A Robust Feature-Based Digital Image Watermarking Scheme

Transcription

1 Chpter 6 A Robust Feture-Bsed Digitl Imge Wtermrking Scheme 6.1 Introduction Attcks hve been developed to destroy wtermrks. These ttcks on wtermrks cn roughly be clssified s geometric distortions nd noise-like signl processing. Geometric distortions re difficult to tckle. They cn induce synchroniztion errors between the extrcted wtermrk nd the originl wtermrk during the detection process, even though the wtermrk still exists in the wtermrked imge. Nowdys, severl pproches tht counterttck geometric distortions hve been developed. These schemes cn be roughly divided into invrint trnsform domin bsed, moment-bsed nd feture extrction bsed lgorithms. Wtermrk embedded in invrint-trnsform domins generlly mintin synchroniztion under rottion, scling nd trnsltion. Exmples of these trnsforms re given in subsection The wtermrk detection process is similr to the pttern recognition process in computer vision, but the originl imges my not be vilble to the wtermrk detector. Moments of objects hve been widely used in pttern recognition. The discussion of moment-bsed wtermrking techniques is found in subsection On the other hnd, the extrcted feture of imge content cn be used s reference points for both wtermrk embedding nd detection s 87

2 illustrted in subsection In this chpter, we develop robust wtermrking scheme. This scheme combines the dvntges of feture extrction nd imge normliztion to resist imge geometric distortion nd to reduce wtermrk synchroniztion problem t the sme time. Section 6. describes the feture extrction method used in the proposed scheme. In Section 6.3, the imge normliztion process developed for pttern recognition is briefly reviewed. Section 6.4 contins the description of our wtermrk embedding procedure. Section 6.5 covers the detils of the wtermrk detection procedure. Simultion results in Section 6.6 will show the performnce of our scheme. Finlly, Section 6.7 concludes this presenttion. 6. Feture Extrction To detect wtermrks without ccess to the originl imges, we look for reference points tht re perceptully significnt nd cn thus resist vrious types of common signl processing, such s JPEG compression nd geometric distortions. These reference points cn lso ct s mrks for (loction) synchroniztion between wtermrk embedding nd detection. In this pper, we will use the term feture points to denote these reference points. In our scheme, we dopt feture extrction method clled Mexicn Ht wvelet scle interction. This method ws originlly used in [6][66][84]. It determines the feture points by identifying the intensity chnges in n imge. Since significnt intensity chnges (edges) my occur t different scled versions of the sme imge, Mrr nd Hildreth suggested tht different opertors should be used t different scles for optimlly detecting significnt intensity chnges. The Mexicn Ht wvelet (Mrr wvelet) [33][34] is rottion invrint wvelet. It hs circulrly symmetric 88

3 frequency response. The computtionl cost is high becuse this wvelet is not seprble. In fct, it is the negtive Lplcin of Gussin function. The wvelet nlysis filter is loclized t different frequencies nd sptil scles (resolutions). The Mexicn-Ht mother wvelet t loction x r is defined by (6.1): r r r x / Ψ ( x) = ( x ) e, (6.1) r. The two-dimensionl Fourier trnsform of ( ) where 1/ x = ( x + y ) ψˆ x r is given by r r r k / ψˆ ( k ) = k e, (6.) where k v represents the -D sptil-frequency. The feture extrction method proposed in [6][66] uses the following quntities: r r r P ( x) M ( x) M ( x), ij = γ (6.3) i i i r M ( x) = ( Ψ( x)) A, i j r (6.4) r where (x) represents the response of the Mexicn Ht wvelet opertor t sptil M i loction x r of scle i, γ is scling prmeter, (x) P ij r is the scle interction between two different scles i nd j, A is the input imge, nd denotes the convolution opertion. Our scheme is designed for both color nd gry-level imges. For color imges, the Y component is extrcted for wtermrk embedding. The Mexicn Ht wvelet filtering is implemented in the frequency domin using the FFT. An input imge is first zero-pdded to in size. We void selecting feture points locted ner borders of n imge. Hence, prohibited zone long the imge border is predefined. Thus, border effects re negligible in extrcting the feture points. Exmples of filtered imges t two different scles re shown in Figs. 6.1() nd 6.1(b). The difference of these two filtered imges is the Mexicn Ht scle 89

