The Difference between DCT, DWT, DFT Watermarking Techniques by using Multiple Attacks
Ahmed Adnan Mohammed Al-Azzawi
University of Diyala
ahmedadnan5060@gmail.com
Abstract
Internet evolution, along with the advancement of digital multimedia tools has created a major impact in making the storage and distribution of multimedia content a straightforward tasks. Thus the security of multimedia contents becomes a vital issue and there is a need for protecting the digital content against counterfeiting, piracy, and malicious manipulations. Digital watermarking is an evolving field that requires continuous effort to find the best possible method of protecting multimedia content. In this study, we introduced the methods DCT, DWT and DFT based algorithm for watermarking in digital images. In order to compare the imperceptibility and robustness of the algorithms make use of several attacks.
Keywords: Watermarking, Multimedia, Multiple Attacks, Discrete Wavelet Transform, Discrete cosine Transform, Discrete Fourier Transform.
Introduction
The success of the Internet and digital consumer devices has greatly changed our society and daily lives through making the transmission, storage and get of digital data extremely easy and convenient. However, this raises a big concern is how to secure these data and preventing unauthorized use. This issue has become problematic in many fields. For example, the music and video industry loses millions of dollars yearly because to illegal copying and downloading of copyrighted material from the Internet. As a solution, digital watermarking is used frequently. Thus, digital watermarking becomes very attractive research topic. Digital watermarking is a technology that creates and detects invisible markings, which can be used to trace the originality and legal usage of digital data. Ideally, they should be hard to notice, difficult to reproduce, and impossible to remove without destroying the cover they protect. In the future, the main development of digital watermarking can be as follows: copyright protection, pirate tracking, copying protection, image authentication, cover-up communication [1].
In terms of the embedding domain, watermarking algorithms are mainly divided into two groups: spatial domain methods which embed the data by directly altering the pixel values of the original image and transform domain method which embed the data by modifying the transform domain coefficients. A frequency-domain watermarking, the value of certain frequencies are altered from their original & embeds the watermark into the transformed image. This is more robust than the spatial domain technique. In frequency-domain technique multiple transforms used for the watermarking purpose such as DCT, DFT, DWT. The most usually used transforms for digital watermarking are DFT (Discrete Fourier Transform) DCT (Discrete Cosine Transform) and DWT (Discrete Wavelet Transform). Now frequency domain watermarking is more advantageous for all practical internet applications. Watermarks and watermarking techniques can be divided into different categories in various ways. The watermarks can be applied in the spatial domain. An alternative to spatial domain watermarking is frequency domain watermarking. It has been pointed out that the frequency domain methods are more.
Watermarking techniques can be divided into four categories according to the type of document to be watermarked as follows.
‘ Image Watermarking
‘ Video Watermarking
‘ Audio Watermarking
‘ Text Watermarking
According to the human perception, the digital watermarks can be divided into three different types as follows.
‘ Visible watermark
‘ Invisible-Robust watermark
‘ Invisible-Fragile watermark
‘ And one another type called Dual watermark
The visible watermark is a secondary translucent overlay into the primary image. The watermark appears visible to a casual viewer on a careful inspection. The invisible-strong watermark is embedded in such a way that alternations made to the pixel value are perceptually not noticed and it can be recovered only with appropriate decoding mechanism. The invisible-fragile watermark is embedded in such a way that any manipulation or modulation of the image would change or destroy the watermark. Dual watermarking is a combination of a visible and an invisible watermark. In this type of watermark, an invisible watermark is used as a backup for the visible watermark as shown from the following diagram.
Figure 1: Schematic representation of dual watermarking
Discrete Cosine Transform
With the character of discrete Fourier transform (DFT) Discrete cosine transform (DCT) turn over the image edge to make the image turn into the form of even function. It is one of the most common linear transformations in digital signal processor technology. Two-dimensional discrete cosine transform (2D-DCT) is defined as:
The corresponding inverse transformation (Whether 2D-DCT) is defined as:
The 2D-DCT can not only concentrate the main information of the original image into the smallest low-frequency coefficient but also it can cause the image blocking effect is the smallest, which can realize the good compromise between the information centralizing and the computing complication. Thus, it obtains the wide spreading application in the compression coding.
Discrete Wavelet Transform
The wavelet transform is a time domain localized analysis method with the window's size fixed and shapes convertible. There is the quite good time differentiated rate in high-frequency part of signals DWT transformed. Also, there is quite good frequency differentiated rate in its low-frequency part. It can distil the information from signal effectively.
The main idea of discrete wavelet transform (DWT) in image process is to multi-differentiated decompose the image into sub-image of the different spatial domain and independent frequency district [5] [6]. Then transform the coefficient of Sub-image. After the original image has been DWT transformed, it is decomposed into 4 frequency districts which are one low-frequency district(LL) and three high-frequency districts (LH,HL,HH). If the information of low-frequency area is DWT transformed, the sub-level frequency district information will be obtained. A two-dimensional image after three-times DWT decomposed can be shown in Fig.1. Where L represents low-pass filter, H represents a high-pass filter. An original image can be decomposed of frequency areas of HL1, LH1, and HH1. The low-frequency district information also can be decomposed into sub-level frequency area information of LL2, HL2, LH2 and HH2. Through doing this the original image can be decomposed for n level wavelet transformation.
