Robust Multiple Watermarks for Medical Image Based on DWT and DFT Jingbing Li
Chunhua Dong
College of Information Science and Technology Hainan University Haikou , China
[email protected]
College of Information Science and Technology Hainan University Haikou, China
[email protected]
Xianhua Han
Yen-wei Chen
College of Information Science and Engineering Ritsumeikan University Kasatsu-shi, Japan
[email protected]
College of Information Science and Engineering Ritsumeikan University Kasatsu-shi, Japan
[email protected]
Abstract—Medical images must be stored in a secure way to preserve unauthorized disclosure of patient data. This paper proposes an algorithm of robust multiple watermarks to serve these purposes using DWT and DFT. A part of sign sequence of DWT and DFT coefficients are used as feature vector for enhancing the robustness against Totation attacks, scaling attacks, translation attacks and cropping attacks. Moreover, the content of medical image remains unchanged with our proposed algorithm which is one kind of the zero-watermarking technology. We describe how to extract the feature vector of medical image, and then, embed and extract the multiple watermarks. The results of experiment indicate that the watermark scheme has strong robustness, and can embed much more data compared with the existing watermarking techniques.
2) Reversible watermarking. In the reversible watermarking, once the embedded content is read, the watermarking can be removed from the image allowing retrieval of the original image[5]. Unfortunately, most of the reversible watermarking is fragile. Its robustness is poor and the capacity is still way below the embedding capacity of non-reversible watermarking technique. 3) Classical watermarking. In this method, watermarking is often embedded in the least significant bit (LSB) [6], or in the low or middle frequency coefficients in the frequency domain(DCT,DFT or DWT). However, compared to the previous two methods, the capacity of the embedded watermark easily affects the content of Region of Interest(ROI). It is necessary to control the amount of the embedded watermarking to avoid wrong diagnosis of the doctors. In addition, the classical watermarking has low robustness especially against geometric attacks. Therefore, in this paper we present a DWT-DFT based multiple watermarks. With the proposed algorithm, the watermarking does not affect the quality of medical images and has good robustness.
Keywords-DWT; DFT; Multiple watermarks; Medical image
I.
INTRODUCTION
In a modern integrated health care environment, digital information systems are playing an important role. However, it is fairly easy for malicious adversary to intercept sensitive medical data when the public network is being used for telemedicine. It is an urgent need of security measures in medical information system. With the invisibility and robustness properties of watermarks, patient information, doctor diagnosis and Electronic Patient Records can be embedded in the medical imagesas hidden watermarks[1]. Medical image watermarking is usually divided into the following three types [2]. 1) RONI(Region of non-interest)-based medical image watermarking. The content of medical images is unable to tolerate significant changes when watermarking is embedded. Hence, the watermarking information is embedded in the RONI of the medical images [3][4]. However, the capacity of hidden information is limited because most of the RONI area of the image is the black background..
II.
THE DISCRETE WAVELET TRANSFORM(DWT) AND FOURIER TRANSFORM(DFT)
A. The Discrete Wavelet Transform(DWT) The wavelet transform, first proposed by Daubechies and Mallat in 1988, is a new signal analysis theory and is a Ātimefrequencyā method. Let \ L2 (R) , be the dilated function, and can be defined by: 1 / 2 \ a,b (t ) a \ ((t b) / a)ǂǂa, b R, ǂa z 0 (1) Any basis function can be obtained from \ by first dilating by the factor a, and then translating by the factor b. The wavelet transform of f L 2 ( R ) by \ is defined as:
895
³
W f ( a ,b )
R
f (t ) \
a ,b
( t ) dt
f ( x, y ) is the value of the medical image at the point ( x, y) and F (u , v ) corresponds to the DFT coefficientat point (u,v)
(2)
The decomposing equation of the Mallat algorithm is as follows:
in frequency domain. III.
¦ c j ,n h n 2 k ǂ k z
c j 1 , k
d j 1,k
(3)
n z
¦c j ,n g n2 k ǂǂkz
A. The extracting algorithm of feature vector from medical image Firstly, DWT is applied on the original medical image to obtain the approximated subband LL1. Then, DFT of the whole LL1 is computed and the DFT coefficient matrix is acquired. We choose 5 low-frequency DWT-DFT coefficients (F(1,1), …F(1,5)), which are shown in Table I. It can be seen that the value of the low-frequent coefficients may change after the image has undergone an attack, particularly some geometric attacks such as rotation, scaling, and transformation. However, the signs of the coefficients remain unchanged even with strong geometric attacks, as shown in Table I. Here, two signs are generated from one complex coefficient. The different attacked images are shown in Fig. 1(b)-(e). Let “1” represents a positive or zero coefficient(including real and imaginary part), and “0” represents a negative coefficient, and then we can obtain the sign sequence of low-frequency coefficients, as shown in the column “C7”, “Sequence of coefficient signs”, in Table I. It can be seen that the sign sequence is unchanged after geometric attacks, and the normalized cross-correlation (NC) is equal to 1.0, as shown in column “C8”.
