 11 watermark bits. Therefore, the quality of watermarked image was seriously distorted. Su et al. [13]
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presented a digital watermarking algorithm; this watermarking algorithm embedded the digital color watermark into carrier image successfully, which could resist many common attacks.
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However, the algorithm requires two times operations of two-dimensional Discrete Cosine Transform (2D-DCT), so the computational complexity is high. Song et al. [19] proposed a robust digital image watermarking scheme which is using the QR decomposition and chaotic system, this method has excellent robustness and it can resist a variety of attacks. However, as we all know, the number and magnitude of modified pixel values can directly affect the watermark invisibility. 4
Since the pixel values are modified extensively during the watermark embedding process in [19], its invisibility performance is not good. The requirements of a good digital watermark include invisibility, robustness, security, watermark capacity, blind extraction and so on. However, many watermarking techniques still cannot meet these requirements better. Therefore, how to devise a blind watermarking technology for meeting the requirements of robustness, invisibility, and security has become a hot research
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topic.
A color digital image blind watermarking algorithm based on 2D-DCT is proposed in this
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paper. This presented algorithm selects the special middle coefficients of image blocks after
2D-DCT, and modifies the size relationship between the selected middle coefficients to fulfill the
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watermark embedding and extracting process. At first, dividing the carrier image and color
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watermark image into red, green and blue three color layers; then, dividing each layer of the watermark image into non-overlapping pixel blocks. Afterwards, the block to be embedded of
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color carrier image is selected by pseudo-random sequence and transformed by 2D-DCT, and then embedding the scrambled watermark into the specific position of the DCT coefficients following
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zig-zag order. This presented watermarking algorithm has better performance on watermark
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invisibility and robustness, which is suitable for digital image copyright protection.
The remainder of this paper is organized as follows: the relevant knowledge is described in
part 2, which includes Arnold scrambling transformation, randperm function and 2D-DCT. Part 3 shows the process of watermark embedding and watermark extraction. Part 4 shows simulation attacks result and analysis. At last, the conclusion is given in part 5.
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2 Preliminaries
2.1 Arnold scrambling transformation Arnold scrambling transformation is usually used as pretreatment of information hiding. The digital watermark is scrambled before watermark embedding, which can greatly improve the watermarking security. Therefore, Arnold scrambling transformation is widely used in the
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scrambling of watermark image to ensure watermarking algorithm security. Arnold scrambling transformation is defined as follows: u ' 1 1 u mod P . v ' 1 2 v
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(1)
where, u, v, u', v' ∈{0, 1, 2,…, P-1}, P is the size of the watermark image to be scrambled, (u, v)
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is the position of pixel in watermark image before scrambling, (u', v') is the position of pixel in
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watermark image after scrambling. Arnold transformation can move the pixel value of digital watermark image from the original position (u, v) to the new position (u', v').
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Using Arnold transformation to scramble the original watermark image can realize the hiding of image information. The scrambling times can be used as the private key Kai, which can
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strengthen the confidentiality and security of the watermarking scheme.
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Correspondingly, for restoring the original watermark image, the corresponding inverse Arnold scrambling transformation is as follows: u 2 1 u ' P mod P. v 1 1 v ' P
2.2 Randperm function 6
(2)
For improving the security of watermarking algorithm, we use the randperm function to choose the non-overlapping blocks randomly for embedding watermark information. Randperm function, as a build-in function in MATLAB, can scramble a number sequence randomly. For example, randperm(n, m) means select m numbers from {1, 2,…, n} randomly, where n is greater than m, and m, n is often viewed as the private key. Therefore, we reuse the randperm function twice time to generate two random sequences to select the non-overlapping embedded block
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randomly.
2.3 Two-dimensional discrete cosine transform (2D-DCT)
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Discrete Cosine Transform (DCT), as a widely used signal decomposition and compression
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technique, is mainly used for data compression and image compression. DCT can convert the signal from the spatial domain to the frequency domain, which has better performance of
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de-correlation. DCT is a special case of the Fourier transform, which avoids the complex operation in the Fourier transform, and it is a transform in real number domain.
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After applying DCT to an image, its coefficients can be divided into a direct component (DC)
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and some altering components (AC). The DC component represents the average brightness, and the AC components concentrate the main energy of the original image block. DCT algorithm has
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the advantages of high speed and accuracy. Therefore, DCT plays a vital role in image processing.
Two-dimensional Discrete Cosine Transform (2D-DCT) means to perform DCT again based
on the one-dimensional DCT. After performing 2D-DCT, the DCT coefficients of matrix A of sized M×N are obtained by Eq. (3):
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M 1 N 1 (2 x 1)u (2 y 1)v F (u, v) c(u )c(v) f ( x, y) cos cos . 2M 2N x 0 y 0
(3)
among them, v 0 1 N c (v ) = . 2 N v 1, 2,..., N 1 u 0 1 M c(u ) = . 2 M u 1, 2,..., M 1
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x and y are the sampling values in spatial domain, and f(x, y) is the pixel value at position (x, y) in spatial domain correspondingly, u and v are the sampling values in frequency domain, and F(u, v)
is the frequency coefficient at position (u, v) after 2D-DCT in frequency domain correspondingly.
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When used in digital image processing, digital image is usually represented by square pixel matrix,
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that is M=N.
The formula of inverse transform of 2D-DCT (2D-IDCT) is given as follows: (4)
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3 Proposed method
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(2 x 1)u (2 y 1)v M 1 N 1 f ( x, y) c(u )c(v) F (u, v) cos cos . 2M 2N u 0 v 0
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The implementation of the presented watermarking algorithm includes into two processes that
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are watermark embedding and watermark extracting. Specific steps of watermark embedding and watermark extracting are described below.
3.1 Process of watermark embedding The specific steps of watermark embedding process are shown in Fig. 1.
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Pre-processing the carrier image
Pre-processing the watermark image
Key Kc
Key Kb
Key Ka Selecting the embedded block of the carrier image Getting binary watermark sequence Selecting the specific middle frequency coefficients of the pixel block
Obtaining the watermarked pixel block
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Obtaining the watermarked image
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Updating the block of watermarked pixels to corresponding position
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Modifying the size relation between middle frequency coefficient pairs
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Fig. 1 The diagram of watermark embedding process.
Step1: Preprocessing of the color carrier image and color watermark image.
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At first, dividing the color carrier image H which size is M×M into three layer carrier images Hi of red (R), green (G), and blue (B) color, and then dividing each layered image Hi into
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non-overlapping pixel blocks which size is 8×8. Secondly, dividing the watermark image which size
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is N×N into three layer watermark images Wi of R, G, and B color. Then scrambling each layered watermark image Wi using Arnold transformation which is based on the key Kai to enhance the security of watermarking algorithm, transforming all pixel value with decimal format to binary information. Afterwards, all the binary information is connected to form the watermark bit sequences SWi. The length of sequence SWi is 8N2, where i = 1, 2, 3, and it is the R, G, and B three layer images, respectively. 9
Step 2: Choosing the embedded pixel block from color carrier image. The pseudo-random sequences generated by randperm function based on the key Kbi and Kci are used to generate two random numbers that are the row and column coordinates of the pixel block to be embedded, then the pixel block A is selected from the layer carrier image Hi, where i =1, 2, 3, and it is the R, G, and B three layer images. Step 3: Selecting the specific middle-frequency coefficients of the pixel block after
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two-dimensional Discrete Cosine Transform (2D-DCT).
According to Eq. (5), 2D-DCT is carried out on the chosen pixel block A for obtaining the
transformation matrix dctA, and four pairs of DCT middle-frequency coefficients (cp1, cp2) of the
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transformation matrix dctA are selected by the zig-zag order, p =1, 2, 3, 4, respectively:
dctA dct2( A).
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(5)
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where, dct2 (.) is the DCT function, the selected four pairs of DCT middle-frequency coefficients have their fixed positions, which are position (4, 2) and (3, 3), (2, 4) and (1, 5), (4, 3) and (3, 4), (2,
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5) and (1, 6).
Step 4: Modifying the size relation between DCT middle-frequency coefficient pairs.
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Selecting four watermark bits wp from SWi successively and using Eq. (6) and Eq. (7) to modify the size relation between DCT middle-frequency coefficient pairs (cp1, cp2) for embedding the
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watermark bit wp, where p =1, 2, 3, 4, respectively. The modified DCT middle-frequency coefficient pairs (cp1*, cp2*) are obtained as follow:
signc (c p1 ) (avg 0.3 T ), if w '1' and abs (c p 2 ) abs (c p1 ) T * c p1 = signc (c p1 ) ( avg 0.7 T ), if w '0 ' and abs (c p1 ) abs (c p 2 ) T . c ， else p1
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(6)
if w '1' and abs (c p 2 ) abs (c p1 ) T signc (c p 2 ) (avg 0.7 T )， * c p 2 = signc (c p 2 ) ( avg 0.3 T )，if w '0 ' and abs (c p1 ) abs (c p 2 ) T c ， else p2
.
