Local Geometric Distortions Resilient Watermarking Scheme Based on Symmetry
Zehua Ma, Weiming Zhang, Han Fang, Xiaoyi Dong, Linfeng Geng, Nenghai Yu
11 Local Geometric Distortions ResilientWatermarking Scheme Based on Symmetry
Zehua Ma, Weiming Zhang, Han Fang, Xiaoyi Dong, Linfeng Geng, and Nenghai Yu
Abstract —As an efficient watermark attack method, geometricdistortions destroy the synchronization between watermark en-coder and decoder. And the local geometric distortion is a famouschallenge in the watermark field. Although a lot of geometricdistortions resilient watermarking schemes have been proposed,few of them perform well against local geometric distortionlike random bending attack (RBA). To address this problem,this paper proposes a novel watermark synchronization processand the corresponding watermarking scheme. In our scheme,the watermark bits are represented by random patterns. Themessage is encoded to get a watermark unit, and the watermarkunit is flipped to generate a symmetrical watermark. Then thesymmetrical watermark is embedded into the spatial domain ofthe host image in an additive way. In watermark extraction, wefirst get the theoretically mean-square error minimized estimationof the watermark. Then the auto-convolution function is appliedto this estimation to detect the symmetry and get a watermarkunits map. According to this map, the watermark can beaccurately synchronized, and then the extraction can be done.Experimental results demonstrate the excellent robustness of theproposed watermarking scheme to local geometric distortions,global geometric distortions, common image processing opera-tions, and some kinds of combined attacks.
Index Terms —digital watermark, watermark synchroniza-tion, local geometric distortions, random bending attack, auto-convolution function
I. Introduction D IGITAL watermark is widely used for ownership pro-tection, authentication, annotation, etc. [1], [2]. An ef-ficient watermarking scheme should be robust to a varietyof distortions. Besides the robustness towards common imageprocessing, the robustness towards geometric distortions isequally significant. Common image processing, for example,filtering or compression, weakens the watermark by changingthe value of pixels. However, geometric distortions destroythe synchronization between watermark encoder and decoder.Under such distortions, the decoder can no longer decodethe watermark without resynchronization even through thewatermark still exists.The geometric distortions can be divided into two cate-gories. One is global geometric distortion, such as rotation,scaling, translation, and cropping. The other is local geometricdistortion, like random bending attacks (RBA) of Stirmark[3], [4]. The local geometric distortions are more complicated
All the authors are with CAS Key Laboratory of ElectromagneticSpace Information, University of Science and Technology of China, Hefei,230026, China. (e-mail: [email protected], [email protected],[email protected]) Corresponding author: Weiming Zhang.This work was supported in part by the Natural Science Foundation of Chinaunder Grant U1636201 and 61572452, and by Anhui Initiative in QuantumInformation Technologies under Grant AHY150400. and harder to recover. And it has been an open problemfor years that designing a watermarking scheme performingwell under local geometric distortions. Besides, many cross-media watermarking schemes have been proposed recently, forexample, print-scanning watermarking schemes [5], [6], print-camera watermarking schemes [7]–[9], and screen-camerawatermarking schemes [10]–[13]. Considering that the cross-media process will introduce unnoticeable local geometricdistortions [3], a watermark synchronization process resilientto local geometric distortions may improve the performanceof such schemes.A lot of geometric distortions resilient watermarkingschemes have been proposed. And they can be divided intothe following five categories. The first category is the water-marking scheme using image normalization to resist geometrictransforms [14]–[18]. By normalizing the image accordingto a set of predefined moment criteria, watermarked imageachieves invariance under affine transformation. But imagenormalization based methods have weak performance undercropping distortions. Because cropping changes the momentscalculated from the whole image. Meanwhile, most imagenormalization based methods have only one-bit capacity andhigh computational cost.The second category is based on template [19]–[21]. Atemplate is embedded in the Fourier domain. Before water-mark extraction, the affine transformation can be estimatedby comparing the detected template with the original one.Then the inverse affine transformation is implemented andthe watermark can be extracted with a traditional method.However, the performance of template based watermark highlydepends on the detection accuracy of the template. Besides,such watermark is vulnerable to template removal attack [22].The third category is the watermarking scheme embeddingthe watermark in the geometric invariant domain [5], [23]–[26]. A rotation, scaling and translation (RST) invariant do-main is obtained by applying the Fourier-Mellin transform(discrete Fourier transform and log-polar mapping). The RSToperations in the spatial domain can be converted into param-eter translation in the Fourier-Mellin domain. By embeddingand extracting the watermark in the Fourier-Mellin domain,there is no need to estimate and invert the geometric distor-tions. And the translation can be easily recovered by usingtracking sequences embedded along with the informative wa-termark. Kang et.al [5] proposed a uniform log-polar mapping(ULPM) based watermarking scheme which eliminates theinterpolation distortion and interference distortion introducedin the embedding process. Besides, Urvoy et.al proposed aperceptual Discrete Fourier Transform (DFT) watermarking a r X i v : . [ c s . MM ] J u l (a) The host image. (b) The image attacked by RBA.(c) A regular grid. (d) The grid attacked by the sameRBA (red).Fig. 1: Two images attacked with the same RBA. scheme [27], whose embedding strategy can help these DFT-based watermarking schemes get perceptually optimal visibil-ity.However, local geometric distortion is still a challenge to thewatermarking schemes belonging to the aforementioned threecategories. Comparing Fig. 1(b) to Fig. 1(a), the distortioncaused by RBA is almost unnoticeable. But the distortion issevere as shown in Fig. 1(d). Frequency values and momentswhich are calculated from the whole image will also changeseverely after RBA, which severely limits the performance ofthese watermarking schemes.The feature based watermarking schemes belong to thefourth category [28]–[34]. By binding the watermark withthe global or local geometrically invariant features, the water-marking scheme would obtain the corresponding robustness.Most of them are one-bit watermark scheme. In [34], a multi-bit watermarking scheme was proposed based on local daisyfeature transform (LDFT). It is resilient to many kinds of localgeometric distortions. However, its robustness to commonimage processing operations and global geometric distortionsis weak. A possible reason is that local geometrically invariantfeatures are not robust enough to other distortions. Besides,comparing to other watermarking schemes, feature basedmethods usually have higher computational cost.The last category is the watermark scheme using periodicwatermark itself as calibration signal [35]–[39]. A watermarkunit is periodically tiled to generate a periodic watermark.In watermark extraction, the period can be detected by auto-correlation function (ACF) or magnitude spectrum (MS) andsuch period can act as a reference to recover the global geo-metric distortions. Considering that local geometric distortions can be regarded as a set of affine transformations in the localregion, Voloshynovskiy et.al [39] proposed using local ACFto detect and restore local geometric