SVD-based Digital Image Watermarking on approximated
Orthogonal Matrix
Yevhen Zolotavkin and Martti Juhola
Computer Science, School of Information Sciences, University of Tampere, Kanslerinrinne 1, Tampere, Finland
Keywords: Digital Image Watermarking, Singular Value Decomposition, Robustness, Distortions, Transparency.
Abstract: A new watermarking method based on Singular Value Decomposition is proposed in this paper. The method
uses new embedding rules to store a watermark in orthogonal matrix that is preprocessed in advance in
order to fit a proposed model of orthogonal matrix. Some experiments involving common distortions for
grayscale images were done in order to confirm efficiency of the proposed method. The robustness of
watermark embedded by our method was higher for all the proposed rules under condition of jpeg
compression and in some cases outperformed existing method for more than 46%.
1 INTRODUCTION
Multimedia is becoming increasingly important for
human communication. In some cases the protection
of multimedia from unauthorized usage is a critical
requirement. Existing and widely used techniques in
Digital Right Protection (DRP) do not always
provide reliable defence against cybercriminals. One
of the main difficulties is connected with
degradation of quality of media content caused by
application of DRP related tools. Indeed value of
perceptual content of media is of the same
importance as the question of ownership. The
situation is complicated by increasing number of
multimedia processing tools that do not contradict
officially with DRP policy, but can introduce some
specific distortions like, for example, compression.
New and more sophisticated methods are needed to
satisfy the requirements which complexity is
growing.
One of the branches of DRP is Digital Image
Watermarking (DIW). The needs of DIW could be
different depending on a particular application. For
example, it might be required that a watermark
resists as much influence as possible (robust
watermarking) (Barni, 1997), resists some kinds of
influence and indicates presence of other kinds
(semi-fragile watermarking) (Altun, 2006); (Pei,
2006), and just indicates (fragile) (Fridrich, 2002).
In order to increase robustness under some
constraint that somehow represents invisibility (or
transparency) many methods have been proposed
during the last 20 years (Cox, 2007). The most
successful among them are methods operating in
transform domain. Widely used transforms are DFT,
DCT, DWT (Fullea, 2001); (Lin, 2000). Those well-
known transforms are parameterized in advance and
do not depend on an image fragment being
transformed. Therefore only a set of coefficients is
important to represent a fragment according to a
particular transform. However usually few
coefficients in the set are used for watermarking.
The drawback is that number of significant
coefficients of transformed fragment (and
significance of some coefficients as well) could vary
between different fragments (Xiao, 2008).
Consequently different parts of a watermark could
be embedded with non-equal robustness that
worsens the total extraction rate under an
assumption of some kind of distortion.
Another concern is that embedding of a
watermark requires quantization of coefficients. A
proper robustness-transparency trade-off for a
particular application requires different quantization
steps for different fragments. However information
about quantization steps should be transmitted
separately.
Different type of transform is provided by
Singular Value Decomposition (SVD). It assures
that the number of coefficients encapsulating image
fragment’s features is small and constant. These
coefficients form a diagonal in a matrix of singular
values. However SVD is a unique transform which
321
Zolotavkin Y. and Juhola M..
SVD-based Digital Image Watermarking on approximated Orthogonal Matrix.
DOI: 10.5220/0004507903210330
In Proceedings of the 10th International Conference on Security and Cryptography (SECRYPT-2013), pages 321-330
ISBN: 978-989-8565-73-0
Copyright
c
2013 SCITEPRESS (Science and Technology Publications, Lda.)
is different for every fragment and information about
the transform is in left and right orthonormal
matrices. Utilization of singular values for
watermarking provides good trade-off between
robustness and invisibility (Yongdong, 2005).
Though, elements of left and right orthonormal
matrices could also be used for watermarking. The
main complication for modification of elements of
left and right orthonormal matrices is that matrices
can become non-orthogonal. This considerably
worsens robustness of a watermark.
The main contribution of this paper is to provide
a watermarking method that modifies left
orthonormal matrix in a way it remains orthonormal.
Another contribution is utilization of different
embedding rules that provide different robustness-
transparency trade-off which improves flexibility
(adjustability) of watermarking.
