IMAGE AUTHENTICATION USING HIERARCHICAL

SEMI-FRAGILE WATERMARKS

Yuan-Liang Tang* and Chun-Hung Chen

Department of Information Management

Chaoyang University of Technology

168, Jifong E. Rd., Wufong Township, Taichung County 41349, Taiwan (R.O.C.)

Keywords: Image authentication, Digital watermarking, Semi-fragile watermarks, Wavelet transformation.

Abstract: In this paper, a semi-fragile watermarking technique operating in the wavelet domain is proposed. A

hierarchy of the image blocks is constructed and the image features are extracted such that relationships

among image blocks are established in order to enhance the security and robustness of the system. With

such a hierarchy, the image can be authenticated at different levels of resolution, hence providing a good

property of tamper localization. In addition, by varying certain parameters, the system is able to control the

degree of robustness against non-malicious attacks. The proposed algorithm thus provides a fine trade-off

between security and localization, and is also robust to common image processing operations.

1 INTRODUCTION

With the advance of network technologies and the

popularity of digital multimedia, it is very easy to

create, duplicate, transmit, and modify digital

products. However, serious problems also arise

along with such convenience, that is, unauthorized

modification on digital products becomes very easy,

too, and detection of such tampering is extremely

difficult. If the digital products are images, we face

the problem of image authentication, namely, to

identify if an image has experienced malicious

tampering. One of the solutions referred to as exact

authentication embeds fragile watermarks (Lin,

1999) in the image and they break easily even if the

image experiences only tiny modification. The

applications of exact authentication are very limited

because manipulations which preserve the semantics

of the image should be acceptable. Such a

requirement leads to another solution known as

inexact authentication, in which semi-fragile

watermarks (

Bartolini, 2001) are embedded in stead

of fragile ones. Semi-fragile watermarks are

relatively robust to content-preserving manipulations,

while fragile to malicious modification.

This research is supported by a grant from National

Science Council, Taiwan, R.O.C.

(NSC92-2213-E-324-024).

There are a number of works related to

semi-fragile watermarks. For example, Queluz (

1999)

generated digital signatures, based on moments and

edges, to protect the image. An image may be

corrupted without affecting their moments, but their

edges will certainly be changed. This property is

used to authenticate the image content. Yu et al.

(2000) used the Gaussian distribution to model the

amount of modification on wavelet coefficients

which is introduced by incidental distortions or

malicious attacks. The number of coefficients

necessary for watermark embedding is optimized as

well. Lin et al. (2000) embedded a pseudorandom

m-sequence into the median frequency DCT

coefficients for image authentication. They used

correlation values to determine the authenticity of an

image.

284

Tang Y. and Chen C. (2004).

IMAGE AUTHENTICATION USING HIERARCHICAL SEMI-FRAGILE WATERMARKS.

In Proceedings of the First International Conference on E-Business and Telecommunication Networks, pages 284-289

DOI: 10.5220/0001380902840289

 SciTePress

In addition to authenticating an image as a whole,

it is also desirable to pinpoint the locations of

tampering. Most localized authentication methods

rely on some form of block-wise authentication

(Wong, 1999), in which the image is divided into

disjoint spatial regions and each of them is

authenticated independently. The spatial acuity with

which a block-based authentication system localizes

tampering depends on the block size, thus it might

be desirable to reduce the block. However, as

indicated by Holliman and Memon (2000), there are

potential security risks associated with smaller block

sizesthe system is vulnerable to the collage attack

(Wong, 1999; Yeung, 1997). Therefore, there exists a

trade-off between security and localization. In this

paper we describe a semi-fragile watermarking

technique operating in the wavelet domain. A

hierarchy of the image blocks is constructed and the

image features are extracted such that the

relationships among image blocks are established in

order to resist the collage attack. The hierarchy is

based on the work done by Celik et al. (2002), and

with such a hierarchy the image can be authenticated

at different levels of resolution, hence providing a

good localization property. In addition, the proposed

system is designed in such a way that by varying

certain parameters, it is possible to control the

degree of robustness against non-malicious attacks.

Therefore our algorithm provides a fine trade-off

between security and localization and is also robust

to common image processing operations.

2 THE PROPOSED SYSTEM

Figure 1 delineates the embedding and

authentication processes of our system. In the

embedding process, a hierarchical structure is first

constructed for the original image, X, and then the

features are extracted from such a hierarchy. The

features represent the image content and are

embedded as a watermark into the

wavelet-transformed image, X

, resulting in X

Finally, X

is inversely transformed back to the

original format, producing the watermarked image

. The embedding process also requires a private

key to ensure the security of the system. During

authentication, both the image features and the

watermark are extracted using the same methods as

in the embedding process. These two pieces of data

are then compared against each other to determine if

the image blocks are authentic. The locations of

tampering, if any, will be reported as well.