The information of low-frequency area is an image close to the original image. Most signal information of the original image is in this frequency district. The frequency areas of LH, HL and HH respectively represents the level detail, the upright detail and the diagonal detail of the original image.
According to the character of HVS, human eyes are sensitive to the change of smooth district of the image, but not sensitive to the tiny change of edge, profile, and streak. Therefore, it’s difficult to conscious that putting the watermarking signal into the big amplitude coefficient of high-frequency band of the image DWT transformed. Then it can carry more watermarking signal and has a good concealing effect.
Discrete Fourier Transform
Discrete Fourier transform is a frequency domain localized analysis method.
Given a 2D discrete function g (u, v) defined on an (M x N) grid, the DFT is defined as:
The inverse again is just a change of sign inside the Exponent:
Algorithms Evaluation
We make the evaluation of the watermark techniques depending on the PSNR values the PSNR is an engineering term for the ratio between the maximum possible power of a signal and the power of corrupting noise that impacts the fidelity of its representation.
Embedding and Extracting
Let I(i,j) be N X N Embedding Domain of Cover image, I'(i,j) the watermarked image, (a) is a factor which determines the strength of the watermark and W(i,j) the watermark image:
1) DCT
Embedding Equation I'(i,j)=I(i,j)+a*W(i,j).
Where: I(i,j) 8×8 blocks of the Cover image, I'(i,j) represent the Watermarked 8×8 blocks of the Cover image.
Extraction Equation W(i,j)= (I'(i,j)- I(i,j))/a.
2) DWT
Embedding Equation I'(i,j)=I(i,j)+a*W(i,j).
Where: I(i,j) LL sub-band of the Cover image, I'(i,j) represent the Watermarked LL sub-band of the Cover image.
Extraction Equation
W(i,j)= (I'(i,j)- I(i,j))/a.
3) DFT
Embedding Equation I'(i,j)=I(i,j)+a*W(i,j).
where: I(i,j) represent the Magnitude of the Cover image, I'(i,j) represent the Watermarked Magnitude of the Cover image.
Extraction Equation
W(i,j)= (I'(i,j)- I(I,j))/a.
Results
In this study, we used the cover image (Lena 512×512) and watermark image (Best) as shown in Fig.3 and Fig.4.
Fig. 3 Cover image Lena 512×512. Fig. 4 watermark image. Fig. 5 watermarked image.
Attacks results:
We used the following attacks Gaussian noise Attack, Mean Filter Attack, Scaling Attack, Rotate Attack, Histogram Attack, intensity Attack, Gamma correction Attack, Crop attack and Compression attack.
1. Gaussian attack (mean=0, Variance=0.001)
TABLE I
PSNR VALUES FOR GAUSSIAN ATTACK
DCT PSNR DWT PSNR DFT PSNR
29.5856 29.9336 29.9939
2. Mean Filter Attack (Mask size=3×3)
TABLE 2
PSNR VALUES FOR MEAN FILTER ATTACK
DCT PSNR DWT PSNR DFT PSNR
32.3503 29.7364 32.2960
3. Scaling Attack (minimize percentage 75%)
TABLE 3
PSNR VALUES FOR SCALING ATTACK
DCT PSNR DWT PSNR DFT PSNR
29.5791 32.4841 29.9210
4. Rotate Attack (20”)
TABLE 4
PSNR VALUES FOR ROTATE ATTACK
DCT PSNR DWT PSNR DFT PSNR
13.9563 11.4282 14.7093
5. histogram Attack equal (Automatic)
TABLE 5
PSNR VALUES FOR histogram ATTACK
DCT PSNR DWT PSNR DFT PSNR
14.7093 11.4282 12.1563
6. intensity Attack ([l=0 h=0.8],[b=0 t=1])
TABLE 6
PSNR VALUES FOR intensity ATTACK
DCT PSNR DWT PSNR DFT PSNR
19.0173 17.2322 17.2906
7. Gamma correction Attack (1.5)
TABLE 7
PSNR VALUES FOR Gamma ATTACK
DCT PSNR DWT PSNR DFT PSNR
19.0173 17.2322 17.2906
8. Crop Attack (both sides)
TABLE 8
PSNR VALUES FOR Crop ATTACK
DCT PSNR DWT PSNR DFT PSNR
16.3523 17.3939 14.7956
9. JPEG Compression Attack (Q=25)
TABLE 9
PSNR VALUES FOR JPEG Compression ATTACK
DCT PSNR DWT PSNR DFT PSNR
31.3859 34.4156 29.103
Conclusion
In this study we made a comparison and evaluation of three Transform Domain Watermarking Techniques DCT, DWT, and DFT.
We used the cover image (Lena 512×512) and one watermark binary image (Best) the evaluation operation depended on 9 attacks and attack force was measured by using PSNR value.
Depending on PSNR values we can conclude:
‘ In Gaussian attack and Rotate attack DFT better than DWT and DCT.
‘ In Scale attack, Crop attack and JPEG compression attack DWT better than DCT and DFT.
‘ In histogram attack, intensity attack, Gamma attack and Mean Filter attack DCT better than DFT and DWT.
References
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