3d-dct video watermarking using quantization-based methods...3d-dct video watermarking using...

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


(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,

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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.

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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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