2.1 Construction of the Hierarchy

and Feature Extraction

Celik et al. (2002) proposed a hierarchical structure

in which the original image is first divided into

disjoint blocks which constitute the bottom level of

the hierarchy. And then successive levels are formed

by combining distinct groups of blocks at a

preceding level. Without loss of generality, we

assume that 8-bit grayscale square images are dealt

Figure 1: The embedding and authentication processes.

Watermark

Extraction

Feature

Extraction

Comparison

Watermark

Non-authentic

blocks

Wavelet

Transform

Features

Authentication:

Wavelet

Transform

Original

Image, X

Feature

Extraction

Watermark

Embedding

key

Features

(watermark)

Inverse Wavelet

Transform

Embedding:

key

Hierarchy

Construction

Hierarchy

Construction

IMAGE AUTHENTICATION USING HIERARCHICAL SEMI-FRAGILE WATERMARKS

285

with. Given an N×N image X, if X is divided into

M×M blocks at the bottom level, we have a

hierarchy of L = log

M + 1 levels. Let X

denote a

block at level l, l = 0..L–1, where indices ij represent

the spatial position. Assuming that 2×2 blocks at a

given level of the hierarchy are combined to create a

block at the next level, we have













−

12,12

2,12

12,2

2,2

for l = 1..L–1. The top level thus consists of only one

block X

L–1

= X. Based on Celik’s hierarchy, for

each block, X

, we first compute the mean, m

, of

pixel intensities of the block. Due to the limitation of

capacity, the bottom-level mean, m

, is quantized

into 64 levels, i.e., a 6-bit intensity instead of the

ordinary 8-bit intensity. In addition, since tampering

with a block may not affect the mean when the block

size is large, we introduce the polarity to improve

the sensitivity as well as the reliability of detection.

The four-bit polarity, p

, of X

is obtained by

comparing the parent block’s mean with those of its

4 children:







≥

−

otherwise 0,

if ,1

),(

2,2

yjxi

yxp

for l = 1..L–1 and x, y = 0..1. Denoting | ⋅ | as the

length in bits, we have |m

| = 6, |m

| = 8, and |p

| =

4 (l = 1..L–1), respectively. These intensity means

and polarities, denoted by A

= m

and A

|| p

, l = 1..L–1), are regarded as the image

features (i.e., the authentication data or watermark)

and are embedded back into the image for content

protection.

2.2 Watermark Embedding

The coefficients in frequency band LL

of the

wavelet-transformed image are selected for

embedding. These coefficients are good candidates

in that they represent the perceptually significant

part of the image and it is impossible for an attacker

to tamper with the image without gross

modifications to its appearance. The high level

authentication data is spread over a number of lower

level blocks and the accumulated payload is inserted

at the lowest level of the hierarchy by wavelet

coefficient modification. This is done by partitioning

into a number of smaller strings:

{} {} { }

,1)( ,1)(||...||1 ,0||0 ,0 −Λ−Λ= llAAAA

where Λ(l) = 2

. The payload of a block on the

lowest level is formed by concatenating the units

inherited from higher level blocks:

{

}

{}

,)(),(||...

||)(),(||

11)(),(

jCjiCiA

jCjiCiAAD

LLjCiC

jCiCijij

−−

−−=

−−

where C

(x) =



x/2



. After the above preparation,

wavelet coefficients corresponding to each block on

the lowest level of the hierarchy are embedded with

payload bits. To increase the security level of the

system, we use the pseudo-random number

generator (PRNG), initialized by a private key, to

establish the correspondence between an image

block and the wavelet coefficients. This is illustrated

in Figure 2, in which the watermark is embedded in

the corresponding 4×4 coefficients in subband LL

Kundur and Hatzinakos (1999) embed the

watermark by first defining the quantization

function:







±±±=+<≤

±±=+<≤

... 5 ,3 ,1for )1( if ,0

... 4 ,2 ,0for )1( if ,1

),(

kqkfkq

qfQ

where f is the wavelet coefficient and q denotes the

size of the quantization interval. They update f by











≤≠−∆

>≠+∆

=+∆

qrbqfQqf

bqfQqf

5.0 and ),( if ,5.0

5.0 and ),( if ,5.1

),( if ,5.0

where ∆f =



f/q



⋅ q, r = f−∆f (quantization noise),

and b is the watermark bit. Obviously, the result of

such update will locate at exactly the middle of the

quantization step, which makes it very easy to

identify the watermarked coefficients. To overcome

this security risk, we modify the coefficient update

function as follows:











≤≠+−∆

>≠−+∆

−<=−+∆

+>=++∆

+≤≤−=

qrbqfQsqf

zqrbqfQsqf

zqrzqbqfQf

5.0 and ),( if ,5.0

5.0 and ),( if ,5.1

)5.0( and ),( if ,5.0

)5.0()5.0( and ),( if ,

where s is a random number in the range [1..z] and z

is the randomness tuner (z =



q/6



in our

experiments). The result of such new update will

look random and therefore is more secure. Normally,

a larger q gives a more robust watermark and it

should vary according to the host image. However, a

larger q also creates more visual impact. In order to

search for an appropriate value, dozens of

well-known images were tested to obtain the

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140

190

240

290

340

100 90 80 70 60 50 40 30 20

JPEG Quality Factor (%)

Figure 3: Watermark robustness as a relationship between

quantization intervals and compression quality factors.

