Journal of Information Security, 2012, 3, 138148 http://dx.doi.org/10.4236/jis.2012.32016 Published Online April 2012 (http://www.SciRP.org/journal/jis) New Video Watermark Scheme Resistant to Super Strong Cropping Attacks Ming Tong, Tao Chen, Wei Zhang, Linna Dong School of Electronic Engineerin, Xidian University, Xi’an, China Email: mtong@xidian.edu.cn Received January 14, 2012; revised February 28, 2012; accepted March 20, 2012 ABSTRACT Firstly, the nonnegative matrix factorization with sparseness constraints on parts of the basis matrix (NMFSCPBM) method is proposed in this paper. Secondly, the encrypted watermark is embedded into the big coefficients of the basis matrix that the host video is decomposed into by NMFSCPBM. At the same time, the watermark embedding strength is adaptively adjusted by the video motion characteristic coefficients extracted by NMFSCPBM method. On watermark detection, as long as the residual video contains the numbers of the least remaining subblocks, the complete basis matrix can be completely recovered through the decomposition of the nonnegative matrix of the least remaining subblocks in residual videos by NMFSCPBM, and then the complete watermark can be extracted. The experimental results show that the av erage intensity resistant to the various regular cropping of this scheme is up to 95.97% and that the average intensity resistant to the various irregular cropping of this scheme is up to 95.55%. The bit correct rate (BCR) values of the ex tracted watermark are always 100% under all of the above situations. It is proved that the watermark extraction is not limited by the cropping position and type in this scheme. Compared with other similar methods, the performance of resisting strong cropping is improved greatly. Keywords: Digital Watermarking; Cropping Attack; Geometric Attacks; Nonnegative Matrix Factorization (NMF); Sparseness Constrain 1. Introduction The watermarking robustness has been a focus in multi media research field, and how to resist geometric attacks is the hotspot and difficulty of the study [1]. Geometric attacks destroy the synchronization between the water mark and the videos, which seriously affect the robust ness of the watermarking and pose a deadly threat to the watermarking security. At the same time, with the ap pearance and maturity of a variety of video signal proc essing tools, the video data can be cropped, copied and tampered in various forms and different degrees much more conveniently, faster and more casually. Especially to strong cropping, the embedded watermark information is cropped directly and enormously and the copyright of digital video products is facing serious challenges. How to extract and recover the complete watermark in residual videos has always troubled researchers [2]. Consequently, the research on video watermark methods resisting to strong cropping attacks can help strengthening the copy right authentication and management, standardizing the market of video products, and solving the technology bottleneck problem of commercializing watermark, which has important academic research value and extensive market application prospect. A fourlevel dualtree complex wavelet transform (DT CWT) is applied to every video frame of the host video in [3], which embeds the watermark in the coefficients of low frequency subband. This method takes the advan tage of perfect reconstruction, shift invariance, and good directional selectivity of DT CWT, and can resist the cropping attacks with a certain strength. In [4], the wa termark is embedded into 8 × 8 subblocks of each Iframe, which is robust to row and column cropping attacks with small strength. Since the geometrical distor tions operations for every frame along the time axis in a video sequence are the same [5], the watermark is em bedded into the same position in the video frame by modifying the pixels of texture complex or sports intense area. But the information of the watermarks embedded by this method is less, and the robustness is greatly in fluenced by host carrier characteristics. So this method cannot resist cropping attacks. In [6], the watermark is embedded into the singular value of the coefficient ma trix of nonnegative matrix factorization (NMF). This method is robust to noise, filtering and other general at tacks, but cannot resist strong cropping attacks. Theo retical analysis and experimental results show that most existing video watermarking methods [27] resisting to C opyright © 2012 SciRes. JIS
