Content uploaded by K. Zebbiche
Author content
All content in this area was uploaded by K. Zebbiche
Content may be subject to copyright.
Multibit Decoding of Multiplicative Watermarking for
Fingerprint Images
K.Zebbiche, F.Khelifi, A.Bouridane
School of Electronics, Electrical Engineering and Computer Science
Queen’s University Belfast
Belfast,BT7 1NN
Email: {kzebbiche01, fkhelifi01, A.Bouridane}@qub.ac.uk
Keywords: Multibit decoding, Multiplicative watermark,
Maximum-likelihood.
Abstract
In this paper, we propose an optimum decoder of multibit,
multiplicative watermarks hidden within discrete wavelet
transform (DWT) coefficients of fingerprint images. The
structure of the decoder is based on the maximum-likelihood
(ML) method which requires a probability distribution
function (PDF). Generalized Gaussian PDF is used to model
the statistical behaviour of the DWT coefficients. The
performance of the decoder is tested in realistic scenarios,
where attacks are taken into account. The experiments reveal
that the proposed decoder provides very attractive results and
the decoding error is within an acceptable range of tolerance.
1 Introduction
With the widespread utilisation of fingerprint-based
identification systems, establishing the authenticity of
fingerprint data itself has emerged as an important research
issue. Watermarking is a possible technique that can be used
to increase the security of the fingerprint images [8] and may
be used in applications like protecting the originality of
fingerprint images stored in databases against intentional and
unintentional attacks, fraud detection, guaranteeing secure
transmission of acquired fingerprint images from intelligence
agencies to a central database,…etc.
Watermarking is defined as embedding information such as
ID, origin, destination, access level,…etc in the host data. The
embedded information may be recovered later on and used to
check the authenticity of the host data. Two processes can be
defined at this stage: (i) the detection stage, which aims to
decide whether a given watermark has been inserted in the
host image, referred to as one-bit watermark detection, and
(ii) given that a watermark is embedded into the host image,
the decoding aims to extract bit by bit the hidden information,
referred to as multibit watermarking decoding. In practice,
since a watermarked image is altered by several attacks, the
hidden information cannot be completely extracted and errors
may occur, thus a good decoder should be able to estimate the
hidden information with a low probability of error.
Optimum decoding of multibit watermark has been proposed
in [2, 5, 6]. Hernandez et al. [5, 6] proposed an optimum
multibit decoder for image watermarking operating in the
discrete cosine transform (DCT) domain and used
Generalized Gaussian PDF to model the distribution of the
DCT coefficients. However, this decoding scheme refers to
the additive watermarking and thus cannot be applied when a
different embedding rule is used. Barni et al. [2] proposed an
optimum decoding and detecting technique for a multibit,
multiplicative watermark hosted in the magnitude-of-DFT
domain, modelled by Weibull distribution.
In this work, we propose an optimum decoding of a multibit,
multiplicative watermark embedded in the DWT coefficients
of fingerprint images. By assuming equally probable
information bits, optimum decoding is considered as a
maximum-likelihood (ML) estimation scheme which allows
the derivation of the structure of the decoder based on the
parametric model of the PDF of the DWT coefficients. A
Generalized Gaussian PDF is used to model the statistical
behaviour of the coefficients. The performance of the
proposed decoder is examined through a number of
experiments using real fingerprint images with different
quality to derive the error of decoding probability. We have
also used the Bose–Chaudhuri–Hochquenghem (BCH) code
[3, 7] to increase the successful rate of decoding. Further
experimentations have been carried out to assess the
performance of the decoder in more realistic scenarios, where
different attacks are taken into account.
The rest of the paper is organized as follows: Section 2
explains how the watermark is embedded within DWT
coefficients. The optimum decoder is derived for the
Generalised Gaussian distribution as described in section 3
while the experimental results are provided in Section 4. The
conclusion is presented in Section 5.
2 Information encoding and watermark casting
The multibit watermarking technique presented here is an
extension of the one-bit watermarking scheme developed in
[1]. The watermark is embedded into the DWT subbands
coefficients. Let b= {b1…bNb} be the information bit
sequence to be hidden (assuming value +1 for bit 1 and -1 for
bit 0) and m= {m1m2…mN} a pseudo-random set uniformly
distributed in [-1, 1], which is generated using a secret key K.
The information bits b are hidden as follows: (i) the DWT
subband coefficients used to carry the watermark are
partitioned into Nb non-overlapping blocks {Bi: 1 ≤ i ≤ Nn}.