distortions. Moreover, asstated in the paper proposing template removal attack [22],methods in this category are resilient to this attack.In this paper, a watermark synchronization process basedon symmetry is proposed, which is similar to the methodsbelonging to the last category mentioned above. However,we believe the difference between symmetry and periodicitymakes symmetry have some advantages as the watermark cal-ibration signal. And the corresponding watermarking schemeis proposed, which performs well under global geometricdistortions, common image processing operations, and somecombined attacks.The rest of this paper is organized as follows. In Section II,a universal watermark synchronization process based on peri-odicity is illustrated first. Then the difference between it andthe proposed synchronization process based on symmetry isdiscussed. In Section III and IV, we illustrate the watermarkembedding process and the extraction process of the proposedwatermarking scheme respectively. The experimental resultsare shown and discussed in Section V. Section VI draws theconclusion.II. Watermark Synchronization Process AnalysisIn this section, we will discuss and compare periodicity andsymmetry, and their application on watermark synchronizationto illustrate the advantages of symmetry as the watermarkcalibration signal. A. A Universal Periodic Watermark Synchronization Process
The periodic watermark schemes, as mentioned in Section I,have been widely used. Among them, the scheme proposed byVoloshynovskiy et.al [39] is one of the most representativeschemes, as the unique periodic watermark scheme robust tolocal geometric distortions, or random bending attack. We firstillustrate its watermark synchronization process to support thelater discussion.In [39], the watermark unit, named macro-block, consistingof informative watermark and reference watermark. As shownin Fig. 2(a), the watermark unit is tiled to generate a peri-odic watermark. In the case of rectangular macro-block, thewatermark W has the following property: W ( x , y ) = W ( x + m T len , y + n T wid ) (1)where m , n are integers, and T len , T wid are the size of themacro-block. The periodicity P of W is commonly defined asthe auto-correlation of W : P ( i , j ) = (cid:213) x (cid:213) y W ( x , y ) W ( x + i , y + j ) (2)in which P ( i , j ) represents the correlation between W and the W translated by vector ( i , j ) . P can also be computed by thefrequency form of ACF: P = I FFT [ FFT ( W ) FFT ( W ) ∗ ] (3) (a) A example of watermark generating. (b) The corresponding state change of (a).Fig. 2: (a) is an example of generating a 4 × × where FFT represents the fast Fourier transform,
I FFT isthe corresponding inverse transform, and ∗ operator denotescomplex conjugation. The periodicity will change along withthe global geometric distortions.The case of global geometric distortion is considered first.Most global geometric distortions can be uniquely describedby an affine transformation, and the affine transformationcan be represented by a linear component matrix A , plus atranslation component v . Considering that the translation canbe separately recovered, Voloshynovskiy et.al [39] propose touse an approach based on penalized Maximum Likelihood(ML) estimation to estimate the linear component A :ˆ A = arg min A ∈ Φ (cid:40) ρ (cid:32)(cid:32) x (cid:48) y (cid:48) (cid:33) − A (cid:32) x y (cid:33)(cid:33) + µ Ω ( A ) (cid:41) (4)where ˆ A is the optimal estimation within the set of possiblesolutions A ∈ Φ , ρ denotes the cost function, and ( x , y ) , ( x (cid:48) , y (cid:48) ) represent the Cartesian coordinates of ACF peaksbefore and after affine transformation. The last term µ Ω ( A ) is a weighted prior knowledge, restricting the variations ofparameters in A . After recovering the linear transformationof the affine transformed watermark, the translation v canbe easily recovered, for example based on an intercorrelationbetween the extracted watermark and the reference watermarkmentioned above.Considering that the local geometric distortions, like RBAand perspective transformation, can be approximated as affinetransformations in the local region, and local geometric distor-tions can be approximated by a similar process. We can furthersummarize the watermark synchronization process proposed in [39] as the flowchart in Fig. 3.It should be noted that even though flipping appeared inthe scheme proposed by Voloshynovskiy et.al [39] for somepurposes, the synchronization process of the scheme is stillbased on periodicity and follows the above discussion. B. The Proposed Symmetrical Watermark SynchronizationProcess
However, we believe that the watermark synchronizationprocess based on symmetry may have some advantages overthe one based on periodicity. These advantages come from thedifference between symmetry and periodicity and contributeto a simpler watermark synchronization process as shownin Fig. 4. Similarly, we define symmetrical watermark andits symmetry first. In our scheme, as shown in Fig. 2(a),the symmetrical watermark W is generated by flipping therectangular watermark unit, and it satisfies: W ( x s − x , y s − y ) = W ( x s + x , y s + y ) (5)where ( x s , y s ) are the coordinates of one symmetrical center of W . In the symmetrical watermark W , the symmetrical centersare the corners of the watermark unit. Similar to periodicity,the symmetry S of the watermark about a point ( i , j ) can bedefined by: S ( i , j ) = (cid:213) x (cid:213) y W ( i − x , j − y ) W ( i + x , j + y ) . (6) S ( i , j ) is actually the correlation between W and the W flippedaround point ( i , j ) .We believe the most important difference between symmetryand periodicity is that there is a clearer mapping between (a) Original (b) Rotation (c) Scaling (d) Translation (e) Cropping (f) Affinetransformation (g) PerspectivetransformationFig. 5: Top row:
The grids under the same geometric distortions with watermarks, representing the states of the watermark units;
Middle row:
The symmetry of the symmetrical watermark in Fig. 2(a) under geometric distortions;
Bottom row:
The periodicity of the periodic watermark in Fig. 2(a) under geometric distortions. symmetrical peaks and watermark position. Periodicity is acharacteristic about translation, and symmetry is a character-istic about position. To be specific, in Eq. (2), the coordinatesof P represent a translation or a vector, and the correspondingvalue in P denotes the possibility that the period of W is thatvector. The coordinates of P and W have different meanings.But in Eq. (6), the coordinates of S and W have the samemeaning, indicating the position. Given a point ( i , j ) , the valueof S ( i , j ) represents the possibility that point ( i , j ) is one ofthe symmetrical centers of W . In the ideal case, the positionsof symmetrical peaks in S are the positions of symmetricalcenters in W .Considering that symmetrical centers are corners of wa-termark units, knowing the position of symmetrical peaksis equivalent to knowing the position of watermark unitsand corresponding geometric distortions. Fig. 5 shows theperiodicity of periodic watermark and the symmetry of sym-metrical watermark under various geometric distortions, inwhich the watermarks in Fig. 2(a) are used as samples andtheir periodicity and symmetry are calculated respectively byEq. (2) and Eq. (6). Observing these peaks in Fig. 5, wefind that symmetrical peaks show the position of the currentwatermark units and the experienced geometric distortionsmore clearly. Moreover, knowing the four corner points of awatermark unit, the position of the unit can be determinedand most of its geometric distortions can be recovered, evenincluding perspective transformation, just like Fig. 5(g). So thewatermark synchronization process based on symmetry shownin Fig. 4 becomes simpler.As a summary of the above discussion, the advantages of thewatermark synchronization process based on symmetry can belisted as follows:1) The process needs not the step of estimating