50 90 130 170 210 250 290 330 370

PSNR (dB)

Figure 4: PSNR versus quantization intervals.

relationship between q and the JPEG quality factors

(QFs). Figure 3 shows the results, in which, for a

specified value of QF, any quantization intervals set

below the curve will cause our system to produce

false positives. For instance, if we want to validate

the watermarked image that can withstand JPEG

compression of 80% QF, q should be greater than 85,

otherwise such an operation will be identified as a

malicious attack instead of common processing. In

order to obtain a more general form, those curves are

approximated by a second order non-linear equation

using the regression technique, and the following

equation is obtained:

q = 393 – 6.014QF + 0.027QF

The equation above actually defines the lower bound

of the quantization interval. On the other hand, to

determine upper bound, the PSNRs as a function of

q are computed for each watermarked image. Figure

4 shows the results and, because PSNR ≥ 30 is

generally acceptable, q should be less than 200,

namely, the upper bound. Since the lower bound

produces least visual impact on an image, it is a

good candidate when determining q. As a

consequence, our system allows determining the

quantization interval automatically, depending on

the visual quality requirement of JPEG compression.

2.3 Image Authentication

The authentication process is analogous to the

embedding process. Let

denote a block of the

image that may have been tampered with. The

watermark bit is extracted by

(

qfQb =

, where

is the corresponding coefficient. The partitioning

algorithm used during embedding is reversed to

recover the authentication data

, which is further

partitioned to obtain

and

. The same feature

Figure 2: Concatenation of blocks to form a payload and placement of resulting payload in wavelet domain of the image.

Payload

Wavelet version:

PRNG

key

4×4

IMAGE AUTHENTICATION USING HIERARCHICAL SEMI-FRAGILE WATERMARKS

287

extraction is also applied to obtain

and

for

each block. And finally, the difference between the

extracted features and watermark is calculated. Let

;

mmT −=

is determined as non-authentic

TT >

, where T

is the threshold and it varies

according to the size of the block. At the bottom

level, since we have ignored the 2 least significant

bits when collecting the authentication data, we set

= 8 (3 bits) to increase the robustness.

Furthermore, because tampering with a small area

may have little influence on the intensity mean of a

large-sized block, the threshold should be smaller. In

our experiments, we set T

= 6, T

= 4, and T

= 2

for l = 3..L–1 to accommodate such a situation.

For polarity checks,

and

are compared

against each other bit by bit. Any bit difference

signifies a non-authentic block. However, if the

intensity means of the two blocks are similar,

non-malicious modification may easily reverse their

polarity. Based on such reasoning, when the

intensity difference between the parent block and the

child block is small, say less than 4, that bit is

ignored during comparison. In summary, a block is

authentic only when it passes both intensity mean

and polarity tests.

3 EXPERIMENTAL RESULTS

In our experiments, the 512×512 grayscale Lena

image is used as the host image, as shown in Figure

5(a). We set the size of the lowest level block to be

16×16 pixels, which results in a 6-level hierarchy.

Figure 5(b) shows the watermarked image, whose

PSNR value is about 38 dB. The degradation of the

watermarked image depends on the amount of the

embedded data and the embedding strength. To

demonstrate the effectiveness of our technique, we

modify the image by placing a tattoo (apple) on

Lena’s arm (Figure 5(c)). As can be seen in Figure

5(d), the tampered blocks are correctly detected, in

which non-authentic blocks at lower levels are

shown in darker shades, while those at upper levels

are shown in lighter shades. Furthermore, we

perform several non-malicious manipulations to test

the robustness of our system, including 80%-QF

JPEG compression, blurring, sharpening, and

addition of Gaussian noise with zero mean and

variance of 20. As expected, our system didn’t make

any false positive errors and Table 1 shows the

results.

4 CONCLUSION

We have presented in this paper an image

authentication technique using semi-fragile

watermarks. The authentication data is embedded in

the image and is arranged in a hierarchical structure

so that the whole contents of image are tightly

connected in order to overcome the security

weakness of block-based techniques. The system is

insensitive to common image processing techniques

in that robust image features are selected and a

variable quantization interval further controls the

degree of robustness. The system is also secure

because not only the block-dependence property

significantly discourages the collage attack, but also

the random correspondence between blocks and

coefficients prohibits brute-force attacks. The

experimental results demonstrated that our system is

very effective.

(a) (b)

Figure 5: (a) Original image, (b) watermarked (q = 110),

Table 1: Experimental results of various attacks.

Attack

Quantization

Interval

Authentic?

JPEG (QF = 20%~100%)

Blurring

Sharpening

Gaussian noise addition

By formula

160

190

120

Yes

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