The rest of the paper is organized as following: a
short review of relevant watermarking methods
exploiting SVD is given in the Section 2; Section 3
bears our own approach which is described in detail;
then, some experimental results are represented in
Section 4 followed by a discussion of their
importance in Section 5; finally, in Section 6 the
paper is concluded by general remarks regarding
relevance of our approach and its influence on future
research.
2 SVD-BASED WATERMARKING
Watermarking methods utilizing SVD have become
especially popular during the last 10 years.
This transform decomposes image fragment on
two orthogonal matrices and and diagonal
matrix containing singular values:
∙∙
.
(1)
Virtually any component from such decomposition
can be used for watermark embedding. There are
SVD-based watermarking methods that are blind
(Modaghegh, 2009), semi-blind (Manjunath, 2012)
and non-blind (Dharwadkar, 2011). In spite of that
the classification is quite clear, some methods, for
example, state they do not require for extraction any
additional media except a key, but during
watermarking the region of embedding is carefully
chosen to optimize robustness-transparency trade-off
(Singh, 2012). Evidently it is not absolutely fair to
compare performance of pure blind methods with
random key toward performance of such region
specific methods as the latter require new key
(different size) for each new image which is a lot of
additional information.
Starting from the first methods modifying just
the biggest singular value of decomposed image
fragment (Sun, 2002), continued further by more
sophisticated methods combining DCT-SVD (Lin,
2000); (Manjunath, 2012); (Quan, 2004), DWT-
SVD (Dharwadkar, 2011); (Fullea, 2001); (Ganic,
2004) and methods optimizing trade-off between
robustness and transparency for SVD-based
watermarking (Modaghegh, 2009) only few among
those approaches consider for embedding orthogonal
matrices and . The papers discussing blind
embedding in orthogonal matrix are (Chang, 2005)
(Tehrani, 2010) where watermarking methods that
operate on are proposed. The difference between
them is that in (Tehrani, 2010) some additional
block-dependent adjustment of a threshold is done.
Realizations and computational requirements for
both methods are quite simple. However, their
impact is not only in increased robustness compared,
for example, to (Sun, 2002). The methods also could
be modified in order to embed larger watermarks.
The idea to switch from standard approach of
modification of one singular value (as it is usually
done in most SVD-based watermarking schemes) to
modification of the first column in provides better
adaptation to robustness-transparency requirement.
The first column contains several elements that are
of equal significance. Their significance is the same
as it is for the biggest singular value which is clear
when equation (1) is rewritten in a different form:
∑
,
∙
∙
, (2)
where
and
are corresponding columns of
and respectively. Being constructed from
different significance layers image fragment has
scaling factor
,
on each layer. Adoptive
quantization of the first scaling factor is not always
the best alternative for watermarking because it
requires transmission of additional information
about quantization steps. Therefore it would be more
beneficial to modify the first layer in a more
sophisticated manner that provides adaptation which
purely corresponds to blind strategy. Such attempt is
made by Chang (2005) and Tehrani (2010) by
introducing a rule with a threshold. The rule is
applied to a pair of elements in the first column of
and can be used for embedding with different
robustness-transparency rate for each block.
Nevertheless approaches presented by Chang
(2005) and Tehrani (2010) have some disadvantages
because the authors did not develop a tool to achieve
orthogonality and normalization of modified matrix
SECRYPT2013-InternationalConferenceonSecurityandCryptography
322
. On the other hand SVD guarantees that during
extraction of a bit of a watermark from a square
block all three resulting matrices are orthogonal.
Therefore matrices that were used to compose a
block during embedding phase are not equal to the
matrices calculated during extraction phase. This
fact obviously could cause misinterpretation of a bit
of a watermark. Another disadvantage of Chang’s
(2005) and Tehrani’s (2010) approaches is that they
used only one embedding rule that considers only
two out of four elements in a column. Obviously
there is a better way to minimize distortions of
embedding if more elements are taken into account.
In order to increase the performance of SVD-
based blind watermarking in domain some
improvements are proposed in this paper. First we
provide that modified -matrix is orthonormal
which improves robustness. Second we propose
different embedding rules that maintain different
robustness-transparency trade-off which improves
flexibility. Third we minimize embedding
distortions which reduces visual degradation of
original image.
