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3D-DCT VIDEO WATERMARKING USINGQUANTIZATION–BASED METHODS
Patrizio Campisi and Alessandro NeriDip. Elettronica
Applicata
Università degli Studi Roma TREVia della Vasca Navale 84, 00146
Roma, Italy
phone: +39.06.55177064, fax: +39.06.55177026e-mail: (campisi,
neri)@uniroma3.it
ABSTRACTVideo watermarking methods operating in the
three-dimensional discrete cosine transform (3D-DCT) domain us-ing
quantization–based embedding techniques are here pre-sented.
Specifically, after having partitioned a video se-quence into
spatio-temporal units, they are projected ontothe 3D-DCT domain. A
set of transformed coefficients aretaken according to a selection
rule, ordered according to apredefined scan order, and eventually
marked. Two em-bedding methods are here considered: Quantization
IndexModulation watermarking (QIM) and Rational Dither Mod-ulation
(RDM). A perceptual criterion is also used to definethe “local”
quantization steps to be used in QIM. Finally, theinverse 3D
inverse DCT (IDCT) is performed thus obtainingthe marked video
shot. Robustness of the proposed methodagainst a variety of both
intentional and unintentional videoattacks has been observed
through experimental results.
1. INTRODUCTION
In this paper we deal with the problem of copyright protec-tion
of digital video sequences by using digital watermark-ing. This
issue is rising more and more concerns becauseof the development of
the digital multimedia market and ofthe always decreasing price of
storage devices and digitalsupports. Extensive surveys dealing with
video watermark-ing applications, attacks and methodologies can be
found in[1], [2].
The video temporal dimension is not exploited in thefirst
developed video watermarking methods, where a videois considered as
a succession of digital still images. There-fore existing schemes
employed for still image watermarkinghave been employed by
watermarking each frame indepen-dently of the others. A real time
watermarking algorithmrobust to video coding, D/A and A/D
conversion, formatconversion and limited editing, using a
bidimensional spreadspectrum approach operating in the spatial
domain is pre-sented in [3]. A spread spectrum approach to embed
digitalwatermarks in both the uncompressed domain and the
com-pressed MPEG-2 domain is presented in [4]. An attemptto exploit
the static and dynamic temporal components of avideo has been
performed in [5] where a wavelet transformis applied along the
temporal axis of the video to designa robust watermarking system.
In order to make the em-bedding of the mark imperceptible, methods
exploiting per-ceptual information have been presented in the
recent past(see for example [6], [7]). In [7] a perceptual
watermarkingmethod, operating in the 2D-DCT domain, for
embedding
the mark into MPEG-2 compressed video streams, has
beenpresented. However, in order to design video
watermarkingmethods robust to both non-hostile and hostile video
pro-cessing operations such as video format conversion, tem-poral
desynchronization, video editing, and video collusionframe-by-frame
watermarking strategy are not appropriate.In [8] collusion issues
are discussed when frame-by-frameembedding strategies are enforced
for video watermarking.In the recent past, to overcome the
drawbacks related toframe-by-frame watermarking methods, approaches
operat-ing in three dimensional transform domains have been
pro-posed. A watermarking approach operating in the 3D dis-crete
Fourier transform domain has been proposed in [9]. Awatermarking
method operating in the wavelet domain andmaking use of BCH codes
and 3D interliving is presented in[10]. In [11] a watermarking
method operating in the 3D-DWT domain, by using pseudo random
linear statistics ofpseudo random connected regions in the DC
subband of the3D wavelet domain is described. In [12] a perceptual
basedvideo watermarking technique, operating in the 3D
discretewavelet transform (3D-DWT) domain, that jointly
exploitsboth the spatial and the temporal dimension of a video
se-quence is described. Quantization based methods are usedin [13]
to mark 3D subbands in the 3D-DWT domain. In[14] a video
watermarking technique using the 3D discretecosine transform has
been described.
Attempts to account for human visual attention in or-der to
better localize video’s regions where to transpar-ently embed the
mark have been recently used to designsaliency-based watermarking
techniques. In [15] the pay-load is embedded in those regions that
receive less attentionby a viewer, so that the perception of the
scene is not al-tered. Among the factors impacting the human visual
atten-tion there are: contrast, color, object size and shape,
mo-tion, and many more. Although several factors have
beenidentified, their relative importance is not yet
determined.However, in many studies, the temporal features are
consid-ered as characterizing the importance of a region in terms
ofhuman perception of quality [16]. For instance, foregroundmoving
objects are prone to attract viewers’ attention mak-ing impairments
in the background more difficult to detect.At the same time, when
objects move faster with respectto the average motion of the scene,
impairments in the ob-ject would have minor impact on the subject
quality assess-ment. This would allow to increase the watermark
strengthin “low”-motion and “high”-motion areas, while reducing
itfor regions with “medium” temporal activity.