M. TONG ET AL. 139 geometric attack can resist cropping attacks with smaller strength, but are sensitive to strong cropping attacks. Nonnegative matrix factorization (NMF) is a matrix factorization method under the condition that all the ele ments of the matrix are nonnegative, which can greatly reduce the dimensions of the data. The decomposition characteristics meet the experience of human visual per ception, and the decomposition results have interpretabil ity and clear physical meaning. Since it is proposed, N MF has been paid to great attentions, and it succeeds in the application to pattern recognition, computer vision and image engineering etc [811]. This paper proposes a new video watermarking scheme based on nonnegative matrix factorization with sparseness constraints on parts of the basis matrix (NMFSCPBM), in which the watermark is embedded into the basis matrix of NMFSCPBM. It uses video motion coefficients to adaptively control the watermark embedding strength. This scheme can resist various highintensity cropping attack, and experimental results show the effectiveness of this scheme. 2. Complete Basis Matrix Recovery and Video Motion Components Extraction Based on NMFSCPBM The NMF with sparseness constraints (NMFSC) method is proposed in [12], which uses a nonlinear projection operator to achieve the precise control of the sparseness by adding sparseness constraints in all basis vectors. But the data is described insufficiently under higher sparse ness constraints. A NMFSCPBM method is proposed in this paper, in which controllable sparseness constraints are added in the part of basis vectors. Not only can the NMFSCPBM method extract video motion components quickly and correctly, and filter out the static background interference completely, but also solve the problems of the NMFSC method under higher sparseness constraints. Meanwhile it reduces the decomposition error and speeds up the convergence rate. 2.1. NMFSCPBM Model Construction Sparse matrix is the matrix that most of the elements are zero or approach to zero and only a few are nonzero. The sparse degree of a vector is defined as Equation (1). 2 1 ii ny y n mn r 2 , ij ij ij DBWHB WH sparseness y (1) where n is the dimension of y [12]. So the NMFSCPBM can be transformed into the fol lowing constrained optimization problem that given a nonnegative matrix B of size , solve the basis matrix W of size and coefficient matrix H of size , where r is the decomposition dimension of B. If squared Euclidean distance D of primitive matrix and reconstructed matrix is defined as the target evaluation function, shown as Equation (2), which is used to de scribe the error between primitive matrix B and recon structed matrix WH, W and H should satisfy the condi tion of Equation (3). m rn (2) min , ,0,0 sparseness(), 1, 2, , ii DBWH WH wsi zzr w w , 0 0, ij ijjk ik k ij ij ij ii WW WHBH WifW Welse wLw (3) where i is the ith column of the basis matrix I, and si is the expected sparseness of . i The iteration rules of NMFSCPBM are described as follows: 1) Basis matrix W: (4) where Lw w i is performing nonlinear projection opera tion to [12]. i 2) Coefficient matrix H: T kj kjkj T kj WB HH WWH W wWsparseness(, )ws k wk w Wdw (5) Firstly, the definitions of some parameters used in it erative process are given. L is iterations. s is sparseness degree. new is the sparse constraint matrix to be added. k is the kth column of new . k is the adding sparseness constraints with the sparseness degree s for . is the column vector after the sparse con straint. newj is sparseness constraints matrix. is intermediate variable, is penalty factor. is pen alty factor threshold. is the convergence error thre shold of objective function. T is transpose operation. Therefore, the iterative steps of NMFSCPBM can be described below. The algorithm input is B, r, and L. The output is W and H. Step 1. Initialize , set the loop variable I = 1, and initialize W and H to random positive matrices. Step 2. T T WB HH WWH ,2 , DBWHB WH . T dwWHBH , Step 3. 12, . 1j new WW dw Step 4. Add partly sparseness constraints to W and start the iteration. (a) . Copyright © 2012 SciRes. JIS
