- Email: [email protected]
A method of processing color image watermarking based on the Haar wavelet
J. Vis. Commun. Image R. 64 (2019) 102627
Contents lists available at ScienceDirect
J. Vis. Commun. Image R. journal homepage: www.elsevier.com/locate/jvci
A method of processing color image watermarking based on the Haar wavelet q Jianyu Wang, Zhiguo Du ⇑ College of Business and Commerce, Rongchang Campus, Southwest University of Chongqing, 402460, China
a r t i c l e
i n f o
Article history: Received 4 June 2019 Revised 26 August 2019 Accepted 26 August 2019 Available online 26 August 2019 Keywords: Color image watermarking Discrete Wavelet Transform (DWT)
a b s t r a c t Despite the fact that traditional digital watermarking technology is relatively mature, there are still some areas that have not been fully involved in. For example, image watermarking technology and the certification are still in its infancy at early times. The bottleneck problem of digital product safety protection all solved theoretically with the combination of computing theory as well as traditional digital watermarking technology and point out a new direction for the research of information security industry. Inspired by the traditional algorithm of image watermarking and based on the Haar wavelet function along with algorithm of 2-D discrete wavelet transform and selection, this article presents the techniques of watermark embedding and extraction of color images. The main appraisal criteria of the watermark include invisibility and robustness, and some other standards. Image watermarking is relatively simple in the spatial domain, where it cannot resist geometrical attacks. In the transform domain, this approach can resist both geometrical attacks and image processing attacks. Only when the carrier image suffers from severe damage with the image quality hugely compromised will the extracted watermark become unrecognizable. As a result, the algorithm presented in this article can well embed the color image in the carrier image, and has good resistance to attack operations such as loss compression and adding of noise. Ó 2019 Elsevier Inc. All rights reserved.
1. Introduction 1.1. Overview of the evolution of image watermarking technology Nowadays, digital information has become the mainstream of the era, and consequently protecting the copyright of such information becomes an urgent issue that needs to be tackled with more secure dissemination. Digital watermarking technology is widely used, such as copyright protection, medical image protection, legal evidence protection, inheritance certification, etc. These may be tampered or attacked in the process of transmission over the network or during the actual shipping process. Network and information security become an increasingly prominent issue in our daily lives. In this sense, digital watermarking technology is of vital importance. Excellent algorithm support is very essential in digital watermarks. In addition, it can extract the embedded watermark to achieve the goal of watermark authentication. In this Abbreviations: DWT, Discrete Wavelet Transform; RGB, Red Green Blue; LSB, Least Significant Bit. q
This paper has been recommended for acceptance by ‘Luming Zhang’.
⇑ Corresponding author.
E-mail address: [email protected] (Z. Du). https://doi.org/10.1016/j.jvcir.2019.102627 1047-3203/Ó 2019 Elsevier Inc. All rights reserved.
context, traditional cryptography no longer meets the contemporary needs of our society. Instead, digital watermarks have emerged and become one of the research hotspots in recent years. Digital watermarking technique can protect the copyright of digital media in an effective manner and it has attracted more and more attention and a variety of algorithms have been put forward one after another in recent years. For digital images, the embedding process can be accomplished in either spatial domain or frequency domain. As far as the frequency domain scheme is concerned, it is shown that better compromise of robustness and transparency can be obtained with this scheme adopted. As to frequency domain transforms, DCT, DFT and Discrete Wavelet Transform are very common to see. Traditional algorithms of watermarking generally include the discrete Fourier transform algorithm, the discrete cosine algorithm, among other algorithms. These algorithms well conceal the image watermark to a certain extent, and meanwhile it is not easy to destroy the carrier image quality. However, the watermark extracted through such algorithms has poor anti-attack capacity; subsequent to the adding of noise and the loss compression by the attacker, they cannot be well recognized.
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J. Wang, Z. Du / J. Vis. Commun. Image R. 64 (2019) 102627
This article presents an algorithm based on the latest method of wavelet analysis. The author adopts the multi-scale 2-D discrete wavelet algorithm and the corresponding selection algorithm. First, the watermark image is adaptively embedded into the high-energy part of the carrier image so as to minimize the effect on the quality of the carrier image. Second, the algorithm proposed in this article can well extract the watermark image subsequent to the noise attack and the loss compression by the attacker. Therefore, it is applicable to the field of image information security against the backdrop of the rapid development of the Internet [1]. 1.2. Overview of the image watermarking technology We have witnessed an explosive growth of Information data over the Internet and the common use of digital media in virtue of fast development of multimedia applications over the Internet. As a result, multimedia documents can be transferred by data across the Internet conveniently which results in the increase in the public concern to protect the copyright of content. Both control access techniques and encryption are adopted to protect the ownership of media in the early days. Nevertheless, as watermarking algorithms embed the watermark into digital data and we can prevent the unauthorized copying by the application of these watermark, the watermarking techniques are adopted to avoid unauthorized copying after the media have been successfully transmitted and decrypted in recent years. The image watermarking technology is defined as embedding a picture with special information into another image (In most cases, it is referred to as the original image), and the embedded image poses no effect on the senses in the original image. Image watermarking technology is a critical branch of information security and has been well adopted in the field of copyright and confidentiality. The image watermarking is generally divided into the visible watermark and the invisible one. Visible watermarks are used in video images. As for invisible watermarks, they are mostly adopted in audio signals and static signals. This article focuses on the static color watermark image. Therefore, the invisible watermark is selected in this thesis which possesses optimal privacy and proves to be resistant to different physical attacks to some extent [2]. As a pattern of bits, a digital watermark can be inserted into an image, audio or video file. The name originates from the text or graphics that are almost invisibly imprinted on stationery which is used to identify the manufacturer of the stationery. The applications of watermarking are various, for instance, Device control, Transaction tracking, Owner identification, Copy control, Broadcast monitoring, Proof of ownership, etc. The watermarking techniques put forward in the present literature can be grouped into two types: that is the transform domain methods and the spatial-domain methods. A great deal of techniques has been put forward in the spatial domain, for example the LSB (least significant bit) insertion method, the patchwork method and the texture block coding method. These techniques can be adopted to process the luminance as well as the location of the image pixel in a direct manner. LSB method is characterized by its main disadvantage, that is the easy damage of the least significant bits, for example the random flip of lossy compression or the lower bits. A transform-domain method, such as the Fourier Transform, Discrete Cosine Transform are on the basis of special transformations, and processes the coefficients in the frequency domain for hiding data. Among all these methods, the watermark is hidden in the middle frequency coefficients or high frequency coefficients of the protected image. Filtration such as noise is very declined to result in the suppression of the low frequency coefficients. As a consequence, the high frequency coefficients of the protected