In this paper we propose a novel video watermarking
©2007 EURASIP 2544
15th European Signal Processing Conference (EUSIPCO 2007),
Poznan, Poland, September 3-7, 2007, copyright by EURASIP
-
technique operating in the 3D-DCT domain, thus jointly
ex-ploiting both the spatial and the temporal dimension of avideo
sequence. Specifically, the video is projected ontothe 3D-DCT
domain, and the coefficients selection is per-formed by taking into
account the energy compaction prop-erty of the DCT transform.
Eventually, the selected co-efficients set is marked by using two
quantization-basedapproaches: the quantization index modulation
(QIM) wa-termarking [17] and the rational dither modulation
(RDM)[18]. The quantization-based approaches, which are gain-ing
always increasing consensus with respect to other ap-proaches such
that spread spectrum based watermarkingmethods, consists in
quantizing the selected coefficients bymeans of a quantizer chosen
in a set on the basis of thecoefficient to embed. We propose to
perceptually design thequantization steps by using a qualitative
Human Visual Sys-tem (HVS) model. After a brief review of the
3D-DCT andof its inverse transform given in Section 2, the proposed
wa-termarking methods are detailed in Section 3.
Experimentalresults and conclusions are drawn in Sections 4.
2. 3D-DCT
Given a 3D real valued function f [n1,n2,n3], being n1,n2,and n3
integers assuming values in the set 0 ≤ n1 < N1,0≤n2 < N2,
and 0 ≤ n3 < N3, its forward 3D-DCT [20],F [k1,k2,k3], is given
by:
F [k1,k2,k3] = α(k1 ,k2,k3)N1−1∑
n1=0
N2−1∑
n2=0
N3−1∑
n3=0f [n1,n2,n3]·
· cos (2n1 +1)k1π2N1
cos(2n2 +1)k2π
2N2cos
(2n3 +1)k3π2N3
(1)
being
α(k1,k2,k3) =√
8N1N2N3
C(k1)C(k2)C(k3) (2)
and
C(ki) =
⎧⎨⎩1√2
ki = 0
1 otherwise(3)
with 0 ≤ ki < Ni, being i = 1,2,3.The 3D IDCT [20], is given
by:
f [n1,n2,n3] =N1−1∑
k1=0
N2−1∑
k2=0
N3−1∑
k3=0α(k1,k2,k3)F [k1,k2,k3]·
· cos (2n1 +1)k1π2N1
cos(2n2 +1)k2π
2N2cos
(2n3 +1)k3π2N3
(4)
where α(k1 ,k2,k3) and C(ki) are given by (2) and (3)
re-spectively.
It is worth pointing out that the 3D-DCT (3D-IDCT)is a separable
transform, which implies that it can be im-plemented as a series of
1D-DCT (1D-IDCT). Therefore itscomputation can be performed by
means of the fast algo-rithms which have been devised for computing
the 1D-DCT(1D-IDCT). The 3D-DCT (3D-IDCT) computational com-plexity
and computing time can be further reduced when fast3D-DCT (3D-IDCT)
algorithms are employed as discussedin [21].
3. THE PROPOSED WATERMARKING METHOD
The video sequence is first segmented into
non-overlappingspatio-temporal plot units, called shots, that
depict differ-ent actions. Each shot is characterized by no
significantchanges in its content which is determined by the
back-ground and the objects present in the scene. Although sev-eral
video segmentation algorithms which detect the abruptscene changes
[23], [24], [25], have been proposed in lit-erature, for the sake
of simplicity, we have segmented thevideo sequence into shots of
fixed length. Then each shotis projected onto the 3D-DCT domain and
the coefficientswhere to embed the mark are selected and ordered
accordingto a specific criterion. The selected coefficients are
markedusing either QIM or RDM, and eventually the 3D-IDCT
isperformed, thus obtaining the marked shot. Specifically, letus
consider the m-th video sequence shot, fm[n1,n2,n3], with0≤ n1 <
N1,0≤ n2 < N2, and 0≤ n3 < N3, composed by N3frames of
dimension N1 ×N2 pixels. Let us indicate withFm[k1,k2,k3] the
3D-DCT of fm[n1,n2,n3] obtained using(1).