M. TONG ET AL. JIS 140 , . kzzr (b) . sparseness, ,1, kk wws Copyright © 2012 SciRes. (c) 2 newj B WH, newj DBW H. (d) If H, , DBW newj or DBW H , then newj , turn to Step 5. Otherwise, return to Step 4(a), and set WW 2 , . 1jj Step 5. If 2 BWH F or i, then exit. Oth erwise, return to Step 2, and set . L 1ii H b 2.2. Complete Basis Matrix Recovery Based on the Least Remaining SubBlocks First of all, the definition of least remaining subblocks is given, followed by the Theorem 1 and its proof, which is the theoretical basis of resisting strong cropping attack of this scheme. Here, the residual video is defined as the remaining of the watermarked video after it is suffered from cropping attacks. The number of least remaining subblocks is defined as the number of the least complete video subblocks needed to recover the complete basis matrix from the residual video. Set the basic NMF modelmnmr rn . i is the ith column of B. i is the ith column of H. BW h 12mn n and, , , bBbb 12rn , , , n hh h are substituted in the basic model of NMF, then: 12 , , , nmr bbbW 12 , , , n hh h (6) Outspread Equation (6), then Equation (7) is obtained. 1, ri hi n aaK im bW (7) Firstly, perform blocking preprocessing to video, shown as Figure 1. The rules of blocking are as follows. Divide original video V into subblocks with size of along the temporal axis, and outspread each subblock as one column of nonnegative matrix B. Let C mod () 2, 1, 2,,kK 2, , c be the jth subblock of V, then: directly set to 0, shown as Figure 2. Let c denote the number of remaining complete subblocks after strong cropping attacks. For convenience, the remaining com plete subblocks are rearranged from 1, B ac cording to blocking order. Then the data matrix , the coefficient matrix and the base matrix W corre sponding to the remaining subblocks are as follows: 11 121 21 222 12 c c mm mc bb b bbb B bb b See the Equation (8). where denotes rounding operation toward 0, denotes modulus operation, K is the number of video frames, , and . 2 , iKa1, Actually, cropping attacks may occur in anywhere of the video. If video subblocks at its position suffer from cropping attacks, the corresponding data in the data matrix 11 121 21 222 12 c c rr rc hhh hh h H hh h 11 121 21 222 12 r r mm mr ww w ww w W ww w , , r 'BWH , where is the dimension of nonnegative matrix factorization. According to Equa tion (7), Equation (9) is obtained. (9) B Equation (9) shows that after the video suffers strong cropping attacks, is obtained by Equation (8) and ' and complete matrix W can be obtained by the iteration rules of NMFSCPBM. Therefore, the following Theorem 1 is established. Theorem 1: When the watermarked video suffers from strong cropping attacks, as long as the residual video contains the number of least remaining subblocks and meets, the complete basis matrix W can be recovered from residual video uniquely and correctly. cr '' TT T Theorem 1 is proved as follows. Transpose Equation (9) to obtain Equation (10). WB B (10) , Take ' and W into Equation (10), then Equa tion (11) is obtained. See the Equation (11). Let ,, , ,, , , , then Equation (11) is converted into: 11112 1 T r wwww 22122 2 T r www w 12 T mmmmr wwww 111121 T c bbb b 22122 2 T c bbbb 12 T mmm mc bbb b mod, ,1, mod, 0 ,1, mod, 0 j j Ciaiaakkifia Caiaa kkifia (, )Bi j 11 2111121111 211 2221222212222 1 212 rmm rmm crcrrmrc cmc hhhwwwbbb h wwwbbb h wwwbbb (8) 12 12 c hh hh (11)
M. TONG ET AL. 141 1 2 K a aa a 12 n v B= v v aaK Frame number Column Column Column Column Figure 1. Video blocking of this paper. 12 ,, ,,, vn b bb b 1,,,0,,0,,, vn b bb b Original videoBlocking Strong cropping attacks 1,,,,, vn bbbb Figure 2. Vide suffer from strong cropping. 12 'T 12mm www bb b 'T (12) Let H, then Equation (12) can be converted to the following linear equations, shown as Equation (13), where A is the coefficient matrix of each equations and 12 m w w 11 22 mm T Ww is the unsolved unknown vectors. wb wb wb (13) What follows is: taking the linear equation 11 wb as example, the existence and uniqueness of its solution is discussed. By the uniqueness of nonnegative matrix decomposition results, we know that, 11 wb is solv able and has a unique solution. In fact, the necessary and sufficient conditions of rdimensional homogeneous linear equations are RA RA r, where 11 'T Ab H b is the augmented matrix of A, and RA RA are the rank of A and respec tively, , and min ,r cRA RA min 1,rc r . It can be divided into three cases. 1) If c and RA cRA r, 11 wb has infinite solutions; 2) If and cr RARAr, 11 wb has infi nite solutions. The above two cases violate to uniqueness of the nonnegative matrix factorizing results, the solu tions are rejected. 