4 interction imge (with γ =1), shown in Fig. 6.1(c). The two scles we choose re suggested by [6][66]; tht is, i = nd j =4. Feture points re defined s locl mxim inside disks in the scle interction imge. The disk rdius is chosen to be 45, which is determined experimentlly. Feture points locted in regions of smll vrince re discrded for reducing wtermrk visibility. A flowchrt of the feture extrction method is given in Fig. 6.. Among the mny feture extrction lgorithms proposed in the literture, we hve dopted the scheme proposed in [6][66] for severl resons. First, since the Mexicn Ht wvelet scle interction is formed by two scles, it llows different degrees of robustness (ginst distortion) by choosing proper scle prmeters. Second, since locl vritions such s cropping or wrping generlly ffect only few feture points in n imge, the unffected feture points cn still be used s references during the detection process. Third, this wvelet function is rottionlly-invrint. It mens tht most feture points my not chnge fter imge rottion. Fourth, since the Mexicn Ht wvelet is essentilly bnd-limited, the noise sensitivity problem in feture extrction cn be reduced. Finlly, the extrcted feture points do not shift their loctions much under high-qulity JPEG compression s discussed in [66]. These feture points re the centers of the disks tht re to be used for wtermrk embedding (s described in the next section). Exmples of disks re shown in Fig. 6.1(d). Since these disks should not interfere with ech other, we only select the feture points tht re wy from ech other to crete non-overlpped disk set. In our scheme, feture point hs higher priority for wtermrk embedding if it hs more neighboring feture points inside its disk. 90

5 () (b) (c) (d) Fig () Mexicn Ht wvelet filtered imge t scle i =. (b) Mexicn Ht wvelet filtered imge t scle i =4. (c) The difference imge between () nd (b). (d) The center of ech disk is feture point. 91

6 Originl Imge Zero Pdding -D FFT Extrcted Feture Points Mexicn Ht Wvelet Filtering t Scle i Mexicn Ht Wvelet Filtering t Scle j Identify Nonoverlpped Points -D IFFT -D IFFT Serch for Locl Mximum Feture Points Recover the Originl Imge Size Recover the Originl Imge Size Mexicn Ht Wvelet Scle Interction Fig. 6.. Feture extrction by Mexicn Ht wvelet scle interction. 6.3 Imge Normliztion The imge normliztion technique developed for pttern recognition cn be used for digitl wtermrking s suggested in [58]. Severl geometric centrl moments re computed to trnsform the input imge to its normlized form. The normlized imge (object) of rotted imge (object) is the sme s the normlized imge of the originl imge (if no pdding or cropping occurs). Since objects re rottionlly invrint in the normlized imge, the wtermrk detection process cn be much simplified when it is pplied to the normlized imge. On the other hnd, becuse imge normliztion is sensitive to locl imge vritions, detection is more ccurte when pplied to individul objects rther thn the entire imge. In our scheme, we pply the imge 9

7 normliztion process to ech non-overlpped locl disk seprtely. The centers of these disks re the extrcted feture points described in Section II. Imge normliztion technique is used for selecting the loction of the wtermrks. However, wtermrks re not embedded in the normlized imges. This is becuse sptil interpoltion is necessry for mpping the originl imge pixels to the normlized imge pixels, nd vice-vers. This interpoltion process induces significnt mount of distortions nd thus reduces wtermrk detectbility. The detils of the imge normliztion process cn be found in [85]. Here, we only briefly describe its computtionl steps. The prmeters below re computed once for ech imge disk. 1) Men vector [ C xc ] T y, where C x = Ω p( x, y) xf ( x, y) dxdy, C y = Ω yf ( x, y) dxdy, f ( x, y) =, p( x, y) dxdy Ω where p( x, y) denotes the gry-level vlue t loction ( x, y), ndω is the region of interest. u u 0 11 k r ) Covrince mtrix M =, where u = Ω ( x C ) ( y C ) f ( x, y dxdy. 11 3) Centrl moments u 30, u1, u1, u03 of the originl disk. u u 0 kr x y ) T 4) Eigenvlues λ1, λ nd their ssocited eigenvectors [ e 1x e 1y ] of M. 5) Two ffine trnsformtion coefficient mtrices 93