image are used to embed the watermark. The way to choose the best frequency portions of the image for hiding watermark is an important and difficult issue. In contrast with the spatial-domain method, the transform-domain method is more robust against compression, cropping, as well as jittering. In the transform domain, the robustness is kept at the expense of imperceptibility. 1.3. Characteristics of image watermarking Generally speaking, the image watermarking is required to demonstrate the following characteristics: that is robustness, invisibility, extractability, safety. (1) Robustness. The image watermark can still maintain partial integrity and be accurately identified subsequent to either unintentional or intentional procedures of signal processing. It indicates the resistance of the mark against cropping as well as scaling, these attacks can be intentional or unintentional. (2) Invisibility. The watermarked image does not vary from the original image by a significant margin. It indicates that the quality of the image should not be reduced significantly in the watermarking process. (3) Extractability. The watermark owner can easily extract the watermark through the key. (4) Safety. Only the watermark owner can recognize the embedding and extraction of the watermark images and grasp its knowability, and it is hard to tamper or forge such images. 1.4. Methods of watermark processing Most of the algorithms of image watermarking feature the adoption of spread spectrum communication. Digital watermarks based on the spatial domain have limited watermark capacity, which results in the rarity of information bits that ready to be embedded. In contrast, frequency domain-based techniques allow the embedding of large amounts of bits of data without causing imperceptible defects. Generally speaking, this method is based on the changes of the value of some coefficients in the frequency domain; at the same time, the method involves the use of similar spread spectrum image technology to conceal the digital watermark information. These techniques are generally on the basis of commonly used image transformations, either locally or in whole [3]. A majority of the existing watermarking systems put forward in the preset research results can be grouped in accordance with the corresponding domain, for example, the spatial domain or the watermarking domain. For the former domain, the pixels are altered in a direct manner. For the latter domain, the embedding takes place in this domain. In all these transforms, DCT, DWT as well as DFT are very common to see. The frequency domain method has three advantages as follows in contrast with the spatial domain method: (1) It facilitates the distribution of the energy of the watermark in the frequency domain to every pixel of the carrier image, which helps safeguard the privacy of the watermark; (2) Some features of the HVS can be applied to the frequency domain, and the watermark can be coded more efficiently and simply; meanwhile the method minimizes the influence on the quality of the carrier image; (3) The frequency domain method can be compatible with international data compression standards, thus facilitating a watermarking algorithm in the compressed domain, and it is also capable of resisting the corresponding loss compression [4]. However, the wavelet transform and the inverse wavelet transform in the frequency domain can
J. Wang, Z. Du / J. Vis. Commun. Image R. 64 (2019) 102627
cause damage. The anti-attack capacity of the watermark embedding algorithm in the frequency domain is stronger than that of the previous traditional algorithms. 2. Proposed method 2.1. Discrete wavelet transform
ible with compression standards such as JPEG. The watermark embedded with the wavelet transform has good resistance to multiple attacks and sensory experience [5–7]. 2.1.2. Definition of the formula of the discrete wavelet transform The Wavelet Function WðtÞ refers to the functions with shock characteristics and rapid decay of energy to 0:
Z The image is divided into various bands on a logarithmic scale with bandwidth which is nearly equal. That is to say, the image is divided into several components of approximately equal bandwidth to one octave which resembles the retina of the human eye. It is assumed that the application of Discrete Wavelet Transform for watermarking can produce watermark that is difficult to detect. The fundamental principle of the DWT for a two-dimensional image is described as below. By using a subcomponent filters, the image is first decomposed into four parts (i.e., LL1, HL1, LH1, HH1). The subcomponents labeled HL1, LH1, and HH1 indicates the finest scale wavelet coefficients. The subcomponent LL1 is further decomposed and critically subsampled. In order to obtain the next coarser scaled wavelet components, this process should be conducted again and again which depends on the application at hand. In this thesis, three-dimensional DWT decomposition is adopted to improve the Signal to Noise Ratio by minimizing the influence of noise on overlay image. In this embedding process, high frequency components should be taken into consideration as they contain edge information and the subtle changes are not easily detectable by the HVS. The key of watermarking algorithms lies in how to select this component for the embedding process apart from invisibility of the watermark. In this way, it facilitates the survival of it in condition of the possible attacks that the image may go though. 2.1.1. Background of the wavelet transform In the description of signals, Wavelet transform provides flexibility that contains regions of various frequency contents which is of key importance for variable load applications as well as power quality problems. A wavelet transform is a specified waveform that extends into a space defined by a group of functions, which can be interpreted as the wavelets. Wavelet if referred to as a small wave, ‘‘small” indicates that the wavelet is feeble. ‘‘Wave” implies its volatility. Afunction w form a function cluster {w a b} through scaling and translation: A function is named as the basic wavelet, as the derivative form of w, {wa b} is names as wavelet. The frequency information of the wavelet depends on the called scale parameter and this parameter changes the filter bandwidth. In the transformation results, the time domain information depends on b represents the location parameter. It can be concluded that, as a function, the wavelet function has characteristics of both the time and the frequency domain. Recently, wavelet basis that is the wavelet function is put forward by researchers, such as Beylkin wavelets, vector wavelet, and so on. Wavelet analysis which originates from Fourier analysis plays vital role in the development history of Fourier analysis. It has an advantage over Fourier analysis. The analysis of the signal processing of the Wavelet transform is a theory known to the academic circle only in the last decades. In 1988, inspired by the tower algorithm and the multi-argument analysis, Mallat invented the Mallat algorithm. It not only improves the analysis on the theories about wavelets in signal analysis but also simplifies the calculations in the process of wavelet analysis. In terms of the application of image watermarking, the discrete wavelet transform not only better matches the characteristics of HVS (Human Visual System), but also proves to be compat-