3.1 Host coefficients selection
The host coefficients where to embed the mark must bechosen in
such a way to guarantee both the robustness andthe imperceptibility
of the mark. Therefore, the low fre-quency coefficients, which
usually present the higher energy,are left unaltered to guarantee
transparency. To achieve ro-bustness, similar rule applies to the
high frequency coef-ficients, which are usually drastically
quantized by videoencoders due to their low energetic content.
Following thiscriterion, the watermark is embedded in the DCT
coeffi-cients that correspond to the middle spatial and
temporalfrequencies. Specifically, the coefficients choice is
per-formed by selecting those coefficients, in the 3D-DCT vol-ume,
whose indices (k1,k2,k3) belong to the region R limitedby the two
hyperboloids (k1 + 1)(k2 + 1)(k3 + 1) = Cl and(k1 + 1)(k2 + 1)(k3 +
1) = Cu, being Cl < Cu two properlychosen constants.
Once the embedding region has been selected, its coeffi-cients
are ordered in a vector VR = [v1,v2, · · · ,vL], accordingto a
predefined scan order, which we assume known at thereceiving side.
In our approach the coefficients scan is madeby picking the
coefficients, belonging to the region R, firstalong the direction
k1, then along the direction k2, and fi-nally along the direction
k3. This scan order is determinedby the observation that in most
cases the coefficients arespread over the smaller values of k3.
3.2 Perceptual QIM watermark embedding
The mark embedding, based on the use of the QIM approach,relies
on the quantization of the selected host coefficients bymeans of a
quantizer chosen among a set of quantizers ac-cording to the data
to be embedded. However, to minimizethe distortion perception
produced by the watermarking, thequantizers can be designed taking
into account the spatio-temporal properties of the HVS.
Specifically, the HVS haslow contrast sensitivity for high
horizontal (k1), vertical (k2),and temporal (k3) frequencies, and
even lower sensitivity forhigh joint frequencies (k1
−k2,k1−k3,k2−k3,k1−k2 −k3).Therefore the quantization step should
increase with an in-crease of (k1), (k2), and (k3), and increase
even more for
©2007 EURASIP 2545
15th European Signal Processing Conference (EUSIPCO 2007),
Poznan, Poland, September 3-7, 2007, copyright by EURASIP
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(k1 − k2,k1 − k3,k2 − k3,k1 − k2 − k3) [19]. These qualita-tive
considerations on the HVS allow us properly choosingthe
quantization step as a function of the coefficient index(k1,k2,k3)
as follows:
∆(�k) = ∆(k1,k2,k3) = �∆4 (1+ kp1 + k
p2 + k
p3 )�. (5)
Then, given the coefficients to be marked, ordered in thevector
VR = [v1,v2, · · · ,vL], the corresponding quantizationsteps,
defined according to (5) are collected in the vector∆R = [∆1,∆2, ·
· · ,∆L].
Given a binary representation b = {bi,1≤ i ≤ L} of thewatermark,
and the host coefficients VR = {vi,1≤ i≤L} theperceptual QIM system
we define consists of quantizing viby letting bi choose between one
of two uniform quantizersU0 and U1 defined as:
U0 = {u = l∆i +d|l ∈ Z}U1 = {u = l∆i +∆i/2+d|l ∈ Z} (6)
being ∆i ∈ ∆R the quantization step and d ∈ [0,1) a keyused to
improve security. It is straightforward to note thatthis method can
be expressed in terms of additive water-marking. In fact, by
posing
qi = Q∆i
[vi −∆i
(bi2
+d)]
−[vi −∆i
(bi2
+d)]
, (7)
being Q∆i a uniform quantizer of step ∆i, the watermarkeddata
can be expressed as
vwi = vi +qi. (8)
The so obtained marked coefficients, are first grouped inthe
vector VwR = [vw1 ,v
w2 , · · · ,vwL ], then inserted back in the
selected region R in the DCT volume according to the de-fined
scan order, thus obtaining the marked 3D-DCT vol-ume Fwm
[k1,k2,k3]. Eventually, the 3D-IDCT is performedaccording to (4)
thus obtaining the marked m-th video se-quence shot f wm
[n1,n2,n3].