3) If and cr RA rRA, 11 wb has the unique solution. Similarly, other equa tions have the same conclusions. We can see from the above solution process, if cr RA RA r, , , m ww w crW and , 12 separately has unique solution, or the base matrix W has a unique solution. In other words, when the watermarked video suffers from strong cropping attacks, as long as the re sidual video contains complete video subblocks and the number meets , the complete basis matrix can be recovered from residual video uniquely and correctly. Namely, Theorem 1 is established. Experimental results of this paper verify the correctness of theoretical analysis. 2.3. Video Motion Components Extraction Based on NMFSCPBM The basis matrix and coefficient matrix can be obtained by nonnegative matrix factorizing. Basis matrix repre sents the major features of video. Coefficient matrix is the linear projection of nonnegative matrix to basis ma trix and represents the local feature weights of video. Video frames can be seen as linear weighted sum of the static components and motion components. In general, the static components are nonsparse, while the motion components are sparse. So motion component can be separated from the static background by controlling sparseness constrains of the basis matrix, and then extract the motion components. The motion component extrac tion processes based on NMFSCPBM includes: 1) Video preprocessing. Take the target frame of the movement components to be extracted as the center for the original video Vm mK 21 l xy and choose the for ward and the next l frames separately. Let the total . frames compose of a video frame group V Outspread V onedimensionally as one column of non Copyright © 2012 SciRes. JIS
M. TONG ET AL. 142 negative mix B, shown as Equation (14), where the size of video frame is atr y mm , 1, 2, , y imm, 1, 2, , 21jl. The p chosen too large, calculation is risen significantly. Ifl is chosen too small, there have no obvious motion information between video frames. arameter l needs a reason able choice. If l is , , mod, , Bi jVimimj xx factorization. Perform (14) 2) NMFSC NMFSCPBMPBM to matrix B, and set r as the factorization dimension. Add sparseness constraints to the 1r basis vectors, so the basis vectors constrained spars 1,2, , 1 i wi r represents the motion components o 3) Solving Video motion components. Motio eness f video [12]. n com ponents of target frame can be obtained by weight ing and mming to the 1r su motion components, shown as Equation (15). 1r ,1 1 iil i MwH eighting coefficient o ,1 is the w spon (15) il Hf basis vectors e where, tar i w corrding to target frame. For each pixels of the get frame, there is one element in which is cor responding to it, has the same size with target frame, the bigger of the element in , the more intensity of the corresponding pixels movinn target frame. Motion components extracted by the NMFS g i and other similar methods are shown in Figure 3. It can be seen that, the motion components in Figure 3(b) ex tracted by the proposed method filter out the static back ground interference completely, and show the trajectory clearly compared with Figure 3(a). Figure 3(c) cannot distinguish the moving target from static background and cannot show the trajectory. Figure 3(d) has improved a little compared with Figure 3(c), but still cannot separate the moving target from static background completely. To quantitatively assessment the effectiveness of the motion components extraction of this paper, the matching rate [13] τ is defined to evaluate as follows: CPBM , ,, ,SMD, ,, SMD,SMD, xy R xy RxyR Ixy xy I xyIxyxyxy (16) SMD , y is the motion components extracted, where , xy R is the manually specified target motion area, and is the target frame. The more the is close to 1, the more matching of the extracted motion features compared with the features specified motion area. When the extracted motion features are exactly the same with the features specified motion area, 1 . The experiment chooses “hall”, “stefan” and “tennis” as test videos. (http://trace.eas.asu.edu/yuv/index.html). (a) (b) (c) (d) . ults obtained byFSCPBM method and other similar methods. (a) Original Figure 3Motion components extraction res NM video; (b) Motion components extraction results obtained by NMFSCPBM; (c) Motion components extraction results ob tained by NMFSC; (d) Motion components extraction results obtained by NMF. Copyright © 2012 SciRes. JIS