(4)
nz
The reconstruction equation of the Mallat algorithm is given by: c j ,k
¦ d j 1, n g k 2 n ǂ ǂǂ kz ¦ c j 1,n hk 2 n ǂ nz
(5)
nz
By the one-layer wavelet decomposition of the original image, four subband images LL1, LH1, HL1, and HH1 can be obtained. Therein, LL1 is the approximated subband image with low frequency characteristics that are robust against attacks. The others subband images (LH1, HL1, and HH1) with high frequency characteristics are easily affected by changes. Therefore, embedding the watermarking into the LL can provide better robustness. In this paper the original medical image was decomposed by DWT (set layer=1), and the watermarking was embedded in the LL. Since both the new Joint Photographic Experts Group 2000 (JPEG2000) and new Moving Picture Experts Group 4 (MPEG-4) use DWT, a watermarking algorithm that uses DWT is compatible with them.
B. The embedding and detracting algorithms of multiple watermarks First, k groups of independent binary pseudo-morph sequences are generated for the watermarks. W are the multiple watermarks to be embedded with W= ^wk ( j) w( j) 0,1; ǂǂ 1 d j d L, 1 d k d N` ,where L and N are length
B. The Discrete Fourier Transform (DFT) The discrete Fourier transform is a signal analysis theory. The M u N medical image’s DFT is defined by: M 1 N 1
F (u , v )
¦ ¦ f ( x, y ) e
j 2 S xu / M
e
j 2 S yv / N
and number of multiple watermarks, respectively. We select the tenth slice of the used medical volume data as the original medical image. It is described as F= { f (i, j ) , 1İiİN1, 1İj İN2},where f (i, j ) denotes the value of medical image at the point (i, j ) . To facilitate the operation, we assume N1=N2 = N.
x 0 y 0
x
0,1,..., M 1; y
DWT AND DFT BASED ROBUST MULTIPLE WATERMARKS FOR MEDICAL IMAGE
0,1,..., N 1
TABLE I CHANGE OF DWT-DFT LOW-FREQUENCY COEFFICIENTS WITH RESPECT TO DIFFERENT ATTACKS
C1
C2 [103]
C3 [103]
C4 [103]
C5 [103]
C6 [103]
C7
C8
Image processing
F(1,1)
F(1,2)
F(1,3)
F(1,4)
F(1,5)
Original image
405.11+0i
-238.19-13.6i
-1.77-0.07i
34.66+4.60i
9.57+5.38i
Sequence of coefficient signs 1100001111
Rotation (20e)
405.06+0i
-220.69-39.62i
-12.67-11.79i
22.79+11.13i
10.61+14.00i
1100001111
1.0
Scaling (x 2)
101.55+0i
-59.46-4.88i
-0.57-0.05i
8.50+1.77i
2.26+1.60i
1100001111
1.0
Scaling (x 0.5)
NC 1.0
1623.10+0i
-953.91-42.71i
-7.99-0.21i
138.64+13.28i
39.74+19.86i
1100001111
1.0
Translation (7% ,down)
405.11+0i
-238.19-13.56i
-1.77-0.07i
34.66+4.60i
9.57+5.38i
1100001111
1.0
Cropping(10%) (from Y direction˅
381.05+0i
-218.67-12.78i
-11.11-0.98i
35.39+5.11i
11.41+5.13i
1100001111
1.0
896
(a)
(b)
(c)
(d)
(e)
Fig. 1. Different geometrical attacks: (a) Original image; (b) Rotation(20eclockwise); (c) Scaling(0.5times); (d) Translation(7%,down);(e)Cropping(10%,from y direction)
1) Embedding multiple watermarks Setp1: Acquire a robust feature vector of the original medical image using DWT and DFT. Firstly, DWT is used to decompose the original medical image, F(i,j), to get coefficients matrix FA(i,j). Then, DFT of the whole approximated subband LL1, FAL(i,j) , is computed and the DFT coefficient matrix, FF(i,j), is acquired. Next, the frequency sequence Y(j), from low to high frequency, can be obtained. Finally, the feature vector V {v( j ) | v( j ) 0,1; 1 d j d L ǂ }ǂis achieved as the signs sequence of the low-frequency DWT-DFT coefficients, where the value of L can tune the robustness and capability of the embedded watermarking. The procedure is described as: FA(i , j ) DWT 2( F (i , j )) (7) FF (i , j ) V ( j)
DFT 2( FAL (i , j )) Sign( FF (i , j ))
W k ' ( j ) V ' ( j ) key k ( j )
Where Wk’(j) is the k-th watermarking, V’(j) is the feature vector of the tested image, and Keyk(j) was obtained from the above process of watermarkingembedding. The k-th key corresponds to k-th watermarking. The NC between the original W and the extracted watermarks W’ can be calculated. In addition, the hidden information (watermarking) can be extracted without the original medical image, which is advantageous to protect the safety of the medical image. IV.