3
þ1
1
WðtÞdt ¼ 0
ð2:1Þ
Based on the stretching and translation transformation, WðtÞ we can derive a family of functions:
tb ða; b 2 R; a–0Þ a
1
Wa;b ðtÞ ¼ pffiffiffiffiffiffi W jaj
ð2:2Þ
In this function, a means the scale factor, b means the shift factor. If Wa;b ðtÞ satisfies the (2.2) equation, then for signals with limited energy f ðtÞ 2 L2 ðRÞ, the continuous wavelet transform (CWT) function will be:
Z wf ða; bÞ
þ1
1
f ðtÞWa;b ðtÞdt
ð2:3Þ
In the function, Wa;b ðtÞ means Wa;b ðtÞ the function of complex conjugate. The formula of the inverse transform of the Eq. (2.3) is specified as follows:
ZZ f ðtÞ ¼
1 wf ða; bÞWa;b ðt Þ a2
ð2:4Þ
As the computational complexity of the continuous wavelets far exceeds the capacity of computers, the author has introduced the discrete wavelet transform to meet the actual demands [2]. The discrete wavelet transform (DWT) uses Wa;b ðt Þa; b based on the coefficient and in accordance with the existing standards. In addition, the author has selected some discrete points. Usually we adopt the method of power series transformation to discretize m the points, i.e, rendering a ¼ am 0 ; b ¼ nb0 a0 , generally rendering b0 ¼ 1; a0 ¼ 2. Therefore, for any function f ðtÞ ¼ L2 ðRÞ, the discrete wavelet will be transformed into:
Z Dðm; nÞ ¼
þ1
1
f ðtÞWm;n ðt Þdt
ð2:5Þ
Its inverse transform will be:
f ðtÞ ¼
þ1 X
þ1 X
Dðm; nÞWm;n ðtÞ
ð2:6Þ
m¼1 n¼1
2.2. Algorithm of the color image watermarking 2.2.1. General thinking Due to the conflict between robustness and invisibility of the watermark information, it is necessary to compromise invisibility for higher robustness, and vice versa. According to the multivariate analysis, the low-frequency subbands of the image concentrate most of the energy of the image, whereas the high-frequency parts correspond to the edges and textures of the image. If the water mark is inserted in to the low frequency part of the image, it will highly influence the quality of original picture and further undermine the invisibility of watermark, therefore makes it easier for people to sense it; if the watermark is fully inserted into the high frequency part of the image, it helps to give full play to the concealing function of high frequency picture. But in this way the robustness of watermark will be greatly influenced, too. The attackers will greatly damage the watermark through lossy
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J. Wang, Z. Du / J. Vis. Commun. Image R. 64 (2019) 102627
compression and Gaussian noise. Therefore, we decided to insert the watermark into the middle and low frequency wave range through selection algorithm. In this way, the fidelity of the original picture is guaranteed and the quality of inserted watermark is also secured. Through the analysis above, if we transfer the colorful static image from RGB model to YIQ model with the Haar wavelet function, and then use a two-dimensional discrete wavelet within one scale to decompose the YIQ model, four coefficient matrixes can be obtained and they are approximately wavelet coefficient matrix A (a,b), horizontal detailed coefficient matrix H(a,b), vertical detailed coefficient matrix V (a,b) and diagonal detailed coefficient matrix D (a,b). These four matrixes correspond optimal approximations of the original picture under different scales and resolutions and deliver relevant information of the original picture. Likely, we transform the approximate images with wavelet which is resulted from two dimensional discrete transformation within one scale, that is to process the approximate images with two-dimensional discrete wavelet transformation within two scales. In this way, we have the second level approximate coefficients and detailed coefficients A2(a,b), H2(a,b), V2(a,b), D2(a,b). We also have scale M that is resulted from scale M-1. If we conduct one scale two-dimensional discrete transformation on the colorful watermark image, we will have one approximate matrix and three detailed matrixes. We will insert the watermark in different scales of the original picture through specific selection algorithm. Finally, we made the watermarked image of the original picture through two-dimensional inverse discrete transformation within two scales.
Fig. 2. Watermarking image.
can get the approximate matrix A(a,b) and three detailed matrix H(a,b), V(a,b),D(a,b).(Each group is comprised of 32 32 coefficient matrix.) (4) We partitioned each matrixes in (2), (3) and the scale of each part is 32 32. (As it is shown in Picture 3) and the we have 8 8 little matrixes. (5) As Cox and many others believe that the watermark should be placed on the core part of the HVS, we got a pair of contrast sensibility in the spatial frequency domain by using the HVS model raised by Dooley.
cðu; v Þ ¼ 5:05e0:178ðuþv Þ e0:1ðuþv Þ 1
With the function (2.7), we can fix the intensity of the watermark image embedding. The detailed calculative process is as follows: reconstruct the 32 32 coefficient matrixes we obtained in (3) and then we got corresponding image blocks of the matrixes, after that we conducted discrete wavelet transformation within two scales on those image blocks respectively and got jwi ðm; nÞj2 . By using the function (2.7), we can calculate the contrast sensibility matrix C ðu; v Þ of each image block, and u = 1:32, v = 1:32. Then we can know the saliency of each image block (see Fig. 3):
Fi ¼ 2.2.2. Water imbedding algorithm We chose a 256 256 color picture, a 64 64 color water image and the Haar wavelet function. As it is shown in Figs. 1 and 2. (1) Transform the carrier image and watermark image from RGB model to YIQ model respectively. (2) Transform the 256 256 color image by two dimensional discrete wavelet changing within three scales. And we can get the third-level approximate matrix zA3(a,b) and the first, second and third-level detailed matrixes zHi, zVi, zDi (when i = 1, 2, 3; and i = 1, the scale of the matrix is 128 128; when i = 2, the matrix is 64 64; when i = 3, the scale of the matrix is 32 32). (3) Transform the 64 64 color watermark image with one scale two-dimensional discrete wavelet changing. And we
Fig. 1. Original image.
ð2:7Þ
XX u
v
Cðu; v Þjwi ðm; nÞj2 i ¼ 1; 2; ; 32
ð2:8Þ
(6) We calculated FH, FV, FD, which are the maximum value of the saliency of the image blocks that are composed of different detailed matrixes at all levels. The letter i represents the number of horizontal detailed coefficient matrixes, letter j represents the number of vertical detailed coefficient matrixes, and letter k represents the number of diagonal detailed coefficient matrixes, and i þ j þ k ¼ 32. According to the saliency of the carrier image, the function of the adaptive watermarking embedding algorithm is as follows: 0
zA3 ða; bÞ ¼ zA3 ða; bÞ þ aAða; bÞ
ð2:9Þ
sffiffiffiffiffiffi Fi Hða; bÞ zHi ða; bÞ ¼ zHi ða; bÞ þ a FD 0
ð2:10Þ
$
+
9
'
Fig. 3. Carrier Image coefficient is partitioned based on watermark image coefficient.