8 c λ e x e 1 1 1y = c 1 e y e 0 1 1x λ c c e1 x e1 y = λ1 λ1 c c e1 y e1 x λ λ c 0 b1 = λ e x e y C x b c e1 y e1 x C y 0 λ 11 1 Cx = 1 C y where 1/ 4 c = ( λ1 λ ). 6) Centrl moments for clculting rottionl invrint trnsformtion: u' u' u' u' = = = = u u u u ( + ( 1 111u u u 03 1 u ) u 1 ) u ( + ( 3 u ) u ) u u u ) Tensors: t u' 1 + u' 30, t = u' 03 + u' 1 1 t Angle: α = tn ( ) t =. 1 8) Tensor t = t sin α + t cosα 9) If < 0 then α = α + π t. 1 Finlly, the normlized imge is computed from the originl imge bsed on the following coordinte trnsformtion: x cosα = y sinα sinα cosα c λ e 1 c e λ x 1y e 1y e 1x x C y C x y, where ( x, y) is the originl disk coordintes, nd ( x, y) is the normlized disk 94

9 coordintes. The normlized imge object is insensitive to trnsltion, scling nd rottion of the originl imge object [85]. After coordinte trnsformtion, ech disk becomes disk. Rectngulr windows used to hold wtermrks in the originl imge disks re constructed s follows. Two 3 3 blocks in ech (originl) imge disk re chosen for wtermrk embedding. The loctions of these 3 3 blocks re determined through the use of the normlized imge disk. Two ordered points A nd B re chosen t integer coordintes inside the normlized imge (disk) s shown in Fig. 6.3(). The loctions of these two points re chosen secretly but re known to the wtermrk detector. The loctions of A nd B re chosen close to the boundry of the normlized disk, nd the distnce between these two points is 3. Points nd b locted in the originl imge re the inverse mpping of A nd B (on the normlized imge) s shown in Fig. 6.3(b). Usully, points of the inverse mpping of A nd B do not hve integer coordintes, nd thus, points nd b re quntized to integers. They re connected to form line segment b. Although the distnce between points A nd B is 3, the distnce between nd b is generlly different due to the normliztion process. Therefore, b is shortened or extended to the line segment b ', which hs length 3. Usully, point b ' is not the sme s point b, but these two points re close. Then, 31 line segments prllel to b ' re creted running towrds the center of the disk. Finlly, b ' nd its 31 prllel line segments of length 3 form 3 3 block in the originl imge s shown in Fig. 6.3(c). Since the 3 points tht line segment psses through do not lwys hve integer coordintes, we choose 3 integer-coordinte pels nerest to the line segment to form the discrete-grid line segment s shown in Figs. 6.4() nd 6.4(b). The crossing points of grid represent integer-coordinte pels in the originl imge (disk). If the bsolute vlue of the slope of line segment is less thn 1, its discrete-grid pproximtion is 95

10 constructed long the horizontl direction s shown in Fig. 6.4(). Otherwise, the verticl direction is used s shown in Fig. 6.4(b). Two 3 3 blocks re selected for ech disk s shown in Fig. 6.3(d). To reduce the impct of feture point shift due to wtermrk embedding, these blocks should not contin the disk center (feture point). All the loction informtion of these two blocks is determined on the normlized imge (disk). After the coordintes of A nd B re determined s described bove, the coordintes of C nd D will be the symmetric pels with respect to the symmetric center C e (Fig. 6.3()). C e is not necessry the center of the disk. Point E is the middle point of A nd B. AB is perpendiculr to EC e. The distnce between points A nd C e is less thn 45 but greter thn 3. The distnce between E nd C e hs to be greter thn 3. Next, the corresponding pels c nd d in the originl imge disk re computed by the inverse normliztion trnsformtion. A shortened or extended line segment of cd is c' d, which contins 3 pels. The blocks selected for the imge Len re shown in Fig Occsionlly, tiny corner (very few pels) of 3 3 block my be outside the originl imge disk. If this hppens, these pels re not wtermrked. Another potentil problem is tht lthough the extrcted feture points (center of the disk) re locted in high-contrst regions, the two 3 3 selected blocks my be prtly locted in smooth regions. Therefore, to keep wtermrk imperceptibility, such disk is not wtermrked if the vrince of one 3 3 block in n originl imge disk is smll. In our experiment, there re only 8 qulified disks (Fig. 6.5) for wtermrk embedding lthough there re 11 feture points (disk centers) re extrcted on the Len imge (Fig. 6.1(d)). 96