(7)
where, signc (.) is defined as below: sign( x), signc( x) 1,
if x 0 else
.
where, sign (.) is sign function, avg=(abs(cp1)+abs(cp2))/2, abs(.) is absolute value function, T is the quantization step of this presented algorithm.
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Step 5: Embedding watermark.
Replacing the original DCT middle-frequency coefficient pairs (cp1, cp2) with the modified
DCT middle-frequency coefficient pairs (cp1*, cp2*) to obtain the watermarked transformation matrix
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dctA*, where p =1, 2, 3, 4, and it is the p-th pair of DCT middle-frequency coefficient, respectively.
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Step 6: Updating the block of watermarked pixels to the corresponding locations of the layered
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carrier image.
According to Eq. (8), inverse transform of 2D-DCT (2D-IDCT) is performed on the
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watermarked transformation matrix dctA* to obtain the watermarked pixel block A*, and the watermarked pixel block A* are updated to their corresponding locations of the layered carrier image
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Hi, where i =1, 2, 3, and it is the R, G, and B three layer images, respectively:
A* idct2(dctA* ).
(8)
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where idct2 (.) is the inverse 2D-DCT function. Step 7: Repeating. The steps 2 to 6 are repeated until embedding all the watermark information, and the layered watermarked image Hi* is obtained. At last, the layered watermarked images Hi* are combined to get final watermarked image H*, where i =1, 2, 3, and it is the R, G, and B three layer images. 11
3.2 Process of watermark extraction Since this presented algorithm is belong to blind watermarking algorithm, in the watermark extraction process, watermark information can be extracted from final watermarked image H* and doesn’t need the original data. The specific steps of watermark extraction are given in Fig. 2. Pre-processing the watermarked image
Obtaining the extraction block of the watermarked image
Key Kc
Selecting the middle frequency coefficients of watermarked pixel block
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Key Ka
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Extracting watermark bit
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Key Kb
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Getting binary watermark sequence
Obtaining the extracted watermark
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Fig. 2 The diagram of the process of watermark extraction.
Step 1: Preprocessing of obtained watermarked image.
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At first, dividing watermarked image H* into three layered images Hi* of R, G, and B color. At the same time, dividing each layered image Hi* into non-overlapping pixel blocks which size is
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8×8, where i =1, 2, 3, and it is the R, G, and B three layers, respectively. Step 2: Obtaining extracted block from the watermarked image. Using pseudo-random sequences generated by randperm function with the key Kbi and Kci to choose the pixel block A* from the layered watermarked image Hi*, where i =1, 2, 3, and it is respectively the R, G, and B three layers. 12
Step 3: Selecting the specific middle-frequency coefficients from the chosen watermarked pixel block after two-dimensional Discrete Cosine Transform (2D-DCT). Applying 2D-DCT to the watermarked pixel block A* in order to obtain the transformation matrix dctA*. Four pairs of DCT middle-frequency coefficients (cp1*, cp2*) corresponding to the embedding process are selected following zig-zag order in the transformation matrix dctA*, where p
Step 4: Extracting watermark bit.
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=1, 2, 3, 4, and it is the p-th pair of the DCT middle-frequency coefficient, respectively.
According to the size relation between DCT middle-frequency coefficient pairs (cp1*, cp2*), the watermark bit is extracted from the watermarked block by Eq. (9):
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abs(c p1 ) abs(c p 2 ) '1', if wp * . '0', else
(9)
Step 5: Repeating.
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middle-frequency coefficients, respectively.
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where, abs(.) is absolute value function, p =1, 2, 3, 4, and it is the p-th pair of the DCT
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The steps 2 to 4 are repeated to get the binary extraction watermark sequence SWi* of each layer watermarked image Hi*, dividing each 8-bit binary information in the watermark bit sequences
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SWi* into a group, converting it to decimal pixel values, and getting the decimal sequence, where i
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=1, 2, 3, and it is respectively the R, G, and B layer. Step 6: Obtain final extracted watermark. Using inverse Arnold transform which is based on key Kai on the decimal pixel sequence of
three layers respectively to get the extracted layered watermark Wi*. At last, the extracted layered watermark Wi* is recombined to get the final extracted watermark W*, where i =1, 2, 3, and it is the R, G, and B layer, respectively. 13
4 Experimental results
For testing the performance in terms of invisibility, robustness, security, and embedding capacity of the presented algorithm, ten color digital images of sized 512×512 given in Figs. 3(a)-(j) are selected as the carrier images in this paper. All the carrier images are chosen from two public standard image databases, that is CVG-UGR [17] and USC-SIPI [18]. Two color digital images of
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sized 32×32 given in Figs. 4(a)-(b) are selected as digital watermark images. Then the selected images are used in a series of experiments, and the presented algorithm is compared to some
relevant methods. For example, a color digital image watermarking method based on two times
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operations of two-dimensional Discrete Cosine Transform (2D-DCT) [13], a robust digital image
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watermarking method using chaotic system and QR decomposition [19], and a novel fast and robust spatial-domain watermarking algorithm [21]. The presented algorithm is frequency-domain
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watermarking method based on 2D-DCT in this paper. So, we selected algorithms [13] and [19] as comparative method, because the algorithm [13] is also used 2D-DCT to complete the operations
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of watermark embedding and extraction, and algorithm [19] is also a frequency-domain
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watermarking algorithm. In addition, in order to prove the presented watermarking algorithm has better performance compared with the spatial-domain watermarking algorithm, the algorithm [21]
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is also selected as comparative method.
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(a)
(b)
(c)
(f)
(d)
(g)
(e)
(h)
(i)
(j)
Fig. 3 Carrier images: (a) Lena, (b) Peppers, (c) Kid, (d) SailBoat, (e) Baboon, (f) Bear, (g) Barbara, (h) Couple,
(a)
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(i) Avion, and (j) House.
(b)
Fig. 4 Watermark images: (a) watermark 1, and (b) watermark 2.
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The imperceptibility and robustness performance of the presented watermarking algorithm are
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evaluated by specific performance indexes in following experiments. For example, peak
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signal-to-noise ratio (PSNR) is an important objective evaluation index of watermarked image distortion measurement, is usually used to calculate the similarity between the original carrier image and watermarked image. It can be defined as follows: M N max{[ H (u, v, j )]2 }
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PSNR j 10 lg
M
N
[ H (u, v, j) H * (u, v, j)]2
.
(10)
u 1 v 1
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among them, H (u, v, j ) , H * (u, v, j ) are the pixels whose coordinates are (u, v) in layer j of
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original carrier image and the watermarked one, M, N are respectively the row and column size of the test image. The PSNR of color image is defined by: (11)
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PSNR PSNR j . j 1
Due to the specific structure of natural signals and the strong interrelationship between pixels, a new evaluation standard, i.e. structural similarity index measurement (SSIM), is proposed from the 15
perspective of human visual system [22]. The value of SSIM can measure the image quality effectively, and it is defined as follows: SSIM ( H , H * ) l ( H , H * )c( H , H * ) s( H , H * ).
(12)
where, l ( H , H * ) (2 H H * C1 ) ( H2 H2 * C1 ) * 2 2 . c( H , H ) (2 H H * C2 ) ( H H * C2 ) * s( H , H ) ( HH * C3 ) ( H H * C3 )
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l ( H , H * ) , c( H , H * ) and s( H , H * ) is the luminance comparison, contrast comparison and structure
comparison function, respectively.
In addition, as an evaluation criterion, normalized cross-correlation (NC) can estimate the
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robustness of watermarking algorithm effectively. As for color digital watermark, Eq. (13) is used to
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calculate the NC value in order to evaluate the robustness of the watermarking algorithm. The
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NC
m
n
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calculation of NC is defined as follows:
(W (u, v, j ) W * (u, v, j)) j 1 u 1 v 1
3
m
n
3
m
n
W (u, v, j) W 2
j 1 u 1 v 1
(u, v, j )
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j 1 u 1 v 1
*
(13)
.
2
where W* is extracted color digital watermark, and W is original digital watermark, 1
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m and n represent the row and column size of color digital watermark respectively, j represents the
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j-th layer of color digital watermark.