J. Wang, Z. Du / J. Vis. Commun. Image R. 64 (2019) 102627
sffiffiffiffiffiffi 0 Fj zV j ða; bÞ ¼ zV j ða; bÞ þ a V ða; bÞ FD
ð2:11Þ
sffiffiffiffiffiffi Fi zDk ða; bÞ ¼ zDk ða; bÞ þ a Dða; bÞ FD 0
ð2:12Þ
In the function above, a represents the energy intensity of the embedded watermarked image. Through a large number of experiments, we find that when a is 10%, and i þ j þ k ¼ 32, optimal balance can be achieved between the influence on the image and the robustness of the watermark. (7) We conducted inverse two-dimensional discrete wavelet 0
0
transformation within three scales on zA3 ða; bÞ; zHi ða; bÞ; 0
0
zV j ða; bÞ; zDk ða; bÞ, the four new coefficient matrixes we obtained in (6) and then we can get the watermarked image (Fig. 4).
5
By testing the similarity between the carrier image and the watermarked carrier image, we know that the P = 94.54%, which is above the standard influence of the embedded watermark on the original image. (The similarity between the watermarked image and the original one should be 90.00%). Fig. 5 demonstrates the details above through diagrams. 2.2.3. Watermark extraction algorithm By conducting inverse transformation of the watermark embedding algorithm mentioned in 2.2.2, we can get the extracted watermarked image (Fig. 6). To test the similarity of the watermark, we usually use function (2.13).
PP 0 XX P ¼ PP P P 0 2 1=2 1=2 ð X2Þ ð X Þ
Fig. 4. Test results of original image after embedding watermarking.
Fig. 5. Process Mapping.
ð2:13Þ
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J. Wang, Z. Du / J. Vis. Commun. Image R. 64 (2019) 102627
Fig. 6. Test results of extracting watermarks.
In function (2.13), X means the original watermarked image, and X0 represents the extracted watermarked image. Through analysis, we find that the similarity P between the extracted watermarked image and the original watermarked image is 87.27%. And this means we can well extract the original color watermarked image.
similarity of the watermarked image and the original one, P, is as high as 83.94%. This demonstrates that the algorithm can resist noise in an effective way (Fig. 8). 3.3. Testing on filtering We conducted smoothing filtering and Wiener filtering on the watermarked color image and found that the quality of the watermarked carrier image was undermined greatly, but the similarity of the image still stood at 70.87%, exceeding the standard (Fig. 9).
3. Simulation testing 3.1. Testing on resistance to compression After we conducted lossy JPEG compression on the embedded watermarked color image (the compression ratio is 5%), we extracted the watermark and get a watermarked image. By testing the similarity of the watermarked image and the original one, we found that the P is 75.74%, 5.74% above the standard. This demonstrates that the extracted watermarked image can resist lossy compression in an effective manner (Fig. 7). 3.2. Testing on resistance to noise Gaussian noise is added into the watermarked color image and the watermark is extracted. After this, it can be found that the
4. Discussion and experiments The article introduces a new watermark embedding algorithm of color images. This algorithm includes transforming the color carrier image and watermarked image from RGB model to YIQ model respectively, then conducting two-dimensional discrete wavelet transformation within one scale on the watermarked image and two-dimensional discrete wavelet transformation within scale M on the carrier image until the dimension of the latter equals the dimension of the former (we choose Haar wavelet function as the wavelet function). By using the Human Vision Model proposed by Dooley, we choose the embedded matrix and
Fig. 7. Compression resistance testing.
J. Wang, Z. Du / J. Vis. Commun. Image R. 64 (2019) 102627
7
Fig. 8. Anti-noise detection.
Fig. 9. Filter processing detection.
fix the energy of the watermark to achieve the optimal balance between the robustness of the watermark and invisibility. This algorithm has little influence on the carrier image after the embedding of watermark into color images. It can well resist attacks like Gaussian noise, lossy compression and is very practical.
All authors take part in the discussion of the work described in this paper. These authors contributed equally to this work and should be considered co-first authors.
5. Conclusions
Funding
This thesis proposes a novel DWT-based color image watermark embedding algorithm on the basis of the latest method of wavelet analysis. Both the multi-scale 2-D discrete wavelet algorithm and the corresponding selection algorithm are adopted in this algorithm. In addition, Haar wavelet function is selected as the wavelet function and the embedded matrix and fix the energy of the watermark to achieve the optimal balance between the robustness of watermark and invisibility. As this algorithm has little influence on the carrier image after the embedding of watermark into color images, it can resist attacks like Gaussian noise, lossy compression, it is applicable to the field of image information security in the context of rapid growth of multimedia applications over the Internet.
The authors wish to thank Southwest University. This article supported by ‘‘Fundamental Research Funds for the Central Universities” (project number: XDJK2016C048).
Author’s contributions
Declaration of Competing Interest We have no conflict of interest. Acknowledgements The authors thank the editor and anonymous reviewers for their helpful comments and valuable suggestions.
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J. Wang, Z. Du / J. Vis. Commun. Image R. 64 (2019) 102627
References [1] F. Cao, S.M. Zhao, Optical encryption scheme with double secret keys based on computational ghost imaging, Opt. Sin. 37 (2017) 0111001. [2] Yongfu Shi, Deguo Yang, Zhi Li, A new algorithm of watermarking of digital image based on wavelet transformation, J. Central China Normal Univ. (Nat. Sci. Ed.) 47 (04) (2013) 479–482. [3] Jun Meng, Tongli Wei, Jin Wu, Changyuan Chang, Principle on the discrete wavelet transformation of digital image and analysis on its hardware implementation, J. Southeast Univ. (Nat. Sci. Ed.) 06 (2002) 842–847. [4] C.T. Hsu, J.L. Wu, Hidden digital watermarks in images, Trans. Image Process. 8 (1) (1999) 58–68. [5] Shuai Han, Yasuyuki Matsushita, Imari Sato, et al. Camera spectral sensitivity estimation from a single image under unknown illumination by using fluorescence. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Book Series: IEEE Conference on Computer Vision and Pattern Recognition Pages, 2012, pp. 805–812. [6] Xiang-Feng Meng, Lu-Zhong Cai, Xiu-Lun Yang, et al., Information security system by iterative multiple-phase retrieval and pixel random permutation, Appl. Opt. 45 (14) (2006) 3289–3297. [7] Qingtang Su, Gang Wang, Xiaofeng Zhang, et al., A new algorithm of blind color image watermarking based on LU decomposition, Multidimensional Syst. Signal Process. 29 (3) (2018) 1055–1074.
Jianyu Wang born in 1998, male, who studies at the Business College of Southwest University, researching image processing and applied mathematics.