11 C A D C e E B c b d () (b) c' d b' b' (c) (d) Fig () Two ordered points A nd B in the normlized imge (disk). (b) Two corresponding points nd b in the originl imge (disk). (c) A 3 3 block is constructed in the originl imge disk. (d) Two symmetric 3 3 blocks in the originl imge disk re formed. () (b) Fig The crossing points of the grid represent the integer pel loctions on the originl disk. () If the slope (bsolute vlue) of line segment is less thn or equl to 1, the integer pels closest to the line segment horizontlly re chosen to form the dt line segment. (b) If the slope (bsolute vlue) of line segment is greter thn 1, the integer pels closest to the line segment verticlly re chosen to form the dt line segment. 97

12 Fig Ech disk contins two 3 3 blocks for wtermrk embedding (Len). 6.4 DFT Domin Wtermrk Embedding Our wtermrk is designed for copyright protection. We view ll blocks s independent communiction chnnels. To improve the robustness of trnsmitted informtion (wtermrk bits), ll chnnels crry the sme copy of the chosen wtermrk. The trnsmitted informtion pssing through ech chnnel my be disturbed by different types of trnsmission noise due to intentionl nd unintentionl ttcks. During the detection process, we clim the existence of wtermrk if t lest two copies of the embedded wtermrk re correctly detected. Originl Imge Extrct Feture Points Compute Imge Normliztion Prmeters on Disks in the Originl Imge Trnsform Coordintes of Selected Points from Normlized Imge bck to the Originl Imge Construct Two 3x3 Blocks in Ech Qulified Disk in the Originl Imge Wtermrked Imge Replce the Disks in Originl Imge by the Wtermrked Ones -D IFFT Wtermrk Embedding -D FFT on 3x3 Blocks Wtermrk nd Secret Key K Fig Wtermrk embedding scheme. 98

13 The wtermrk embedding process is outlined in Fig First, the feture extrction method genertes reference centers of disks for wtermrk embedding nd detection. We then perform the imge normliztion technique on disks in the originl imge. The coordinte trnsformtion coefficients between the originl imge disks nd the normlized disk imges re generted. The loction of blocks in the originl imge for wtermrk embedding is determined from the normlized imge. Then, coordintes of selected points re trnsformed from normlized imge bck to the originl imge. As result, the wtermrk synchroniztion problem during the detection process is reduced. Next, -D FFT is pplied to these 3 3 blocks on ech qulified disk in n originl imge. The wtermrk is embedded in the trnsform domin. Lst, the wtermrked blocks re -D IFFT converted bck to the sptil domin to replce the originl imge blocks. The procedure of selecting nd modifying the mgnitude of DFT coefficients for wtermrk embedding is illustrted below. First, the FFT is pplied to ech 3 3 selected block. Then, severl middle DFT coefficients re selected ccording to the secret key K. Middle frequency components re generlly more robust in resisting compression ttcks. A modified version of [6] is used to embed wtermrk bits into DFT coefficients. Selected pirs, x, y ) nd y i, x ) ( i i ( i upper hlf DFT plne (Fig. 6.7) re modified to stisfy, o F '( xi, yi ) F '( yi, xi ) α if wmi F '( x, y ) F '( y, x ) α if wm i i i i i 90 prt, locted on the = 1 = 0, where F '( x i, y ) nd F' ( y i, x ) re the mgnitudes of the ltered coefficients t i i loctions x, y ) nd y i, x ) in the DFT trnsform domin, α is the wtermrk ( i i ( i strength, nd wm i is the binry wtermrk bit, which is either 0 or 1. The phse of the selected DFT coefficients is not modified. If the wtermrk bit is 1 nd the originl mplitude difference between points x, y ) nd y i, x ) is greter thn α, 99 ( i i ( i