M. TONG ET AL. 143 ompute the matching rate of the 25th fame and the 55th C frame in “hall”, the 26th frame and the 30th frame in “ste fan”, and the 16th frame and the 18th frame in “tennis”, respectively. The experiment sets 5l, and experimen tal results are shown in Figure 4. It can be seen that the matching rates of this paper are more close to 1 compared with other methods. The average matching rate of this paper is 0.8907, NMF is 0.5371, and NMFSC is 0.4070. 3. Watermark Embedding and Extraction ds Watermark embedding. The general watermark metho based on the NMF attempt to change the coefficient ma trix by various signal processing operations to accom plish watermark embedding [6], but the robustness is subjected to comparative limitation. As a linear expres sion method, the significant advantage of NMF lies in that the basis matrix is changeable [10] and that is robust to cropping attack [9]. Therefore, this scheme embeds the watermark into the basis matrix that is decomposed into by NMFSCPBM. When the watermarked video suffers from strong cropping attacks, known by Chapter 2.2 of this paper, as long as the residual video contains the numbers of least remaining subblocks, the complete basis matrix 'W can be completely recovered and then Figure 4. Comparative analysis of matching rate of the mo atermark can be extracted. The watermark cessing. Perform blocking preproc es 2.2 of this pape MFSCPBM decomposition to B. C tion components obtained by NMFSCPBM method and other similar methods. the complete w embedding schematic diagram of the proposed scheme is shown in Figure 5. 1) Video prepro sing to the original video xy Vm mK . According to the blocking rules Chapterr, obtain the nonnegative matrix B. 2) Performing the N alculate the decomposition error according to Equation (17), and retain W for watermark extraction. BWH (17) 3) Watermark encryption. Sel qu 1 ,1, 2, , tt t Pks kukkN (18) 4) Watermark embedding. The proposed scheme ch ect pseudorandom se ence U as the secret key, perform encryption to wa termark signal S, and gain the secret information P, shown as Equation (18). l ooses the N biggest elements 12 , ww w of the basis matrix W as the positions for embedding, embeds watermark by Equation (19) multiplicative rules, and gains the watermarked basis matrixW. '1 nn n ww Ip watermark (19) 5) Watermark embedding strength m adaptively adjust ent. Perform the blocking processing to video accord ing to Chapter 2.2 of this paper. Extract the video motion components according to Chapter 2.3 of this paper. Calculate theotion feature coefficient i m w of the row where the ith coefficients locate according to Equa tion (20). Therefore, the watermark embedding strength of the ith coefficient is 1, 2,, ii wFwi N , where is the motion d 0.0 masking weighting factor an 13 is selected by the experiments. 2 a , i j xy wMij mm (20) 6) Performing nonnegative matrix synthesis by NM FSCPBM. Perform nonnegative matrix synthesize to 'W, , E as Equation (21). ''BWHE (21) Basis matrixW Coefficient matrix H，Error matrix E NMFSCPBM Factorization NMFSCPBM Synthesize W Secret key U Watermark Original viWatermarked video deo Preprocessing Watermark embedding Video reconstruct Embed position select Basis matrix W storage Embed strength control Motion component extraction Figure 5. Watermark embedding sche me of this paper. Copyright © 2012 SciRes. JIS
M. TONG ET AL. 144 7) Video reconstructiocon lter mark extraction. The watermark extraction sche m sid in W 2), 1if ww (22) 4. Experiment and Analysis is paper, the videos 4.1. Transparency Tests frame video captures of and after the watermark is em 4.2. Bit Rate Constancy Tests e bit rate constancy of n. Restruct 'B according to of video coding before b ocking rules, and then output the wamarked video finally. Water atic diagram of the proposed scheme is shown in Fig ure 6. Firstly, perform the blocking preprocessing for the watermarked video that has been attacked according to Chapter 2.2 of this paper, obtaining the nonnegative ma trix B constituted by the remaining complete subblocks in reual video. Secondly, perform the NMFSCPBM decomposition toB, getting the watermarked complete basis matrix 'W residual video. Finally, by compar ing W with ', the encrypted watermark is extracted as Eation (2 and then it is decrypted by the secret key U. From the process of watermark extraction, we know that the watermark extraction of this scheme does not need original video. So it is a blind watermark scheme. 