Zhiguo Du, born in 1977. Associate professor at the college of business, Southwest University. His current research interests include wireless sensor networks and network communication, and information security.
Contents lists available at ScienceDirect
J. Vis. Commun. Image R. journal homepage: www.elsevier.com/locate/jvci
A method of processing color image watermarking based on the Haar wavelet q Jianyu Wang, Zhiguo Du ⇑ College of Business and Commerce, Rongchang Campus, Southwest University of Chongqing, 402460, China
a r t i c l e
i n f o
Article history: Received 4 June 2019 Revised 26 August 2019 Accepted 26 August 2019 Available online 26 August 2019 Keywords: Color image watermarking Discrete Wavelet Transform (DWT)
a b s t r a c t Despite the fact that traditional digital watermarking technology is relatively mature, there are still some areas that have not been fully involved in. For example, image watermarking technology and the certification are still in its infancy at early times. The bottleneck problem of digital product safety protection all solved theoretically with the combination of computing theory as well as traditional digital watermarking technology and point out a new direction for the research of information security industry. Inspired by the traditional algorithm of image watermarking and based on the Haar wavelet function along with algorithm of 2-D discrete wavelet transform and selection, this article presents the techniques of watermark embedding and extraction of color images. The main appraisal criteria of the watermark include invisibility and robustness, and some other standards. Image watermarking is relatively simple in the spatial domain, where it cannot resist geometrical attacks. In the transform domain, this approach can resist both geometrical attacks and image processing attacks. Only when the carrier image suffers from severe damage with the image quality hugely compromised will the extracted watermark become unrecognizable. As a result, the algorithm presented in this article can well embed the color image in the carrier image, and has good resistance to attack operations such as loss compression and adding of noise. Ó 2019 Elsevier Inc. All rights reserved.
1. Introduction 1.1. Overview of the evolution of image watermarking technology Nowadays, digital information has become the mainstream of the era, and consequently protecting the copyright of such information becomes an urgent issue that needs to be tackled with more secure dissemination. Digital watermarking technology is widely used, such as copyright protection, medical image protection, legal evidence protection, inheritance certification, etc. These may be tampered or attacked in the process of transmission over the network or during the actual shipping process. Network and information security become an increasingly prominent issue in our daily lives. In this sense, digital watermarking technology is of vital importance. Excellent algorithm support is very essential in digital watermarks. In addition, it can extract the embedded watermark to achieve the goal of watermark authentication. In this Abbreviations: DWT, Discrete Wavelet Transform; RGB, Red Green Blue; LSB, Least Significant Bit. q
This paper has been recommended for acceptance by ‘Luming Zhang’.
⇑ Corresponding author.
E-mail address: [email protected] (Z. Du). https://doi.org/10.1016/j.jvcir.2019.102627 1047-3203/Ó 2019 Elsevier Inc. All rights reserved.
context, traditional cryptography no longer meets the contemporary needs of our society. Instead, digital watermarks have emerged and become one of the research hotspots in recent years. Digital watermarking technique can protect the copyright of digital media in an effective manner and it has attracted more and more attention and a variety of algorithms have been put forward one after another in recent years. For digital images, the embedding process can be accomplished in either spatial domain or frequency domain. As far as the frequency domain scheme is concerned, it is shown that better compromise of robustness and transparency can be obtained with this scheme adopted. As to frequency domain transforms, DCT, DFT and Discrete Wavelet Transform are very common to see. Traditional algorithms of watermarking generally include the discrete Fourier transform algorithm, the discrete cosine algorithm, among other algorithms. These algorithms well conceal the image watermark to a certain extent, and meanwhile it is not easy to destroy the carrier image quality. However, the watermark extracted through such algorithms has poor anti-attack capacity; subsequent to the adding of noise and the loss compression by the attacker, they cannot be well recognized.
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J. Wang, Z. Du / J. Vis. Commun. Image R. 64 (2019) 102627
This article presents an algorithm based on the latest method of wavelet analysis. The author adopts the multi-scale 2-D discrete wavelet algorithm and the corresponding selection algorithm. First, the watermark image is adaptively embedded into the high-energy part of the carrier image so as to minimize the effect on the quality of the carrier image. Second, the algorithm proposed in this article can well extract the watermark image subsequent to the noise attack and the loss compression by the attacker. Therefore, it is applicable to the field of image information security against the backdrop of the rapid development of the Internet [1]. 1.2. Overview of the image watermarking technology We have witnessed an explosive growth of Information data over the Internet and the common use of digital media in virtue of fast development of multimedia applications over the Internet. As a result, multimedia documents can be transferred by data across the Internet conveniently which results in the increase in the public concern to protect the copyright of content. Both control access techniques and encryption are adopted to protect the ownership of media in the early days. Nevertheless, as watermarking algorithms embed the watermark into digital data and we can prevent the unauthorized copying by the application of these watermark, the watermarking techniques are adopted to avoid unauthorized copying after the media have been successfully transmitted and decrypted in recent years. The image watermarking technology is defined as embedding a picture with special information into another image (In most cases, it is referred to as the original image), and the embedded image poses no effect on the senses in the original image. Image watermarking technology is a critical branch of information security and has been well adopted in the field of copyright and confidentiality. The image watermarking is generally divided into the visible watermark and the invisible one. Visible watermarks are used in video images. As for invisible watermarks, they are mostly adopted in audio signals and static signals. This article focuses on the static color watermark image. Therefore, the invisible watermark is selected in this thesis which possesses optimal privacy and proves to be resistant to different physical attacks to some extent [2]. As a pattern of bits, a digital watermark can be inserted into an image, audio or video file. The name originates from the text or graphics that are almost invisibly imprinted on stationery which is used to identify the manufacturer of the stationery. The applications of watermarking are various, for instance, Device control, Transaction tracking, Owner identification, Copy control, Broadcast monitoring, Proof of ownership, etc. The watermarking techniques put forward in the present literature can be grouped into two types: that is the transform domain methods and the spatial-domain methods. A great deal of techniques has been put forward in the spatial domain, for example the LSB (least significant bit) insertion method, the patchwork method and the texture block coding method. These techniques can be adopted to process the luminance as well as the location of the image pixel in a direct manner. LSB method is characterized by its main disadvantage, that is the easy damage of the least significant bits, for example the random flip of lossy compression or the lower bits. A transform-domain method, such as the Fourier Transform, Discrete Cosine Transform are on the basis of special transformations, and processes the coefficients in the frequency domain for hiding data. Among all these methods, the watermark is hidden in the middle frequency coefficients or high frequency coefficients of the protected image. Filtration such as noise is very declined to result in the suppression of the low frequency coefficients. As a consequence, the high frequency coefficients of the protected