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the value of SSIM/NC
SSIM
NC
1 0.98 0.96 0.94 0.92 0.9 0.88 0.86 0.84 0.82 0.8 16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
quantization step
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Fig. 5 The average values of structural similarity index measurement (SSIM) and normalized cross-correlation (NC) under different quantization steps.
As we all know, the quantization step T is an important parameter. In order to select an
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effective quantization step, we did many experiments. Embedding the color image watermarks as shown in Figs. 4(a) and (b) into the carrier images as shown in Figs. 3(a)-(j) with different
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quantization steps. The experimental results are shown in Fig. 5. SSIM becomes smaller and smaller
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and NC becomes bigger and bigger while the quantization step T is adding, which indicates that the invisibility of watermark becomes worse and worse, while the robustness of watermark becomes
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better and better. Thus, in order to have a good performance in robustness and invisibility
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simultaneously, we choose the quantization step T as 23 in this paper.
4.1 The imperceptibility test and analysis
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The invisibility of digital watermark is the ability that hiding the digital watermark information
in the carrier image. As an effective watermarking algorithm, the invisibility requires the embedded digital watermark cannot be detected by human perception system. The invisibility is an important character of watermarking algorithm. Table 1 shows the value of peak signal-to-noise ratio (PSNR) and structural similarity index measurement (SSIM) of the extracted watermark 17
images after embedding the watermark images in Figs. 4(a) and (b) to the carrier images in Figs. 3 (a)-(j), respectively. Table 1 The invisibility results (PSNR/SSIM) of embedding test watermark images into carrier images watermark 2
Lena
37.5851/0.9350
37.4625/0.9323
Peppers
38.0702/0.9241
38.1277/0.9250
Kid
37.4801/0.9242
37.6455/0.9250
SailBoat
38.1685/0.9403
38.4066/0.9414
Baboon
36.3189/0.9725
36.1885/0.9724
Bear
38.0001/0.9441
38.0903/0.9448
Barbara
37.3726/0.9385
37.4858/0.9395
Couple
38.2239/0.9193
38.2255/0.9196
Avion
37.1426/0.9245
37.2966/0.9255
House
38.2472/0.9149
38.3659/0.9154
Average
37.6609/0.9337
37.7295/0.9341
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watermark 1
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From Table 1 we can see that when watermarks 1 and 2 are respectively embedded into
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different carrier images, the values of PSNR are greater than 36dB, and the values of SSIM are close to 1. This indicates that the watermark is imperceptible through the human visual system after
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embedding watermark information into carrier image. It is proved that the presented watermarking algorithm has good performance of invisibility.
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For comparing the invisibility of this presented watermarking algorithm with other watermarking algorithms, the digital watermark 1 in Fig. 4(a) is respectively embedded into two
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carrier images in Figs. 3(a) and (b), the digital watermark 2 in Fig. 4(b) is respectively embedded
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into two carrier images in Figs. 3(c) and (d) . After embedding the selected watermarks to the color carrier images, the PSNR and SSIM values of different algorithms are shown as Table 2. NC values of different algorithms without the attack are given as Table 3. As can be seen from Table 2, algorithm [13] is a two-level two-dimensional Discrete Cosine Transform (2D-DCT) watermarking algorithm, while the presented algorithm is a one-level 2D-DCT algorithm. Therefore, we select the one-level 2D-DCT part of algorithm [13] for comparing with this paper. Although algorithm [13] 18
has high PSNR and SSIM, which indicated it has high watermark invisibility, as we can see in Table 3, its normalized cross-correlation (NC) is small that means its robustness is weak. On the contrary, in algorithm [19], the PSNR values and SSIM values are much smaller than other algorithms, which mean its invisibility is weak but its robustness is very strong. Because of that, the algorithm [19] is not used as comparison in the analysis of robustness. Good balance between the performance of invisibility and robustness is achieved and satisfies the requirements of the invisibility and
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robustness in the presented watermarking algorithm. As shown in Table 2, the values of PSNR are greater than 37dB, the values of SSIM are close to 1. The experimental result indicates that the presented algorithm has better performance of invisibility.
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Table 2 The invisible comparison results for (PSNR/SSIM) of various watermarking algorithms Algorithm [19]
Algorithm [21]
Algorithm [23]
Lena
48.6761/0.9956
22.5616/0.6332
38.0535/0.9414
39.4385/0.9656 37.5851/0.9350
Peppers
40.7425/0.9708
23.2864/0.7111
37.6262/0.9231
38.3367/0.9299 38.0702/0.9241
Kid
41.6958/0.9857
22.3026/0.6846
36.8241/0.9231
34.4638/0.8650 37.6455/0.9250
SailBoat
45.7757/0.9933
18.7103/0.6301
37.7440/0.9458
34.2340/0.8766 38.4066/0.9414
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Algorithm [13]
Presented Algorithm
Table 3 The compare results for NC values of various watermarking algorithms Algorithm [13]
Algorithm [19] Algorithm [21]
Algorithm [23]
Presented Algorithm
1.0000
1.0000
0.9937
1.0000
0.9475
Peppers
0.8568
0.9975
1.0000
0.9826
1.0000
Kid
0.8441
1.0000
1.0000
0.9771
0.9997
SailBoat
0.8746
1.0000
1.0000
0.9817
1.0000
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Lena
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4.2 The robustness test and analysis The robustness of digital watermark refers to the digital watermarking algorithm has the ability
to resist various linear and nonlinear filtering operations, common geometric transformations and other common transformations attacks. The robustness of watermark is also one of the important characteristics of watermarking technology. In this part, for measuring robustness of the presented watermarking algorithm, a series of 19
simulation attacks are preceded, such as JPEG compression, adding noise, filtering, scaling, cropping. As we all know, as an objective similarity measure of the final extracted watermark W* and original watermark W, normalized cross-correlation (NC) value is used to estimate the robustness of watermarking algorithm effectively. After a serious of attacks, watermarks were extracted from watermarked image namely “Lena” and “Peppers”. Fig. 6 shows the visual effect of extracted watermarks and its NC values under various attacks respectively.
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For proving the robustness of this algorithm further, we embedded the watermarks in Fig. 4(a) and (b) to carrier digital image “Lena” in Fig. 3(a) and carried out a series of attacks and compared with other relevant algorithms [13], [21], [23]. The simulation results are given in Figs. 7-10. Salt &
Butterworth
Peppers
low-pass
Attack
JPEG 2000 JPEG (40)
Median
white noise (5:1)
Cropping
Zoom-in
(25%)
(4:1)
filtering
noise (0, 0.001)
filtering
(3×3)
(0.2%)
(100, 5)
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Watermark
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Gaussian
0.9929
0.9999
0.9714
0.9351
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Fig.3 (b)
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Fig.3 (a)
0.9997
0.8590
0.9755
0.8199
0.9737
0.8456
0.9999
0.9643
0.8502
0.9451
0.9615
0.9999
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Fig. 6 Extract the watermarks from the watermarked image “Lena” after various attacks and their NC values
Image compression is a common processing method, and JPEG compression attack and JPEG
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2000 compression attack are effective methods to measure the robustness of watermarking schemes. Fig. 7 shows the experimental results of watermarked images after image compression attacks on JPEG and JPEG 2000. As shown in Fig. 7 that this presented algorithm has better robustness compared with other watermarking algorithms and it can resist different image compression attacks.
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Algorithm [13] 1
Algorithm [21]
Algorithm [23]
Presented Algorithm
0.9
NC value
0.8 0.7 0.6 0.5 0.4 0.3 JPEG 60
JPEG 2000 (4：1)
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Fig. 7 The comparison of NC value between various algorithms after compression attacks.
Then, Fig. 8 gives the experimental results after Salt & Peppers noising attack with a noise
intensity of 0.2% and Gaussian noise with a variance of 0.001. As Fig. 8 shows that the presented
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algorithm has stronger robustness than other compared algorithms relatively in terms of resisting
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different noise attacks. Fig. 9 gives the experimental results after median filtering attack and
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Butterworth low-pass filtering attacks. The median filtering attack which window size is 3×3 and the Butterworth low-pass filtering attack which filter order is 10 are respectively carried out on the
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watermarked images. It is indicated that this presented watermarking algorithm can effectively against the filtering attacks. Algorithm [13]
Algorithm [23]
Presented Algorithm
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1
Algorithm [21]
0.9
NC value
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0.8 0.7 0.6 0.5 0.4 0.3
Salt & Peppers noise (0.002)
Gaussian noise (0,0.001)
Fig. 8 The comparison of NC value between various algorithms after noising attacks. 21
Algorithm [13]
Algorithm [21]
Algorithm [23]
Presented Algorithm
1 0.9 0.8 0.7
NC value
0.6 0.5 0.4 0.3 0.2 0.1 0 Median filtering (3×3)
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Butterworth low-pass filtering (100,10)
Fig. 9 The comparison of NC value between various algorithms after filtering attacks.
