A DWT-SVD BASED PERCEPTUAL IMAGE FIDELITY METRIC

FOR WATERMAKING SCHEMES

Franco Del Colle and Juan Carlos G´omez

Laboratory for System Dynamics and Signal Processing

FCEIA, Universidad Nacional de Rosario, Rosario, Argentina

CIFASIS, CONICET, Rosario, Argentina

Keywords:

Perceptual distortion metrics, Discrete wavelet transform, Singular value decomposition, Image watermarking.

Abstract:

In this paper, a novel DWT-SVD perceptual ﬁdelity metric for the evaluation of watermarking schemes is

introduced. The proposed metric is based on a widely used Human Visual Model in the Discrete Wavelet

Transform domain accounting for the frequency sensitivity, and the local luminance and contrast masking

effects of the human eye. A relationship between the visual model in the DWT domain and the modiﬁcation

of the wavelet coefﬁcients’s singular values is derived. The proposed metric is validated through subjective

assessment and its performance is compared to several state-of-the-art perceptual image distortion metrics.

The paper focus on Image Adaptive Watermarking methods in the Discrete Wavelet Transform Domain since

they yield better results regarding robustness and transparency than other watermarking schemes.

1 INTRODUCTION

Digital Watermarking refers to techniques that im-

perceptibly embed information (the watermark) into

the original data in such a way that always remains

present and detectable. One of the main require-

ments that should be met by any watermarking tech-

nique is the perceptual transparency that refers to the

property of the watermark of being imperceptible in

the sense that humans can not distinguish the wa-

termarked images from the original ones by simple

inspection (Barni and Bartolini, 2004), (Cox et al.,

2002).

The assessment of watermarked image ﬁdelity is

one of the key aspects in the evaluation of image wa-

termarking insertion methods. Basically, the ﬁdelity

is a measure of the similarity between the images be-

fore and after the watermark insertion. Many works

exist in the literature dealing with quality assessment

mainly focused on compression applications. Never-

theless, visual quality assessment should include spe-

cial requirements that depend on the application con-

text. An extended review of image quality assessment

techniques in watermarking and data hiding applica-

tions can be found in (Le Callet et al., 2008).

Generally speaking, image ﬁdelity assessment can

be performed by following two different approaches:

subjective evaluation and objective evaluation. In

the subjective assessment a number of observers are

asked to rank the distortion of the images in a given

scale and a Mean Opinion Score (MOS) is obtained.

This type of evaluation is time consuming and it can

be inﬂuenced by experimental conditions (such as

lighting, monitor characteristics, etc.), and lack of

motivation and mood of the participants. On the other

hand, in the objective assessment approach, a distor-

tion metric is mathematically deﬁned and computed

from the original and watermarked images, and is

then used to quantify the watermarked image ﬁdelity

in an automatic way, without the involvement of hu-

man beings. This classiﬁcation of the different ap-

proaches for image ﬁdelity assessment is considered

within the framework of the so-called full reference

image quality evaluation techniques, where both the

original and the distorted images are assumed to be

available for the computation.

Among the objective image quality metrics, two

different classes can be distinguished: metrics based

only on the characteristics of the image, usually called

pixel-based metrics, and metrics that take also into

account perceptual characteristics of the Human Vi-

sual System (HVS), which for this reason are called

perceptual quality metrics. Within the ﬁrst class the

widely used mean squared error (MSE), the peak sig-

nal to noise ratio (PSNR), the root mean squared error

(RMSE), the mean absolute error (MAE), the signal-

187

Del Colle F. and Carlos Gómez J. (2010).

A DWT-SVD BASED PERCEPTUAL IMAGE FIDELITY METRIC FOR WATERMAKING SCHEMES.

In Proceedings of the International Conference on Signal Processing and Multimedia Applications, pages 187-192

DOI: 10.5220/0002881701870192

 SciTePress

to-noise ratio (SNR), the Universal Image Quality In-

dex (UQI) proposed in (Wang and Bovik, 2002), and

the metric based on Singular Value Decomposition

(SVD) introduced in (Shnayderman et al., 2006), can

be mentioned. Within the second class, the struc-

tural similarity metric (SSIM) introduced in (Wang

and Lin, 2004), and the Komparator metric proposed

in (Le Callet and Barba, 2003), can be mentioned.