3.3 QIM Watermark extractionAt the receiving side, the m-th shot
of the received markedvideo sequence, f̂ wm [n1,n2,n3], is 3D-DCT
transformed. Theregion R, where the mark has been embedded, is then
se-lected according to the aforementioned criterion. The
coef-ficients belonging to the region R are then extracted and
or-dered in the vector V̂wR = [v̂w1 , v̂
w2 , · · · , v̂wL ]. Given the generic
element v̂wi belonging to V̂wR , and the quantization steps
vec-
tor ∆R = [∆1,∆2, · · · ,∆L], the decoded value b̂i is obtainedby
first extracting yi according to the following rule:
yi = Q∆i [v̂wi −d∆i]− [v̂wi −d∆i] , (9)
and then by using hard-decision decoding. Because of theadopted
embedding rule (7), the values yi should be close tozero when the
bit bi to be embedded is equal to 0 and closeto ±∆i/2 when bi = 1.
Therefore, the decoded value b̂i canbe obtained according to the
following decision rule:
b̂i ={
0 |yi| < ∆i/41 |yi| ≥ ∆i/4. (10)
3.4 RDM watermark embeddingHowever, as well known QIM based
watermarking schemesare largely vulnerable to amplitude scalings.
Therefore, in[18] a variation of the QIM embedding approach robust
toamplitude scalings while still retaining the simplicity of theQIM
method has been presented. Specifically, given the i-thinformation
symbol, bi ∈ {−1,1}, and the host coefficientsvector VR = [v1,v2, ·
· · ,vL], the embedding rule is expressedas follows:
vwi = g(Vi−1)Qbi
(vi
g(Vi−1)
)(11)
where Qbi represents the quantizers induced by the lattices:
U-1 = {u = 2l∆−∆/2|l ∈ Z}U1 = {u = 2l∆+∆/2|l ∈ Z}. (12)
The vector Vi−1 contains the past W samples of vector Vtaken at
instant i− 1 that is V i−1 = {vi−1,vi−2, · · · ,vi−W}.The function
g(·) is chosen within the functions such thatfor any ρ > 0,
g(ρVi) = ρg(Vi). Some functions satisfyingthis constraint are the
lp vector-norm:
g(Vi) =
(1W
k−1∑
m=k−W| vm |p
)1/p. (13)
The so obtained marked coefficients, are first collected in
thevector VwR = [vw1 ,v
w2 , · · · ,vwL ], then inserted back in the DCT
volume according to the defined scan order. Eventually,
the3D-IDCT is performed thus obtaining the marked m-th
videosequence shot f wm [n1,n2,n3].
3.5 RDM watermark extractionAt the receiving side, the region R
where the mark hasbeen embedded is selected after having 3D-DCT
trans-formed the m-th shot of the received marked video sequencef̂
wm [n1,n2,n3]. Let us indicate with V̂wR = [v̂w1 , v̂
w2 , · · · , v̂wL ] the
coefficients belonging to the marked region R.The decoding is
performed using a minimum Euclidean
distance rule:
v̂i = argmin−1,1
∣∣∣∣(
vi
g(V̂wi−1)
)−Qbi
(vi
g(V̂ wi−1)
)∣∣∣∣∣2
. (14)
4. EXPERIMENTAL RESULTS ANDCONCLUSIONS
Experimentations have been performed on uncompressedvideos
composed by N3 = 384 frames each of size (N1 ×N2) = (352 × 288)
pixels (CIF format). The employedtest sequences comprise news
programs, computer generatedvideos, musical videos, as well as
sport video clips. Eachvideo has been partitioned into shots having
fixed lengthequal to 20 frames. The region R limited by the two
hy-perboloids, where to embed the watermark, is specified
byconsidering Cl = 300 and Cu = 400, thus selecting a
middle-frequency region in the 3D-DCT domain. A watermarkcomposed
by 600 bits, drawn from a uniform distribution,
©2007 EURASIP 2546
15th European Signal Processing Conference (EUSIPCO 2007),
Poznan, Poland, September 3-7, 2007, copyright by EURASIP
-
Figure 1: Performance of both the proposed watermarkingmethods
(3D-DCT QIM and 3D-DCT RDM) in comparisonwith the method proposed
in [14] when the video is MPEG-2compressed.
Figure 2: Performance of both the 3D-DCT QIM and3D-DCT RDM
proposed methods in comparison with themethod proposed in [14] when
the video is MPEG-4 com-pressed.
is embedded in the selected region by using the
approachdescribed in Section 3.