3 PROPOSED METHOD
Taking into account disadvantages of previously
proposed SVD-based watermarking methods new
approach is considered in this section. The
improvements incorporated in our approach provide
that altered matrix is orthogonal and normalized.
Different embedding rules are also proposed.
Satisfying orthogonality requirement would
consequently imply better robustness as all the
changes introduced to the most robust part of a
matrix (the first column) would not have projections
on other dimensions (defined by second, third and
fourth columns) except the dimension defined by
that part. In order to provide this a special kind of
approximation of an initial orthogonal matrix is
proposed.
Another improvement considered to enhance
robustness while preserving most of an original
image is normalization of altered orthogonal matrix.
Even in case each of original orthogonal matrices
defined by SVD is normalized, embedding of a
watermark according to (Chang, 2005); (Tehrani,
2010) cancels this quality. In contrast to that our
embedding method assures each watermarked
orthogonal matrix is normalized.
The way watermark bits are interpreted also
significantly influences robustness. The only kind of
matrix elements interpretation described in (Chang,
2005), (Tehrani, 2010) is the comparison of absolute
values of the second and the third elements in the
first column. In some cases we could greatly benefit
from different ways of interpretation that take into
account more elements. Our method of embedding
utilizes five different embedding rules where each
rule has an advantage under an assumption of some
kind of distortion.
3.1 Approximation of Orthogonal
Matrix
The approximation of an initial orthogonal matrix
proposed in this paper is based on 4x4 matrix that
can be described by 4 variables in different
combinations. Each combination creates an entry in
a set. One matrix from the possible set is
represented as following:
.
(3)
This matrix is always orthogonal and under an
assumption single row (or column) is normalized the
whole matrix is normalized too. Similarly to widely
used basis functions this matrix is described
compactly (just 4 variables) but in contrast to them
each separate element in a row (or column) is free
from being functionally dependent on others. Such a
quality makes these matrices quite suitable for
accurate and computationally light approximations
of original orthogonal matrices obtained after SVD
of square image fragments. Moreover every matrix
from the set is a distinctive pattern which could be
used to assess the distortions introduced after
watermark is embedded. Optionally this distinction
could be used to determine during extraction which
matrix from equally suitable and caries
watermark’s bit. The whole set of proposed
orthogonal matrices and option to choose between
embedding in or is necessary to achieve
minimal total distortion that consists of an
approximation error and a distortion caused by
embedding according to some rule.
There could be several approximation strategies
considering models from the proposed set of
orthogonal matrices. The main idea of embedding is
to provide extraction of watermark bits from
orthogonal matrices obtained after SVD with highest
possible rate while preserving high enough image
quality. Extraction is possible if during embedding a
watermarked image fragment is composed using one
diagonal matrix and two orthogonal matrices
SVD-basedDigitalImageWatermarkingonapproximatedOrthogonalMatrix
323
and (here
is defined to store a bit).
Suppose now we are preparing (or
approximating) the first orthogonal matrix for
embedding, so the result is
, but the second
orthogonal matrix remains unchanged. As we do
not embed in singular values there is no need to care
about the content of the diagonal matrix except the
requirement that it should be diagonal. So let
modified matrix of singular values be
∗
and
possibly different from original . Having the
original image fragment of size 4x4 it can be
written:
∙∙
∗
.
(4)
Note that in case of such approximation strategy it is
only required to satisfy twelve off-diagonal elements
of
∗
are as small as possible (in Least Squares
sense). Then after approximation is done those
twelve elements should be put to zero, so
approximation error causes some distortion of image
fragment before the actual embedding.
Another approximation strategy is to provide
both and are unchanged. In that case it is
necessary to approach:
∙∙
.
(5)
This is more challenging task as it is required to
match sixteen pixels as close as possible using the
same model of orthogonal matrix defined by just
four variables. However, this kind of approximation
strategy could have some advantage in perceptual
sense because singular values are preserved.
For our particular realization of watermarking
method it was decided to limit watermark
embedding by the first kind of approximation only.
In order to show in more details the approximation
with proposed orthogonal matrix let us substitute the
matrix product ∙ in (4) with 4x4 matrix :
∙
∗
.
(6)
Now let’s substitute
with orthogonal matrix
A in (3):
∙
∗
.