In addition, image cropping and zooming are the common image geometric attack and will
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directly affect the image quality. Fig. 10 givens the NC values of the watermarked image attacked
by cropping with a cropping ratio of 50% and scaling with a scaling ratio of 400%. The results show
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that the presented algorithm can against both the cropping and zooming attacks. As a whole, the
Algorithm [13]
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presented watermarking algorithm can meet the requirements of robustness better.
Algorithm [21]
0.9
0.7
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NC vlaue
0.8
Presented Algorithm
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1
Algorithm [23]
0.6
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0.5 0.4 0.3
Cropping (50%)
Zoom in (400%)
Fig. 10 The comparison of NC value between various algorithms after cropping and zoom in attacks.
In order to estimate performance of robustness of the presented watermarking algorithm accurately, the comparison of the mentioned algorithms’ average NC values in Figs. 7-10 are given 22
by Fig. 11. As we can see from Fig. 11, the values of average NC of these mentioned algorithms are 0.7694, 0.9423, 0.7156, and 0.9430, respectively. Comparing with other algorithms, the average NC value of the presented algorithm is the highest. These results show that the robustness of the presented algorithm is better than other relevant algorithms [13], [21], and [23].
1 0.9430
0.9423
0.95
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0.9
NC value
0.85 0.8
0.7694
0.75
0.7156
0.65 0.6 Algorithm [21]
Algorithm [23]
Presented Algorithm
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Algorithm [13]
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0.7
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Fig. 11 The average NC of different algorithms after various attacks.
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4.3 The security analysis
In order to improve the security and robust performance of watermarking algorithm, this
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paper divided the color watermark image into red, green, and blue layered watermark images, and then using Arnold transformation with private key Kai to scrambe the layered watermark images.
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The key Kai is decided by integer number, and the integer number range is 1-32767, so the length of every layered key Kai is 15, in other word, the key space of every layered key Kai is 215. Therefore, for the color digital watermark, its key space is 245. In addition, the pseudo-random sequences generated by the randperm function based on the keys Kbi and Kci are used to choose the embedding block of the color carrier image, the key Kbi 23
and the key Kci are determined by two integers respectively. Since the key space of each factor determined by integer is 215. Therefore the key space of Kbi is 230 which is as same as the key space of Kci. Thus, the key space of the embedding block includes the key space of red, green and blue three layers is 2180. Thus, the key space of this watermarking algorithm determined by the key Kai, Kbi and Kci is
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2225, and the presented algorithm has higher security.
4.4 The embedding capacity analysis
We calculated maximum embedding capacity of our presented watermarking algorithm and
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other relevant watermarking algorithms to compare the watermark embedding capacity of them.
Usually, the embedded watermark bits and the pixels number of carrier image are used to calculate
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the embedding capacity. The embedding capacities of the mentioned algorithms are shown in Table
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4. In the presented algorithm, the color watermark image which size is 32×32 was embedded into the color carrier image which size is 512×512, therefore the maximum embedding capacity of the
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presented algorithm can be calculate by dividing the watermark length by the number of carrier image pixels. As we can see from Table 4, the maximum embedding capacity of this presented
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algorithm is equal to algorithms [21] and [23]. Algorithm [13] embedded eight watermark bits in
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one image block. In detail, it embedded one watermark bit to direct component (DC) coefficient and embedded seven watermark bits to the altering components (AC) coefficients at the same time. Moreover, the size of its color digital watermark is 64×64. Thus, the embedding capacity of algorithm [13] is bigger than other algorithms.
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Table 4 The result of maximum embedding capacity of various algorithms Algorithm
Watermark image (Bit)
Carrier image (Pixel)
Bit/Pixel
Algorithm [13]
98304
786432
0.12500
Algorithm [21]
24576
786432
0.03125
Algorithm [23]
24576
786432
0.03125
Presented Algorithm
24576
786432
0.03125
5 Conclusion
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A new image blind watermarking algorithm based on two-dimensional Discrete Cosine Transform (2D-DCT) is presented for protecting the digital color image copyright in this paper. This method selects four pairs of middle-frequency coefficients from the pixel block after 2D-DCT, and
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completes the embedding watermark and extracting watermark by modifying the size relationship between the selected middle-frequency coefficients. Moreover, the carrier image and watermark
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image used in this method are both color images. As can be seen from simulation results, this
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presented watermarking algorithm not only has good invisibility, but also has strong robustness, high security and large embedded capacity, which is suitable for digital image copyright protection
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with color logo of company in the future. In detail, this novel watermarking algorithm can embed the registered color trademark of company into the protected color digital image, which has an
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important value in terms of application and can be implemented in the industry of digital image
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copyright protection in the near future.
Declaration of interest statement The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work report in this paper.
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Acknowledgements The research was supported by the National Natural Science Foundations of China (No. 61771231, 61772253, 61872170, and 61873117), and the Key Research and Development
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Program of Shandong Province (No. 2019GGX101025, 2019GGX101032).
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https://doi.org/10.1109/TIP.2003.819861. [23] N. E. H. Golea, R. Seghir, R. Benzid, A bind RGB color image watermarking based on singular value decomposition, in: IEEE/ACS International Conference on Computer Systems and Applications (AICCSA), 2010, pp. 1–5, https://doi.org/10.1109/AICCSA.2010.5586967. [24] A. A. Attari, A. A. B. Shirazi, Robust audio watermarking algorithm based on DWT using Fibonacci numbers, Multimedia Tools & Applications 77 (19) (2018) 25607-25627,
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PII:
S0030-4026(19)32051-0
DOI:
https://doi.org/10.1016/j.ijleo.2019.164152
Reference:
IJLEO 164152
To appear in:
Optik
Received Date:
25 October 2019
Revised Date:
18 December 2019
Accepted Date:
28 December 2019
Please cite this article as: Yuan Z, Liu D, Zhang X, Su Q, New image blind watermarking method based on two-dimensional Discrete Cosine Transform, Optik (2019), doi: https://doi.org/10.1016/j.ijleo.2019.164152
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New image blind watermarking method based on two-dimensional Discrete Cosine Transform
Zihan Yuan1, Decheng Liu1, Xueting Zhang1, Qingtang Su1* [email protected] 1 School
of Information and Electrical Engineering, Ludong University, Yantai 264025, China
*
Corresponding author: Tel.: +86-535-6672343 , (Qingtang Su)
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Highlights
The size relationship between the selected middle frequency coefficients of 2D-DCT is used to embed and extract watermark information;
Comparing with traditional algorithms which are based on DCT, the watermark capacity of this algorithm is larger;
The proposed algorithm is a blind watermarking algorithm, and the original data or original watermark is not needed in the process of watermark extraction;
Comparing with other relevant algorithm, the proposed algorithm has higher invisibility and stronger robustness, which is suitable for digital image copyright protection.
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Abstract: In this paper, a new image blind watermarking method based on two-dimensional Discrete
Cosine Transform (2D-DCT) is presented to realize copyright protection of color image. At first,
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2D-DCT is performed on the selected image blocks, and some fixed coefficients in the middle
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frequency are selected as embedding position of watermark. Then, the watermark embedding and extraction procedure are completed by modifying the relationship of size between the selected middle-frequency coefficients with the proposed rules. The advantages of the presented algorithm include the following two points: 1) the relationship of size between the selected middle-frequency coefficients of 2D-DCT is used to fulfill the process of watermark embedding and extraction; 2) the presented algorithm uses color digital image as carrier image and watermark image, which is not 1
same as most watermarking techniques. In recent years, most of the watermarking algorithms used gray or binary image as watermark. In this presented algorithm, all the digital carrier images are chosen from two public standard image databases, i.e. CVG-UGR and USC-SIPI. A series of simulation results prove that this presented algorithm not only satisfies the invisibility of watermarking algorithm, but also makes good performance of robustness, security and embedding capacity.