0if ww qu ' p In order to verify the validity of th “football”, “motherdaughter”, “tempete”, “mobile”, “aki yo”, “hall”, “foreman” and “soccer” with the format of CIF and the length of 300, 260, 260, 300, 300, 300, 300 and 300 frames are selected as the host video for ex pe riment respectively. A 64 × 64 binary image is selected as the watermark, the size of subblock is 8 × 8, the de composition dimension r of NMFSCPBM is 32, and the experimental software environment is matlab 7.2. The experiment conducts the test and analysis about the transparency, bit rate constancy, robustness, realtime property, and the algorithm efficiency etc. for this scheme respectively. Due to the length limitation of this paper, only a partial list of results are listed such as the transpar ency, bit rate constancy, and strong cropping attacks etc. Figures 7(a) and (b) are the I the original frame and watermarked frame from football sequence. It can be seen that there is no significant visual perceptive distortion before and after the watermark is embedded. From the quantization assessment data shown in Tab le 1, we also know that the difference value ΔPSNR bedded decreases only by average 0.025dB (PSNR, Peak Signal to Noise Ratio of video coding) and that there is no influence on visual perception. The reason is that the proposed scheme sufficiently considers the visual mask ing features for watermark embedding position selection and strength control, embeds the watermark into the big coefficients of the basis matrix, and meanwhile embeds comparatively strong strength watermark into the regions where the motion is intense [14], eliminating the flicker influence and guaranteeing the transparency of the method. Table 2 shows the test results of th this paper. The experiment is assessed by the bit in creased rate (BIR) before and after the watermark is em bedded, as Equation (23). _ BIR watermarked B _ 100 % _ R originalBR original BR (23) where original_BR is the bit rate before the watermark is 4.3. Strong Cropping Attacks Experiments nd ir embedded, and watermarked_BR is the bit rate after the watermark is embedded. It can be seen that the increase in video BIR after the watermark is embedded in this paper is under 0.15%, with a good bit rate constancy. Strong cropping attacks include various regular a regular cropping, such as row and column cropping, edge cropping, top right corner cropping and center cropping etc. The same type and intensity of cropping attacks are synchronously carried out to paper [3], and the compara tive analysis is given. The experimental results are as sessed by the bit correct rate (BCR) of the extracted wa termark, as Equation (24). BCR 100% m (24) where e is the number of correct bits of the extracted e watermark, and m is the number of total bits of the ex tracted watermark. The more the BCR is close to 100%, the more higher of the correct rate. Let the threshold 70.00%T that is determined by experiments. If he watermark is detected. Some figures and BCR >T , t Basis matrix W W Watermarked video Waterma rk Secret key U Strong cropping attacks Residual video NMFSCPBM Factorization Preprocessing Nonnegative Matrix B Watermark extraction Figure 6. Watermark extraction scheme of this paper. Copyright © 2012 SciRes. JIS
M. TONG ET AL. 145 (a) Original video and watermark (b) Watermarked video and extracted waterark(c) Left bottom cropping 95.01%, BCR = 100%m (d) Column corpping 97.73%, BCR = 100% (e) Row and column cropping 97.98%, BCR=100%(f) Row cropping 97.22%, BCR = 100% (g) Row and column cropping 97.98%, (h) Edge cropping 97.73%, BCR=100% (i) Row and column cropping 96.72%, BCR = 100% BCR = 100% (j) Irregular cropping 94.51%, BCR = 100% (k) Irregular cropping 95.04%, BCR = 100% (l) Irregular cropping 95.50%, BCR = 100% (m) Irregular cropping 95.53%, BCR = 100% (n) Irregular cropping 96.17%, BCR = 100% (o)Irregular cropping 96.56%, BCR = 100% . Sis p Table 1. Transparency test results of this paper. Figure 7trong cropping attacks test results of thaper. Table 2. Bit rate constancy tests results of this paper. PSNR (dB) Test video Without wa watermark △PSNR termark With(dB) football 33.25 33.24 0.01 motter fo herdaugh37.90 37.87 0.03 tempete 32.92 32.88 0.04 mobile 32.22 32.17 0.05 akiyo 38.45 38.44 0.01 hall 36.31 36.28 0.03 reman 35.15 35.14 0.01 soccer 34.31 34.29 0.02 Bit rate (kbps) Test video watermarked_BR original_BR BIR football 166768.89 0. .98 160546% mo0.0720% f s therdaughter222.22 222.38 tempete 1101.06 1101.61 0.0500% mobile 1651.80 1651.83 0.0018% akiyo 226.49 226.52 0.0130% hall 415.98 416.05 0.0168% oreman489.58 490.33 0.1500% occer 654.55 655.44 0.1400% Copyright © 2012 SciRes. JIS