14 no chnge is needed. Also, to produce rel-vlued imge fter DFT spectrum modifiction, the symmetric points on the lower hlf DFT plne hve to be ltered to the exct sme vlues, too. A lrger vlue of α nd longer wtermrk sequence length would increse the robustness of the wtermrking scheme. Becuse the 3 3 blocks re selected in the high vrince imge regions, typiclly the embedded wtermrk is less visible for smller α. Hence, there is trdeoff between robustness nd trnsprency. In our cse, we embed 16 bits in ech 3 3 block. ( i y i, x ) 0 y ( x i, yi ) x Fig Two points x, y ) nd y i, x ) ( i i ( i used for embedding one wtermrk bit., o 90 prt, on the upper hlf DFT plne re The secret key K shown in Fig. 6.6 is lso known to the wtermrk detector. This secret key is used s the seed for generting rndom numbers to specify the frequencies of the DFT coefficients used to hide wtermrk bits. 6.5 Wtermrk Detection The block digrm of our wtermrk detection scheme is shown in Fig The wtermrk detector does not need the originl imge. The feture (reference) points re first extrcted. The feture extrction process is similr to tht used in the wtermrk embedding process. All the extrcted feture points re cndidte loctions of embedded bits. Since imge contents re ltered slightly by the embedded mrks 100

15 nd perhps by ttcks too, the loctions of extrcted feture points my be shifted. In ddition, some of the originl feture points my fil to show up during the detection process. If the feture point shift is smll, the embedded wtermrk blocks cn still be extrcted correctly. Received Imge Feture Extrction Compute Imge Normliztion Prmeters on Ech Disk in the Received Imge Trnsform Coordintes of Selected Points from the Normlized Imge bck to the Received Imge Construct Two 3x3 Blocks in Ech Disk of the Received Imge Wtermrk nd Secret KeyK -D FFT Wtermrk Detection Wtermrk Detection Decision Fig Wtermrk detection scheme. Imge normliztion is pplied to ll the disks centered t the extrcted cndidte reference points. Two 3 3 blocks re extrcted in ech disk. The loctions of these 3 3 blocks re the sme s those specified t wtermrk embedding. The coordinte trnsformtion coefficients between the originl imge disk nd the normlized disk imge re generted. Thus, the loction of blocks in the received imge is determined from the normlized imge, nd the coordintes of the selected points re trnsformed from normlized imge bck to the received imge. In ech 3 3 DFT block, 16 wtermrk bits re extrcted from the DFT components specified by the secret key. For n extrcted pir of DFT coefficients, ( i i x, y ) nd y i, x ) formul, ( i, the embedded wtermrk bit is determined by the following 101

16 1 if F"( xi, yi ) F"( yi, xi ) 0 wm =, i 0 if F"( xi, yi ) F"( yi, xi ) < 0 where F ( x i, y ) nd F ( y i, x ) re the mgnitudes of the selected coefficients t " i " i loctions x, y ) nd y i, x ). The extrcted 16-bit wtermrk sequence is then ( i i ( i compred to the originl embedded wtermrk for deciding success detect. Two kinds of errors re possible in the detector: the flse-lrm probbility (no wtermrk embedded but detected hving one) nd the miss probbility (wtermrk embedded but detected hving none). There is trde-off between these two error probbilities in selecting detector prmeters. Typiclly, reducing one will increse the other. It is rther difficult to hve exct probbilistic models of these two kinds of errors. Simplified models re thus ssumed in choosing the detector prmeters s shown below. We first exmine the flse-lrm probbility. For n unwtermrked imge, the extrcted bits re ssumed to be independent rndom vribles (Bernoulli trils) with the sme success probbility, P success. It is clled success or mtch if the extrcted bit mtches the embedded wtermrk bit. We further ssume tht the success probbility, P success, is ½. Let r 1 nd r be the numbers of mtching bits in the two blocks on the sme disk, nd n the length of the wtermrk sequence. Then, bsed on the Bernoulli trils ssumption, r 1 nd r re independent rndom vribles with binomil distribution, nd P 1 = n n! r1!( n r 1 r 1 )! 1 = The men vlues of r 1 nd r re both n/. P n n! r!( n 10 )!. r r A block is climed wtermrked if the number of its mtching bits is greter thn