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Keywords: Blind watermarking; Color image; Discrete Cosine Transform; Frequency domain
1 Introduction
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In recent years, as the rapid advancement of the multimedia and Internet, we can obtain more
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required information accurately and efficiently, and many achievements and creations are stored and
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published on the Internet in the form of digit, but it also produced a series of serious problems, such as piracy, infringement, tampering, and so on. Therefore, the protection of intellectual property and
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copyright is extremely urgent [1]-[4], and digital watermarking technology emerges at the historic moment [5]. It is well known that digital watermarking is an important branch of information hiding
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technology [6], which uses data redundancy or visual redundancy of the digital multimedia to embed the digital watermark into the digital multimedia directly by some certain embedding methods. The
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successful embedding and extraction of digital watermarks can effectively solve the problem of protecting copyright. According to the difference of carrier image processing ways, digital watermarking algorithms are divided into the spatial-domain watermarking algorithm [7, 8] and frequency-domain watermarking algorithm [5, 9, 16]. The spatial-domain watermarking algorithm 2
refers to modify the image pixel value directly in order to embed watermark information. Spatial-domain watermarking algorithm is simple and efficient in execution, but its robustness is relatively weak. For example, Abraham et al. [7] presented a novel color image watermarking algorithm using spatial-domain technique, and generated a watermarked image with excellent quality. Furthermore, the frequency-domain watermarking algorithms embed watermark information in frequency-domain coefficients, which makes good use of the human vision,
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auditory and other characteristics. This watermarking method has good robustness, but its
calculation is more complex. The frequency-domain watermarking algorithms often use Discrete Wavelet Transform (DWT) [10, 15, 24], Discrete Cosine Transform (DCT) [9, 12, 13, 16],
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Discrete Fourier Transform (DFT) [11, 21], and matrix factorization [5, 14, 19, 20, 23] and so on.
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than the spatial watermarking method [13].
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In a word, the watermarking method in frequency domain has better invisibility and robustness
Therefore, considering the invisibility and robustness of watermark, many watermarking
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algorithms based on the frequency domain have been presented to protect the copyright over the years. For instance, Ernawan et al. [9] presented a DCT-based digital image watermarking method
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which used the best psychovisual threshold. The watermark information was not embedded to the DCT coefficients directly as other watermarking methods. In this algorithm, the watermark
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information was embedded by modifying the correlation coefficients based on specific rules. This watermarking algorithm has better robustness and invisibility. However, the used carrier image is gray-scale image [16], and the used watermark image is binary image in this method. As we all know, digital color images are more vivid, bright and informative, and its utilization rate far exceeds that of gray-scale images. 3
Pradhan et al. [10] proposed a non-blind digital watermarking algorithm using DWT and cross chaos. This method belongs to non-blind watermarking algorithm since the original data is needed in watermark extraction process. Nevertheless, in practice, obtaining the primary data is not easy when detecting watermark in most cases. Therefore, non-blind watermarking method has certain defects, and blind watermarking method has more practical value and application prospect. Hence, Roy et al. [12] proposed a blind DCT-based watermarking scheme which can embed
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multiple watermark images. This watermarking scheme can extract the watermark information without the need of original data, so it belongs to blind watermarking scheme. In addition, the watermarking scheme embedded multiple watermark information into middle-frequency
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coefficients based on zig-zag order, and it has high robustness. This method can against common
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image processing attacks mainly include image enhancement such as low-pass filtering, median
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filtering, image sharpening, adding noise; geometric processing such as rotation, cropping, scaling; and compression attacks such as JPEG compression, JPEG2000 compression. But, it is needed to
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modify 22 coefficients of middle-frequency of DCT in [12] so each image block can embed 11 watermark bits. Therefore, the quality of watermarked image was seriously distorted. Su et al. [13]
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presented a digital watermarking algorithm; this watermarking algorithm embedded the digital color watermark into carrier image successfully, which could resist many common attacks.
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However, the algorithm requires two times operations of two-dimensional Discrete Cosine Transform (2D-DCT), so the computational complexity is high. Song et al. [19] proposed a robust digital image watermarking scheme which is using the QR decomposition and chaotic system, this method has excellent robustness and it can resist a variety of attacks. However, as we all know, the number and magnitude of modified pixel values can directly affect the watermark invisibility. 4
Since the pixel values are modified extensively during the watermark embedding process in [19], its invisibility performance is not good. The requirements of a good digital watermark include invisibility, robustness, security, watermark capacity, blind extraction and so on. However, many watermarking techniques still cannot meet these requirements better. Therefore, how to devise a blind watermarking technology for meeting the requirements of robustness, invisibility, and security has become a hot research
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topic.
A color digital image blind watermarking algorithm based on 2D-DCT is proposed in this
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paper. This presented algorithm selects the special middle coefficients of image blocks after
2D-DCT, and modifies the size relationship between the selected middle coefficients to fulfill the
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watermark embedding and extracting process. At first, dividing the carrier image and color
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watermark image into red, green and blue three color layers; then, dividing each layer of the watermark image into non-overlapping pixel blocks. Afterwards, the block to be embedded of
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color carrier image is selected by pseudo-random sequence and transformed by 2D-DCT, and then embedding the scrambled watermark into the specific position of the DCT coefficients following
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zig-zag order. This presented watermarking algorithm has better performance on watermark
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invisibility and robustness, which is suitable for digital image copyright protection.
The remainder of this paper is organized as follows: the relevant knowledge is described in
part 2, which includes Arnold scrambling transformation, randperm function and 2D-DCT. Part 3 shows the process of watermark embedding and watermark extraction. Part 4 shows simulation attacks result and analysis. At last, the conclusion is given in part 5.
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2 Preliminaries
2.1 Arnold scrambling transformation Arnold scrambling transformation is usually used as pretreatment of information hiding. The digital watermark is scrambled before watermark embedding, which can greatly improve the watermarking security. Therefore, Arnold scrambling transformation is widely used in the
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scrambling of watermark image to ensure watermarking algorithm security. Arnold scrambling transformation is defined as follows: u ' 1 1 u mod P . v ' 1 2 v
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(1)
where, u, v, u', v' ∈{0, 1, 2,…, P-1}, P is the size of the watermark image to be scrambled, (u, v)
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is the position of pixel in watermark image before scrambling, (u', v') is the position of pixel in
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watermark image after scrambling. Arnold transformation can move the pixel value of digital watermark image from the original position (u, v) to the new position (u', v').
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Using Arnold transformation to scramble the original watermark image can realize the hiding of image information. The scrambling times can be used as the private key Kai, which can
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strengthen the confidentiality and security of the watermarking scheme.
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Correspondingly, for restoring the original watermark image, the corresponding inverse Arnold scrambling transformation is as follows: u 2 1 u ' P mod P. v 1 1 v ' P
2.2 Randperm function 6
(2)
For improving the security of watermarking algorithm, we use the randperm function to choose the non-overlapping blocks randomly for embedding watermark information. Randperm function, as a build-in function in MATLAB, can scramble a number sequence randomly. For example, randperm(n, m) means select m numbers from {1, 2,…, n} randomly, where n is greater than m, and m, n is often viewed as the private key. Therefore, we reuse the randperm function twice time to generate two random sequences to select the non-overlapping embedded block
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randomly.
2.3 Two-dimensional discrete cosine transform (2D-DCT)
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Discrete Cosine Transform (DCT), as a widely used signal decomposition and compression
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technique, is mainly used for data compression and image compression. DCT can convert the signal from the spatial domain to the frequency domain, which has better performance of
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de-correlation. DCT is a special case of the Fourier transform, which avoids the complex operation in the Fourier transform, and it is a transform in real number domain.
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After applying DCT to an image, its coefficients can be divided into a direct component (DC)
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and some altering components (AC). The DC component represents the average brightness, and the AC components concentrate the main energy of the original image block. DCT algorithm has
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the advantages of high speed and accuracy. Therefore, DCT plays a vital role in image processing.
Two-dimensional Discrete Cosine Transform (2D-DCT) means to perform DCT again based
on the one-dimensional DCT. After performing 2D-DCT, the DCT coefficients of matrix A of sized M×N are obtained by Eq. (3):
7
M 1 N 1 (2 x 1)u (2 y 1)v F (u, v) c(u )c(v) f ( x, y) cos cos . 2M 2N x 0 y 0
(3)
among them, v 0 1 N c (v ) = . 2 N v 1, 2,..., N 1 u 0 1 M c(u ) = . 2 M u 1, 2,..., M 1
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x and y are the sampling values in spatial domain, and f(x, y) is the pixel value at position (x, y) in spatial domain correspondingly, u and v are the sampling values in frequency domain, and F(u, v)
is the frequency coefficient at position (u, v) after 2D-DCT in frequency domain correspondingly.
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When used in digital image processing, digital image is usually represented by square pixel matrix,
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that is M=N.
