digital image watermarking using discrete wavelet transform

DIGITAL IMAGE WATERMARKING USING DISCRETE WAVELET TRANSFORM:
PERFORMANCE COMPARISON OF ERROR CORRECTION CODES
Nataša Terzija, Markus Repges, Kerstin Luck, Walter Geisselhardt
Faculty of Engineering Sciences, Institute of Information Technology,
Gerhard-Mercator-Universität Duisburg, Duisburg, Germany
{nterzija,m.repges,k.luck}@uni-duisburg.de
Abstract. In this paper the influence of different error
correction codes on the robustness of image watermarks is
investigated. To encode the watermark three different
error correction codes are considered: the Hamming, the
BCH and the Reed-Solomon code. Following the idea of
the JPEG2000 standard the encoded watermark is
embedded by a method based on Discrete Wavelet
Transform (DWT). Availability of the original image is
presumed for extraction. The sensitivity against attacks on
the watermarked image is investigated. The types of
attacks applied are: the removal, denoising and
compression attack. It is shown that the Hamming and the
Reed-Solomon code yield better results than the BCH
code. Due to the higher correction capability the Reed-
Solomon code behaves better than the Hamming code.
Keywords: Robust image watermarking, discrete
wavelet transform, error correction codes, attacks.
1. Introduction
With the development of the JPEG2000 standard digital
image watermarking schemes that are based on Discrete
Wavelet Transform (DWT) are becoming more and more
interesting. The majority of watermarking schemes
consider Discrete Cosine Transform (DCT) as the method
of choice. An overview can be found in [1]. Though, there
is evidence that DWT could enhance robustness of the
watermark against intentional and unintentional attacks,
work based on DWT for watermarking is comparatively
rare but exists, e.g. [2]. The reason mainly being that the
former JPEG standard relied on DCT. With the advent of
JPEG 2000 schemes based on DWT are gaining interest.
Though, watermark robustness varies with the
underlying transform algorithms, provisions must be
taken to harden a watermark against attacks. Ways are,
e.g. multiple embedding [3] and the application of error
correction codes (ECC) [4] are in use to regain the
embedded watermark.
Robustness of watermarking schemes being far from
satisfactory this paper investigates application of DWT in
conjunction with ECC. In this paper three different error
correction codes are applied to the ASCII representation
of the text "Universitaet Duisburg" being used as
watermark. The encoded data streams are embedded into
an image by a DWT based watermarking method. After
running several attacks on the watermarked image the
influence of the ECCs are compared and evaluated.
Error correction codes used were the (7,4)-Hamming
code, the (15,7)-BCH and (15,7)-Reed-Solomon code,
respectively. By considering these ECCs we try to find a
tradeoff between the number of bits to be embedded and
the number of bit errors that can be corrected. The
advantage of the Hamming code is that the number of bits
to be embedded (294) is less than that one the BCH (315)
and Reed-Solomon code (360) require. Whereas the
Hamming code allows to correct only one error, the BCH
and Reed-Solomon code allow correction of two and four
errors, respectively.
After embedding the watermark several attacks were
executed on the images to investigate the influence of the
error correction codes. To run the attacks the MATLAB
program Checkmark has been used. Checkmark consists
of about six categories of attacks [5]. We focus on
template removal, denoising and compression attacks. The
denoising attacks are represented by several filtering
attacks using, for instance, a Gaussian or a Wiener filter.
The compression attacks contain several JPEG and
Wavelet compressions. Considering these compressions
we include the mostly used image transformations in our
investigations.
The paper is organized as follows. In section 2 the main
idea of the Discrete Wavelet Transformation is
introduced. Section 3 consists of the description of the
watermarking method that is used to embed information
into an image. The method is based on the DWT. A short
overview of the attacks that are used to destroy the
watermark and that are part of the program Checkmark is
given in section 4. In section 5 the embedding method and
the error correction codes applied are considered and their
impact on the robustness of the encoded watermarks is
presented. In the following section 6 we draw a
conclusion and give an outlook.