M. TONG ET AL. 146 quann assesslts oobu perime shown ie 7 and. for various curve of BCRs of the pr and paper [3] for strong cropping attacks. tificatioment resuf the rstness ex ent arn Figur Table 3 It can be seen from Figure 7 and Table 3 that, 1) the BCRs of the proposed scheme are all 100% regular and irregular strong cropping attacks. The scheme can recover the complete watermark without any damage, and has a very strong ability to resist strong cropping attacks. Analysis of the main reasons is that, based on the strong robustness of basis matrix to crop ping attacks, this scheme embeds the encrypted water mark into the big coefficients of the basis matrix that the host video is decomposed into by NMFSCPBM. When the watermarked video suffers from strong cropping at tacks, the complete basis matrix can be completely re covered through decomposition of the residual video by NMFSCPBM, and then the complete watermark can be extracted. The selection of the big coefficients of the basis matrix and the adaptive control of the watermark embedding strength based on the video motion feature coefficients, further increase the watermark embedding strength and improve the robustness. The spread spec trum encryption processing for watermark also increases the robustness while increases the watermark invisibility. 2) About various regular and irregular cropping attacks listed in the experiment, with the same attack intensity compared with this paper, the BCRs of the paper [3] are completely not up to 70% of the threshold requirements. Take the example of the “football” test video, when the row regular cropping is 97.22%, the BCR of the paper [3] Table 3. Robustness comparison of this scheme is 51.25%. When the edge cropping is 97.73%, the BCR of the paper [3] is 48.82%. For various irregular cropping attack, as Figures 7(j)(o) shown, the BCRs of the paper [3] are between 47.07%  56.35%, which can not meet the threshhold 70%. The same conclusion is obtained from the motherdaughter, tempete, mobile, akiyo, hall, foreman and soccer test videos. Figure 8 shows the relation oposed scheme with the cropping attack intensity. It can be seen that the inflexion where the BCR is less than 100% appears on the point with the cropping intensity 97.98%, while the cropping intensity is maximum and the number of the remaining complete subblocks in the residual video is c = 32, neither more nor less than equal ing to the dimension of NMF r = 32. Further analysis shows that, with the further increase of the cropping in tensity, the BCR decreases rapidly. It is mainly because the number of the remaining complete subblocks in the residual video c is less than 32, which indeed does not meet the least number of the remaining complete sub blocks required in the Theorem 1 of this paper. This fact makes e that is the number of correct bits of the extracted watermark decrease rapidly and causes the BCR decrease rapidly. The above analysis and results are fully consis tent with the results of the theoretical analysis in Chapter 2.2 of this paper. BCR (%) football motherdaughtertempetemobakiyo hall foreman soccer ile Attacks O OrOrOurOur er OrOr ur Paper [3] Our Paper [3] ur Pape [3]ur Pape [3] rPape [3] Pap [3] ur Pape [3] ur Pape [3] No attacks 100 100 100 100 100100100100100100100 100 100 100 100100 Row 00% C Row8% To B Irregular cropping 94.51% cropping 94.100 56.30 100 57.3810059.0710055.4810052.86100 56.21 100 54.4010055.03 Row cropping 97.22% 100 51.25 100 51.3610052.8210051.2110045.65100 51.29 100 53.1510054.25 olumn cropping 95.45%100 59.76 100 57.2310057.1510056.3210052.80100 51.25 100 50.5310053.29 Column cropping 97.73% 100 52.05 100 55.1510047.4110051.2610048.99100 47.26 100 53.3410051.77 and column cropping 97.9100 52.55 100 52.5810049.0910052.1010051.67100 46.54 100 48.5510049.85 Edge cropping 97.73% 100 48.82 100 50.0610050.1510050.2310052.27100 49.36 100 47.7310047.76 p corner cropping 95.01%100 50.44 100 49.5610052.7110051.8510053.59100 50.45 100 52.01 100 50.31 ottom corner cropping 95.01%100 47.85 100 49.9810051.6410050.3610052.52100 43.56 100 53.1910052.24 Centre cropping 93.56% 100 53.55 100 50.2510050.3910050.8510049.86100 51.19 100 54.0510049.12 100 52.80 100 52.0110051.2610051.3610050.71100 48.57 100 52.16 10048.58 Irregular cropping 95.04% 100 51.89 100 52.5410054.5510049.9510051.45100 51.26 100 53.15 10051.36 Irregular cropping 95.50% 100 55.39 100 54.6010056.2510050.2610055.32100 51.35 100 51.14 10052.25 Irregular cropping 95.53% 100 50.85 100 50.7610052.3510051.2510048.07100 49.68 100 51.65 10054.33 Irregular cropping 96.17% 100 52.92 100 56.3510054.3510055.3510054.17100 48.69 100 47.65 10047.07 Irregular cropping 96.56% 100 51.31 100 52.1610053.6310052.8610050.95100 50.25 100 51.23 10048.25 Copyright © 2012 SciRes. JIS