The formula of inverse transform of 2D-DCT (2D-IDCT) is given as follows: (4)
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3 Proposed method
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(2 x 1)u (2 y 1)v M 1 N 1 f ( x, y) c(u )c(v) F (u, v) cos cos . 2M 2N u 0 v 0
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The implementation of the presented watermarking algorithm includes into two processes that
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are watermark embedding and watermark extracting. Specific steps of watermark embedding and watermark extracting are described below.
3.1 Process of watermark embedding The specific steps of watermark embedding process are shown in Fig. 1.
8
Pre-processing the carrier image
Pre-processing the watermark image
Key Kc
Key Kb
Key Ka Selecting the embedded block of the carrier image Getting binary watermark sequence Selecting the specific middle frequency coefficients of the pixel block
Obtaining the watermarked pixel block
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Obtaining the watermarked image
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Updating the block of watermarked pixels to corresponding position
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Modifying the size relation between middle frequency coefficient pairs
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Fig. 1 The diagram of watermark embedding process.
Step1: Preprocessing of the color carrier image and color watermark image.
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At first, dividing the color carrier image H which size is M×M into three layer carrier images Hi of red (R), green (G), and blue (B) color, and then dividing each layered image Hi into
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non-overlapping pixel blocks which size is 8×8. Secondly, dividing the watermark image which size
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is N×N into three layer watermark images Wi of R, G, and B color. Then scrambling each layered watermark image Wi using Arnold transformation which is based on the key Kai to enhance the security of watermarking algorithm, transforming all pixel value with decimal format to binary information. Afterwards, all the binary information is connected to form the watermark bit sequences SWi. The length of sequence SWi is 8N2, where i = 1, 2, 3, and it is the R, G, and B three layer images, respectively. 9
Step 2: Choosing the embedded pixel block from color carrier image. The pseudo-random sequences generated by randperm function based on the key Kbi and Kci are used to generate two random numbers that are the row and column coordinates of the pixel block to be embedded, then the pixel block A is selected from the layer carrier image Hi, where i =1, 2, 3, and it is the R, G, and B three layer images. Step 3: Selecting the specific middle-frequency coefficients of the pixel block after
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two-dimensional Discrete Cosine Transform (2D-DCT).
According to Eq. (5), 2D-DCT is carried out on the chosen pixel block A for obtaining the
transformation matrix dctA, and four pairs of DCT middle-frequency coefficients (cp1, cp2) of the
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transformation matrix dctA are selected by the zig-zag order, p =1, 2, 3, 4, respectively:
dctA dct2( A).
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(5)
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where, dct2 (.) is the DCT function, the selected four pairs of DCT middle-frequency coefficients have their fixed positions, which are position (4, 2) and (3, 3), (2, 4) and (1, 5), (4, 3) and (3, 4), (2,
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5) and (1, 6).
Step 4: Modifying the size relation between DCT middle-frequency coefficient pairs.
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Selecting four watermark bits wp from SWi successively and using Eq. (6) and Eq. (7) to modify the size relation between DCT middle-frequency coefficient pairs (cp1, cp2) for embedding the
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watermark bit wp, where p =1, 2, 3, 4, respectively. The modified DCT middle-frequency coefficient pairs (cp1*, cp2*) are obtained as follow:
signc (c p1 ) (avg 0.3 T ), if w '1' and abs (c p 2 ) abs (c p1 ) T * c p1 = signc (c p1 ) ( avg 0.7 T ), if w '0 ' and abs (c p1 ) abs (c p 2 ) T . c ， else p1
10
(6)
if w '1' and abs (c p 2 ) abs (c p1 ) T signc (c p 2 ) (avg 0.7 T )， * c p 2 = signc (c p 2 ) ( avg 0.3 T )，if w '0 ' and abs (c p1 ) abs (c p 2 ) T c ， else p2
.
(7)
where, signc (.) is defined as below: sign( x), signc( x) 1,
if x 0 else
.
where, sign (.) is sign function, avg=(abs(cp1)+abs(cp2))/2, abs(.) is absolute value function, T is the quantization step of this presented algorithm.
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Step 5: Embedding watermark.
Replacing the original DCT middle-frequency coefficient pairs (cp1, cp2) with the modified
DCT middle-frequency coefficient pairs (cp1*, cp2*) to obtain the watermarked transformation matrix
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dctA*, where p =1, 2, 3, 4, and it is the p-th pair of DCT middle-frequency coefficient, respectively.
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Step 6: Updating the block of watermarked pixels to the corresponding locations of the layered
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carrier image.
According to Eq. (8), inverse transform of 2D-DCT (2D-IDCT) is performed on the
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watermarked transformation matrix dctA* to obtain the watermarked pixel block A*, and the watermarked pixel block A* are updated to their corresponding locations of the layered carrier image
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Hi, where i =1, 2, 3, and it is the R, G, and B three layer images, respectively:
A* idct2(dctA* ).
(8)
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where idct2 (.) is the inverse 2D-DCT function. Step 7: Repeating. The steps 2 to 6 are repeated until embedding all the watermark information, and the layered watermarked image Hi* is obtained. At last, the layered watermarked images Hi* are combined to get final watermarked image H*, where i =1, 2, 3, and it is the R, G, and B three layer images. 11
3.2 Process of watermark extraction Since this presented algorithm is belong to blind watermarking algorithm, in the watermark extraction process, watermark information can be extracted from final watermarked image H* and doesn’t need the original data. The specific steps of watermark extraction are given in Fig. 2. Pre-processing the watermarked image
Obtaining the extraction block of the watermarked image
Key Kc
Selecting the middle frequency coefficients of watermarked pixel block
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Key Ka
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Extracting watermark bit
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Key Kb
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Getting binary watermark sequence
Obtaining the extracted watermark
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Fig. 2 The diagram of the process of watermark extraction.
Step 1: Preprocessing of obtained watermarked image.
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At first, dividing watermarked image H* into three layered images Hi* of R, G, and B color. At the same time, dividing each layered image Hi* into non-overlapping pixel blocks which size is
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8×8, where i =1, 2, 3, and it is the R, G, and B three layers, respectively. Step 2: Obtaining extracted block from the watermarked image. Using pseudo-random sequences generated by randperm function with the key Kbi and Kci to choose the pixel block A* from the layered watermarked image Hi*, where i =1, 2, 3, and it is respectively the R, G, and B three layers. 12
Step 3: Selecting the specific middle-frequency coefficients from the chosen watermarked pixel block after two-dimensional Discrete Cosine Transform (2D-DCT). Applying 2D-DCT to the watermarked pixel block A* in order to obtain the transformation matrix dctA*. Four pairs of DCT middle-frequency coefficients (cp1*, cp2*) corresponding to the embedding process are selected following zig-zag order in the transformation matrix dctA*, where p
Step 4: Extracting watermark bit.
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=1, 2, 3, 4, and it is the p-th pair of the DCT middle-frequency coefficient, respectively.
According to the size relation between DCT middle-frequency coefficient pairs (cp1*, cp2*), the watermark bit is extracted from the watermarked block by Eq. (9):
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abs(c p1 ) abs(c p 2 ) '1', if wp * . '0', else
(9)
Step 5: Repeating.
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middle-frequency coefficients, respectively.
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where, abs(.) is absolute value function, p =1, 2, 3, 4, and it is the p-th pair of the DCT
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The steps 2 to 4 are repeated to get the binary extraction watermark sequence SWi* of each layer watermarked image Hi*, dividing each 8-bit binary information in the watermark bit sequences
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SWi* into a group, converting it to decimal pixel values, and getting the decimal sequence, where i
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=1, 2, 3, and it is respectively the R, G, and B layer. Step 6: Obtain final extracted watermark. Using inverse Arnold transform which is based on key Kai on the decimal pixel sequence of
three layers respectively to get the extracted layered watermark Wi*. At last, the extracted layered watermark Wi* is recombined to get the final extracted watermark W*, where i =1, 2, 3, and it is the R, G, and B layer, respectively. 13
4 Experimental results
For testing the performance in terms of invisibility, robustness, security, and embedding capacity of the presented algorithm, ten color digital images of sized 512×512 given in Figs. 3(a)-(j) are selected as the carrier images in this paper. All the carrier images are chosen from two public standard image databases, that is CVG-UGR [17] and USC-SIPI [18]. Two color digital images of
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sized 32×32 given in Figs. 4(a)-(b) are selected as digital watermark images. Then the selected images are used in a series of experiments, and the presented algorithm is compared to some
relevant methods. For example, a color digital image watermarking method based on two times
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operations of two-dimensional Discrete Cosine Transform (2D-DCT) [13], a robust digital image
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watermarking method using chaotic system and QR decomposition [19], and a novel fast and robust spatial-domain watermarking algorithm [21]. The presented algorithm is frequency-domain
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watermarking method based on 2D-DCT in this paper. So, we selected algorithms [13] and [19] as comparative method, because the algorithm [13] is also used 2D-DCT to complete the operations
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of watermark embedding and extraction, and algorithm [19] is also a frequency-domain
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watermarking algorithm. In addition, in order to prove the presented watermarking algorithm has better performance compared with the spatial-domain watermarking algorithm, the algorithm [21]
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is also selected as comparative method.