2. Discrete Wavelet Transform (DWT)
The basic idea of DWT for one-dimensional signals is
briefly described. A signal is split into two parts, usually

the high frequency and the low frequency part. This
splitting is called decomposition. The edge components of
the signal are largely confined to the high frequencies
part.
The signal is passed through a series of high pass filters
to analyze the high frequencies, and it is passed through a
series of low pass filters to analyze the low frequencies.
Filters of different cutoff frequencies are used to analyze
the signal at different resolutions. Let us suppose that x[n]
is the original signal, spanning a frequency band of 0 to π
rad/s. The original signal x[n] is first passed through a
halfband highpass filter g[n] and a lowpass filter h[n].
After the filtering, half of the samples can be eliminated
according to the Nyquist’s rule, since the signal now has
the highest frequency of π/2 radians instead of π. The
signal can therefore be subsampled by 2, simply by
discarding every second sample. This constitutes one level
of decomposition and can mathematically be expressed as
follows:
y [ k]
x[
k]
g[
2k
− n]
and
where yhigh[k] and ylow[k] are the outputs of the highpass
and lowpass filters, respectively, after subsampling by 2.
The above procedure can be repeated for further
decomposition.
The outputs of the highpass and lowpass filters are
called DWT coefficients and by these DWT coefficients
the original image can be reconstructed. The reconstructed
process is called the Inverse Discrete Wavelet Transform
(IDWT).
The above procedure is followed in reverse order for the
reconstruction. The signals at every level are upsampled
by two, passed through the synthesis filters g’[n], and
h’[n] (highpass and lowpass, respectively), and then
added. The analysis and synthesis filters are identical to
each other, except for a time reversal. Therefore, the
reconstruction formula becomes (for each layer)
To ensure the above IDWT and DWT relationship the
following orthogonality condition on the filters H(ω) and
G(ω) must hold:
where
∑
high
∑
= n
∑
y [ k]
x[
k]
h[
2k
− n]
low
= n
x[
n]
( y high [ k]
g[
−n
+ 2k]
+ y
= n
and
low
2
2
| H( ω)|
+ |G( ω)|
= 1
∑
H ( ω ) h[
n]
e
= n
∑
= n
− jnω
G(
ω ) g[
n]
e
[ k]
h[
−n
+ 2k])
.
− jnω
An example of such H(ω) and G(ω) is given by
1 1 − jω
H ( ω)
= + e
2 2
and
1 1 − jω
G(
ω)
= − e
2 2
which is known as the Haar wavelet filters.
The DWT and IDWT for an one-dimensional signal can
be also described in the form of two channel treestructured
filterbanks. The DWT and IDWT for a twodimensional
image x[m,n] can be similarly defined by
implementing DWT and IDWT for each dimension m and
n separately DWTn[DWTm[x[m,n]], which is shown in
Figure 1.
x[m,n]
Figure 1 DWT for two-dimensional images [2]
An image can be decomposed into a pyramidal
structure, which is shown in Figure 2, with various band
information: low-low frequency band LL, low-high
frequency band LH, high-low frequency band HL, highhigh
frequency band HH.
LL 2
LH 2
H*(ω) 2 ↓
m m
G*(ω)
m
LH 1
2 ↓
m
HL 2
HH 2
H*(ω) 2 ↓
n n
G*(ω) 2 ↓
n n
H*(ω) 2 ↓
n n
G*(ω) 2 ↓
n n
HL 1
HH 1
Figure 2 Pyramidal structure
3. Embedding Method based on DWT
Watermarking in the DWT domain can be split into the
two procedures: embedding of the watermark and
extraction of the watermark.
For embedding a bit stream is transformed into a
sequence w(1)...w(L) by replacing the 0 by –1, where L is
the length of the bit stream and w(k)∈ {-1,1} (k=1,...,L).
This sequence is used as the watermark.