transla-tion. Comparing Fig. 5(a) and Fig. 5(d), symmetricalpeaks show the position of watermark unit after trans- lation while periodic peaks keep the same. Reducingthe estimation steps contributes to a simpler synchro-nization process, which means less computational costand higher accuracy. Meanwhile, the redundancy forestimating translation, like reference watermark, is nolonger needed in the proposed watermark unit.2) The process performs better under local geometric dis-tortions. In the proposed synchronization process, thegeometric distortion on a watermark unit is regardedas a perspective transformation and will be recoveredbased on the detected four corners of the watermarkunit. Meanwhile, as we have mentioned, the synchro-nization process based on periodicity uses affine trans-formations to approximate local geometric distortions,including perspective transformation and RBA. Compar-ing to affine transformation, we think that perspectivetransformation has more parameters and will fit betterwhen approximating local geometric distortions.Besides, the proposed watermark synchronization processbased on symmetry has the potential to become an improvedversion of the one based on periodicity. Generating the water-mark by flipping rather than tiling and detecting the watermarkby symmetrical peaks rather than periodic peaks, most periodicwatermark schemes following the synchronization process inFig. 3 can be modified to the corresponding symmetricalwatermark schemes. If the modification does not introducenew disadvantages, these modified watermark schemes willperform better.Actually, these disadvantages do exist and may limit theperformance of synchronization process based on symmetry.These disadvantages can be listed as follows:1) The current process lacks a fast method to calculatesymmetry. Calculating symmetry in space domain likeEq. (6) is inefficient, especially when the host imageis large. This problem also exists in the document Fig. 6: Watermark embedding process.Fig. 7: An example of using R to spread spectrum. watermark scheme proposed by Fang et.al [7].2) The flipping introduces additional states of the wa-termark unit, as shown in Fig. 2(b), which need tobe determined before decoding. A common solutionis introducing predefined redundancy in the watermarkas a reference. But such solutions will bring back theredundancy again, which is released from estimatingtranslation.In Section III and IV, the proposed watermarking schemebased on symmetry is illustrated, which overcomes the disad-vantages mentioned above. To be specific, we discover the rela-tionship between symmetry and auto-convolution function, justlike periodicity and auto-correlation function, and conclude alower computational cost version of Eq. (6). Meanwhile, wepropose to use hypothesis testing to determine the state ofthe watermark rather than introducing redundancy. And theadvantages of symmetry are retained in the proposed schemeto get better performance.III. Watermark EmbeddingFig. 6 shows the framework of the proposed watermarkembedding process. And it can be divided into three mainmodules: watermark unit generating, symmetrical watermarkgenerating, and watermark embedding. The implementationdetails of these modules are illustrated as follows. A. Watermark Unit Generating
By applying a key, we generate a 2-D bipolar random matrix r of size L r , r i , j ∈ {-1,1}, i , j = , , ..., L r . Then r is doubly upsampled to get R . Comparing to r , the components of R ismainly distributed in the middle frequency and more robustto common image processing operations. And the size of R is L R , L R = L r . Watermark sequence is first encoded using anerror correction code (ECC) to obtain the message m of length L m . Then we reshape m to a 2-D matrix of size p × q , where p × q ≥ L m . After that m is spread spectrum encoded using R to get a watermark unit w . As Fig. 7 shows, in w , bit ‘1’ ispresented as + × R and bit ‘0’ is presented as − × R . So thesize of w is L R times the size of m . Specifically, the lengthand width of w are defined as m and n , where m = p × L R , n = q × L R . In the end, w is masked with a mask matrix K , which is also generated from a key and doubly upsampledto the same size of w . The masked watermark unit w m iscalculated by w m ( i , j ) = w ( i , j ) K ( i , j ) (7)where i , j denote the index of the matrix. The maskingoperation is effective and necessary because it can1) Offer basic informative security. Without K , even thewatermarking scheme is a white box, the adversarialcannot accurately extract the message.2) Eliminate the impact of weak messages. Similar to aweak key in cryptography, a weak message refers to akind of message makes the watermark synchronizationprocess behave in some undesirable ways. For example,a symmetrical 2-D message is a kind of weak message.Because the symmetry of the message itself and thesymmetry generated by flipping will be both detectedand confuse the watermark synchronization. To elimi-nate the impact of weak messages, watermark unit w is masked with a mask matrix K . Because of spread-spectrum matrix, the information rate of K is L R timesthat of w . The difference of information rate makes theproperties of masked watermark unit w m more dependon R rather than w . So after masking, most propertiesof the message are eliminated, and w will be closeto a random matrix. As a result, weak messages willno longer impact the synchronization process and theproposed watermarking scheme can reach its theoreticalinformation rate.3) Help judge the state of the watermark unit. This partwill be illustrated in Section IV-C. Fig. 8: An example of generating symmetry by flipping watermark unit.
B. Symmetrical Watermark Generating
We flip the masked watermark unit w m to create thecomplete watermark W . In this paper, flipping vertically isdefined as flipping along the central horizontal axis of theblock and flipping horizontally is defined as flipping along thecentral vertical axis of the block. Fig. 8 shows an exampleof generating symmetry by flipping watermark unit in whichwe use symbol ‘p’ to represent the watermark unit. Thesymmetrical watermark is generated by following a flippingrule : • flipping rule : The next horizontally adjacent watermarkunit is generated by flipping the elder one horizontally,and the next vertically adjacent watermark unit is gener-ated by flipping the elder one vertically.To a specific image I , w m is flipped repeatedly until thesize of W is larger than the size of I . Then we crop W to thesize of I to get the watermark for embedding.Note that the flipping process is self-consistent. Differentflipping order will generate the same symmetrical watermark W . To this W , the adjacent line of two watermark units is thesymmetrical axis of W and adjacent point of four watermarkunits is the symmetrical center of W . C. Watermark Embedding in Spatial Domain
Watermark is embedded into the luminance of the hostimage with an additive way. In case that input is a color image,we will convert it to
YCbCr space and take component Y as the luminance, called I . To balance the robustness andimperceptibility, an adaptive watermark strength strategy isa common solution, for example, the adaptive embeddingstrategy proposed in [40]. In this paper, we use a simplestrategy that embedding watermark with higher strength onthe region with complex texture and with lower strength onthe region with simple texture. The complexity of the imagecould be measured by the local variance of I . So the adaptivewatermark strength s is defined as follows: s ( i , j ) = F ( σ I ( i , j )) (8)where σ I is the local variance of I and F is a nonlinearfunction. In the proposed scheme, F is defined as: F ( x ) = (cid:40) α , i f lo g ( x ) < α lo g ( x ) , other w ise (9)where α is a global embedding strength and set to 2 in ourscheme. Then the watermarked image I w is generated by I w ( i , j ) = I ( i , j ) + s ( i , j ) W ( i , j ) . (10) Fig. 9: Watermark extraction process.