k k (10) Key ( j ) V ( j ) W ( j ) Where V(j) denotes the feature vector of the original medical image, Wk(j)denotes the multiple watermarks to be embedded, and “” is the exclusive-OR operator. The k-th key, Keyk (j), corresponds to k-th watermarking, Wk(j). After the binary logical sequence, Keyk(j) is abained, we should store it for extracting the multiple watermarksfrom the watermarked medical image. Furthermore, Keyk(j) can be regarded as a secret key and registered to the third part to preserve the ownership of the original medical image [7]. 2) Extract the multiple watermarks from the tested image Step 3: Acquire the feature vector V’(j) using the DWTDFT of the whole tested image F’(i,j), This process of acquiring the feature vector V’(j) is similar to step 1 of the above algorithm for embedding the watermarking. The obtained feature vector is V ' {v'( j) | v'( j) 0,1; 1d j d L} ǂ, which consists of the siges sequence of the DWT-DFT coefficients with the same meaning of L as previously. The procedure is described as follows˖ FA'(i , j ) DWT 2( F '(i , j )) (11)
DFT 2( FAL '(i , j ))
V '( j ) Sign ( FF '(i , j )) Step 4: Extract multiple watermarks Wk’(j)
EXPERIMENTS
In our experiments, 1000 groups of independent binary pseudomorph sequences are used. Every sequence consists of 32 bits. In the experiment, three groups which are the 300th group, 500th group and 700th are selected at random from the 1000 groups as the embedded multiple watermarks. The medical image is the tenth slice of one medical volume data and its size is 128x128. The original medical image is denoted as F(i,j), where 1 i, j 128. The corresponding DWT-DFT coefficient matrix is FF(i,j). Taking the robustness and the capacity of one-time embedding into consideration, we select the 32bitsigns sequence of 16 low frequencies coefficient as the feature vector V(j) selected from FF (i,j), where 1 i, j 4. In order to measure the quantitative similarity, the normalized cross-correlation (NC) is used in this paper, defined as:
(8) (9)
Step 2˖Utilize the multiple watermarks Wk(j) and feature vector V(j) to generate the logical sequence, Keyk(j);
FF '(i , j )
(14)
NC
¦¦[W(i, j) W'(i, j)] ¦¦[W(i, j)] , 2
i
j
i
j
(15)
Where W denotes the embedded watermarking and W’ denotes extracted watermarking. The higher the NC value, the more similarity there is between the embedded and extracted watermarking. A. Rotation attacks. Fig. 2(a) shows the medical image rotated clockwise by 15q. PSNR of the rotated medical image is 12.70dB. Fig. 2(b) shows that the multiple watermarks can be detected, with quantitative similarity NC1=0.85, NC2=0.90 and NC3=0.90. Table II gives the PSNR and NC when the medical image has been rotated by different angles. When the angle of rotation is up to 25q clockwise. the multiple watermarks can still be detected, with NC1=0.69, NC2=0.82 and NC3=0.83. Therefore we can conclude that our scheme is robust against rotation attacks.
(12) (13)
897
(a)
(b)
Fig. 2. Under rotation attack (angle is 15q): (a) an image with rotation attack; (b) multiple watermarks detector TABLE II THE PSNT AND NC UNDER ROTATION ATTACKS
Rotation (clockwise) PSNR(dB) NC1 NC2 NC3
5嘙
10嘙
15嘙
20嘙
25嘙
16.19 1.00 1.00 1.00
13.49 0.85 0.90 0.90
12.70 0.85 0.90 0.90
12.38 0.75 0.86 0.86
12.16 0.69 0.82 0.83
B. Scaling attacks. Fig. 3(a) shows the medical image with a scale factor of 4.0. Fig. 3(b) shows that the multiple watermarks can be detected, NC1=1.0, NC2=1.0 and NC3=1.0. Table III gives the PSNR and NC when the medical image has been scaled by
different scaling factors. If the scale factor drops to 0.4, the multiple watermarks can still be detected, NC1=0.74, NC2=0.75 and NC3=0.74. Therefore our proposed algorithm of multiple watermarks is robust against scaling attacks.