The original image is first decomposed into several
bands using the discrete wavelet transformation with the
pyramidal structure. Decomposition is performed through
two decomposition levels using the ”Haar filter”. The
watermark is added to the largest coefficients in all bands
of details which represent the high and middle frequencies
of the image. Let f(m,n) denote the DWT coefficients
which are not located at the approximation band LL2 of
the image. The embedding procedure is performed
according to the following formula:
f΄(m,n) = f(m,n) + αf(m,n)w(k),
where α is the strength of the watermark controlling the
level of the watermark w(1)...w(L). By this, DWT
coefficients at the lowest resolution which are located in
the approximation band are not modified. The
watermarked image is obtained by applying the inverse
discrete wavelet tansform (IDWT).
In the watermark extraction procedure both the received
image and the original image are decomposed into the two
levels. It is assumed that the original image is known for
extraction.
The extraction procedure is described by the formula
wr(k)=(fr΄(m,n)-f(m,n))/(αf(m,n)),
where fr΄(m,n) are the DWT coefficients of the received
image. Due to noise added to the image by attacks or
transmission over the communication channel the
extracted sequence wr(1)...wr(L) consists of positive and
negative values. Hence, it is better to take the extracted
watermark as:
we(k)=sgn(wr(k)).
After extraction of the watermark the bit stream is
reconstructed according to the replacement rule at the
beginning.
Figure 3 shows the block diagram of the embedding
method.
message
Xr
w1...wL
encode embedding
fr(m,n)
f(m,n)
DWT
f(m,n)
wr1... wrL
f‘(m,n)
X-original image
IDWT
X-original image
we1... weL
DWT extraction sgn(wr) decode
DWT
original watermark
w1...wL
X’ - watermarked image
Xr - received image, distorted after attacks
extracted
message
Figure 3 Block diagram of the embedding method
X'
attacks
Xr
4. Watermark attacks
To investigate the robustness of the encoded watermark
some alterations have to be made to the watermarked
image. The alterations are caused by using the MATLAB
program Checkmark. Checkmark consists of six
categories of attacks: Denoising, denoising followed by
perceptual remodulation (DPR), denoising followed by
bending, copy attack, template removal and compression
[5]. We neglect the copy attack and the denoising
followed by bending and focus on the remaining
categories.
The denoising attacks are several filtering attacks as
Gaussian filter, Wiener filter etc.. The Wiener Filtering,
the Hard Thresholding and the Soft Thresholding are
considered as MAP estimates corresponding to a Gaussian
image, gamma goes to 0 in the generalized Gaussian
model, and a Laplacian image. The noise – i.e. the
embedded data – is assumed to be Gaussian [6]. The
median, midpoint and trimmed mean filtering are
considered as ML estimates. The Sharpening is a high
pass filter that is applied to the image to accentuate edges.
And the Gaussian filters are applied to the image to blur
and to remove noise [7]. By running an attack using
Thresholding the image is converted from grayscale to
black and white.
Denoising and remodulation with different windows for
Wiener filtering and denoising and remodulation
assuming a correlated watermark belong to the DPR
attacks.
For the template removal attack the template composed
of peaks and used to recover the watermark is considered.
The watermark is estimated, the peaks are detected and
then removed. Finally a small transformation is applied
[5].
The compression attacks consist of several JPEG and
wavelet compressions. By considering all these
compressions we include most of the alterations of the
image that result from standard image processing
operations. The image is JPEG-compressed with varying
quality factors where the bit rate decreases as the quality
factor decreases. Compression with varying bitrates using
JPEG2000 wavelet compression and, in particular, the
JASPER compression program [7] is also investigated.
All these attacks can be part of intentional and
unintentional alterations of the watermarked image.
5. Experiments and results
For the experiments a picture of the university (Fig. 4) is
converted into grayscale values. The message
“Universitaet Duisburg” is converted into ASCII code.
The German umlaut “ä” is changed into “ae” to be able to
use only seven-bit ASCII instead of eight-bit ASCII
values. This allowed the use of (15,7)-BCH and Reed
Soloman code. The resulting bits are embedded in four
different ways: without ECC and protected by Hamming,
BCH and Reed-Solomon code. The embedding is done in

all bands shown in the pyramidal structure except for the
approximation band LL2.
