International Journal of Computer and Electrical Engineering, Vol.3, No.1, February, 2011
1793-8163
8
Abstract– As DC coefficients are perceptually most
significant and more robust to many unintentional attacks
(signal processing) and intentional attacks (unauthorized
removal), in this paper we proposed a robust non-blind
watermarking algorithm based on DC coefficients for color
images. DC coefficients are obtained by applying discrete
wavelet transformation technique (DWT) followed by block
based Discrete Cosine Transformation (DCT) technique. The
RGB color spaces of the cover image are decomposed into
different frequency bands using wavelet decomposition and
block based DCT is applied. DC matrix is SVD decomposed to
obtain singular values in which watermark is to be hidden. The
proposed algorithm increases the watermarking capacity of
cover data watermark and provides robustness against many
signal processing operations and intentional attacks. The
quality of the extracted watermark from green and blue color
spaces is very good. The measured psnr and NC values are
tabulated.
Index Terms— Digital Watermarking, Discrete Wavelet
Transform (DWT), Discrete Cosine Transform (DCT) and
Singular Value Decomposition (SVD).
I. I
NTRODUCTION
With the development of web communication and
multimedia technology, more and more digital multimedia
signal can be transmitted through Internet which in turn
vulnerable to various attacks. Among today’s information
security techniques, multimedia watermarking techniques
have been developed greatly and become a kind of powerful
tool for protecting multimedia content. Watermarking is the
process of embedding data into a multimedia content such as
an image, audio or video file for the purpose of copy right
protection, ownership verification, broadcast monitoring,
authentication etc. The important properties of watermarking
algorithm include imperceptibility, robustness, security and
watermark recovery with or without the original data [1]. In
order to be robustness, it is preferred to embed the watermark
in perceptually most significant components, but this may
affect the visual quality of the image and watermark may
become visible. If perceptually insignificant coefficients are
selected for embedding then the watermark may be lost by
common signal processing operations. Thus determining the
place of watermark is a conflict between robustness and
fidelity and it is purely application dependent.
Manuscript received February 12, 2010.
V.Santhi is with the VIT University, Vellore, TamilNadu, India, 632 014
phone: +91 9688138634 , e-mail: vsanthi@ vit.ac.in
Arunkumar Thangavelu is with VIT University, Vellore,Tamil Nadu,
India, 632 014 . e-mail: arunkumar.thangavelu@gmail.com.
Generally information could be hidden either by directly
modifying the intensity value of pixels or frequency
coefficients of an image. The former technique is called
spatial domain technique and later is called frequency
domain technique. To obtain frequency components of an
image, it needs to be transformed using any one of the
transformation techniques such as Discrete Fourier
Transformation (DFT), Discrete Cosine Transformation
(DCT) [3]. Discrete wavelet Transformation (DWT)[4]. In
transform domain casting of watermark can be done in full
frequency band of an image or in specific frequency band
such as in low frequency band or in high frequency band or in
middle frequency band.
In this paper we proposed a new robust watermarking
algorithm that combines the features of discrete wavelet
transform, singular value decomposition and discrete cosine
transformation techniques. The advantages of the proposed
method are its robustness and its capacity. Robustness is
achieved through embedding of watermark in most
significant coefficients (DC coefficients) and capacity is
increased by using three channels (RGB) of color image. The
proposed algorithm is tested against various signal
processing operations and many attacks and found that the
algorithm is robust. The robustness is tested by measuring the
similarity of original and extracted watermark which is more
than 90 percent for all kinds of attacks except the rotation
attack.
The rest of the paper is organized as follows; Review of
related works is given in section II. Preliminaries of
DWT-DCT-SVD techniques are discussed in section III.
Proposed algorithm is discussed in section IV. Performance
evaluation is elaborated in section V. Concluding remarks are
given in section VI.
II. R
EVIEW OF
R
ELATED
W
ORKS
Review of literature survey has been conducted on
discrete wavelet transformation (DWT), discrete cosine
transform (DCT) combined with singular value
decomposition (SVD) techniques for hiding information in
digital color images. In [2] the image is divided into many
block of size 8x8 and it is block transformed using DCT
technique. These transformed blocks are randomly shuffled
to decorrelate and to spread the watermark across the entire
image. The mid band blocks are selected from the permuted
blocks to embed watermark. This system is more robust than
SVD based method. In [3] the cover is decomposed into four
bands. The high frequency band is inverse transformed to
obtain high frequency image and it is SVD decomposed to
DC Coefficients Based Watermarking Technique
for color Images Using Singular Value
Decomposition
V.Santhi Member, IACSIT, Prof. Arunkumar Thangavelu
International Journal of Computer and Electrical Engineering, Vol.3, No.1, February, 2011
1793-8163
9
embed watermark by modifying high frequency components.
