A ROBUST IMAGE WATERMARKING TECHNIQUE BASED ON

SPECTRUM ANALYSIS AND PSEUDORANDOM SEQUENCES

Anastasios L. Kesidis and Basilios Gatos

Computational Intelligence Laboratory, Institute of Informatics and Telecomunications

National Center for Scientific Research “Demokritos”, GR-153 10 Agia Paraskevi, Athens, Greece

Keywords: Image watermarking, invisible watermark, blind watermarking, pseudorandom noise sequences, geometric

distortions, attacks, data hiding, information embedding.

Abstract: In this paper a watermarking scheme is presented that embeds the watermark message in randomly chosen

coefficients along a ring in the frequency domain using non maximal pseudorandom sequences. The

proposed method determines the longest possible sequence that corresponds to each watermark bit for a

given number of available coefficients. Furthermore, an extra parameter is introduced that controls the

robustness versus security performance of the encoding process. This parameter defines the size of a subset

of available coefficients in the transform domain which are used for watermark embedding. Experimental

results show that the method is robust to a variety of image processing operations and geometric

transformations.

1 INTRODUCTION

Nowadays the size of the available digital media is

increasing rapidly. This fact leads to an urgent need

for an efficient copyright protection of the digital

content. Digital image watermarking can offer

watermarks may be visible or invisible, where a

visible watermark is easily detected by observation

while an invisible watermark is designed to be

transparent to the observer and detected using signal

processing techniques. In the literature, there are two

main invisible watermarking categories: (i) spatial

domain watermarking and (ii) spectrum domain

watermarking. In the spatial domain watermarking,

the watermark is embedded by directly modifying

the pixels of an image (Kimpan, 2004, Hyung,

2003). Spectrum domain techniques are applied to

transform domains such as the Discrete Cosine

Transform (DCT), Discrete Fourier Transform

(DFT) and Discrete Wavelet Transform (DWT). Cox

et al. (Cox, 1997) have proposed a watermarking

technique based on embedding a watermark in the

DCT domain using the concept of spread spectrum

communication. In order to obtain a robust

watermark, the watermark is embedded in the low-

frequency components of the image. The technique

proposed in (Alturki, 2000) is based on modifying

the sign of a subset of low frequency, image

transform coefficients (DCT, DFT and Hadamard

transforms) with high to moderate magnitudes. In

(Dugad, 1998), the spread spectrum image

watermarking technique in the DWT domain is

proposed. A watermark with a constant weighting

factor is embedded into the perceptually significant

coefficients in the high frequency sub bands in order

to preserve invisibility. In (Kumsawat, 2005), the

spread spectrum image watermarking algorithm

using the discrete multi wavelet transform is

proposed. In this approach, performance

improvement with respect to existing algorithms is

obtained by genetic algorithms optimization.

In this paper a watermarking scheme is presented

that uses the frequency domain in order to embed a

watermark that is previously encoded using

pseudorandom noise sequences. In order to increase

the security of the watermarking process a parameter

of the algorithm defines a subset of randomly

selected frequency coefficients where the watermark

will be embedded. Furthermore, the proposed

method determines the longest possible

pseudorandom sequence that corresponds to each

watermark bit for a given number of candidate

coefficients in order to increase the method’s

121

L. Kesidis A. and Gatos B. (2007).

A ROBUST IMAGE WATERMARKING TECHNIQUE BASED ON SPECTRUM ANALYSIS AND PSEUDORANDOM SEQUENCES.

In Proceedings of the Second International Conference on Computer Vision Theory and Applications - IFP/IA, pages 121-126

 SciTePress

robustness. The parameter of the algorithm that

defines the number of watermarked coefficients also

controls the robustness versus security performance

of the encoding process. Several experimental

results show that the watermarked images are robust

to a variety of image processing operations and

geometric transformations. The rest of the paper is

organized as follows: section 2 provides a brief

introduction to pseudorandom noise sequences and

section 3 determines the coefficients of the

frequency domain where the method is applied as

well as the parameters that control the performance

of the embedding method. Sections 4 and 5 present

the embedding and the detection algorithm,

respectively. Section 6 provides some experimental

results while section 7 concludes the paper.