As pointed out in (Eskicioglu, 2000) and (Winkler,

1998), pixel-based metrics do not correlate well with

human visual distortion perception. The same conclu-

sion is drawn in (Marini et al., 2007), where a compar-

ison of several perceptual and non perceptual metrics

in the framework of image watermarking is carried

out.

In this paper, a new perceptual metric for ﬁdelity

evaluation of watermarked images is presented and

validated through subjective tests. The metric re-

sorts to a widely used perceptual model of the HVS

introduced in (Watson et al., 1997), which takes

into account frequency sensitivity, local luminance

and contrast masking effects to determine an image-

dependent quantization matrix. This model provides

the maximum possible quantization error in the DWT

coefﬁcients which is not perceptible by the HVS. A

relationship between these maximum quantization er-

rors in the DWT domain and the maximum variation

of the wavelet coefﬁcients’s singular values is derived.

The performance of the proposed metric is compared

with two state-of-the-art perceptual ﬁdelity metrics,

namely, the Komparator metric introduced in (Le Cal-

let and Barba, 2003), and the SSIM metric introduced

in (Wang et al., 2004). No non perceptual quality

metrics are considered in this paper, since they have

shown to have poor correlation with the results of sub-

jective assessment.

A wide variety of watermarking schemes have

been proposed in the literature. Among the different

approaches, the ones in the Discrete Wavelet Trans-

form domain where the watermark strength is adapted

locally to the particular image, called hereafter Im-

age Adaptive Discrete Wavelet Transform (IADWT)

watermarking schemes, have proved to have bet-

ter performance regarding robustness against attacks

and ﬁdelity. For this reason, IADWT watermarking

schemes will be considered in this paper. In partic-

ular, the IADWT schemes introduced in (Podilchuk

and Zeng, 1998) and in (Del Colle and G´omez, 2007)

will be employed for the evaluation of the proposed

ﬁdelity metric.

The rest of the paper is organized as follows. In

section 2, a brief review of the Singular Value De-

composition and its application in image processing

is presented. In section 3, the new perceptual ﬁdelity

metric based on DWT and SV decompositions is in-

troduced. The general conditions for the subjective

tests used to validate the different ﬁdelity metrics are

described in section 4. The results of the subjec-

tive evaluation applied on two IADWT watermark-

ing schemes, together with the results of the proposed

objective metric are presented in section 5. Finally,

some concluding remarks are given in section 6.

2 SINGULAR VALUE

DECOMPOSITION

Any real matrix A can be decomposed into a prod-

uct of three matrices as A = UΣV

, where U and

V are orthogonal matrices (U

U = I, V

V = I), and

Σ = diag(σ

, σ

, . . . σ

). The diagonal entries σ

of Σ

are called the singular values of A, while the columns

of U and the columns of V are called the left and

right singular vector of A, respectively (Golub and

Van Loan, 1996). This decomposition is known as the

Singular Value Decomposition (SVD) and has many

applications in signal and image processing. In par-

ticular, in the area of image processing, the SVD of

an image is an optimal decomposition, in the sense

that most of the signal energy is concentrated in few

coefﬁcients (singular values). In addition, the SVD

has properties of stability, proportion invariance and

rotation invariance.

The SVD has also been used in recent years in

watermarking applications, see for instance (Liu and

Tan, 2002), (Chang et al., 2005), (Zhang and Li,

2005), (Mohammad et al., 2008), (Xiong et al., 2008),

(Pei and Liu, 2008), (Changzhen et al., 2009), where

different watermarking schemes based on modiﬁca-

tion of the singular values are presented. More re-

cently, the SVD has been used in combination with

the DWT decomposition in different watermarking

schemes. For instance, in (Bhartnagar and Raman,

2009) a semi-blind reference watermarking scheme

for copyright protection using gray scale logos as wa-

termarks is presented. For the watermark embedding,

the original image is transformed using DWT, a ref-

erence image is obtained, and then the watermark is

embedded into the reference image by modifying its

SVs, using the SVs of the watermark. In (Li et al.,

2007), a hybrid DWT-SVD watermarking scheme that

considers Human Visual properties is introduced. The

embedding is done by DWT decomposing the host

image into four subbands, applying SVD to each sub-

band, and then modifying the SVs using the SVs of

the watermark. The watermark strength is determined

by the HVS model proposed in (Lewis and Knowles,

1992).