Results show that the system is withstanding certain attacks
including geometric attacks.
In [4] Image is transformed by DWT technique to K level.
The middle frequency band LH and HL are SVD transformed
and watermark is hidden. Similarly in low frequency and
high frequency band the watermark is embedded using
distributed discrete wavelet transform method (DDWT).
Both algorithms are tested against attacks ad proved that they
are robust against cropping attacks. For attacks such as
Gaussian Noise, contrast adjustment, sharpness, histogram
equalization, and rotation the proposed scheme is robust by
exploiting the advantage of the SVD watermarking technique.
In [5], three level decomposition of DWT is applied on image
to get ten bands of frequencies. All ten bands of frequency
coefficients are SVD transformed to embed watermark. A
new watermarking scheme for images based on Human
Visual System (HVS) and Singular Value Decomposition
(SVD) in the wavelet domain is discussed. Experimental
results show its better performance for compression,
cropping and scaling attack.
In [6] two level decomposition of DWT is applied to
transform an image into bands of different frequency and a
particular band is selected and converted into blocks of size
4x4 for embedding data. Each of those the blocks are SVD
transformed and watermark is hidden into diagonal matrix of
every block. The similarity between the original watermark
and the extracted watermark from the attacked image is
measured using the correlation factor NC. The algorithm
shows that when DWT is combined with SVD technique the
watermarking algorithm outperforms than the conventional
DWT algorithm with respect to robustness against Gaussian
noise, compression and cropping attacks. In [7] a new
algorithm is proposed for embedding watermark in color
images. The blue color channel of the image is decomposed
to obtain four frequency bands and the selected band is SVD
transformed to to hide watermark. This scheme performs well
for JPEG compression attacks. In [8] the new non-invertible
method is proposed by combining DWT and SVD technique.
The performance evaluation shows that the algorithm is
robust against attacks such as cropping, Gaussian noise,
JPEG compression. In [9] human visual system is exploited
while embedding watermark. In [10], DWT and SVD
techniques are combined to embed watermark in YUV
channel. YUV channels are decomposed by applying wavelet
transformation technique followed by SVD technique. Since
the watermark is hidden in full band of YUV channel, the
DSFW is robust to many signal processing attacks. In [12],
the DWT technique is applied to decompose input image and
LL band is converted into many blocks for DCT
transformation. Only DC coefficients are selected and a new
matrix is formed , this new matrix is SVD decomposed for
watermark embedding
Based on the review performed many works are existing
for embedding watermark by combining DWT and SVD
techniques for intensity images. In the proposed work the
watermark is embedded in the DC components of
transformed color image. In order to increase the robustness,
the low frequency band can be selected. But to increase the
capacity of the watermark full band can also be used. The
selected band is divided into block of size 2x2 which in turn
DCT transformed to obtain only DC coefficients. These DC
coefficients are SVD transformed to embed watermark in
singular values.
III. P
RELMINARIES
A. Discrete Cosine Transform
DCT is another important transformation technique which
is widely used due to its energy compaction and decorrelation
properties. DCT technique is faster than discrete Fourier
transform since the bases are cosine function for the former
technique and complex function for the later technique
The transformed matrix consists of both AC and DC
coefficients. If the DCT technique is applied on block of size
NxN then it is called block DCT. In DCT transformed block
the left top corner element is called as DC coefficient which
is perceptually significant and the remaining coefficients are
called AC coefficients which are perceptually insignificant.
These coefficients are zigzag scanned to obtain frequency
components of an image in decreasing order. These DC and
AC components are modified to embed watermark in it
[3][11]. Equ. 1 and 2 are used for taking transformation and
inverse transformation of an image.
0,0
√
∑∑
,
,
√
∑∑
,
cos
п
cos
п
(1)
Where u = 1,…,M-1 , v = 1,…,N-1.
The inverse transform is
,
1
√
0,0
2
√
,
cos
2 1
п
2
cos
2 1
п
2
(2)
B. Discrete Wavelet Transform
DWT is a transformation technique is used to represent an
image in a new time and frequency scale by decomposing the
input image into low frequency, middle and high frequency
bands. The value of low frequency band is the averaging
value of the filter whereas the high frequency coefficients are
wavelet coefficients or detail values. [4].
The DWT can be used to decompose image as a multistage
transform. In the first stage, an image is decomposed into
four subbands LL1, HL1, LH1, and HH1, where HL1, LH1,
and HH1 represent the finest scale wavelet coefficients,
while LL1 stands for the coarse level coefficients, i.e., the
approximation image. Fig.1 shows the one level wavelet
decomposition of an image [12].