(ii) the watermark sequence m is split into Nb non-overlap
chunks {Mi: 1≤ i ≤ Nn} (where the number of elements in Bk
is equal to the number of elements in chunk Mk), so that, each
block Bk and each chunk Mk will be used to carry one
Figure 1: Block diagram of the watermark embedding process
information bit. (iii) each chunk Mk is multiplied by +1 or -1
according to the information bit bk to get an amplitude-
modulated watermark. Finally, the watermark is embedded
using the multiplicative rule, given by:
(
)
k
Bkk
k
BxbMy
γ
+= 1 (1)
where
{
}
k
NB
k
B
k
B
k
Bxxxx L
21
= and
{
}
k
NB
k
B
k
B
k
Byyyy L
21
=are
the DWT coefficients of an original image and the associated
watermarked image belonging to the block Bk, respectively. γ
is a value used to control the strength of the watermark by
amplifying or attenuating the watermark at each DWT
coefficient so that the watermark energy is maximized while
the alterations suffered by the image are kept invisible. The
embedding process is summarized in Figure 1.
3 Watermark decoding
The main issue in the decoding process is to obtain a good
estimateb
ˆof the information bit hidden within an image and
this can be achieved by developing a criterion that minimizes
the probability of error. The decoding process is presented in
Figure 2. By assuming that all possible 2Nb information bits
sequences are equally probable, a maximum-likelihood (ML)
criterion can be used to derive a close structure of an
optimum decoder. Thus, an estimation of the hidden
watermark is obtained by looking for the sequence that
maximizes fy(y|m, b), so that:
(
)
lyN
lbmyfb ,maxarg
ˆ21L=
= (2)
where y={y1y2…yN} represents the set of DWT coefficients of
the watermarked image, fy(y|m,b) is the PDF of the set y
conditioned to the events m and bl. Assuming that the
information bits b and the coefficients in m are independent of
each other, as well as the DWT coefficients used to carry the
watermark, equation (2) can be expressed by:
(
)
∏
=
=
=b
N
klkk
k
B
k
B
yN
lbMyfb 1
21 ,maxarg
ˆ
L (3)
where K
B
yindicates the DWT coefficients of the block Bk
carrying the bit bk, and Mk represents the set of the random
coefficients from m used to represent the bit bk. The decision
criterion for the bit bk can be expressed as:
{ }
(
)
kkii
k
Bi y
k
b
kbMyfb ,maxarg
ˆ1,1 ∏
∈
+−∈
=
(
)
( )
−
+
=∏
∏
∈
∈
k
Bi kiiy
k
Bi i
kiy
Myf
Myf
sign 1,
1, (4)
The PDF of the marked coefficients yi conditioned to the
value Mk and bk, can be expressed by:
( )
++
=ki
i
x
ki
kiiy bm
y
f
bm
bmyf
γγ
11 1
, (5)
where fx(x) represents the PDF of the original DWT
coefficients. An initial investigation using various
distributions such as Laplacian, Gaussian and Generalized
Gaussian has found that the Generalized Gaussian PDF is the
best distribution that can reliably model the DWT coefficients
of the fingerprint images. The central Generalized Gaussian
PDF is defined as:
( )
( )
(
)
β
α
β
αββα
iiX xxf −
Γ= exp
1
2,; (6)
where Γ() is the Gamma function, i.e., Γ(z) =∫e-t tz-1dt, z>0.
The parameters α and β represent the scale and the shape
parameters, respectively, and are estimated as described in
[4]. Also, the Generalized Gaussian can be used to model
each block Bk. The PDF of the marked coefficients
conditioned to the event Mk and the bk= +1 is given by:
( )
( )
+
−
+
Γ
=+ ∏
∈
k
B
ki
i
k
B
k
B
k
Bi ki
k
B
k
B
k
B
kiy
M
y
M
Myf
β
β
γ
α
γ
β
α
β
1
1
exp
1
1
2
1,
and the PDF of the marked coefficients conditioned to the
event Mk and bk= -1 is given by:
( )
( )
−
−
−
Γ
=− ∏
∈
k
B
ki
i
k
B
k
B
k
Bi ki
k
B
k
B
k
B
kiy
M
y
M
Myf
β
β
γ
α
γ
β
α
β
1
1
exp
1
1
2
1,
(7)
(8)
Secret key K
PRS
Generator
Original Image
DWT x Partitioning k
B
x
m Dividing Mk
Information bit
Encoder bk
Strength γ
k
B
y
Reconstructing y IDWT
Watermarked
Image
Figure 2: Block diagram of the watermark decoding process.