image are used to embed the watermark. The way to choose the best frequency portions of the image for hiding watermark is an important and difficult issue. In contrast with the spatial-domain method, the transform-domain method is more robust against compression, cropping, as well as jittering. In the transform domain, the robustness is kept at the expense of imperceptibility. 1.3. Characteristics of image watermarking Generally speaking, the image watermarking is required to demonstrate the following characteristics: that is robustness, invisibility, extractability, safety. (1) Robustness. The image watermark can still maintain partial integrity and be accurately identified subsequent to either unintentional or intentional procedures of signal processing. It indicates the resistance of the mark against cropping as well as scaling, these attacks can be intentional or unintentional. (2) Invisibility. The watermarked image does not vary from the original image by a significant margin. It indicates that the quality of the image should not be reduced significantly in the watermarking process. (3) Extractability. The watermark owner can easily extract the watermark through the key. (4) Safety. Only the watermark owner can recognize the embedding and extraction of the watermark images and grasp its knowability, and it is hard to tamper or forge such images. 1.4. Methods of watermark processing Most of the algorithms of image watermarking feature the adoption of spread spectrum communication. Digital watermarks based on the spatial domain have limited watermark capacity, which results in the rarity of information bits that ready to be embedded. In contrast, frequency domain-based techniques allow the embedding of large amounts of bits of data without causing imperceptible defects. Generally speaking, this method is based on the changes of the value of some coefficients in the frequency domain; at the same time, the method involves the use of similar spread spectrum image technology to conceal the digital watermark information. These techniques are generally on the basis of commonly used image transformations, either locally or in whole [3]. A majority of the existing watermarking systems put forward in the preset research results can be grouped in accordance with the corresponding domain, for example, the spatial domain or the watermarking domain. For the former domain, the pixels are altered in a direct manner. For the latter domain, the embedding takes place in this domain. In all these transforms, DCT, DWT as well as DFT are very common to see. The frequency domain method has three advantages as follows in contrast with the spatial domain method: (1) It facilitates the distribution of the energy of the watermark in the frequency domain to every pixel of the carrier image, which helps safeguard the privacy of the watermark; (2) Some features of the HVS can be applied to the frequency domain, and the watermark can be coded more efficiently and simply; meanwhile the method minimizes the influence on the quality of the carrier image; (3) The frequency domain method can be compatible with international data compression standards, thus facilitating a watermarking algorithm in the compressed domain, and it is also capable of resisting the corresponding loss compression [4]. However, the wavelet transform and the inverse wavelet transform in the frequency domain can
J. Wang, Z. Du / J. Vis. Commun. Image R. 64 (2019) 102627
cause damage. The anti-attack capacity of the watermark embedding algorithm in the frequency domain is stronger than that of the previous traditional algorithms. 2. Proposed method 2.1. Discrete wavelet transform
ible with compression standards such as JPEG. The watermark embedded with the wavelet transform has good resistance to multiple attacks and sensory experience [5–7]. 2.1.2. Definition of the formula of the discrete wavelet transform The Wavelet Function WðtÞ refers to the functions with shock characteristics and rapid decay of energy to 0:
Z The image is divided into various bands on a logarithmic scale with bandwidth which is nearly equal. That is to say, the image is divided into several components of approximately equal bandwidth to one octave which resembles the retina of the human eye. It is assumed that the application of Discrete Wavelet Transform for watermarking can produce watermark that is difficult to detect. The fundamental principle of the DWT for a two-dimensional image is described as below. By using a subcomponent filters, the image is first decomposed into four parts (i.e., LL1, HL1, LH1, HH1). The subcomponents labeled HL1, LH1, and HH1 indicates the finest scale wavelet coefficients. The subcomponent LL1 is further decomposed and critically subsampled. In order to obtain the next coarser scaled wavelet components, this process should be conducted again and again which depends on the application at hand. In this thesis, three-dimensional DWT decomposition is adopted to improve the Signal to Noise Ratio by minimizing the influence of noise on overlay image. In this embedding process, high frequency components should be taken into consideration as they contain edge information and the subtle changes are not easily detectable by the HVS. The key of watermarking algorithms lies in how to select this component for the embedding process apart from invisibility of the watermark. In this way, it facilitates the survival of it in condition of the possible attacks that the image may go though. 2.1.1. Background of the wavelet transform In the description of signals, Wavelet transform provides flexibility that contains regions of various frequency contents which is of key importance for variable load applications as well as power quality problems. A wavelet transform is a specified waveform that extends into a space defined by a group of functions, which can be interpreted as the wavelets. Wavelet if referred to as a small wave, ‘‘small” indicates that the wavelet is feeble. ‘‘Wave” implies its volatility. Afunction w form a function cluster {w a b} through scaling and translation: A function is named as the basic wavelet, as the derivative form of w, {wa b} is names as wavelet. The frequency information of the wavelet depends on the called scale parameter and this parameter changes the filter bandwidth. In the transformation results, the time domain information depends on b represents the location parameter. It can be concluded that, as a function, the wavelet function has characteristics of both the time and the frequency domain. Recently, wavelet basis that is the wavelet function is put forward by researchers, such as Beylkin wavelets, vector wavelet, and so on. Wavelet analysis which originates from Fourier analysis plays vital role in the development history of Fourier analysis. It has an advantage over Fourier analysis. The analysis of the signal processing of the Wavelet transform is a theory known to the academic circle only in the last decades. In 1988, inspired by the tower algorithm and the multi-argument analysis, Mallat invented the Mallat algorithm. It not only improves the analysis on the theories about wavelets in signal analysis but also simplifies the calculations in the process of wavelet analysis. In terms of the application of image watermarking, the discrete wavelet transform not only better matches the characteristics of HVS (Human Visual System), but also proves to be compat-