The symmetrical watermark can be slightly pre-distorted toresist against spatial averaging and removal attack [39]. Thispredistortion will not significantly affect the symmetry of thewatermark used for the recovering of geometric distortions. Inthe end, a
YCbCr to RGB transform will be applied if thehost image is a color image.IV. Watermark ExtractionAs a blind watermarking scheme, the watermark extractorhas no prior knowledge of the host image. However, the keyis shared between encoder and decoder, so the extractor cangenerate the same spread-spectrum matrix R and the maskmatrix K . The watermark extraction process is illustrated inFig. 9 and can be divided into four main modules: watermarkestimation, watermark synchronization, watermark state deter-mining, and watermark decoding. These modules are furtherexplained as follows. A. Watermark Estimation
Part of the discussion in this section refers to [41]. Thewatermark component is predicted from the attacked water-marked image J received by the extractor. We denote thedistortion and noise as n . Then J can be represented as: J ( i , j ) = I ( i , j ) + W ( i , j ) + n ( i , j ) . (11) n is assumed to be zero-mean white noise for the purpose oftractability. Considering w m is almost a random matrix and W is generated by w m , W is similar to an additive random noisejust like n . So J and I have the same local mean µ . Eq. (11)can be further represented as: J (cid:48) ( i , j ) = I (cid:48) ( i , j ) + W ( i , j ) + n ( i , j ) (12)where I (cid:48) and J (cid:48) are residual components such that I (cid:48) = I − µ , J (cid:48) = J − µ . We hope to find a kind of h so that W can beestimated as follows: (cid:99) W = J (cid:48) ⊗ h (13) where ⊗ represents the convolution operation and (cid:99) W is anestimate of W . h is the convolution kernel which can minimizethe mean-square error: h = arg min E {( W − (cid:99) W ) } (14)where E {·} represents the expectation. Substituting (cid:99) W withEq. (13), the mean square error can be rewritten as: E {( W − (cid:99) W ) } = E {( W − J (cid:48) ⊗ h } . (15)Substituting J (cid:48) with Eq. (12), Eq. (15) can be rewritten infrequency domain as: E {( W − (cid:99) W ) } = E {( W − J (cid:48) H ) } = E {( W − ( I (cid:48) + W + N ) H ) } = E {( W ( − H ) − I (cid:48) H − N H ) } = E { W ( − H ) + I (cid:48) H + N H + Z } (16)where I (cid:48) , J (cid:48) , W , N , H are the frequency form of I (cid:48) , J (cid:48) , W , n , h , respectively. Z is the summation of the cross product.Specifically, Z = − W ( − H ) I (cid:48)∗ H ∗ − W ∗ ( − H ) ∗ I (cid:48) H − W ( − H ) N ∗ H ∗ − W ∗ ( − H ) ∗ N H + I (cid:48) H N ∗ H ∗ + I (cid:48)∗ H ∗ N H = − W I (cid:48)∗ ( − H ) H ∗ − W ∗ I (cid:48) ( − H ) ∗ H − W N ∗ ( − H ) H ∗ − W ∗ N ( − H ) ∗ H + I (cid:48) N ∗ H H ∗ + I (cid:48)∗ N H ∗ H . (17)Note that the cross-correlation of two variables can becalculated by the conjugate product of their frequency form.Because the watermark W , residual component I (cid:48) and noise n are independent, the expectation of their cross-correlationshould be zero. So the expectation of Z is E { Z } = − E { W I (cid:48)∗ }( − H ) H ∗ − E { W ∗ I (cid:48) }( − H ) ∗ H − E { W N ∗ }( − H ) H ∗ − E { W ∗ N }( − H ) ∗ H + E { I (cid:48) N ∗ } H H ∗ + E { I (cid:48)∗ N } H ∗ H = . (18)Combining Eq. (16) and Eq. (18), we have: E {( W − (cid:99) W ) } = E { W }( − H ) + E { I (cid:48) } H + E { N } H + E { Z } = P W ( − H ) + P I (cid:48) H + P N H + = P W ( − H ) + ( P I (cid:48) + P N ) H (19)where P W , P I (cid:48) , P N are the power spectrum of W , I (cid:48) , N . Wefind that the mean-square error is a quadratic function about H . To find the minimum error value, the derivative of Eq. (19)is calculated and set to zero. Then we have: H = P W P W + P I (cid:48) + P N = P W P J (cid:48) (20)where P J (cid:48) is the power spectrum of J (cid:48) . From Eq. (20), we canget that h ( i , j ) is a scaled impulse given by: h ( i , j ) = P W P J (cid:48) δ ( i , j ) (21) where δ is a unit impulse. Substituting the right side ofEq. (13) with Eq. (21), the watermark W within the localregion can be expressed as: (cid:99) W = J (cid:48) ⊗ P W P J (cid:48) δ = ( J − µ ) P W P J (cid:48) . (22)Considering J (cid:48) and W are both zero mean in the local region,their power spectrum are their local variance. So the mean-square error minimized estimation of W can be calculated by: (cid:99) W = ( J − µ ) σ W σ J (cid:48) . (23)where σ W , σ J (cid:48) are the local variance of W and J (cid:48) . We cancalculate σ J (cid:48) from the attacked watermarked image J . Notethat W is similar to a random noise so its local variance σ W depends on its embedding strength s , which can be estimatedfrom J using Eq. (8). B. Watermark Synchronization based on Symmetry
To synchronize the masked watermark unit w m , the symme-try of (cid:99) W should be calculated first. In Section. II-B, We havedefined the symmetry of symmetrical watermark and proposedEq. (6) to calculate it. Also in Section. II-B, we believe thata lower computational cost version of Eq. (6) is needed.First of all, the Eq. (6) can be rewritten as: S ( i , j ) = (cid:213) x (cid:213) y (cid:98) W ( i − x , j − y ) (cid:98) W ( i + x , j + y ) = (cid:213) x (cid:213) y (cid:98) W ( x , y ) (cid:98) W ( i − x , j − y ) (24)where x and y run over all values that lead to legal subscriptsof (cid:99) W . Defining a temporary matrix T , T ( i , j ) = S ( i , j ) , wehave: T ( i , j ) = (cid:213) x (cid:213) y (cid:98) W ( x , y ) (cid:98) W ( i − x , j − y ) T ( u , v ) = (cid:213) x (cid:213) y (cid:98) W p ( x , y ) (cid:98) W p ( u − x , v − y ) (25)where (cid:99) W p is (cid:99) W zero-padding to doubly the original size.We discover that T is the auto-convolution of (cid:99) W p . Just likeperiodicity and auto-correlation function (ACF), symmetryhas a relationship with auto-convolution function. In thispaper, A uto- C o N volution F unction is abbreviated as ACNFto distinguish it from ACF. So the convolution theorem couldbe used to get the frequency form of Eq. (25) as follows: T = I FFT [ FFT ( (cid:99) W p ) FFT ( (cid:99) W p )] (26)where FFT represents the fast Fourier transform and
I FFT is the corresponding inverse transform. According to thedefinition of T , T is actually the doubly upsampling of S ,so the symmetry S of (cid:99) W can be calculated by: S = D( I FFT [ FFT ( (cid:99) W p ) FFT ( (cid:99) W p )]) (27)where D(·) is a downsampling function which scales its inputmatrix to the half size. Using the frequency form of ACNF, (a) Original symmetrical peaks. (b) Uniform symmetrical peaks.Fig. 10: Original and uniform symmetrical peaks generated from the samesymmetrical watermark. The symmetrical watermark has 4 × from Eq. (24) to Eq. (27), the computational cost of calculating S is greatly reduced.Another problem is that, in Eq. (24), different i , j willcontribute different summation size. As a result, S has higherpeaks in the middle region, as shown in Fig. 10(a). Thisphenomenon is also reflected in the brightness of symmetricalpeaks in Fig. 5. Actually, in the spatial domain, the uniform S (cid:48) is easy to get by dividing S by its summation size as follows: S (cid:48) ( i , j ) = (cid:205) x (cid:205) y (cid:98) W ( i + x , j + y ) (cid:98) W ( i − x , j − y ) (cid:205) x (cid:205) y S (cid:48) ( i , j ) is a uniform symmetry generated by scaling S ( i , j ) to the unit value. It is hard to find the frequency formof Eq. (28) directly. Kang et.al [5] propose customized phasecorrelation to solve a similar problem and get an approximatesolution. In our scheme, we first calculate the numerator anddenominator of Eq. (28) separately and then calculate theirquotient. We note that the denominator also has frequencyform just like the numerator. So the uniform symmetry S (cid:48) canbe calculated by: S (cid:48) = D (cid:32) I FFT [ FFT ( (cid:99) W p ) FFT ( (cid:99) W p )] I FFT [ FFT ( O p ) FFT ( O p )] (cid:33) (29)where O p is the zero-padding of O and O is a matrix of oneshaving the same size with (cid:99) W . Fig. 10 shows the symmetricalpeaks of original S and uniform S (cid:48) . The peaks of S (cid:48) havesimilar height.To separate symmetrical peaks from noise peaks and getwatermark units map M , an adaptive threshold is applied asfollows: M = (cid:40) , i f S (cid:48) > µ S (cid:48) + β σ S (cid:48) , other w ise (30)where µ S (cid:48) and σ S (cid:48) denote the local average and the standarddeviation of S (cid:48) , respectively. And β is an empirical coefficientwhich is set from 3.0 to 4.3. M is a binary matrix in whichelement 1’s represent the possible corner points of watermarkunits and we can use it to resist various geometric distortions.As shown in Fig. 11, M clearly shows the position of thewatermark units under geometric distortions. (a) Watermarked image rotated by15 ◦ , translated by (-16,-16), andcropped to 75%. (b) M corresponding to (a).(c) Watermarked image attacked byRBA. (d) M corresponding to (c).Fig. 11: Watermarked images under geometric distortions and theircorresponding watermark units map M . The embedded symmetricalwatermark has 16 ×
16 watermark units. state 1 state 2 state 5 state 6state 3 state 4 state 7 state 8
Fig. 12: Four original states and four extra states generated by rotation.