Figure 4 University of Duisburg
In the uncoded version we implement 147 bits according
to 21 characters à 7 bits. In the Hamming scheme we use
a Hamming code with a codeword length of 7 bits and a
message length of 4 bits. According to this code format
the uncoded message is 168 bits instead of 147 bits long.
The Hamming coded watermark has an amount of 294
bits. For the BCH and the Reed-Solomon code is again
the 147 bit-long message used. The encoded watermark
length for BCH is 315 bits, the one for Reed-Solomon is
360 bits. Both codes use a codeword length of 15 bits and
a message length of 7 bits.
This means that with Reed-Solomon coding more than
twice as much bits have to be inserted than without ECC
which may result in problems with the capacity of the
watermarked image. This problem, however, can be
solved by spreading the watermark over some bands. The
resulting four images are manipulated by some attacks
using Checkmark as described in section 4. These attacks
are chosen under the prerequisite that the image size has
to be kept. The extraction of the watermark is done
separately for every band so that the correctness of the
watermark does not depend on the other bands. The
compression methods are a problem for the watermark
only for higher compression rates, especially for LH2 and
HL2. An error-free watermark is also obtained for the
images after Template Removal, Gaussian and Wiener
Filtering and Hard Thresholding. The error rate with the
other attacks is so high that the capabilities of the ECCs
are difficult to evaluate.
Three diagrams give an overview of the impact of ECC
according to the different attacks in LH2. Diagrams 1 and
2 show the compression methods and diagram 3 deals
with some other attacks. Not all of the performed attacks
are shown because the error amount is too high to gain
useful results. The best results – with the least number of
Errors
Errors
30%
25%
20%
15%
10%
errors – can be obtained by using band LH2 and HL2.
Conclusion from results is that the gain in robustness from
Hamming is better than with BCH. According to the
highest error correction capability Reed-Solomon shows
the best results. If the error rate is not greater than 1%,
BCH is able to reconstruct the embedded message
correctly. With the Hamming code an error rate of up to
2% can be tolerated and for Reed-Solomon even rates of
up to 4 and 5% allowed extraction of the correct message.
The ECCs considered are not able to deal with error rates
greater than 10-20%.
It is possible that a shorter codeword length is more
suitable for the use of ECC in watermarking. To verify or
disprove this assumption more tests with shorter Reed-
Solomon codes are necessary.
5%
0%
60%
50%
40%
30%
20%
10%
0%
JPG50
without ECC
Hamming
BCH
Reed-Solomon
JPG40
JPG30
Attacks
Diagram 1 Impact of ECCs after JPEG compression
WVC80
without ECC
Hamming
BCH
Reed-Solomon
WVC60
WVC50
WVC40
Attacks
Diagram 2 Impact of ECCs after Wavelet compression
JPG25
WVC30
JPG15
WVC20
JPG10
WVC10

Errors
60%
50%
40%
30%
20%
10%
0%
gauss1
without ECC
Hamming
BCH
Reed-Solomon
gauss2
wien1
wien2
tprem
Attacks
Diagram 3 Impact of ECCs after several other attacks
6. Conclusion and outlook
In this paper a method for improving the robustness of
digital image watermarks is investigated. For small error
rates and a distribution of the errors according to the
chosen error capabilities the considered ECCs can be used
effectively to improve the robustness of the watermark.
Although the ratio of error correction capability and
codeword length is almost the same BCH behaves worse
than Hamming code and according to the higher ratio the
Reed-Solomon code behaves best. For some applications
Hamming code could be preferable because with
Hamming code there are less bits to be embedded.
The use of error correction codes for digital
watermarking is still an open problem. It requires the
design of codes which are able to take into account many
different kinds of attacks. We are currently investigating
the impact of different codeword lengths with same ratio
sharp
hard1
hard2
soft1
soft2
according to error correction capability. Additionally,
convolutional codes may be part of further research.
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