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3 DWT-SVD METRIC PROPOSAL

In this section, a new image distortion metric based

on DWT and SVD decompositions is introduced. The

metric beneﬁts from the advantages of the Discrete

Wavelet Transform Decomposition regarding space-

frequency resolution and of the Singular Value De-

composition of an image regarding the compactness

of the representation of the signal energy in a few co-

efﬁcients. The metric resorts to a widely used percep-

tual model of the HVS introduced in (Watson et al.,

1997), which takes into account frequency sensitivity,

local luminance and contrast masking effects to deter-

mine an image-dependent quantization matrix, which

provides the maximum possible quantization error in

the DWT coefﬁcients which is not perceptible by the

HVS. These values are the so-called Just Noticeable

Difference (JND) thresholds.

In a ﬁrst stage, a 1-level DWT decomposition is

performed for both the original and the watermarked

images, using the biorthogonal 7/9 wavelet (Mal-

lat, 1998), resulting in the coefﬁcient matrices C

, C

for the original image and C

, C

for the watermarked image. Here, the

subindexes LL, HL, LH and HH indicate approxima-

tion, and vertical, horizontal and diagonal details, re-

spectively.

The Singular Value Decomposition of each coef-

ﬁcient matrix is then performed, resulting in four sin-

gular values matrices for each subband of the original

image, namely Σ

, Σ

and Σ

, and four sin-

gular values matrices for each subband of the water-

marked image, namely, Σ

, Σ

and Σ

. Then,

the absolute difference of the singular values matrices

for each subband is computed (element-wise) accord-

ing to

∆Σ

( j, k) , |Σ

( j, k) − Σ

( j, k)|, (1)

with i = LL, LH, HL, HH.

The watermark in the watermarked image will be

imperceptible if the variation of the wavelet coefﬁ-

cients associated to the singular value differences in

(1) do not exceed the JND thresholds of the DWT

domain HVS model. An SVD decomposition of

the DWT perceptual thresholds for the ith-subband,

JND

, permits to obtain the singular value perceptual

thresholds as follows,

JND

= U

JND

⇒ Σ

JND

= U

JND

, (2)

with i = LL, LH, HL, HH.

A variation of the singular values of a speciﬁc sub-

band will then be perceptible if the difference ∆Σ

(1) exceeds the singular value perceptual thresholds

JND

A matrix Thresh(∆Σ

) can be deﬁned from ∆Σ

zeroing the entries which are below the perceptual

thresholds Σ

JND

, and then, a single value of distor-

tion for each subband can be deﬁned as follows:

kThresh(∆Σ

kΣ

, i = LL, LH, HL, HH (3)

where k·k

stands for the Frobenius norm of a matrix,

and the normalization by kΣ

has been performed in

order for the distortions d

to be in the range [0, 1].

Finally, to provide a unique parameter quantifying

the distortion, a pooling of the four subband distortion

measures is needed. An objective ﬁdelity metric can

then be deﬁned as the complement of the linear com-

bination of the four distortion measures in (3), i.e.,

f , 1− (k

+ k

(4)

where the coefﬁcients k

, k

and k

must

satisfy the constraint

+ k

= 1, (5)

in order for f to be in the range [0, 1].

A schematic representation of the algorithm for

the computation of the objective ﬁdelity metric is

shown in Fig. 1.

4 METRIC VALIDATION

In this section, the experiments for the subjective val-

idation of the proposed ﬁdelity metric are described.

As pointed out before the straightforward way to

assess the ﬁdelity of watermarked images is to run

a subjective test. There are standardized techniques

to perform subjective tests for general image qual-

ity assessment. For instance the Recommendation

ITU-R BT.500-11 (ITU, 2002) speciﬁes a methodol-

ogy for the subjective assessment of still image qual-

ity. On the other hand no standards are available

for subjectiveassessment of watermarked image qual-

ity. Since watermarked images can be considered

as the result of some processing operations (the wa-

termark embedding algorithms) applied to the origi-

nal image, these generalsubjectivequality assessment

techniques could be applied to watermarked images.

In this paper, the Double Stimulus Impairment Scale

(DSIS) protocol, described in (ITU, 2002), is used.

This protocol has also been used by Marini and coau-

thors in (Marini et al., 2007) in the same context.

The experiments were carried out in a room

designed according to the recommendation ITU-R

BT.500-11 (ITU, 2002). Fifteen observers were en-

rolled to do the test and ﬁfteen different natural im-

ages were watermarked using two state-of-the-art Im-

age Adaptive DWT insertion schemes. Namely, the

A DWT-SVD BASED PERCEPTUAL IMAGE FIDELITY METRIC FOR WATERMAKING SCHEMES

189

Watermarked Image

1-level

DWT

1-level

DWT

SVD SVD

abs(.)