C. Watermark State Determining
Before despread spectrum and decoding the masked water-mark unit w m , the state of w m should be determined. Flip-ping offers the watermark symmetry but introduces additionalstates. As Fig. 12 shows, the original watermark unit has fourstates. And if rotation is considered, the states increase toeight. Rather than introducing a reference watermark in thewatermark unit, we propose a state determining method bycombining mask matrix K and the statistical characteristics of w m .The state of w m without any flipping and rotation isdenoted as state 1 and the rest are denoted as state 2 to .Firstly, according to the watermark units map M , we select awatermark unit and restore its geometric distortions to get w s , whose state is unknown. Before de-masking w s with K , w s should be flipped and rotated from current state to state 1 . Setup a null hypothesis as follows: H : w s is not state 1 .Contrary to H , w s is de-masked with K directly to get w r .According to H , w s is wrong de-masked so w r is almost arandom matrix and has no property of spread-spectrum matrix R . We divide w r into non-overlapped small blocks which havethe same size with R , and use w i , jr to represent the small block i -th in row and j -th in column. Then w i , jr is normalized to themean value of 0 and the variance of 1. It should be noted that R is also zero-mean and one-variance. Matrix x is defined by: x ( p , q ) = w i , jr ( p , q ) R ( p , q ) (31)where p , q are integer ranging from 1 to L R . According to H , w i , jr ( p , q ) is independent to R ( p , q ) . So the expectation and thevariance of x ( p , q ) are: µ x = E { x ( p , q )} = E { w i , jr ( p , q )} E { R ( p , q )} = σ x = D { x ( p , q )} = E {( w i , jr ( p , q ) R ( p , q )) } − E { w i , jr ( p , q ) R ( p , q )} = D { w i , jr ( p , q )} D { R ( p , q )} − E { w i , jr ( p , q )} E { R ( p , q )} = . (33)Consider the following equation: y = (cid:113) L R σ x L R (cid:213) p L R (cid:213) q ( x ( p , q ) − µ x ) = L R L R (cid:213) p L R (cid:213) q x ( p , q ) . (34)If the size of R is sufficiently large, y will be a random variablefollowing a standard normal distribution N ( , ) by exploitingthe central limit theorem. One selected watermark unit w s canoffer a few samples and we can roughly evaluate whether y follows N ( , ) according to these samples.Note that H actually makes hypothesis to all blocks’ statebesides the state of w s because the states of watermarkunits are related. For example, according to the flipping rule mentioned in Section III-B, a watermark unit w on right sideof w s is generated by flipping w s horizontally. So if w s is state 1 , the w on right side of w s will be state 2 . And if w s is not state 1 , the w on right side of w s will not be state2 . Similarly, combining H and flipping rule, it is easy toconclude an equivalent null hypothesis H (cid:48) : H (cid:48) : w s is not state 1 ; w on right side of w s is not state 2 ; w on upper side of w s is not state 3 ;. . . . H (cid:48) makes hypothesis to all watermark units. To every block,we can get a set of samples of y . So we have enough samples (a) not state 1 (b) not state 2 (c) not state 3 (d) not state 4 (e) not state 5 (f) not state 6 (g) not state 7 (h) not state 8 Fig. 13: Different distribution of y with different null hypotheses of w s when w s is state 1 actually. The red line follows N ( , ) . of y from these blocks and could evaluate the distribution of y accurately. Fig. 13(a) shows the distribution of y with H (cid:48) when the selected w s is state 1 . It is obvious that y deviateson a large scale from N ( , ) , so H (cid:48) is rejected. And H isalso rejected since H and H (cid:48) are equivalent. Finally, we canget the conclusion that w s is state 1 .Meanwhile, as Fig. 13 shows, if we make a different nullhypothesis, y will follow N ( , ) . In practice, we use Kullback-Leibler divergence (KLD) to measure the distance between y and N ( , ) . To eight different null hypotheses, the distancebetween y and N ( , ) will be calculated respectively. Then thehypothesis corresponding to the farthest distance is rejected,and the state of w s will be determined. D. Watermark Decoding
Now we get the states of all watermark units and restoreall available watermark units to state 1 . All these availableblocks are accumulated to get (cid:98) w . Similarly, (cid:98) w is divided tonon-overlapped small blocks which have the same size withspread-spectrum matrix R and they are denoted as (cid:98) w i , j . Todespread (cid:98) w , the correlation value ρ i , j between (cid:98) w i , j and R isobtained as: ρ i , j = L R (cid:213) p L R (cid:213) q (cid:98) w i , j ( p , q ) R ( p , q ) (35)Then the message bit is determined by: (cid:98) m i , j = (cid:40) , ρ i , j < , ρ i , j ≥ (cid:98) m i , j is the extracted message bit. The obtained messagematrix (cid:98) m is now reshaped and ECC decoded to recover theembedding message m (cid:48) .V. Experimental ResultsIn this section, the proposed watermarking scheme based onsymmetry is compared with some state-of-art watermarkingschemes. The experimental parameters, setup of comparativeexperiment and test database are described in Section V-A.In Section V-B, V-C, and V-D, the robustness in differentaspects is compared between the proposed scheme and otherwatermarking schemes. Fig. 14:
Top row:
Host images;
Bottom row:
Watermarked images generated by the proposed scheme.