(a)
(b)
Fig. 3. Under scaling attack(scaling factor 400%): (a) an image with scaling attack; (b) multiple watermarks detector. TABLE III THE NC UNDER SCALING ATTACKS
Scaling factor
0.4
0.5
0.8
1.0
1.2
2.0
4.0
NC1
0.74
1.00
0.92
1.00
1.00
1.00
1.00
NC2
0.75
1.00
0.88
1.00
1.00
1.00
1.00
NC3
0.74
1.00
0.87
1.00
1.00
1.00
1.00
C. Translation attacks. Fig. 4(a) shows the medical image under translation down by 3%. The PSNR of the translated medical image is 13.82dB. Fig. 4(b) shows that the multiple watermarks can be detected, NC1=0.9, NC2=0.93 and NC3=0.93. Table IV gives the PSNR and NC when the medical image has been translated by
different distance. If the translation down by 7%, the multiple watermarks can still be detected, NC1=0.62, NC2=0.68 and NC3=0.67. The results show that the scheme is also robust against translation.
(a)
(b)
Fig. 4. Under translation attack(translation 3%): (a) an image with translation attack; (b) multiple watermarks detector.
898
TABLE IV THE PSNR AND NC UNDER TRANSLATION ATTACKS
Horizontal Translation(Left)
Vertical Translation(Down)
Distance(%)
3%
4%
5%
6%
7%
3%
4%
5%
6%
7%
PSNR(dB)
12.28
11.51
11.38
11.27
11.14
13.82
12.59
12.39
12.33
12.20
NC1
0.85
0.79
0.54
0.54
0.54
0.90
0.75
0.69
0.69
0.62
NC2
0.90
0.82
0.62
0.62
0.62
0.93
0.82
0.75
0.75
0.68
NC3
0.90
0.82
0.63
0.63
0.63
0.93
0.80
0.74
0.74
0.67
been cropped. The results show if the watermarked image is cropped by 20 % from y axis, we still can obtain NC1 of 0.68, NC2 0f 0.77 and NC3 of 0.74. It can say that the scheme is robust against cropping.
D. Cropping attacks Fig. 5(a) shows the medical image cropping from y axis at the ratio of 18 %. Fig. 5(b) shows that the multiple watermarks can be detected, NC1=0.82, NC2=0.90 and NC3=0.87. Table V contains the values of NC when the medical image has
(a)
(b)
Fig. 5. Under cropping attack (From the Y axis, 18%): (a) an image with cropping; (b) multiple watermarks detector. TABLE V THE PSNR AND NC UNDER TRANSLATION ATTACKS
Cropping ratio NC1 NC2 NC3
V.
4% 0.90 0.95 0.95
6% 0.82 0.90 0.87
8% 0.82 0.90 0.87
10% 0.82 0.90 0.87
14% 0.75 0.82 0.80
16% 0.82 0.90 0.87
18% 0.82 0.90 0.87
20% 0.68 0.77 0.74
Hainan University -- Institute of Acoustics, Chinese Academy of Sciences for Joint Training of Special Support.
CONCLUSION
A novel embedding and extracting multiple watermarks algorithm is presented in this paper. The proposed algorithm is based on DWT-DFT, and has no restriction of the number of watermarks. The part of sign sequence of DWT-DFT coefficients is used as feature vector, which is utilized to enhance the robustness against rotation, scaling, translation attacks. Our proposed algorithm can easily embed multiple watermarkes, where different keys correspond to different watermarks. In addition the watermarking can be extracted without the original medical image. Experimental results show that the algorithm is robust to geometrical attack. Moreover, the content of medical image remains unchanged with our proposed algorithm which is one kind of the zerowatermarking technology.
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[2]
[3]
[4]
[5]
ACKNOWLEDGEMENT
[6]
This work is partly supported by 211 Project, by Hainan University Graduate Education Reform Project (yjg0117), and by Natural Science Foundation of Hainan Province (60894), and by Education Department of Hainan Province project (Hjkj2009-03) and by Communication and Information System,
[7]
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