14
(a)
(b)
(c)
(f)
(d)
(g)
(e)
(h)
(i)
(j)
Fig. 3 Carrier images: (a) Lena, (b) Peppers, (c) Kid, (d) SailBoat, (e) Baboon, (f) Bear, (g) Barbara, (h) Couple,
(a)
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(i) Avion, and (j) House.
(b)
Fig. 4 Watermark images: (a) watermark 1, and (b) watermark 2.
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The imperceptibility and robustness performance of the presented watermarking algorithm are
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evaluated by specific performance indexes in following experiments. For example, peak
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signal-to-noise ratio (PSNR) is an important objective evaluation index of watermarked image distortion measurement, is usually used to calculate the similarity between the original carrier image and watermarked image. It can be defined as follows: M N max{[ H (u, v, j )]2 }
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PSNR j 10 lg
M
N
[ H (u, v, j) H * (u, v, j)]2
.
(10)
u 1 v 1
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among them, H (u, v, j ) , H * (u, v, j ) are the pixels whose coordinates are (u, v) in layer j of
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original carrier image and the watermarked one, M, N are respectively the row and column size of the test image. The PSNR of color image is defined by: (11)
3
PSNR PSNR j . j 1
Due to the specific structure of natural signals and the strong interrelationship between pixels, a new evaluation standard, i.e. structural similarity index measurement (SSIM), is proposed from the 15
perspective of human visual system [22]. The value of SSIM can measure the image quality effectively, and it is defined as follows: SSIM ( H , H * ) l ( H , H * )c( H , H * ) s( H , H * ).
(12)
where, l ( H , H * ) (2 H H * C1 ) ( H2 H2 * C1 ) * 2 2 . c( H , H ) (2 H H * C2 ) ( H H * C2 ) * s( H , H ) ( HH * C3 ) ( H H * C3 )
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l ( H , H * ) , c( H , H * ) and s( H , H * ) is the luminance comparison, contrast comparison and structure
comparison function, respectively.
In addition, as an evaluation criterion, normalized cross-correlation (NC) can estimate the
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robustness of watermarking algorithm effectively. As for color digital watermark, Eq. (13) is used to
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calculate the NC value in order to evaluate the robustness of the watermarking algorithm. The
3
NC
m
n
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calculation of NC is defined as follows:
(W (u, v, j ) W * (u, v, j)) j 1 u 1 v 1
3
m
n
3
m
n
W (u, v, j) W 2
j 1 u 1 v 1
(u, v, j )
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j 1 u 1 v 1
*
(13)
.
2
where W* is extracted color digital watermark, and W is original digital watermark, 1
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m and n represent the row and column size of color digital watermark respectively, j represents the
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j-th layer of color digital watermark.
16
the value of SSIM/NC
SSIM
NC
1 0.98 0.96 0.94 0.92 0.9 0.88 0.86 0.84 0.82 0.8 16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
quantization step
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Fig. 5 The average values of structural similarity index measurement (SSIM) and normalized cross-correlation (NC) under different quantization steps.
As we all know, the quantization step T is an important parameter. In order to select an
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effective quantization step, we did many experiments. Embedding the color image watermarks as shown in Figs. 4(a) and (b) into the carrier images as shown in Figs. 3(a)-(j) with different
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quantization steps. The experimental results are shown in Fig. 5. SSIM becomes smaller and smaller
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and NC becomes bigger and bigger while the quantization step T is adding, which indicates that the invisibility of watermark becomes worse and worse, while the robustness of watermark becomes
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better and better. Thus, in order to have a good performance in robustness and invisibility
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simultaneously, we choose the quantization step T as 23 in this paper.
4.1 The imperceptibility test and analysis
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The invisibility of digital watermark is the ability that hiding the digital watermark information
in the carrier image. As an effective watermarking algorithm, the invisibility requires the embedded digital watermark cannot be detected by human perception system. The invisibility is an important character of watermarking algorithm. Table 1 shows the value of peak signal-to-noise ratio (PSNR) and structural similarity index measurement (SSIM) of the extracted watermark 17
images after embedding the watermark images in Figs. 4(a) and (b) to the carrier images in Figs. 3 (a)-(j), respectively. Table 1 The invisibility results (PSNR/SSIM) of embedding test watermark images into carrier images watermark 2
Lena
37.5851/0.9350
37.4625/0.9323
Peppers
38.0702/0.9241
38.1277/0.9250
Kid
37.4801/0.9242
37.6455/0.9250
SailBoat
38.1685/0.9403
38.4066/0.9414
Baboon
36.3189/0.9725
36.1885/0.9724
Bear
38.0001/0.9441
38.0903/0.9448
Barbara
37.3726/0.9385
37.4858/0.9395
Couple
38.2239/0.9193
38.2255/0.9196
Avion
37.1426/0.9245
37.2966/0.9255
House
38.2472/0.9149
38.3659/0.9154
Average
37.6609/0.9337
37.7295/0.9341
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watermark 1
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From Table 1 we can see that when watermarks 1 and 2 are respectively embedded into
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different carrier images, the values of PSNR are greater than 36dB, and the values of SSIM are close to 1. This indicates that the watermark is imperceptible through the human visual system after
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embedding watermark information into carrier image. It is proved that the presented watermarking algorithm has good performance of invisibility.
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For comparing the invisibility of this presented watermarking algorithm with other watermarking algorithms, the digital watermark 1 in Fig. 4(a) is respectively embedded into two
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carrier images in Figs. 3(a) and (b), the digital watermark 2 in Fig. 4(b) is respectively embedded
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into two carrier images in Figs. 3(c) and (d) . After embedding the selected watermarks to the color carrier images, the PSNR and SSIM values of different algorithms are shown as Table 2. NC values of different algorithms without the attack are given as Table 3. As can be seen from Table 2, algorithm [13] is a two-level two-dimensional Discrete Cosine Transform (2D-DCT) watermarking algorithm, while the presented algorithm is a one-level 2D-DCT algorithm. Therefore, we select the one-level 2D-DCT part of algorithm [13] for comparing with this paper. Although algorithm [13] 18
has high PSNR and SSIM, which indicated it has high watermark invisibility, as we can see in Table 3, its normalized cross-correlation (NC) is small that means its robustness is weak. On the contrary, in algorithm [19], the PSNR values and SSIM values are much smaller than other algorithms, which mean its invisibility is weak but its robustness is very strong. Because of that, the algorithm [19] is not used as comparison in the analysis of robustness. Good balance between the performance of invisibility and robustness is achieved and satisfies the requirements of the invisibility and
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robustness in the presented watermarking algorithm. As shown in Table 2, the values of PSNR are greater than 37dB, the values of SSIM are close to 1. The experimental result indicates that the presented algorithm has better performance of invisibility.
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Table 2 The invisible comparison results for (PSNR/SSIM) of various watermarking algorithms Algorithm [19]
Algorithm [21]
Algorithm [23]
Lena
48.6761/0.9956
22.5616/0.6332
38.0535/0.9414
39.4385/0.9656 37.5851/0.9350
Peppers
40.7425/0.9708
23.2864/0.7111
37.6262/0.9231
38.3367/0.9299 38.0702/0.9241
Kid
41.6958/0.9857
22.3026/0.6846
36.8241/0.9231
34.4638/0.8650 37.6455/0.9250
SailBoat
45.7757/0.9933
18.7103/0.6301
37.7440/0.9458
34.2340/0.8766 38.4066/0.9414
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Algorithm [13]
Presented Algorithm
Table 3 The compare results for NC values of various watermarking algorithms Algorithm [13]
Algorithm [19] Algorithm [21]
Algorithm [23]
Presented Algorithm
1.0000
1.0000
0.9937
1.0000
0.9475
Peppers
0.8568
0.9975
1.0000
0.9826
1.0000
Kid
0.8441
1.0000
1.0000
0.9771
0.9997
SailBoat
0.8746
1.0000
1.0000
0.9817
1.0000
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Lena
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4.2 The robustness test and analysis The robustness of digital watermark refers to the digital watermarking algorithm has the ability
to resist various linear and nonlinear filtering operations, common geometric transformations and other common transformations attacks. The robustness of watermark is also one of the important characteristics of watermarking technology. In this part, for measuring robustness of the presented watermarking algorithm, a series of 19
simulation attacks are preceded, such as JPEG compression, adding noise, filtering, scaling, cropping. As we all know, as an objective similarity measure of the final extracted watermark W* and original watermark W, normalized cross-correlation (NC) value is used to estimate the robustness of watermarking algorithm effectively. After a serious of attacks, watermarks were extracted from watermarked image namely “Lena” and “Peppers”. Fig. 6 shows the visual effect of extracted watermarks and its NC values under various attacks respectively.