17 threshold. The thresholds for the two blocks on the sme disk re denoted by T 1 nd T. Clerly, T 1 nd T should be greter thn n/, the men vlues of r 1 nd r. The flse-lrm error probbility of disk is, therefore, the cumultive probbility of the cses tht r1 T1 nd r T. In order to control the level of flse-lrm probbility by one djustble prmeter, third threshold T is introduced. More precisely, the vrible pirs, r 1 nd r, shll stisfy the following two criteri simultneously: (1) r1 T1, r T nd () r 1 + r T. Tht is, P Flse lrm on one disk = r1 = n, r = n 1 n n! 1 n!. (6.5) r1!( n r )! r!( n r )! r1 = T1, r = T 1 r1 + r T n Furthermore, n imge is climed wtermrked if t lest m disks re detected s success. Under this criterion, the flse-lrm probbility of one imge is P Flse lrm on one im ge = N i N i N ( PFlse lrm on one dis k ) (1 PFlse lrm on one dis k ), (6.6) i= m i where N is the totl number of disks in n imge. We cn plot P ginst vrious T vlues s shown in Fig. 6.9 Flse lrm on one mge using (6.6). The other prmeters re chosen bsed on our experiences: n = 16, N = 10, m = 3, T 10 nd T 10. The curve in Fig. 6.9 drops shrply for T > 3. It is often 1 = = desirble to hve very smll P. However, the selection is ppliction Flse lrm on one mge dependent. We ssume tht 5 P should be less thn 10. In this cse, Flse lrm on one mge T should be greter thn or equl to 4 nd t T = 4, 6 P is Flse lrm on one mge We next exmine the miss probbility. In n ttcked wtermrked imge, we gin ssume tht the mtching bits re independent Bernoulli rndom vribles with equl success probbility, P success. This my not be very ccurte model but it seems to be sufficient for the purpose of selecting the detector prmeters. The 103

18 success detection probbility of r 1 bits in block of n wtermrked bits is Similrly, for the second block r! 1 n r n 1 P = ( P ) (1 P ) 1 r1!( n r. r success success 1)! r! n r n P = ( P ) (1 P ) r!( n r. r success success )! The success detection probbility of disk is the cumultive probbility of ll the cses tht r1 T1, r T nd r 1 + r T. Tht is, P Success on one dis k = r = n, r = n 1 r1 r1 = T1, r = T r + r T 1 P P r. (6.7) Recll tht n imge is climed wtermrked if t lest m disks wtermrk detected. Under this criterion, the miss probbility of n imge is P Miss on on e imge = N i N i N 1 ( PSucesss on one disk ) (1 PSucesss on one disk ). (6.8) i= m i It is difficult to evlute the success detection probbility of wtermrked bit, P success. It depends on the ttcks. For exmple, the distortion induced by JPEG compression cnnot be modeled by simple dditive white Gussin source. However, typicl success detection probbility my be estimted from the experiments on rel imges with ttcks. Becuse we like to see the detector performnce under geometric distortion, modertely difficult cse is chosen from Tble imge Len under combined distortions of 1 degree rottion, cropping nd JPEG compression t qulity fctor of 70. The simultion is done using 10 wtermrked imges Len imposed with (rndomly generted) different wtermrks. The selected vlue of P success is the totl number of mtching bits divided by the totl number of embedded bits. In this experiment, we obtin P success = Bsed on 104

19 this P success vlue, we plot the miss probbility of n imge for vrious T s shown in Fig In this experiment, we set gin n = 16, N = 10, m = 3, T 10 1 = nd T = 10. The curve goes up shrply for T > 3. For T = 4, P Miss on one imge is less thn 0.4. Clerly, from Figs. 6.9 nd 6.10 we cn see the trde-off in selecting T. Suppose tht lower flse-lrm probbility is our higher priority in the simultions in Section VI, T is therefore chosen to be 4 so tht P is less thn Flse lrm on o ne mge Fig The flse-lrm probbility of n unwtermrked imge. The probbility is generted for r 1 nd r stisfying the following two conditions: (1) r 1 10, r 10, nd () r 1 + r T. (n =16, m=3, nd N=10.) 105