M. TONG ET AL. 147 Figure 8. Relation curve of BCRs with the cropping attack intensity in the proposed scheme. y and Decomposing Figu he convergence curves of decomposi termarking scheme robust to strong 4.4. Computational Efficienc Errors Experiments of NMFSCPBM Methods re 9 shows t tion error with the number of iterations of NMFSCPBM, NMF and NMFSC for different data sets. The sparseness constraint of NMFSC and NMFSCPBM is 0.6 respec tively and the decomposition dimension is r = 4 respec tively. Due to the length limitation of an article, Figure 9 only shows the fore 1000 iterative results of the “foot ball” test video. It can be seen that, 1) the convergence error of this paper is 0.468, 19.379 for the NMFSC and 1.809 for the NMF; 2) the convergence error comes up to the minimum after 77 iterations for NMFSCPBM, 913 for NMFSC, and 410 for NMF. Therefore, the decom posing error of this paper is the lowest in the similar methods, and the convergence rate is also obviously bet ter than that of the similar methods. Other experimental data of the test videos give the same conclusion. 5. Conclusion A novel video wa cropping is proposed in this paper. It is characterized as follows. 1) The improved NMFSCPBM method is pro posed, which can extract the video motion features accu rately, filter out the static background interference com pletely, and is simple and effective. Solve the problems of the similar methods that cannot describe the data suf ficiently under higher sparseness constraints. Meanwhile, reduce the decomposition error and speed up conver gence rate. 2) Based on the robustness of basis matrix for shearing attacks, this framework innovatively embeds the encrypted watermark into the big coefficients of the basis matrix that the host video is decomposed into by NMFSCPBM. To achieve the greatest strength of the (77 ,0.468) 77 (410 ,1.089) 410 (913 ,19.379) NMFSCPBM NMF NMFSC 913 Error Iterations 000 Iterations Error Error Iterations Iterations Error Figure 9. Decomposing errors and computational efficien cies of NMFSCPBM and other similar methods. ents extra Moment Invariants for Image Watermarking Robust to Geometric Distortions,” IEEE Transacng, Vol. 20, No. 8, 2010, pp. 2189 watermark embedding with no visual perception, this scheme adaptively adjusts the watermark embedding strength by the video motion feature coeffici cted by NMFSCPBM method, improving the robustness further. On watermark detection, as long as the residual video contains the numbers of least remaining subblocks, the complete basis matrix can be completely recovered through decomposition of the nonnegative matrix of the least remaining subblocks in residual videos by NM FSCPBM, and then the complete watermark can be ex tracted. The experimental results show that the perform ance of resisting strong cropping attacks of this scheme is improved greatly compared to existing methods, and that the scheme has good transparency, bit rate constancy and realtime property. It is a blind watermark scheme. How to extract and recover the complete watermark from the incomplete subblocks of the residual video will be as the further research content for authors. REFERENCES [1] H. Zhang, et al., “Affine Legendre tions on Image Processi 2199. doi:10.1109/TIP.2011.2118216 ol. [2] C. V. Serdean, M. A. Ambroze, M. Tomlinso and J. G. Wade, “DWTBased HighCapacity Blind Video Water marking, Invariant to Geometrical Attacks,” IEEE Pro ceedings of the Vision, Image and Signal Processing, V 150, No. 1, 2003, pp. 5158. doi:10.1049/ipvis:20030 159 [3] L. E. Coria, M. R. Pickering, P. Nasiopoulos and R. K. Ward, “A Video Watermarking Scheme Based on the DualTree Complex Wavelet tions on Information Forensic Transform,” IEEE Transac s and Security, Vol. 3, No. 3, 2008, pp. 466474. doi:10.1109/TIFS.2008.927421 [4] Y. L. Wang and A. Pearmain, “Blind MPEG2 Video Copyright © 2012 SciRes. JIS
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