2 PSEUDORANDOM NOISE

SEQUENCES

The watermark is embedded in the form of a

pseudorandom noise (PN) sequence. (PN) sequences

are binary sequences that appear to be statistically

random and have properties similar to random

sequences generated by sampling a white noise

process. (PN) sequences are generated by

pseudorandom number generators using an initial

seed (key). There are several such utilizations

including GoldCodes, m-sequences, Legendre

sequences and perfect maps (O’Ruanaidh, 1998).

Different keys produce different sequences thus,

unless the algorithm and key are known, the

sequence is impractical to predict. If the key consists

of K registers then a sequence is a maximal length

sequence if it has length 2

−1. Maximal length

sequences have pseudo-randomness properties i.e.

over one period, there are 2

K−1

ones and 2

K−1

−1 zeros

(Luby, 1996). Moreover, the autocorrelation

function is binary valued. Specifically, for a

sequence p

…p

of period N the autocorrelation

function, R

(k), is

∑

′′

kiixx

)(

(1)

where

′

=1−2p

and k represents the k-th shifted

version of the sequence. The value of R

(k) equals 1

if k=0 and −1/N otherwise. In other words, the

sequence produced by the generator is uncorrelated

to all of its circular shifts for k≠0.

Let us suppose that a watermark W is a binary

message b

… b

consisting of L bits. Each

symbol b

is encoded to a zero mean pseudorandom

vector of length N. Since there are two states for

each symbol b

, therefore two (PN) sequences of

length N are used, the first one corresponding to

state 0 and its complementary to state 1.

Corresponding each symbol b

to its (PN)

sequence produces the spread spectrum encoded

watermark W

which is a binary sequence of length.

=NL (2)

The spread spectrum version W

of the

watermark forms a symmetric key cryptosystem

since in order to embed or extract the watermark, it

is necessary to know the key used to generate the

pseudorandom sequences.

3 THE 2D FOURIER

TRANSFORM

Let I(x,y) denote the original image defined on a

integer grid where 0≤x<N

and 0≤y<N

. The two

dimensional discrete Fourier transform (DFT) of I is

F(u,v)=

∑∑

−

−−

/2/2

),(

NjvyNjux

eyxI

ππ

(3)

The watermark is embedded in the magnitude

M(u,v)=|F(u,v)| of the Fourier transform. Its phase

P(u,v)=∠ F(u,v) is not affected but only used during

the inversion of the 2D DFT.

Let us assume that the center of the 2D DFT

transform corresponds to the zero frequency term.

Let also R⊂M the set of coefficients where the

watermark is embedded. R corresponds to a ring

determined by radius r

and r

with 0<r

where N

=min{N

}/2. The values for r

and r

must be chosen so that the image deformation

produced by the embedding process is minimal. The

most proper area to embed the watermark is the

middle frequencies of the spectrum since small

radius values affects the low frequencies leading to

visibly image distortions while high radius values

affect the higher frequencies that are most sensitive

to compression attacks (Cox, 1997). It is,

R = {M(u,v): r

≤

vu + ≤ r

}

(4)

In the proposed method the values of r

and r

are in

the range 0.5N

≤ r

, r

≤0.8N

The number L

of coefficients that satisfy equation

(4) is related to the difference between r

and r

. If

the coefficients are sorted according to angle

VISAPP 2007 - International Conference on Computer Vision Theory and Applications

122

θ=arctan(

) then R can be considered as a one

dimensional signal. However, the magnitude of the

Fourier transform is symmetric, that is R(k)= R(k+

/2), where 0≤k<L

/2. Therefore, in order to

preserve symmetry, the watermark is embedded

twice in R. The maximum number of coefficients

candidates where each copy of the watermark can be

embedded is L

= L

/2.