Substituting (7) and (8) in (4), we obtain:
(
)
( )
−
+
−
+
−
=∏
∈
k
B
ki
i
k
B
k
B
k
B
ki
i
k
B
k
B
k
Bi ki
ki
k
M
y
M
y
M
M
signb
β
β
β
β
γ
α
γ
α
γ
γ
1
1
exp
1
1
exp
1
1
ˆ
For further simplification, we take the natural logarithm of
Equation (9), which leads:
+
−
−
+
+
−
=
∑
∑
∈
∈
k
Bi
k
B
ki
i
k
B
ki
i
k
B
k
B
k
Bi ki
ki
k
M
y
M
y
M
M
signb
ββ
β
γγ
α
γ
γ
11
1
1
1
ln
ˆ
By letting
+
−
−
=k
B
ki
i
k
B
ki
i
k
B
k
B
iM
y
M
y
z
ββ
β
γγ
α
11
1 (11)
and
−
+
=ki
ki
iM
M
T
γ
γ
1
1
ln (12)
Equation (10) can be expressed in simple formulation as:
−
>+
=∑ ∑
∈ ∈
otherwise
Tz
bk
Bi k
Bi ii
k,1
,1
ˆ
4 Experimental results
As a first step, one needs to investigate for the bit error rate
(BER) in the absence of attacks and using different values of
γ. To do this, the experiments were carried out using real
fingerprint images of size 448×478 with different quality
chosen from ‘Fingerprint Verification Competition’ (Db3_a,
FVC 2000) [9]. Each image is transformed by DWT using
Daubechies wavelet at the 3rd decomposition level to obtain
low resolution subband (LL3), and high resolution horizontal
(HL3), vertical (LH3) and diagonal (HH3) subbands. For
reasons of imperceptibility and robustness, the watermark
embedding is carried out in the HL3, LH3 and HH3 subbands.
Each subband is partitioned in blocks of size 16×16 (256
coefficients/block). Thus, since the original image is
unknown to the decoder, which is the case in real systems, a
blind watermark decoding is used so that the Generalized
Gaussian distribution parameters α and β of each block used
are directly estimated from the DWT coefficients of the
watermarked image because it was assumed that γ is small
enough to not visually alter the original image. The diagram
shown in Figure 3 has been obtained by averaging the results
obtained on 10 fingerprint images from database [9] and
different pseudo-random sequences, each hosting Nb=36 bits
(12 information bits/subband), for a total of 36000 bits. The
watermark has been inserted into the coefficients with
different values of γ. The same experiments have been carried
out using code correcting error BCH (31,16,5) and the results
are also plotted in Figure 3, where the peak-signal-to-noise
ratio PSNR corresponding to each value of γ is plotted.
0.20(42.55)0.22(41.85)0.24(41.18)0.26(40.60)0.28(39.95)0.30(39.48)
10
-4
10
-3
10
-2
10
-1
Strength
BER
without BCH
with BCH
Figure 3: Comparison between simulation results bit error rate
with and without using BCH code, computed for different
value of the strength γ. The corresponding value of PSNR is
given in round brackets.
The results obtained show that the BER decreases when the
strength γ increases. Visual degradations appear at γ=0.28
(PSNR < 40) and higher, below this value the BER is low and
the proposed decoder yields very attractive results. The BCH
code increases significantly the successful decoding rate. It is
worth mentioning that the use of code correcting error limits
the number of the information bits to be hidden. For our
example Nb=36 without BCH code and Nb=16 with the BCH
code.
To assess the distortions caused by the watermark, Figure
4.(1-5:b) shows the watermarked images of a sample of
(9)
(10)
(13)
Secret key K PRS
Generator
m Dividing Mk
Strength γ
Estimating α and β
DWT x Partitioning k
B
x
Watermarked
Image
Decoding
α ,β
Decoded Information
bit b
ˆ
k
b
ˆ
fingerprint images (Image 20_1, Image 22_1, Image 42_1,
Image 44_6, Image 9_8) marked with γ=0.26 (PSNR>40) as
shown in Figure 4(1-5:a), respectively. The two images are
visually identical. Figure 4.(1-5:c) show the difference
between the host and the corresponding watermarked image,
magnified by a factor of 20. As it can be seen, the watermark
is concentrated in the region of the ridges, which makes the
watermark more secure because any attempt to remove the
watermark will affect the ridges which constitute the region
of interest.
For the sake of completeness, further experiments have been
carried out to evaluate the performance of the proposed
decoder against known watermarking attacks such as filtering,
compression, cropping, resizing, noise degradations … etc.
However, in this paper we only show the results from average
filtering, Additive White Gaussian Noise (AWGN) and JPEG
Compression. The experiments were carried out on 5
fingerprint images (DB3_a, FVC2000) of Figure 4(1-5:a),
chosen to take into account the different quality of fingerprint
images. For each image and each attack, the BER is computed
for both cases with and without BCH code. The value of
PSNR is also computed to assess alteration of the
watermarked images caused by each attack. The value of the
strength γ is fixed for all images at the value 0.26.