(7)
Matrix
∗
for simplicity could be transformed from
4x4 to 1x16 vector
∗
by rearranging elements of
∗
row by row which will lead to the following
equation:
∙
∗
∗
,
(8)
where
∗
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
.
Equation (8) can be simplified by ignoring 1, 6, 11
and 16 columns and elements of
∗
and
∗
respectively because for the current kind of
approximation diagonal elements of
∗
are not
important. By doing so we will get
∗∗
and zero
vector
:
∗∗
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
∙
∗∗
.
(9)
It is natural to suggest that simplest solution for (9)
is 0, but taking into account
requirement for to be normalized the solution is
not as trivial:
∙
∗∗
1
.
(10)
Obviously such a regularized overdetermined system
represents non-linear Least Squares task.
For further embedding it is required to prepare a
set of approximated orthogonal matrices where
matrix is just one possible variant for final
decision.
Five embedding rules were introduced to
improve robustness. Each rule is a condition that
could be satisfied in different ways, so we tried to
minimize distortions introduced on that step too.
Thanks to simplicity of our orthogonal matrix model
minimization of embedding distortions can also be
done quite easily. Suppose that as a result of
watermark embedding matrix has been changed
and become
∗
. Because it is required to keep
∗
normalized we will accept for further simplicity that
there is some vector
∆,∆,∆,∆
with length 1
which is orthogonal to
,,,
and
∗
is formed
from
SECRYPT2013-InternationalConferenceonSecurityandCryptography
324
∗
√
1
∙∙∆,
∗
√
1
∙
∙∆;
∗
√
1
∙∙∆,
∗
√
1
∙
∙∆;
where 01. The result of extraction of a
watermarked image fragment from unwatermarked
will be:
∙
∗
∙
∗
∙
∗
∙
∗
∙
∗
∙
.
(11)
Matrix
∗
is orthogonal as
∗
has the same
structure as . Consequently the Sum of Square
Residuals (SSR) between watermarked and
unwatermarked fragments can be defined as:
∗
∙
,
∗
1
∙∙∆
,
∗
.
(12)
Here ∆ is formed from ∆,∆,∆,∆ and is
normalized. Further simplification taking into
account the previously made assumptions will
produce an equation:
21
√
1
∙
∑
,
∗
. (13)
According to (13) distortion of image fragment
caused by watermark embedding in our method
depends on the length of the vector added to the first
column of orthogonal matrix and does not depend
on a vector’s orientation in contrast to the method
proposed in (Chang, 2005), (Tehrani, 2010). This
quality could greatly simplify procedure for
minimization of watermarking distortions and enable
more different embedding rules to be used. Equation
(13) also provides an understanding that the same
embedding amplitude could lead to different
distortions in different image fragments because of
influence of singular values.
3.2 Embedding Rules
Proposed embedding rules could be split in two
groups. The first group consists of rules 1
, 2
and ∞
that utilize all the four elements of the first
column of orthogonal matrix for both embedding
and retrieving. The second group consists of rules
1
and 2
that utilize just two elements for
retrieving, however, could change four elements for
embedding because optimization takes place under
normalization constraint. Further suppose we are
embedding bit in with a positive non-zero
threshold :
1
:1
∙
,
∗
,
,
∗
,
∗
,
,
∗
;
2
:1
∙
,
∗
,
,
∗
,
∗
,
,
∗
;
∞
:1
∙
,
∗
,
,
∗
,
∗
,
,
∗
; (14)
1
:1
∙
,
∗
,
∗
;
2
:1
∙
,
∗
,
∗
.
For each embedding rule there is the same additional
normalization constraint and the same goal function
to minimize distortions (that is quite simple thanks
to the proposed orthogonal matrix):
,
∗
,
,
∗
,
,
∗
,
,
∗
1
,
∗
,
→
(15)
3.3 Watermarking Procedure
After embedding is done the resulting matrix
∗
should be composed with
∗
and
which produces
watermarked image fragment
∗
. However, it is
necessary to notice that
∗
contains real-valued
pixels instead of integers. There are many possible
kinds of truncation and each kind distorts orthogonal
matrix
∗
, but, for example, simple round operation
is quite negligible to retrieve a bit for some
reasonable (0.02 works well for all the embedding
rules). A diagram of watermark embedding is shown
on Figure 1.