In order to increase the security of the

embedding process, not all of the L

candidate

coefficients are used in each semi-ring. Instead, a

key S

, provided by the user, is used as seed for a

random number generator which selects a subset of

coefficients in each semi-ring. The number

chosen coefficients, where

< L

, is a system’s

parameter and controls the security level. Indeed, the

possible combinations of

elements out of L

RRRRRR

LLL

−

⎟

⎠

⎞

⎜

⎝

⎛

(5)

If for example, L

=1000 and only

=900

elements are used for watermarking then there are

about 6.39×10

139

possible positions where the

encoded watermark W

can be embedded in each

semi-ring.

If a maximal length sequence generated by K

registers is used then according to (2) the longest

encoded watermark W

that fits in has length

=NL=( 12

−

(6)

The value of K

is integer and can be calculated as

(

12 −

)L=

⇒K

⎥

⎦

⎥

⎢

⎣

⎢

+ )1

(log

(7)

where

⎣⎦

x denotes the greatest integer less than or

equal to x. In the spread spectrum encoded

watermark W

each symbol b

is replaced by a (PN)

sequence of length N.

However, applying a maximal length sequence

as above may leave a significant number of

candidate coefficients unused. Indeed, according to

(7) the maximum number of available coefficients is

used only if

2 -1. In case where

−

≤

2 -1 there is a total number of

)12(

−− unused coefficients. For example,

if the watermark string has a typical length L=64 bit

and

=1000 coefficients then according to (6) the

spread spectrum encoded watermark is L

=960 bits

long. On the other hand, if

=950 then L

significantly reduced to L

=448 which leads to a

“loss” of 502 candidate coefficients. In order to

avoid this problem a non-maximal length sequence

is used instead. In that case, the length of the

encoded watermark W

′

=dL

(8)

where d equals to

⎥

⎦

⎥

⎢

⎣

⎢

. The quantity d denotes

the first d digits of a (PN) sequence generated by

′

registers where

′

⎥

⎤

⎢

⎡

(log

. Symbol

⎡

⎤

x denotes the smallest integer greater than or

equal to x. In other words, the (PN) sequence is

generated by

′

registers and only d of its digits

are used for each symbol b

. It should be noticed that

a maximal length sequence is still achieved if

′

2 -1.

The above analysis demonstrates that the proper

choice of

is a trade-off between security level

and robustness. Clearly, according to (5) the number

of possible combinations is maximized as

reaches L

/2. Thus, the best level of security is

achieved if only half of the L

coefficients are used.

On the other side, according to (8), an increased

number of used coefficients allows a watermark of

greater length to be embedded resulting to a more

robust encoding scheme.

4 WATERMARK EMBEDDING

In order to accomplish image watermarking, a

watermark W as well as a private key K are required.

Key K={

′

, S

} consists of the number

′

of registers in the (PN) sequence generator, the

number

of chosen coefficients and the seed S

of the random number generator (see section 3).

As already mentioned, due to the symmetry

of the Fourier transform domain, the encoded

watermark W

is embedded twice in the ring R of

magnitude coefficients. Let

2,1=i

R denote the two

sets of coefficients where the encoded watermark W

will be embedded, one on each semi-ring. The

magnitude of these coefficients is modified as

A ROBUST IMAGE WATERMARKING TECHNIQUE BASED ON SPECTRUM ANALYSIS AND

PSEUDORANDOM SEQUENCES

123

),( vuM

= ),( vuM +g W

(9)

where M(u,v)∈

2,1=i

R .

The constant g is a factor that controls the

strength of the embedded watermark. The

watermarked image

),( yxI

′

is obtained by applying

the inverse Fourier transform

′

(x,y)=

∑∑

−

′

)//(2

),(

NvyNuxj

evuF

(10)

where

),( vuF

′

),(

vujP

evuM .

5 WATERMARK DETECTION

For the detection of the watermark the private key

K={

′

, S

} is used and a two step process is

applied: First the correlation between the marked

(and possibly corrupted due to an attack) coefficients

and the watermark itself is computed in order to

detect the most probable offset position of the

watermark inside each semi-ring. Second, the

coefficients are divided into d length sequences and

compared to the (PN) sequences used during the

embedding process in order to extract the original

watermark message.