A. Implementation Details
In our scheme, the size of spread-spectrum matrix R is animportant parameter. Obviously, bigger R makes the water-mark more robust to common image processing operations.Meanwhile, smaller R means more watermark units withinthe same size area, that is, there are more symmetrical peaksto better approximate the geometric distortions. In our experi-ment, we choose L R = L m =
64. Toevaluate the performance between the proposed scheme andthe state-of-art ones fairly, the message is embedded directlywithout ECC encoded and the bits error quantity (BEQ) isrecorded.As mentioned in Section I, only watermarking schemesbelonging to the last two categories have the possibility thatbeing robust to local geometric distortions. Voloshynovskiy et.al [39] and Tian et.al [34] respectively belong to these twocategories and are resilient to local geometric distortions. Inthe rest categories, the robustness of Kang et.al [5] to globalgeometric distortions and common image processing opera-tions is one of the best. And we compare the proposed schemewith these three schemes. To illustrate the experimental resultsconcisely, in the following part, we use V_ACF [39], T_LDFT[34], and K_ULPM [5] to represent the three watermarkingschemes above.The test host images include eight colorful images, selectedfrom USC-SIPI image database [42] and one hundred grayimages, randomly selected from BOSSBase database [43].Fig. 14 shows part of the host images and their correspondingwatermarked images generated by the proposed scheme. Theaverage peak signal-to-noise ratio (PSNR) of 108 watermarkedimages is 41.35dB. The robustness of the proposed schemeto distortions is evaluated by the average bits error quantity(BEQ) of watermarked images under the corresponding dis-tortions. To other watermarking schemes in the comparativeexperiment, the same experimental setup and process areapplied. As shown in Table I, the average PSNR values ofwatermarked images generated respectively by four differentwatermarking schemes are set to the same level of 41 ± . TABLE I:Average PNSR of Watermarked Images Generated by Different Schemes.
Scheme V_ACF [39]
T_LDFT [34]
K_ULPM [5]
ProposedPNSR(dB)
B. Robustness to Common Image Processing Operations
In this subsection, we compare the capability of V_ACF[39], T_LDFT [34], K_ULPM [5], and the proposed scheme torecover the hidden message under common image processingoperations, including JPEG compression, Gauss noise, and av-erage filtering. The experimental results are shown as follows.
1) Robustness to JPEG Compression:
The watermarkedimages are compressed with JPEG compression with qualityfactor (QF) from 15 to 90. The average BEQ is listed inTable II. The proposed scheme performs well under JPEGcompression with all quality factors. To be specific, the per-formance of the proposed scheme is similar to K_ULPM [5]’sand better than the rest schemes’.
TABLE II:Average BEQ of Watermarked Images under JPEG Compression.
Quality Factor V_ACF [39]
T_LDFT [34]
K_ULPM [5]
Proposed
90 0 6.111 0.037
80 0 16.352 0.343
70 0 20.740 0.482
60 0.046 22.815 0.630
50 0.213 24.102 1.278
40 0.657 26.963 1.954
2) Robustness to Gauss Noise:
The watermarked imagesare corrupted by Gauss noise with the variance from 0.0001to 0.01. As Table III shows, the 64-bit message can be recov-ered with few errors by the proposed watermarking scheme.Meanwhile, V_ACF [39] also performs well. The proposedwatermarking scheme and V_ACF are both spatial watermarkand have a similar framework. Their low BEQ is a result ofaccumulation operation, which is a common spatial watermarkenhancement method. The impact of Gauss noise could beexcellently decreased by accumulating the repeated watermarkunits.
3) Robustness to Average Filtering:
Average filters of differ-ent size are applied on the watermarked images and the averageBEQ is recorded in Table IV. The proposed watermarkingscheme could recover the message without error under 3 × TABLE III:Average BEQ of Watermarked Images under Gauss Noise.
Variance V_ACF [39]
T_LDFT [34]
K_ULPM [5]
Proposed TABLE IV:Average BEQ of Watermarked Images with Average Filtering.
Filter Size V_ACF [39]
T_LDFT [34]
K_ULPM [5]
Proposed × × × C. Robustness to Geometric Distortions
The robustness of watermarking schemes to geometric dis-tortions, including global and local geometric distortions, areinvestigated in this subsection. Besides rotation, scaling, trans-lation, and cropping, affine transformation, lines removal, andaspect ratio change are also set as global geometric distortionsin comparative experiments. Meanwhile, RBA proposed inStirmark is set as local geometric distortion in the comparativeexperiment. There is no specific experiment to translationbecause translation is a basic geometric distortion and usuallyexists along with other geometric distortions, like rotation andcropping.
1) Robustness to Rotation:
The watermarked images arerotated by some specific angles, including some small, preciseangles, to test the robustness of watermarking schemes torotation. The experimental results are listed in Table V. Theproposed scheme almost recovers the message with very fewerrors from all of the rotation angles. And the rest schemeshave higher average BEQ, especially under some specificrotation angles.
TABLE V:Average BEQ of Rotated Watermarked Images.
Rotate Angle V_ACF [39]
T_LDFT [34]
K_ULPM [5]
Proposed . ◦ . ◦ ◦ ◦ ◦ ◦ ◦
2) Robustness to Scaling:
The width and height of wa-termarked images are scaled proportionally with the scalingfactor from 0.5 to 2.0. As shown in Table VI, under all scalingfactors, the average BEQ of the proposed scheme is 0. Ourscheme and V_ACF [39] have similar performance and aremuch better than the rest.
TABLE VI:Average BEQ of Scaled Watermarked Images.
Scaling Factor V_ACF [39]
T_LDFT [34]
K_ULPM [5]
Proposed
3) Robustness to Cropping:
The watermarked images arecropped by the ratio from 1% to 75%. Both width and heightare cropped. For example, if a watermarked image of size512 ×
512 is cropped 75%, only the central region of size128 ×
128 is reserved whose area is only 6 .
25% of theoriginal one. The experimental results are listed in Table VII.The proposed watermarking scheme can recover the messagealmost without error when the cropping ratio is from 1% to50%. When the cropping ratio is 75%, the average BEQ ofthe proposed scheme is only 5.537, much less than the restschemes’.
TABLE VII:Average BEQ of Cropped Watermarked Images.
Cropping Ratio V_ACF [39]
T_LDFT [34]
K_ULPM [5]
Proposed
1% 0.093 0.231 3.917
5% 0 1.157 4.833
10% 0.269 1.083 5.546
25% 0.657 3.000 8.111
50% 0.694 5.444 17.963
75% 9.824 12.778 28.009
4) Robustness to Affine Transformation:
The watermarkedimages are transformed with different affine transformationmatrix as follows: (cid:34) x (cid:48) y (cid:48) (cid:35) = (cid:34) a bc d (cid:35) (cid:34) x y (cid:35) . (37)By adjusting a , b , c , and d , X-shearing, Y-shearing, andXY-shearing of different strengths would be applied to wa-termarked images. According to the experimental results inTable VIII, under all the tested affine transformations, theBEQ of the message recovered by the proposed scheme is0. Meanwhile, under a specific affine transformation, the BEQof V_ACF [39] is 0.407, the BEQ of T_LDFT [34] is 8.269,and the BEQ of K_ULPM [5] is up to 30.870.