When the perceptual QIM embedding approach is used,the embedding
is performed by means of (7)-(8) using avalue for ∆ in (5) equal to
185. The values of both theconstants Cl , Cu and the parameter ∆
have been empiricallychosen, on a wide range of videos, in order to
trade offbetween the imperceptibility of the mark and its
robustnessagainst most intentional attacks.
The imperceptibility of the mark has been tested by us-ing the
Video Quality Metric (VQM) Software [26] used tomeasure the
perceptual effects on the video of impairment
Cl Cu ∆ VQMG200 300 285 0.30300 400 185 0.20700 800 135 0.15
Table 1: VQMG for the QIM watermarked video.
such as blurring, block distortion, unnatural motion, noiseand
error blocks. Specifically, the general model metric,denoted as
VQMG, which can assume values comprised inthe interval [0,1], has
been used. Higher values of the met-ric correspond to higher
distorted scenes. For the valuesof the parameters Cl,Cu,∆ used in
the experimentations avalue VQMG = 0.2 has been observed (see Table
1). Thisvalue guarantees the imperceptibility of the mark as can
beverified by direct observation of the marked video sequence.From
Table 1 it is evident how the video quality degradeswhen both the
embedding region became closer to the ori-gin of the 3D-DCT domain,
thus involving lower frequencycoefficients, and when the
quantization step increases.
When considering the RDM watermark embedding thesame region R
used in the QIM apporach has been consid-ered (Cl = 300 and Cu =
400). Moreover the quantizationstep ∆ = 0.38 together with the
chosen value for (Cl andCu). guarantee a VQMG equal to 0.2, thus
obtaining thesame perceptual transparency obtained by using the
QIMapproach.
The robustness of the proposed methods has been testedusing a
variety of unintentional and intentional video at-tacks such as
MPEG-2 and MPEG-4 compression, collu-sion, transcoding, and frame
dropping. As a figure of merit,the ratio ρ between the number of
correctly decoded wa-termark bits and their total number is
computed. For thesake of comparison, the method described in [14],
operat-ing in the 3D-DCT domain, has been implemented and
theexperimental results have been here reported. In Figs.1, 2the
performance of both the proposed methods and the onepresented in
[14] in terms of the ratio ρ versus the bit rate ofthe marked video
sequence compressed using both MPEG-4and MPEG-2 coder have been
reported. From Figs.1, 2 weobserve that both the presented
approaches are more robustboth against MPEG-2 and MPEG-4
compression than theone proposed in [14]. Type I and type II
collusion videoattacks have also been considered. As for the first
attacka subsequence obtained by picking one frame belonging tothe
marked video sequence every ten is generated. Then, anestimation of
the mark is obtained by averaging the subse-quence’s frames. Type
II collusion is performed by aver-aging two consecutive frames in a
subsequence of ten con-secutive frames drawn from the marked video.
Then thewatermark is estimated by applying the decoding procedureto
the so obtained nine frames sequence. The experimentalresults in
Table 2 point out that the proposed method is ro-bust against the
collusion attacks. This is explained by theconsideration that the
watermark is “spread” along the tem-poral axis since the embedding
is performed in the 3D-DCTdomain. Moreover, this approach exhibits
good performancealso with respect to transcoding attacks and frame
dropping.The methods are sensitive to temporal desynchronization
at-tacks. Robustness to the gain attack is obtained by usingthe RDM
embedding based approach.
©2007 EURASIP 2547
15th European Signal Processing Conference (EUSIPCO 2007),
Poznan, Poland, September 3-7, 2007, copyright by EURASIP
-
ATTACK 3D-DCT 3D-DCT ApproachQIM RDM in [14]
Type I Collusion 0.89 0.87 0.79Type II Collusion 0.90 0.88
0.82
MPEG-2 (2500 Kb/s) →MPEG-4 (600 Kb/s) 0.92 0.83 0.12
MPEG-2 (1000 Kb/s) →MPEG-4 (600 Kb/s) 0.90 0.8 0.10Drop 1 frame
every 5 0.54 0.46 0.16
Table 2: Performance of the proposed video watermarkingschemes
(3D-DCT QIM and 3D-DCT RDM) for differentvideo attacks.
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©2007 EURASIP 2548
15th European Signal Processing Conference (EUSIPCO 2007),
Poznan, Poland, September 3-7, 2007, copyright by EURASIP
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