3
þ1
1
WðtÞdt ¼ 0
ð2:1Þ
Based on the stretching and translation transformation, WðtÞ we can derive a family of functions:
tb ða; b 2 R; a–0Þ a
1
Wa;b ðtÞ ¼ pffiffiffiffiffiffi W jaj
ð2:2Þ
In this function, a means the scale factor, b means the shift factor. If Wa;b ðtÞ satisfies the (2.2) equation, then for signals with limited energy f ðtÞ 2 L2 ðRÞ, the continuous wavelet transform (CWT) function will be:
Z wf ða; bÞ
þ1
1
f ðtÞWa;b ðtÞdt
ð2:3Þ
In the function, Wa;b ðtÞ means Wa;b ðtÞ the function of complex conjugate. The formula of the inverse transform of the Eq. (2.3) is specified as follows:
ZZ f ðtÞ ¼
1 wf ða; bÞWa;b ðt Þ a2
ð2:4Þ
As the computational complexity of the continuous wavelets far exceeds the capacity of computers, the author has introduced the discrete wavelet transform to meet the actual demands [2]. The discrete wavelet transform (DWT) uses Wa;b ðt Þa; b based on the coefficient and in accordance with the existing standards. In addition, the author has selected some discrete points. Usually we adopt the method of power series transformation to discretize m the points, i.e, rendering a ¼ am 0 ; b ¼ nb0 a0 , generally rendering b0 ¼ 1; a0 ¼ 2. Therefore, for any function f ðtÞ ¼ L2 ðRÞ, the discrete wavelet will be transformed into:
Z Dðm; nÞ ¼
þ1
1
f ðtÞWm;n ðt Þdt
ð2:5Þ
Its inverse transform will be:
f ðtÞ ¼
þ1 X
þ1 X
Dðm; nÞWm;n ðtÞ
ð2:6Þ
m¼1 n¼1
2.2. Algorithm of the color image watermarking 2.2.1. General thinking Due to the conflict between robustness and invisibility of the watermark information, it is necessary to compromise invisibility for higher robustness, and vice versa. According to the multivariate analysis, the low-frequency subbands of the image concentrate most of the energy of the image, whereas the high-frequency parts correspond to the edges and textures of the image. If the water mark is inserted in to the low frequency part of the image, it will highly influence the quality of original picture and further undermine the invisibility of watermark, therefore makes it easier for people to sense it; if the watermark is fully inserted into the high frequency part of the image, it helps to give full play to the concealing function of high frequency picture. But in this way the robustness of watermark will be greatly influenced, too. The attackers will greatly damage the watermark through lossy
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J. Wang, Z. Du / J. Vis. Commun. Image R. 64 (2019) 102627
compression and Gaussian noise. Therefore, we decided to insert the watermark into the middle and low frequency wave range through selection algorithm. In this way, the fidelity of the original picture is guaranteed and the quality of inserted watermark is also secured. Through the analysis above, if we transfer the colorful static image from RGB model to YIQ model with the Haar wavelet function, and then use a two-dimensional discrete wavelet within one scale to decompose the YIQ model, four coefficient matrixes can be obtained and they are approximately wavelet coefficient matrix A (a,b), horizontal detailed coefficient matrix H(a,b), vertical detailed coefficient matrix V (a,b) and diagonal detailed coefficient matrix D (a,b). These four matrixes correspond optimal approximations of the original picture under different scales and resolutions and deliver relevant information of the original picture. Likely, we transform the approximate images with wavelet which is resulted from two dimensional discrete transformation within one scale, that is to process the approximate images with two-dimensional discrete wavelet transformation within two scales. In this way, we have the second level approximate coefficients and detailed coefficients A2(a,b), H2(a,b), V2(a,b), D2(a,b). We also have scale M that is resulted from scale M-1. If we conduct one scale two-dimensional discrete transformation on the colorful watermark image, we will have one approximate matrix and three detailed matrixes. We will insert the watermark in different scales of the original picture through specific selection algorithm. Finally, we made the watermarked image of the original picture through two-dimensional inverse discrete transformation within two scales.
Fig. 2. Watermarking image.
can get the approximate matrix A(a,b) and three detailed matrix H(a,b), V(a,b),D(a,b).(Each group is comprised of 32 32 coefficient matrix.) (4) We partitioned each matrixes in (2), (3) and the scale of each part is 32 32. (As it is shown in Picture 3) and the we have 8 8 little matrixes. (5) As Cox and many others believe that the watermark should be placed on the core part of the HVS, we got a pair of contrast sensibility in the spatial frequency domain by using the HVS model raised by Dooley.
cðu; v Þ ¼ 5:05e0:178ðuþv Þ e0:1ðuþv Þ 1
With the function (2.7), we can fix the intensity of the watermark image embedding. The detailed calculative process is as follows: reconstruct the 32 32 coefficient matrixes we obtained in (3) and then we got corresponding image blocks of the matrixes, after that we conducted discrete wavelet transformation within two scales on those image blocks respectively and got jwi ðm; nÞj2 . By using the function (2.7), we can calculate the contrast sensibility matrix C ðu; v Þ of each image block, and u = 1:32, v = 1:32. Then we can know the saliency of each image block (see Fig. 3):
Fi ¼ 2.2.2. Water imbedding algorithm We chose a 256 256 color picture, a 64 64 color water image and the Haar wavelet function. As it is shown in Figs. 1 and 2. (1) Transform the carrier image and watermark image from RGB model to YIQ model respectively. (2) Transform the 256 256 color image by two dimensional discrete wavelet changing within three scales. And we can get the third-level approximate matrix zA3(a,b) and the first, second and third-level detailed matrixes zHi, zVi, zDi (when i = 1, 2, 3; and i = 1, the scale of the matrix is 128 128; when i = 2, the matrix is 64 64; when i = 3, the scale of the matrix is 32 32). (3) Transform the 64 64 color watermark image with one scale two-dimensional discrete wavelet changing. And we
Fig. 1. Original image.
ð2:7Þ
XX u
v
Cðu; v Þjwi ðm; nÞj2 i ¼ 1; 2; ; 32
ð2:8Þ
(6) We calculated FH, FV, FD, which are the maximum value of the saliency of the image blocks that are composed of different detailed matrixes at all levels. The letter i represents the number of horizontal detailed coefficient matrixes, letter j represents the number of vertical detailed coefficient matrixes, and letter k represents the number of diagonal detailed coefficient matrixes, and i þ j þ k ¼ 32. According to the saliency of the carrier image, the function of the adaptive watermarking embedding algorithm is as follows: 0
zA3 ða; bÞ ¼ zA3 ða; bÞ þ aAða; bÞ
ð2:9Þ
sffiffiffiffiffiffi Fi Hða; bÞ zHi ða; bÞ ¼ zHi ða; bÞ þ a FD 0
ð2:10Þ
$
+
9
'
Fig. 3. Carrier Image coefficient is partitioned based on watermark image coefficient.