5) Robustness to Aspect Ratio Change:
The width andheight of watermarked images are scaled respectively withdifferent scaling factors. In Table IX, the height of water-marked images is scaled with the first scaling factor and the TABLE VIII:Average BEQ of Affine Transformed Watermarked Images.
Affine Transform Matrix a b c d
V_ACF [39]
T_LDFT [34]
K_ULPM [5]
Proposed width is scaled with the second one. As Table IX shows,the proposed watermarking scheme can recover the embeddedmessage without error with all aspect ratio change. V_ACF[39] performs as well as the proposed scheme. The averageBEQ of T_LDFT [34] is over 9, and the average BEQ ofK_ULPM [5] is over 31. TABLE IX:Average BEQ of Disproportionally Scaled Watermarked Images.
Scaling Factors V_ACF [39]
T_LDFT [34]
K_ULPM [5]
Proposed . × . . × . . × .
6) Robustness to Lines Removal:
To investigate the robust-ness to lines removal, 1%, 5% and 10% lines in row andcolumn of watermarked images are removed. These removedlines are distributed at regular intervals. As Table X shows,under all tested lines removal, the proposed scheme has BEQof 0, much lower than the BEQ of the rest schemes.
TABLE X:Average BEQ of Watermarked Images under Lines Removal.
Lines Removal Ratio V_ACF [39]
T_LDFT [34]
K_ULPM [5]
Proposed
1% 0 0.426 5.907
5% 0.056 1.241 4.954
10% 0.083 4.185 6.500
7) Robustness to Random Bending Attack:
RBA of Stir-mark is one of the most typical local geometric distor-tions. Considering the randomness of RBA, to specific attackstrength, each watermarked image is attacked 5 times toget the average performance. Thus, each average BEQ inTable XI is calculated from the messages recovered from108 × M , just like Fig. 11(d). TABLE XI:Average BEQ of Watermarked Images under RBA.
Strength of RBA V_ACF [39]
T_LDFT [34]
K_ULPM [5]
Proposed TABLE XII:Average BEQ of Watermarked Images under Combined Attacks.
Combined Attack Types V_ACF [39]
T_LDFT [34]
K_ULPM [5]
Proposed
Average + Gauss 0.111 29.519 1.824
JPEG + Average 0.083 26.130 1.639
JPEG + Gauss 0 28.287 2.102 Cropping + Rotation 1.120 5.556 11.963
Cropping + Scaling 0.713 22.167 9.972 Scaling + Rotation 0.611 18.972 7.963
Cropping + Average 1.157 25.806 8.491
Cropping + Gauss 0.935 24.426 8.148 JPEG + Cropping 1.111 23.917 8.796 JPEG + Rotation 0.731 24.657 5.963
JPEG + Scaling 0 26.037 5.852 Rotation + Average 0.451 24.935 6.685
Rotation + Gauss 0.583 30.759 5.750
Scaling + Average 0.241 28.398 5.657
Scaling + Gauss 0 32.176 5.713 RBA + Average 0.102 25.037 10.278
RBA + Cropping 0.685 8.046 28.102
RBA + Gauss 0.111 31.704 10.324
RBA + JPEG 0.185 24.954 10.037
RBA + Rotation 0.343 16.444 3.389
RBA + Scaling 0.194 22.796 6.769
D. Robustness to Combined Attacks
In this subsection, we select a couple of representative singleattacks, that is, JPEG compression with QF 70, Gauss noisewith variance 0.001, 3 × ◦ , scalingwith factor 0.75, cropping 25%, and RBA with strength 0.3.One combined attack is generated by combining two of thesesingle attacks. The experimental results are listed in Table XII,where parameters of attacks are omitted. The average BEQ ofthe proposed scheme is less than 1, much lower than the restschemes. It is not a surprising result because the proposedscheme, different from others, has better performance underall these single attacks.VI. ConclusionThis paper presents a blind and robust watermarkingscheme, including a novel watermark synchronization process.The proposed synchronization process is based on the symme-try of the symmetrical watermark, which has several advan-tages comparing to prior similar schemes. Besides, we proposeto minimize the mean-square error to get the watermarkestimation, use auto-convolution function to quickly calculatethe symmetry, and apply hypothesis testing to determine thewatermark state. We believe that the proposed watermarksynchronization process based on symmetry has the potential to become an improved version of the one based on periodicityand help similar schemes to improve their performance. Ac-cording to the experimental results, the proposed watermarkingscheme has excellent performance under various distortions,including RBA, global geometric distortions, common imageprocessing operations, and combined attacks. In further work,we will focus on the application of the proposed watermarkingscheme on the print-camera process.References [1] F. A. Petitcolas, “Watermarking schemes evaluation,” IEEE SignalProcess. Mag , vol. 17, no. 5, pp. 58–64, 2000.[2] C. I. Podilchuk and E. J. Delp, “Digital watermarking: algorithms andapplications,”
IEEE Signal Process. Mag , vol. 18, no. 4, pp. 33–46,2001.[3] F. A. Petitcolas, R. J. Anderson, and M. G. Kuhn, “Attacks on copyrightmarking systems,” in
International workshop on information hiding .Springer, 1998, pp. 218–238.[4] F. A. Petitcolas, “Watermarking schemes evaluation,”
IEEE SignalProcess. Mag , vol. 17, no. 5, pp. 58–64, 2000.[5] X. Kang, J. Huang, and W. Zeng, “Efficient general print-scanningresilient data hiding based on uniform log-polar mapping,”
IEEE Trans.Inf. Forensics Security , vol. 5, no. 1, pp. 1–12, 2010.[6] J.-M. Guo, S.-C. Pei, and H. Lee, “Paired subimage matching watermark-ing method on ordered dither images and its high-quality progressivecoding,”
IEEE Trans. Multimedia , vol. 10, no. 1, pp. 16–30, 2007.[7] H. Fang, W. Zhang, Z. Ma, H. Zhou, S. Sun, H. Cui, and N. Yu,“A camera shooting resilient watermarking scheme for underpaintingdocuments,”
IEEE Trans. Circuits Syst. Video Technol , 2019.[8] C. Chen, W. Huang, B. Zhou, C. Liu, and W. H. Mow, “Picode: A newpicture-embedding 2d barcode,”
IEEE Trans. Image Process , vol. 25,no. 8, pp. 3444–3458, 2016.[9] C. Chen, B. Zhou, and W. H. Mow, “RA code: A robust and aestheticcode for resolution-constrained applications,”
IEEE Trans. Circuits Syst.Video Technol , vol. 28, no. 11, pp. 3300–3312, 2017.[10] C. Chen, W. Huang, L. Zhang, and W. H. Mow, “Robust and unobtrusivedisplay-to-camera communications via blue channel embedding,”
