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.