Fig. 1 One level of Wavelet decomposition
C. Singular Value Decomposition
SVD is a mathematical tool used to analyze matrices. In
Input Image
LL1 LH
HL1 HH
DWT
International Journal of Computer and Electrical Engineering, Vol.3, No.1, February, 2011
1793-8163
10
SVD, a given matrix A is decomposed into three matrices
such that, A=USV
T
where U and V are orthogonal matrices
and U
T
U=I, V
T
V=I, I is an identity matrix. The diagonal
entries of S are called the singular values of A, the columns of
U are called the left singular vectors of A, and the columns of
V are called the right singular vectors of A. This
decomposition is known as the singular value decomposition
(SVD) of matrix A. Usually, watermark is embedded in the
singular matrix, and if the watermark is embedded in the
orthogonal matrices of SVD then the perceptibility of host
image is improved it is not robust to many attacks because the
matrix elements of orthogonal matrices are very small.The
three main properties of SVD from the view point of image
processing applications are [4]:
1. The singular values of an image have very good
stability, that is, when a small perturbation is
added to an image, its singular values do not change
significantly.
2. Each Singular value specifies the luminance of an
image layer while the corresponding pair of singular
vectors specifies the geometry of the image.
3. Singular values represent intrinsic algebraic
properties.
IV. P
ROPOSED
A
LGORITHM
Proposed algorithm combines the properties of DWT,
DCT and SVD techniques to increase the robustness and
capacity of the algorithm by selecting significant coefficients
and number of color channels. The procedure for embedding
and extracting the watermark is given below.
A. Watermark embedding algorithm
In the proposed work the Lena color image of size 512 x
512 is considered as cover image. DWT technique is applied
to decompose the color spaces into different frequency bands
using dB1 filter. Watermark size determines the selection of
one or all the frequency bands. Each band is divided into
many blocks of size 4x4 and DCT is applied to all the blocks.
In DCT transformed block the energy is compact in its DC
component only. DC matrix is formed by collecting DC
components of all the blocks and it is decomposed by SVD
technique to get the singular matrix in which watermark is to
be hidden. Watermark embedding and extraction process is
shown in the Fig. 2 and Fig 3. The steps for embedding
watermark are given below.
Let A be the cover image, then
1. Decompose the input image A into RGB color
channels
2. Apply DWT to decompose RGB color channels of
an image into various frequency bands. Size of the
watermark determines the number of color spaces and
number of frequency bands for embedding watermark.
,
,
,
2
,
1
,
,
,
2
,1
,
,
,
2
,
1
3. Divide the middle frequency band into smaller
blocks of size 4x4 and apply DCT to each block,
B
ij
4. Extract the DC coefficients σ
ij
from every DCT
transformed blocks, and build a new matrix C,
which is decomposed by applying SVD,
5. Let W be the watermark and decompose it using
SVD technique
6. Modify the singular values of ‘C’ matrix by using
the singular values of watermark.
7. Combine the modified singular values with the
orthogonal matrices of ‘C’,
2 1
8. Replace the original DC’s σ
ij
by the modified DC’s
σ
ij
in each block B
ij
.Then apply inverse DCT to each
block of low frequency band to reconstruct low frequency
band of DWT decomposed image.
9. Step 3 to step 8 is repeated for hiding watermark in
other bands of a channel.
10. Step 2 to step 9 is repeated for hiding information
in other color channels.
11. Inverse wavelet transformation technique is
applied to get the watermarked color space.
12. The RGB color spaces are combined to reconstruct
the watermarked image A
w
.
B. Watermark Extraction Algorithm
1. Convert the watermarked image into RGB color spaces.
2. Apply DWT to decompose the respective color space of
a cover image in which watermark is hidden.
,,,
2
,
3. Divide middle frequency band into smaller 4x4 blocks
and apply DCT to each block, B
*
ij
.
4. Extract the DC coefficients σ
ij
from every DCT
transformed blocks and construct a new matrix C,
which could be decomposed by SVD technique,
C=U
*
S
*
V
*T
5. Extract the singular values from C matrix, then compare
the difference between the watermarked singular
values and host image singular values, S3=( S
*
-
S)/α.
6. Combine the obtained singular values with the
orthogonal matrices of watermark,
W
*
= U
w
S3 V
w
T
7. Repeat the same procedure to extract the watermark
from other bands.
In the proposed method, to extract the watermark from all
frequency bands, it uses original cover image. So, this
algorithm is can be classified as non-blind watermarking
technique. The above embedding and extraction algorithm
can be tested for all the three color spaces of (RGB) an image.
The embedding of proposed algorithm is shown in Fig.
1.Similarly the extraction process is shown in Fig 2.