IEEETrans. Image Process , vol. 28, no. 1, pp. 156–169, 2018.[11] H. Fang, W. Zhang, H. Zhou, H. Cui, and N. Yu, “Screen-shootingresilient watermarking,”
IEEE Trans. Inf. Forensics Security , vol. 14,no. 6, pp. 1403–1418, 2018.[12] M.-J. Lee, K.-S. Kim, and H.-K. Lee, “Digital cinema watermarking forestimating the position of the pirate,”
IEEE Trans. Multimedia , vol. 12,no. 7, pp. 605–621, 2010.[13] H. Cui, H. Bian, W. Zhang, and N. Yu, “Unseencode: Invisible on-screenbarcode with image-based extraction,” in
IEEE INFOCOM 2019-IEEEConference on Computer Communications . IEEE, 2019, pp. 1315–1323.[14] C.-W. Tang and H.-M. Hang, “A feature-based robust digital imagewatermarking scheme,”
IEEE Trans. Signal Process , vol. 51, no. 4, pp.950–959, 2003.[15] D. Zheng, S. Wang, and J. Zhao, “RST invariant image watermarkingalgorithm with mathematical modeling and analysis of the watermarkingprocesses,”
IEEE Trans. Image Process , vol. 18, no. 5, pp. 1055–1068,2009.[16] J. S. Seo and C. D. Yoo, “Image watermarking based on invariant regionsof scale-space representation,”
IEEE Trans. Signal Process , vol. 54,no. 4, pp. 1537–1549, 2006.[17] P. Dong, J. G. Brankov, N. P. Galatsanos, Y. Yang, and F. Davoine,“Digital watermarking robust to geometric distortions,”
IEEE Trans.Image Process , vol. 14, no. 12, pp. 2140–2150, 2005.[18] H. S. Kim and H.-K. Lee, “Invariant image watermark using Zernikemoments,”
IEEE Trans. Circuits Syst. Video Technol , vol. 13, no. 8, pp.766–775, 2003.[19] A. Herrigel, J. ó Ruanaidh, H. Petersen, S. Pereira, and T. Pun, “Securecopyright protection techniques for digital images,” in
InternationalWorkshop on Information Hiding . Springer, 1998, pp. 169–190.[20] S. Pereira and T. Pun, “Robust template matching for affine resistantimage watermarks,”
IEEE Trans. Image Process , vol. 9, no. 6, pp. 1123–1129, 2000.[21] X. Kang, J. Huang, Y. Q. Shi, and Y. Lin, “A DWT-DFT compositewatermarking scheme robust to both affine transform and JPEG com-pression,”
IEEE Trans. Circuits Syst. Video Technol , vol. 13, no. 8, pp.776–786, 2003. [22] A. Herrigel, S. V. Voloshynovskiy, and Y. B. Rytsar, “Watermarktemplate attack,” in
Security and Watermarking of Multimedia ContentsIII , vol. 4314. International Society for Optics and Photonics, 2001,pp. 394–405.[23] C.-Y. Lin, M. Wu, J. A. Bloom, I. J. Cox, M. L. Miller, and Y. M.Lui, “Rotation, scale, and translation resilient watermarking for images,”
IEEE Trans. Image Process , vol. 10, no. 5, pp. 767–782, 2001.[24] D. Zheng, J. Zhao, and A. El Saddik, “RST-invariant digital imagewatermarking based on log-polar mapping and phase correlation,”
IEEETrans. Circuits Syst. Video Technol , vol. 13, no. 8, pp. 753–765, 2003.[25] J. J. O’Ruanaidh and T. Pun, “Rotation, scale and translation invariantdigital image watermarking,” in
Proceedings of International Conferenceon Image Processing , vol. 1. IEEE, 1997, pp. 536–539.[26] D. He and Q. Sun, “A RST resilient object-based video watermarkingscheme,” in , vol. 2. IEEE, 2004, pp. 737–740.[27] M. Urvoy, D. Goudia, and F. Autrusseau, “Perceptual dft watermarkingwith improved detection and robustness to geometrical distortions,”
IEEE Trans. Inf. Forensics Security , vol. 9, no. 7, pp. 1108–1119, 2014.[28] H.-Y. Lee, H. Kim, and H.-K. Lee, “Robust image watermarking usinglocal invariant features,”
Opt. Eng , vol. 45, no. 3, p. 037002, 2006.[29] P. Bas, J.-M. Chassery, and B. Macq, “Geometrically invariant water-marking using feature points,”
IEEE Trans. Image Process , vol. 11, no. 9,pp. 1014–1028, 2002.[30] P. Dong, J. G. Brankov, N. P. Galatsanos, Y. Yang, and F. Davoine,“Digital watermarking robust to geometric distortions,”
IEEE Trans.Image Process , vol. 14, no. 12, pp. 2140–2150, 2005.[31] X. Gao, C. Deng, X. Li, and D. Tao, “Geometric distortion insensitiveimage watermarking in affine covariant regions,”
IEEE Transactions onSystems, Man, and Cybernetics, Part C (Applications and Reviews) ,vol. 40, no. 3, pp. 278–286, 2010.[32] S. Xiang, H. J. Kim, and J. Huang, “Invariant image watermarking basedon statistical features in the low-frequency domain,”
IEEE Trans. CircuitsSyst. Video Technol , vol. 18, no. 6, pp. 777–790, 2008.[33] J.-L. Dugelay, S. Roche, C. Rey, and G. Doërr, “Still-image watermark-ing robust to local geometric distortions,”
IEEE Trans. Image Process ,vol. 15, no. 9, pp. 2831–2842, 2006.[34] H. Tian, Y. Zhao, R. Ni, L. Qin, and X. Li, “LDFT-based watermark-ing resilient to local desynchronization attacks,”
IEEE Trans. Cybern ,vol. 43, no. 6, pp. 2190–2201, 2013.[35] M. Kutter, “Watermarking resistance to translation, rotation, and scal-ing,” in
Multimedia Systems and Applications , vol. 3528. InternationalSociety for Optics and Photonics, 1999, pp. 423–431.[36] S. Voloshynovskiy, F. Deguillaume, and T. Pun, “Content adaptivewatermarking based on a stochastic multiresolution image modeling,”in . IEEE, 2000,pp. 1–4.[37] F. Deguillaume, S. V. Voloshynovskiy, and T. Pun, “Method for theestimation and recovering from general affine transforms in digitalwatermarking applications,” in
Security and watermarking of multimediacontents IV , vol. 4675. International Society for Optics and Photonics,2002, pp. 313–322.[38] T. Kalker, G. Depovere, J. Haitsma, and M. J. Maes, “Video watermark-ing system for broadcast monitoring,” in
Security and Watermarking ofMultimedia contents , vol. 3657. International Society for Optics andPhotonics, 1999, pp. 103–112.[39] S. Voloshynovskiy, F. Deguillaume, and T. Pun, “Multibit digital wa-termarking robust against local nonlinear geometrical distortions,” in
Proceedings 2001 International Conference on Image Processing (Cat.No. 01CH37205) , vol. 3. IEEE, 2001, pp. 999–1002.[40] Y. Huang, B. Niu, H. Guan, and S. Zhang, “Enhancing image water-marking with adaptive embedding parameter and psnr guarantee,”
IEEETrans. Multimedia , vol. 21, no. 10, pp. 2447–2460, 2019.[41] J. S. Lim,