Specifically, let

),( vuF

′

denote the DFT

transform of a possibly watermarked image and

),( vuM

′

its magnitude. Let also R⊂

′

denote the

ring of coefficients determined as in section 3. The

encoded watermark W

is constructed from the

pseudorandom sequence generator using the same

number of registers

′

as in the encoding phase.

Additionally, in each semi-ring the set

2,1=i

R of

coefficients where the watermark may be

embedded is determined using the same random

seed S

as during the embedding phase.

In order to detect the watermark even in a rotated

image the embedded watermark is cross-correlated

with all possible shifts of the extracted watermark.

Indeed, according to the rotation property of the

Fourier transform, rotating the image through some

angle in the spatial domain causes the rotation of the

Fourier transform space by the same angle

(O’Ruanaidh, 1998). The correlation between R

and

is given by

where N=

-1. The shifted position of the

maximum correlation is at p=arg

max (C

). If p≠0

then W

is shifted p times in order to match R

. The

set R

of coefficients in each semi-ring contains L

(PN) sequences each one of length d. The correlation

of the k-th sequence in R

and W

where k=1… L,

can be estimated by the Pearson correlation

coefficient

)()()1(

))(),())((),((

ksksd

kWjkWkRjkR

ssii

−

−−

∑

(12)

where R

(k,j), W

(k,j) denote element j of the k-th

sequence in R

and W

, respectively, while )(kR

and

)(kW

denote their sample mean values. The

quantities

)(ks

and

)(ks

denote the standard

deviation of R

(k) and W

(k). Clearly, the closer the

coefficient r

is to 1, the stronger the correlation

between the sequences R

(k) and W

(k). The

extracted watermark

′

is calculated by applying

the above estimation process to all

L (PN) sequences

. As already mentioned in section 2 there are

two (PN) sequences used for encoding

, the first

one corresponding to state 0 and its complementary

to state 1. Thus, if

>0 then the k-th bit of

watermark

′

is set to the state of the (PN)

sequence

(k) otherwise to its complementary.

6 EXPERIMENTAL RESULTS

This section presents some experiments that

demonstrate the robustness of the proposed

algorithm against common image processing

operations and geometric transformations.

As already mentioned in section 3 the number of

randomly selected coefficients

is an important

parameter in the proposed watermarking scheme

since it affects both the security level and robustness

of the method. As an example, Table 1 presents the

recovery performance in two cases where different

amounts of coefficients are selected in each semi-

ring. In both cases the standard test Lena image is

used and a watermark message of 96 bits is

embedded. The ring’s radius is intentionally chosen

about 80% of the 2D DFT domain radius which

corresponds to high frequencies that are very

sensitivity to compression attacks but provide better

visual results since the embedding process leaves the

image perceptually unmodified. The capacity of

(m)=

⎪

⎩

⎪

⎨

⎧

<≤−

≤≤+

∑

−

0)(

0)()(

mNmC

NmnWmnR

(11)

VISAPP 2007 - International Conference on Computer Vision Theory and Applications

124

each semi-ring is L

=648 coefficients. In the fist

case, the 90% of these coefficients are randomly

chosen i.e.

=583. Thus, the total number of

coefficients used is

=576 which corresponds to a

(PN) sequence of 6 symbols per watermark bit. In

the second case, the 60% of these coefficients are

used that is

=388 corresponding to L

=384 and a

(PN) sequence of 4 symbols per watermark bit. As

shown in Table 1, there is a significant loss of

robustness comparing the two implementations. For

instance, for a Jpeg compression factor of 70% the

percent of bit correctly recovered falls from 75% to

65%. On the other hand the security level is

significantly raised. Indeed, according to (5) the

possible positions in each semi-ring where the

encoded watermark

can be embedded raises from

2.47

×10

in the first case up to 7.42×10

187

in the

second one. If, however, the maximal length (PN)

sequence were used then according to (6) only 3

symbols per watermark bit would be used. Clearly,

as shown in the last column of Table 1, this

decreases further the recovery performance.