As it follows from the diagram the least distorted
watermarked fragments are chosen in order to
replace the corresponding original fragments of the
image. This is thanks to availability of different
orthogonal matrices in the set used for the
approximation. It is necessary to notice that in the
current realization we utilized constant threshold for
all the blocks, but threshold adaptation can be done
in the future more easily (at once, non-iteratively)
compared to (Tehrani, 2010) as distortion in our
method depends only on the amplitude of a vector
added to the first column of .
To extract a watermark from the watermarked
image it is required to know the key and the rule.
However in contrast to embedding the extraction
SVD-basedDigitalImageWatermarkingonapproximatedOrthogonalMatrix
325
threshold for each rule is zero. The extraction
diagram is given on Figure 2.
Set of 5 Embedding
Rules
SVD of chosen Blocks
(Key)
Block Partition
Set of orthogonal
matrices
Approximation of U
Embedding acc. to Rule
(Watermark, Threshold)
Inverse SVD
Pixels’ truncation
Watermark’s bit
correct?
Calculate Blocks’ distortion
Find minimum distorted
Blocks
Replace original Blocks
Five
watermarked
images
Original
Image
yes
no
Figure 1: Watermark embedding diagram.
Figure 2: Watermark extraction diagram.
In our realization we also avoided embedding
area to be limited only by blocks with greater
complexity as defined in (Chang, 2005), (Tehrani,
2010), because due to some kind of distortion
complexity (namely the number of non-zero singular
values per block) could change and the person
extracting a watermark could mismatch a key on
different set. Another reason is that such a set has
different size for different images which forces to
use synchronized PRNG (Pseudorandom Number
Generator, not steady key as we use) between
embedder and extractor which is impractical.
4 EXPERIMENTAL RESULTS
In order to confirm the improvements of the
proposed watermarking method some experiments
took place. Each result has been compared with the
result provided by the method described in (Chang,
2005) under the same circumstances. Original
images, watermarking key and watermark were
absolutely identical. We tried to adjust parameters so
that Peak Signal to Noise Ratios (PSNRs) between
each original image and the corresponding
watermarked one were very close for both methods.
There were four kinds of distortions used in the
experiment: white Gaussian noise, speckle noise,
“salt&pepper” and Jpeg compression.
Three grayscale host images with dimension
512x512 and bitdepth 8 bit were used for watermark
embedding. Those images appear to be tested quite
widely in papers related to image processing and are
namely: livingroom.tif, mandril.tif and
cameraman.tif (Figure 3-5). The choice of images
for watermarking could be explained in a way that
we tried to compare a performance of the proposed
method on images with different amount of fine
details. Here image livingroom.tif contains some
areas with fine details, mandril.tif has a lot of fine
details and cameraman.tif contains few details while
having quite large areas with almost constant
background.
The watermark for all our tests is the same and is
1024 bit long. For the better visual demonstration of
each method’s robustness it has been prepared in a
form of square binary 32x32 image that depicts
Canadian maple leaf. Each bit of the watermark has
been embedded according to the same key
(generated randomly) for all the images. The key
defines 4x4 image fragments used for watermarking
and is 16384 bit long. Extraction is done using the
same key. Without distortions extraction of the
watermark is absolutely correct for all the methods
and images.
Taking into account that different rules were
used for embedding in our method and the
approximation had been done previously comparison
with the method proposed in (Chang, 2005) is more
complex. The only parameter influencing robustness
in that method is a threshold, but embedding with
the same threshold has different impact on an image
when both methods are used. Therefore, the
threshold for the method proposed in (Chang, 2005)
has been adjusted after embedding by our method is
done in a way that each in a pair of the
corresponding watermarked images has the same (or
very similar) PSNR.
SECRYPT2013-InternationalConferenceonSecurityandCryptography
326
Figure 3: Original grayscale image livingroom.tif.
Figure 4: Original grayscale image mandril.tif.
Figure 5: Original grayscale image cameraman.tif.