BER Without BCH
BER With BCH
PSNR
Image 20_1
4.48×10-2 8.60×10-3 33.17
Image 22_1
6.13×10-2 1.81×10-2 33.81
Image 42_1
7.76×10-2 4.37×10-2 34.45
Image 44_6
5.46×10-2 1.19×10-2 33.88
Image 9_8 6.60×10-2 2.22×10-2 34.82
Average 6.08×
××
×10-2 2.09×
××
×10-2 34.02
Table 1: BER and PSNR under mean filtering 4×4
BER Without BCH
BER With BCH
PSNR
Image 20_1
1.36×10-2 1.00×10-4 34.03
Image 22_1
2.34×10-2 1.70×10-3 33.74
Image 42_1
5.48×10-2 1.36×10-2 31.99
Image 44_6
2.59×10-2 2.70×10-3 31.65
Image 9_8 3.67×10-2 7.40×10-3 32.05
Average 3.08×
××
×10-2 7.24×
××
×10-3 32.69
Table 2: BER and PSNR under AWGN (SNR=25)
BER Without BCH
BER With BCH
PSNR
Image 20_1
1.84×10-2 1.25×10-4 33.19
Image 22_1
2.53×10-2 8.12×10-4 33.83
Image 42_1
4.46×10-2 9.80×10-3 34.45
Image 44_6
2.56×10-2 2.50×10-3 33.91
Image 9_8 3.52×10-2 4.50×10-3 34.03
Average 2.96×
××
×10-2 3.54×
××
×10-3 33.48
Table 3: BER and PSNR under JPEG compression (50%)
Table 1 shows the results for watermarked images blurred
using 4×4 mean filter. In Table 2, the watermarked images are
corrupted by Additive White Gaussian Noise of SNR=25,
while in Table 3, they are compressed by JPEG with a 50% of
quality. The results obtained clearly reveal that the proposed
decoder provides attractive results and the BER is within an
acceptable tolerance. Also, the use of the BCH code enhances
the performance of the decoding process.
Figure 4: Test fingerprint images :(1-5:a) host image (1-5:b)
watermarked Image (1-5:c) Image of the difference magnified
by 20. γ=0.26.
Image 20_1:
Image 42_1:
Image 44_6:
Image 9_8:
(4:a)
Image 22_1:
(1:a)
(5:a)
(2:a)
(3:a)
(1:b)
(5:b)
(4:b)
(3:b)
(2:b) (2:c)
(1:c)
(3:c)
(4:c)
(5:c)
5 Conclusion
In this paper, an optimum decoder for fingerprint images
watermarking in the DWT domain and based on Generalized
Gaussian PDF has been developed. The parameters of the
Generalized Gaussian distribution are directly estimated from
the watermarked image, which makes it more suitable for real
applications. The experiments have revealed that the proposed
decoder provides very attractive results and the BER is within
an acceptable range of tolerance, even in the presence of
attacks like mean filtering, white Gaussian noise addition and
JPEG compression. Also, it has been shown that the
introduction of the BCH code, to correct the eventually errors,
enhances the performance of the proposed decoder.
References
[1] M. Barni, F. Bartolini, A. De Rosa, A. Piva. “A new
decoder for optimum recovery of nonadditive
watermarks”, IEEE Trans. Image Processing, volume
10, pp. 775-766, (2001).
[2] M. Barni, F. Bartolini, A. De Rosa, A. Piva. “Optimum
decoding and detection of multiplicative watermarks”,
IEEE Trans. Signal Processing, volume 51, pp. 1118-
1123, (2003).
[3] T. Brandão, M.P. Queluz, A. Rodrigues. “On the use of
error correction codes in spread based image
watermarking ”, Advances in multimedia information
processing- PCM 2001: second IEEE pacific rim Conf.
on multimedia, volume 2195/2001, pp. 630, (2001).
[4] M. N. Do, M. Vetterli. “Wavelet-based texture retrieval
using generalized Gaussian and Kullback-Leibler”,
IEEE Trans. Image Processing, volume 11, pp. 146-
158, (2002).
[5] J. R. Hernandez, F. Perez-Gonzalez, F. Balado.
“Approaching the capacity limit in image watermarking:
A prespective on coding techniques for data hiding
applications”, signal Processing, volume 81, pp. 1215-
1238, (2001).
[6] J. R. Hernandez, M. Amado, F. Perez-Gonzales. “DCT-
domain watermarking techniques for still images:
Detector performance analysis and a new structure”,
IEEE Trans. Image Processing, volume 9, pp. 55-68,
(2000).
[7] M,-G, Kim, J.H. LEE. “Undetected error probabilities of
binary primitive BCH codes for both error correction
and detection”, IEEE Trans. communication, volume
44, pp. 575-580, (1996).
[8] K. Zebbiche, L.Ghouti, F. Khelifi and A. Bouridane,
“Protecting fingerprint data using watermarking,”, in
Proc. 1st AHS Conf, pp. 451-456, 2006.
[9] Fingerprint Verification Competition
http://bias.csr.unibo.it/fvc2000/download .asp.