Table 1: Percent of recovered bits for two different sets of

selected coefficients.

Jpeg

factor

90%

(6 symbols/bit)

60%

(4 symbols/bit)

maximal length

(PN)

(3 symbols/bit)

90 92 89 85

70 75 65 51

50 59 53 50

30 61 51 47

Embedding the watermark using the longest possible

(PN) sequence allows sufficient recovery even when

several possible attacks are applied to the

watermarked image. For the following experiments

the standard test images Lena and Baboon were

used, both of size 512

×512. The ratio

/ L

is set

up to 0.85 and the ring is located at radius 0.6

The gain factor

g is set to 5 in both cases. Table 2

provides the bits recovery percentage when Jpeg

compression is applied to the watermarked image.

Table 2: Jpeg compression results.

CF Lena Baboon CF Lena Baboon

100 100 100 50 97 100

90 100 100 40 92 100

80 100 100 30 91 100

70 100 100 20 75 100

60 100 100 10 61 94

The 90% of the watermark is retrieved for

compression factors (CF) down to 30 which

correspond to significantly degraded images.

Apparently, the watermark in the Baboon image

appears robust even for CF about 10.

Figure 1 depicts a sub-area of the Lena image in two

color depth resolutions. The left watermarked image

is without color reduction while on the right one the

color depth is reduced to 2 colors leading to a black

& white version of the image. The watermark is

successfully extracted with only 3 wrong bits out of

64 (95% success). Furthermore, in the Baboon

image the watermark is exactly retrieved.

(a)

(b)

Figure 1: Color depth reduction results. (a) original image

(b) black & white (2 colors). The watermark is

successfully detected in both versions.

The method’s robustness has also been tested on

resized and cropped images. Table 3 summarizes the

corresponding watermark retrieval results. Similar

cropping results have been achieved when an

additional offset of (100,100) pixels from the

image’s center is applied.

Table 3: Percent of recovered bits for several resize and

crop attacks.

Resize Crop

% Lena Baboon % Lena Baboon

200 100 100 90 100 100

150 100 100 80 100 100

70 100 100 70 98 100

50 97 98 60 98 98

30 58 59 50 91 84

Another common attack on watermark images is

stretching. Figure 2 depicts several stretched

versions of the Lena image. The detection process

can correctly retrieve the watermark even for

stretching ratios up to 170%

×50%. In the extreme

case of ratio 60%

×180% only 3 bits out of 64 are

incorrectly retrieved from the Lena image.

A ROBUST IMAGE WATERMARKING TECHNIQUE BASED ON SPECTRUM ANALYSIS AND

PSEUDORANDOM SEQUENCES

125

(a) (b)

Figure 2: Several aspect ratios applied to Lena image. (a)

60%×180%, (b) 70%×150%, (c) 120%×80% and (d)

170%×50%.

7 CONCLUSIONS

In this paper a watermarking scheme is presented

that uses randomly chosen coefficients along a ring

in the transform domain in order to embed a

watermark message. The watermark is constructed

using non maximal pseudorandom sequences so that

each watermark bit is encoded by the longest

possible pseudorandom sequence. Furthermore, an

extra parameter is introduced that defines the

amount of randomly chosen coefficients which are

used for watermark embedding. If higher security

levels are required then a fewer number of

coefficients should be used. On the other hand more

watermark coefficients lead to longer pseudorandom

sequences and consequently to an increased

robustness of the encoding process. Experimental

results show that the method is robust to a variety of

image processing operations and geometric

transformations like Jpeg compression, color

reduction down to black & white, cropping with and

without an offset, stretching with aspect ratio

modification and resizing. Future work will focus on

the adaptive determination of the proper set of

frequency coefficients that provides maximal (PN)

sequences for a given watermark length.

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