Four models of distortions applied to the
watermarked images in our experiment could be
split in two types according to the noise nature:
additive and non-additive. Distortions with additive
noise are namely Gaussian and speckle. Before
applying distortions to watermarked images their
pixel values were scaled to match interval [0, 1]. The
mean for Gaussian is 0 and the variance shown in
tables is 0.0006. Speckle noise adds, to each pixel
,
, the term ∙
,
where is distributed uniformly
with mean 0 and variance 0.001. Distortions
utilizing non-additive noise types are “salt &
pepper” and lossy jpeg-compression. In our
experiments we have applied 3% “salt & pepper”
and 75 image quality for jpeg (Matlab realization).
An extraction with the key has been done
afterwards. To compare the results we used the value
1-BER (Bit Error Rate) which indicates the fraction
of correctly extracted bits of a watermark. We have
placed the values 1-BER calculated according to
each method, embedding rule and distortion type in
separate table for each image (Tables 1-3). Each
result has been averaged among 100 runs for all
kinds of distortions except jpeg (as it is
straightforward and does not contain random
component). For better comparability each row with
results from our method was neighbored to a row
containing results with similar PSNR from method
(Chang, 2005). For every pair of rows better
indicator of robustness toward particular distortion is
bolded.
Table 1: Results of watermark extraction for
livingroom.tif.
Method, Rule
Gaussian,
0.0006
Speckle,
0.001
Salt &
pepper,
0.03
Jpeg, 75
1
, 46.13dB
0.9325 0.9823 0.8451
0.9844
Chang,46.02dB
0.9737 0.9997 0.8986
0.9170
2
, 49.68dB
0.8581
0.9288 0.8333
0.9268
Chang,49.60dB 0.8571
0.9464 0.8952
0.7324
∞
, 49.93dB
0.8797 0.9602
0.8805
0.9092
Chang,49.83dB 0.8410 0.9326
0.8967
0.7227
1
, 50.22 dB
0.8833 0.9660 0.8954 0.8076
Chang,50.22dB 0.8063 0.8961 0.8950 0.6865
2
, 50.22 dB
0.8847 0.9662 0.8975 0.8066
Chang,50.22dB 0.8063 0.8961 0.8950 0.6865
Table 2: Results of watermark extraction for mandril.tif.
Method, Rule
Gaussian,
0.0006
Speckle,
0.001
Salt &
pepper,
0.03
Jpeg, 75
1
, 42.37dB
0.9681 0.9902 0.8690
0.9961
Chang,42.29dB
0.9976 1.0000 0.9070
0.9775
2
, 46.12dB
0.9026 0.9469 0.8539
0.9297
Chang,46.11dB
0.9648 0.9988 0.8988
0.8174
∞
, 46.70dB
0.9138 0.9685 0.8837
0.8652
Chang,46.65dB
0.9492 0.9949 0.8981
0.7822
1
, 47.55dB
0.9099
0.9715
0.9000 0.8057
Chang,47.54dB 0.9060
0.9736
0.8979 0.7236
2
, 47.54dB
0.9111
0.9716 0.8978
0.8076
Chang,47.54dB 0.9060
0.9736 0.8979
0.7236
SVD-basedDigitalImageWatermarkingonapproximatedOrthogonalMatrix
327
Table 3: Results of watermark extraction for
cameraman.tif.
Method, Rule
Gaussian,
0.0006
Speckle,
0.001
Salt &
pepper,
0.03
Jpeg, 75
1
, 45.70dB
0.8908 0.9745 0.8322
0.9336
Chang,45.70dB
0.9153 0.9932 0.8918
0.8125
2
, 50.89dB
0.8123 0.8933
0.8104
0.8926
Chang,50.82dB 0.7927 0.8876
0.8471
0.6094
∞
, 51.06dB
0.8419 0.9327 0.8667 0.8467
Chang,51.05dB 0.7808 0.8712 0.8410 0.5840
1
, 52.32dB
0.8377 0.9338 0.8591 0.7227
Chang,52.30dB 0.6716 0.7365 0.8317 0.4922
2
, 52.31dB
0.8419 0.9348 0.8603 0.7217
Chang,52.30dB 0.6716 0.7365 0.8317 0.4922
Images watermarked by the proposed method are
depicted in Figures 6-8. The rule 2
has been used
for this particular demonstration and PSNRs are
49.68 dB, 46.12 dB and 50.89 dB for livingroom.tif,
mandril.tif and cameraman.tif respectively.
Figure 6: Watermarked grayscale image livingroom.tif.
Figure 7: Watermarked grayscale image mandril.tif.