J. Wang, Z. Du / J. Vis. Commun. Image R. 64 (2019) 102627
sffiffiffiffiffiffi 0 Fj zV j ða; bÞ ¼ zV j ða; bÞ þ a V ða; bÞ FD
ð2:11Þ
sffiffiffiffiffiffi Fi zDk ða; bÞ ¼ zDk ða; bÞ þ a Dða; bÞ FD 0
ð2:12Þ
In the function above, a represents the energy intensity of the embedded watermarked image. Through a large number of experiments, we find that when a is 10%, and i þ j þ k ¼ 32, optimal balance can be achieved between the influence on the image and the robustness of the watermark. (7) We conducted inverse two-dimensional discrete wavelet 0
0
transformation within three scales on zA3 ða; bÞ; zHi ða; bÞ; 0
0
zV j ða; bÞ; zDk ða; bÞ, the four new coefficient matrixes we obtained in (6) and then we can get the watermarked image (Fig. 4).
5
By testing the similarity between the carrier image and the watermarked carrier image, we know that the P = 94.54%, which is above the standard influence of the embedded watermark on the original image. (The similarity between the watermarked image and the original one should be 90.00%). Fig. 5 demonstrates the details above through diagrams. 2.2.3. Watermark extraction algorithm By conducting inverse transformation of the watermark embedding algorithm mentioned in 2.2.2, we can get the extracted watermarked image (Fig. 6). To test the similarity of the watermark, we usually use function (2.13).
PP 0 XX P ¼ PP P P 0 2 1=2 1=2 ð X2Þ ð X Þ
Fig. 4. Test results of original image after embedding watermarking.
Fig. 5. Process Mapping.
ð2:13Þ
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J. Wang, Z. Du / J. Vis. Commun. Image R. 64 (2019) 102627
Fig. 6. Test results of extracting watermarks.
In function (2.13), X means the original watermarked image, and X0 represents the extracted watermarked image. Through analysis, we find that the similarity P between the extracted watermarked image and the original watermarked image is 87.27%. And this means we can well extract the original color watermarked image.
similarity of the watermarked image and the original one, P, is as high as 83.94%. This demonstrates that the algorithm can resist noise in an effective way (Fig. 8). 3.3. Testing on filtering We conducted smoothing filtering and Wiener filtering on the watermarked color image and found that the quality of the watermarked carrier image was undermined greatly, but the similarity of the image still stood at 70.87%, exceeding the standard (Fig. 9).
3. Simulation testing 3.1. Testing on resistance to compression After we conducted lossy JPEG compression on the embedded watermarked color image (the compression ratio is 5%), we extracted the watermark and get a watermarked image. By testing the similarity of the watermarked image and the original one, we found that the P is 75.74%, 5.74% above the standard. This demonstrates that the extracted watermarked image can resist lossy compression in an effective manner (Fig. 7). 3.2. Testing on resistance to noise Gaussian noise is added into the watermarked color image and the watermark is extracted. After this, it can be found that the
4. Discussion and experiments The article introduces a new watermark embedding algorithm of color images. This algorithm includes transforming the color carrier image and watermarked image from RGB model to YIQ model respectively, then conducting two-dimensional discrete wavelet transformation within one scale on the watermarked image and two-dimensional discrete wavelet transformation within scale M on the carrier image until the dimension of the latter equals the dimension of the former (we choose Haar wavelet function as the wavelet function). By using the Human Vision Model proposed by Dooley, we choose the embedded matrix and
Fig. 7. Compression resistance testing.
J. Wang, Z. Du / J. Vis. Commun. Image R. 64 (2019) 102627
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Fig. 8. Anti-noise detection.
Fig. 9. Filter processing detection.
fix the energy of the watermark to achieve the optimal balance between the robustness of the watermark and invisibility. This algorithm has little influence on the carrier image after the embedding of watermark into color images. It can well resist attacks like Gaussian noise, lossy compression and is very practical.
All authors take part in the discussion of the work described in this paper. These authors contributed equally to this work and should be considered co-first authors.
5. Conclusions
Funding
This thesis proposes a novel DWT-based color image watermark embedding algorithm on the basis of the latest method of wavelet analysis. Both the multi-scale 2-D discrete wavelet algorithm and the corresponding selection algorithm are adopted in this algorithm. In addition, Haar wavelet function is selected as the wavelet function and the embedded matrix and fix the energy of the watermark to achieve the optimal balance between the robustness of watermark and invisibility. As this algorithm has little influence on the carrier image after the embedding of watermark into color images, it can resist attacks like Gaussian noise, lossy compression, it is applicable to the field of image information security in the context of rapid growth of multimedia applications over the Internet.
The authors wish to thank Southwest University. This article supported by ‘‘Fundamental Research Funds for the Central Universities” (project number: XDJK2016C048).
Author’s contributions
Declaration of Competing Interest We have no conflict of interest. Acknowledgements The authors thank the editor and anonymous reviewers for their helpful comments and valuable suggestions.
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References [1] F. Cao, S.M. Zhao, Optical encryption scheme with double secret keys based on computational ghost imaging, Opt. Sin. 37 (2017) 0111001. [2] Yongfu Shi, Deguo Yang, Zhi Li, A new algorithm of watermarking of digital image based on wavelet transformation, J. Central China Normal Univ. (Nat. Sci. Ed.) 47 (04) (2013) 479–482. [3] Jun Meng, Tongli Wei, Jin Wu, Changyuan Chang, Principle on the discrete wavelet transformation of digital image and analysis on its hardware implementation, J. Southeast Univ. (Nat. Sci. Ed.) 06 (2002) 842–847. [4] C.T. Hsu, J.L. Wu, Hidden digital watermarks in images, Trans. Image Process. 8 (1) (1999) 58–68. [5] Shuai Han, Yasuyuki Matsushita, Imari Sato, et al. Camera spectral sensitivity estimation from a single image under unknown illumination by using fluorescence. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Book Series: IEEE Conference on Computer Vision and Pattern Recognition Pages, 2012, pp. 805–812. [6] Xiang-Feng Meng, Lu-Zhong Cai, Xiu-Lun Yang, et al., Information security system by iterative multiple-phase retrieval and pixel random permutation, Appl. Opt. 45 (14) (2006) 3289–3297. [7] Qingtang Su, Gang Wang, Xiaofeng Zhang, et al., A new algorithm of blind color image watermarking based on LU decomposition, Multidimensional Syst. Signal Process. 29 (3) (2018) 1055–1074.
Jianyu Wang born in 1998, male, who studies at the Business College of Southwest University, researching image processing and applied mathematics.
Zhiguo Du, born in 1977. Associate professor at the college of business, Southwest University. His current research interests include wireless sensor networks and network communication, and information security.