Thresh(.)

|| . ||

Pooling

Original Image

∆Σ

Figure 1: DWT-SVD based image ﬁdelity metric algorithm.

algorithm proposed in (Podilchuk and Zeng, 1998),

and the one introduced in (Del Colle and G´omez,

2007). These techniques in the DWT domain take

into account the image characteristics and a model of

the Human Visual System to adapt the strength of the

watermark to make it imperceptible. These IADWT

techniques have also proved to deliver better results,

regarding robustnessand ﬁdelity, than image indepen-

dent watermarking schemes.

This setup resulted in 20 min sessions where ob-

servers were asked to rate 30 images at an observation

distance (D

obs

) of six times the display size of the im-

ages. The original and the watermarked images were

displayed side by side on the monitor as shown in

Fig. 2, and the observers were asked to rate the quality

of the marked image compared to that of the original

on a scale of ﬁve categories, namely 5=Imperceptible,

4=Perceptible but not annoying, 3=Slightly annoying,

2=Annoying, and 1=Very annoying.

The results of these experiments are included in

section 5.

original image

watermarked image

obs

Figure 2: Subjective Experiment Setup.

5 RESULTS

The metric described in Section 3 is used in

this section to evaluate the ﬁdelity of the two

IADWT watermarking schemes mentioned be-

fore. A set of ﬁfteen (256 × 256) natural color

images was used. The complete image data set

can be downloaded from the authors’s website

(http://www.fceia.unr.edu.ar/lsd/mrg/watermark/).

Four of the images are shown in Fig. 3

Figure 3: Four images in the database.

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190

Three perceptual image ﬁdelity metrics are con-

sidered in this section. Namely, the Komparator met-

ric introduced in (Le Callet and Barba, 2003), the

SSIM metric introduced in (Wang et al., 2004), and

the metric introduced in Section 3.

In order to illustrate which metric provides the

best objective assessment of image quality for both

watermarking methods, the three metrics are com-

puted and compared to the Mean Opinion Score

(MOS) for the ﬁfteen images. The corresponding

97.5 % conﬁdence intervals (CI) were also calculated

to specify intervals of values with the highest likeli-

hood of containing the true value of the general MOS.

These intervals, centered in the MOS, are shown as

blue solid boxes in Fig. 4. The metric f introduced in

this paper is denoted with green triangles, the SSIM

values with orange squares, while the Komparator

values with brown circles. The values in Fig. 4 are

normalized in the range [1, 5].

The number of points that fall outside the conﬁ-

dence intervals and the average distance (δ) of each

metric to the MOS were calculated for both Water-

marking algorithms and the corresponding values are

shown in Table 1. From Fig. 4 and Table 1, it can

be observed that the metric f is the one that best ﬁts

the subjective results, although the Komparator met-

ric gives also acceptable results.

Table 1: Performance of the metrics.

IADWT IADWT

Points δ Points δ

outside CI outside CI

SSIM 9 0.29 2 0.12

Komparator 3 0.26 3 0.20

f 2 0.26 1 0.13

6 CONCLUDING REMARKS

In this paper, a new perceptual metric for ﬁdelity eval-

uation of watermarked images was presented and val-

idated through subjective tests. The proposed metric

resorts to a widely used perceptual model of the HVS,

which provides the maximum possible quantization

error in the DWT coefﬁcients which is not perceptible

by the HVS. A relationship between these maximum

quantization errors in the DWT domain and the max-

imum variation of the wavelet coefﬁcients’s singular

values was derived in the paper. The proposed met-

ric can be adapted to other HVS models in the DWT

domain, like the one in (Lewis and Knowles, 1992).

The Mean Opinion Score for each image is the average

of the scores assigned by all observers.

Figure 4: Comparison of Objective and Subjective Assess-

ment for methods IADWT (top) and IADWT

(bottom).

CI: Blue solid boxes, f: green triangles, SSIM: orange

squares, Komparator: brown circles.

The performance of the proposed metric was

compared with two state-of-the-art perceptual ﬁdelity

metrics showing better correlation with the subjective

tests for the purposes of quantifying still image wa-

termarking ﬁdelity. The experiments were performed

using two IADWT watermark insertion algorithms. It

is the intention of the authors to test the performance

of the metric with other watermarking schemes, in

particular, with some of the SVD-based algorithms

listed in section 2.

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