International Journal of Computer and Electrical Engineering, Vol.3, No.1, February, 2011
1793-8163
11
U
*
S
*
V
*
U
S V
U
W
S
W
V
W
’
R
LL
LH
HL
HH
Color Space Conversion
DWT in one of the
color component
Block
DCT in LH
RT
SVD of host
image
Watermarked
Image
Extraction
DC from all
blocks
SVD in
DC
matrix
Fig. 3 Watermark extraction process
Extracted watermark
G
B
U S V
Watermark
U
w
S
w
V
w
U S
1
V’
R
G
LL
LH
HL
HH
B
Color Space Conversion
DWT in one of the
color component
Block
DCT in LH
RT
DC from all
blocks
LL
LH
HL
HH
SVD
SVD in
DC
matrix
Host image
Inverse SVD
IDCT
IDWT
Modified LH
Watermarked image
Embedding
Color component
concatenation
Watermarked
component
Fig. 2 Watermark embedding process
R
G
B
International Journal of Computer and Electrical Engineering, Vol.3, No.1, February, 2011
1793-8163
12
V. P
ERFORMANCE
E
VALUATION
In this proposed algorithm the Lena image of size 512x512
is taken as test image and the size of watermark considered is
64x64. Selected embedding intensity value is 0.1 for all
frequency bands. Based on particular application the
frequency band and the color channel can be selected. If the
size of the watermark is small then any one of the color
channel can be selected and application decides the
frequency band. This proposed algorithm is tested by
embedding watermark in all frequency band of red , green
and blue color space.
The original image, watermark and watermarked image
are shown in Fig 4(a), 4(b) and 4(c) respectively. Similarly
the extracted watermarks are shown in Fig.5.
In order to test the quality of the extracted watermark and
cover data both subjective and objective measurements are
used. The objective criteria are measured through (3), (4)
and (5).
∑∑
,
,
(3)
10log
(4)
The quality of watermarked image is measured using peak
signal to noise ratio (PSNR) value and it is observed that the
value is 31.0847 db for all color component of RGB color
space. Normalized correlation (NC) is a metric through
which the degree of similarity between original watermark
and extracted watermark is measured. The equation for
measuring NC is shown in (5)
NC =
(5)
If the watermarked image is not altered through intentional
or unintentional attacks then the calculated normalized
correlation (NC) is 1, means that the original and
watermarked image is exactly similar. In the proposed work
the watermark is hidden in red color space of the cover image
using DWT-DCT-SVD technique and robustness is tested
with various attacks such as compression, rotation , salt and
pepper noise, Gaussian noise, image sharpening, histogram
equalization, Gaussian blur, color contrast, cropping and
resizing. These attacks are not aimed at removing the
watermark, but trying to either destroy it or disable its
detection and attempt to break the correlation between the
extracted and the original watermark. This can be
accomplished by shuffling the pixels that is the value of
corresponding pixels in the attacked and the original image is
the same, however, their location has been changed.
Correlation value of extracted watermark after various
attacks from red color space is shown in Table 1. Similarly
correlation value of extracted watermark from green color
space and blue color space after various attacks are shown in
Table 2 and Table 3.respectively
The tabulated results show that the NC value is high when
watermark is extracted from low frequency components and
it is low for high frequency bands for attacks such as salt and
pepper noise, Gaussian noise, compression, color contrast
and cropping. Similarly the results for sharpening and
resizing shows that the NC values for extracted watermark
from high frequency bands are more than low frequency
bands. But for rotation attack NC value is very low for all
frequency components.
TABLE 1.CALCULATED NC VALUES OF EXTRACTED
WATERMARK FROM THE RED COLOR SPACE
ATTACKS
LL
LH HL HH
Salt and peppers
noise
0.99
9
0.996 0.997 0.573
Gaussian noise
0.99
8
0.994 0.995 0.524
Rotation
0.55
0
0.378 0.203 0.479
Sharpening
0.95
7
0.998 0.995 0.997
Histogram
equalization
0.83
9
0.982 0.985 0.978
Cropping
0.99
6
0.436 0.556 0.391
Gaussian blur
0.99
9
0.999 0.999 0.991
Color contrast
0.99
0
0.931 0.958 0.956
Resize
0.84
9
0.973 0.967 0.962
Compression
0.98
1
0.759 0.839 0.741
As per the table 1, when the watermark is hidden in low
and middle frequency band of red color channel the system is
withstanding many attacks but it is not true if high frequency
band is selected for embedding. System is not robust to
cropping. Salt and pepper noise and Gaussian noise attacks
when high frequency band is selected for the place of
watermark. This algorithm withstanding compression attacks
RT
RT RT
Fig.5 Extracted watermark from all Frequencies
RT
RT
(a) Host image (b) watermark (c) Watermarked image
Fig.4