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For proving the robustness of this algorithm further, we embedded the watermarks in Fig. 4(a) and (b) to carrier digital image “Lena” in Fig. 3(a) and carried out a series of attacks and compared with other relevant algorithms [13], [21], [23]. The simulation results are given in Figs. 7-10. Salt &
Butterworth
Peppers
low-pass
Attack
JPEG 2000 JPEG (40)
Median
white noise (5:1)
Cropping
Zoom-in
(25%)
(4:1)
filtering
noise (0, 0.001)
filtering
(3×3)
(0.2%)
(100, 5)
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Watermark
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Gaussian
0.9929
0.9999
0.9714
0.9351
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Fig.3 (b)
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Fig.3 (a)
0.9997
0.8590
0.9755
0.8199
0.9737
0.8456
0.9999
0.9643
0.8502
0.9451
0.9615
0.9999
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Fig. 6 Extract the watermarks from the watermarked image “Lena” after various attacks and their NC values
Image compression is a common processing method, and JPEG compression attack and JPEG
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2000 compression attack are effective methods to measure the robustness of watermarking schemes. Fig. 7 shows the experimental results of watermarked images after image compression attacks on JPEG and JPEG 2000. As shown in Fig. 7 that this presented algorithm has better robustness compared with other watermarking algorithms and it can resist different image compression attacks.
20
Algorithm [13] 1
Algorithm [21]
Algorithm [23]
Presented Algorithm
0.9
NC value
0.8 0.7 0.6 0.5 0.4 0.3 JPEG 60
JPEG 2000 (4：1)
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Fig. 7 The comparison of NC value between various algorithms after compression attacks.
Then, Fig. 8 gives the experimental results after Salt & Peppers noising attack with a noise
intensity of 0.2% and Gaussian noise with a variance of 0.001. As Fig. 8 shows that the presented
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algorithm has stronger robustness than other compared algorithms relatively in terms of resisting
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different noise attacks. Fig. 9 gives the experimental results after median filtering attack and
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Butterworth low-pass filtering attacks. The median filtering attack which window size is 3×3 and the Butterworth low-pass filtering attack which filter order is 10 are respectively carried out on the
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watermarked images. It is indicated that this presented watermarking algorithm can effectively against the filtering attacks. Algorithm [13]
Algorithm [23]
Presented Algorithm
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1
Algorithm [21]
0.9
NC value
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0.8 0.7 0.6 0.5 0.4 0.3
Salt & Peppers noise (0.002)
Gaussian noise (0,0.001)
Fig. 8 The comparison of NC value between various algorithms after noising attacks. 21
Algorithm [13]
Algorithm [21]
Algorithm [23]
Presented Algorithm
1 0.9 0.8 0.7
NC value
0.6 0.5 0.4 0.3 0.2 0.1 0 Median filtering (3×3)
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Butterworth low-pass filtering (100,10)
Fig. 9 The comparison of NC value between various algorithms after filtering attacks.
In addition, image cropping and zooming are the common image geometric attack and will
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directly affect the image quality. Fig. 10 givens the NC values of the watermarked image attacked
by cropping with a cropping ratio of 50% and scaling with a scaling ratio of 400%. The results show
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that the presented algorithm can against both the cropping and zooming attacks. As a whole, the
Algorithm [13]
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presented watermarking algorithm can meet the requirements of robustness better.
Algorithm [21]
0.9
0.7
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NC vlaue
0.8
Presented Algorithm
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1
Algorithm [23]
0.6
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0.5 0.4 0.3
Cropping (50%)
Zoom in (400%)
Fig. 10 The comparison of NC value between various algorithms after cropping and zoom in attacks.
In order to estimate performance of robustness of the presented watermarking algorithm accurately, the comparison of the mentioned algorithms’ average NC values in Figs. 7-10 are given 22
by Fig. 11. As we can see from Fig. 11, the values of average NC of these mentioned algorithms are 0.7694, 0.9423, 0.7156, and 0.9430, respectively. Comparing with other algorithms, the average NC value of the presented algorithm is the highest. These results show that the robustness of the presented algorithm is better than other relevant algorithms [13], [21], and [23].
1 0.9430
0.9423
0.95
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0.9
NC value
0.85 0.8
0.7694
0.75
0.7156
0.65 0.6 Algorithm [21]
Algorithm [23]
Presented Algorithm
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Algorithm [13]
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0.7
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Fig. 11 The average NC of different algorithms after various attacks.
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4.3 The security analysis
In order to improve the security and robust performance of watermarking algorithm, this
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paper divided the color watermark image into red, green, and blue layered watermark images, and then using Arnold transformation with private key Kai to scrambe the layered watermark images.
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The key Kai is decided by integer number, and the integer number range is 1-32767, so the length of every layered key Kai is 15, in other word, the key space of every layered key Kai is 215. Therefore, for the color digital watermark, its key space is 245. In addition, the pseudo-random sequences generated by the randperm function based on the keys Kbi and Kci are used to choose the embedding block of the color carrier image, the key Kbi 23
and the key Kci are determined by two integers respectively. Since the key space of each factor determined by integer is 215. Therefore the key space of Kbi is 230 which is as same as the key space of Kci. Thus, the key space of the embedding block includes the key space of red, green and blue three layers is 2180. Thus, the key space of this watermarking algorithm determined by the key Kai, Kbi and Kci is
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2225, and the presented algorithm has higher security.
4.4 The embedding capacity analysis
We calculated maximum embedding capacity of our presented watermarking algorithm and
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other relevant watermarking algorithms to compare the watermark embedding capacity of them.
Usually, the embedded watermark bits and the pixels number of carrier image are used to calculate
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the embedding capacity. The embedding capacities of the mentioned algorithms are shown in Table
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4. In the presented algorithm, the color watermark image which size is 32×32 was embedded into the color carrier image which size is 512×512, therefore the maximum embedding capacity of the
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presented algorithm can be calculate by dividing the watermark length by the number of carrier image pixels. As we can see from Table 4, the maximum embedding capacity of this presented
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algorithm is equal to algorithms [21] and [23]. Algorithm [13] embedded eight watermark bits in
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one image block. In detail, it embedded one watermark bit to direct component (DC) coefficient and embedded seven watermark bits to the altering components (AC) coefficients at the same time. Moreover, the size of its color digital watermark is 64×64. Thus, the embedding capacity of algorithm [13] is bigger than other algorithms.
24
Table 4 The result of maximum embedding capacity of various algorithms Algorithm
Watermark image (Bit)
Carrier image (Pixel)
Bit/Pixel
Algorithm [13]
98304
786432
0.12500
Algorithm [21]
24576
786432
0.03125
Algorithm [23]
24576
786432
0.03125
Presented Algorithm
24576
786432
0.03125
5 Conclusion
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A new image blind watermarking algorithm based on two-dimensional Discrete Cosine Transform (2D-DCT) is presented for protecting the digital color image copyright in this paper. This method selects four pairs of middle-frequency coefficients from the pixel block after 2D-DCT, and
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completes the embedding watermark and extracting watermark by modifying the size relationship between the selected middle-frequency coefficients. Moreover, the carrier image and watermark
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image used in this method are both color images. As can be seen from simulation results, this
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presented watermarking algorithm not only has good invisibility, but also has strong robustness, high security and large embedded capacity, which is suitable for digital image copyright protection
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with color logo of company in the future. In detail, this novel watermarking algorithm can embed the registered color trademark of company into the protected color digital image, which has an
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important value in terms of application and can be implemented in the industry of digital image
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copyright protection in the near future.
Declaration of interest statement The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work report in this paper.
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Acknowledgements The research was supported by the National Natural Science Foundations of China (No. 61771231, 61772253, 61872170, and 61873117), and the Key Research and Development
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Program of Shandong Province (No. 2019GGX101025, 2019GGX101032).
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