Figure 8: Watermarked grayscale image cameraman.tif.
The threshold for the method proposed in
(Chang, 2005) has been adjusted so that very similar
PSNR has been achieved for each watermarked
image. Compression according to jpeg standard has
been done then. The watermarks extracted from the
watermarked image livingroom.tif by both methods
are shown together with the original watermark
extracted from non-distorted watermarked image
(Figure 9).
(a) (b) (c)
Figure 9: Original and distorted by jpeg compression
watermarks.
The demonstrated binary images represent
watermarks extracted with rates 1 (Figure 9. (a),
both methods, no distortion), 0.9268 (Figure 9. (b),
our method, jpeg 75), 0.7324 (Figure 9. (c), method
(Chang, 2005), jpeg 75).
5 DISCUSSION
Comparing the rate of correct watermark extraction
for our method and the method proposed in (Chang,
2005) and further developed in (Tehrani, 2010) we
can state the following. Robustness demonstrated by
our method against jpeg attack is much better than
those demonstrated by (Chang, 2005). This is true
for all the embedding rules, but to be said separately
rule 2
provides the greatest improvement for all
the trials with jpeg-compression: it is about 27%
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better on livingroom.tif, about 14% better on
mandril.tif and more than 46% better on
cameraman.tif.
For other types of distortions including Gaussian,
speckle, “salt&pepper” noises rules 1
and 2
performed better than others: about 10% outperform
(Chang, 2005) for Gaussian on livingroom.tif, just
1% better than (Chang, 2005) for Gaussian on
mandril.tif, but 27% better than (Chang, 2005) for
speckle on cameraman.tif. There was no
considerable advantage found for “salt&pepper”
noise for any rule. However rules 1
and 2
usually perform worse under conditions with
Gaussian, speckle, and “salt&pepper” noises. The
rule ∞
has considerable advantage on jpeg which
is close to the advantage 2
has and under
conditions with Gaussian, speckle, and
“salt&pepper” noises in some cases performs several
percent better than (Chang, 2005) (livingroom.tif
and cameraman.tif). The highest achievement for
rule 1
is to be 15% better toward (Chang, 2005)
under jpeg-attack for cameraman.tif, but the gaps in
trials with Gaussian, speckle, and “salt&pepper”
noises are sometimes too high, so, it should probably
be rejected from future experiments.
It is possible to issue a short guidance for end-
user that reflects better flexibility of proposed
method utilizing different rules: embedding rules
1
and 2
should be used if there are comparable
chances for each kind of tested distortions to occur;
rule ∞
is better to be used when chances of jpeg
compression are higher; we recommend to use rule
2
in case the only kind of possible distortion is
jpeg.
The threshold used in all our embedding rules
was the same. On the other hand, PSNRs of the
watermarked images are quite high. So, in the future
we would like to experiment with different values of
the threshold (probably greater) and also apply
adaptation for each block as it is proposed in
(Tehrani, 2010). Another direction we might wish to
explore is an embedding in matrix of the blocks of
greater size, but this requires a different model of
orthogonal matrix to be used for approximation.
6 CONCLUSIONS
The watermarking method operating on -domain of
transform was proposed. Its robustness is better
than those for the method proposed in (Chang,
2005). The improvements are due to optimizations
done on two stages of embedding.
The first stage serves for the approximation of
matrix of transformed 4x4 image blocks. The
approximation was done according to the proposed
model that describes orthogonal matrix analytically.
This procedure allows to preserve orthogonality of
matrix after watermark bit is embedded.
Orthogonality of -matrix improves extraction rate.
The second stage represents an embedding
according to one of five proposed embedding rules.
Each of the embedding rules has its own trade-off
between robustness and transparency which allows
to choose the best rule for particular application. A
minimization of embedding distortions was done for
each rule during embedding which reduces
degradation of original image.
Several kinds of attacks were applied to test
robustness. It was experimentally confirmed that for
each kind of attack there is a different embedding
rule which is more preferable than the others.
However, watermarking according to each of the
proposed embedding rules outperforms the method
proposed in (Chang, 2005) under condition of JPEG-
attack.
ACKNOWLEDGEMENTS
The first author is thankful to Tampere Program in
Information Science and Engineering for the
support.
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