20 Fig The miss probbility on imge Len. The plot is generted for r 1 nd r stisfying the following two conditions: (1) r 1 10, r 10, nd () r 1 + r T. (n = 16, m=3, nd N=10.) 6.6 Simultion Results We test the proposed wtermrking scheme on the populr test imges Len, Bboon nd Peppers. We use StirMrk 3.1[78] to test the robustness of our scheme. The StirMrk 3.1 ttcks cn roughly be clssified into two ctegories: common signl processing nd geometric distortions. The difference imges between the originl imges nd the wtermrked imges in the sptil domin re mgnified by fctor of 30 nd shown in Figs (), (b), nd (d). The PSNR vlues between the originl nd the wtermrked imges re 49.4 db, db, nd db for Len, Bboon nd Peppers, respectively. Becuse of their smll mplitudes, the embedded wtermrks re invisible by subjective inspection. Recll tht the rdius of ech disk in the normlized imges is 45, nd tht two 3 3 blocks re chosen in ech disk for wtermrk embedding. In ech 3 3 squre, the embedded 16 frequencies (of the DFT coefficients) re locted within the shded re of Fig

21 All blocks re embedded with the sme 16 bits wtermrk. The wtermrk strength α is set to 0, 15 nd 10 in Bboon, Len nd Peppers, respectively, for compromise between robustness nd invisibility. Since Bboon imge hs more texture, strong wtermrk is less visible thn in Len nd Peppers. The number of wtermrked imge disks is 11, 8 nd 4 in Bboon, Len nd Peppers, respectively. The more textured the imge is, the more extrcted feture points the imge hs. Simultion results for geometric distortions nd common signl processing ttcks re shown in Tbles 6.1 nd 6., respectively. The tbles show the number of correctly detected wtermrked disks nd the number of originl embedded wtermrked disks. As shown in Tble 6.1, our scheme cn resist JPEG compression up to qulity fctor of 30. The JPEG compression quntiztion step size used in StirMrk is defined by Scle = 5000 / qulity 00 qulity, if qulity <, otherwise. 50 QunStepSize[ i] = ( BsicQunMtrix[ i] Scle + 50) /100. Our scheme performs well under other common signl processing ttcks such s medin filtering, color quntiztion, 3 3 shrpening, nd Gussin filtering. It cn lso resist combined signl processing nd JPEG compression ttcks t qulity fctor of 90. Some of the signl processing opertions used in StirMrk 3.1 re detiled below. Color quntiztion is similr to tht in GIF compression. The 3 3 Gussin filter mtrix is The 3 3 sptil shrpening filter mtrix is The wtermrk robustness ginst common signl processing is much improved with stronger wtermrk strength, but there is the trdeoff between wtermrk robustness nd invisibility. An dditive noise ttck ws lso pplied to the wtermrked imge. The ttcked 107

22 imge is: L' ( x, y) = L( x, y) (1 + β n( x, y)), where L ( x, y) is the luminnce pixel vlue of n input imge t ( x, y), β is prmeter tht controls the strength of the dditive noise, n ( x, y) is noise with uniform distribution, zero men, nd unit vrince, nd L '( x, y) is the luminnce pixel vlue of the ttcked imge t ( x, y). In our experiment, the dditive noise is visible especilly in the imges Len nd Peppers, when β is greter thn 0.1. The wtermrk cn be detected when β is less thn 0.. As stted in Section 6., the noise sensitivity problem in feture extrction is reduced due to the essentilly bnd-limited property of Mexicn Ht scle interction scheme with proper prmeter settings. The PSNR vlue (comprison between the wtermrked imge nd the ttcked imges) in Tble 6.3 is computed by N mxi X i PSNR = 10log10, N ( X i X ' i ) i= 1 where N is the imge size, i is the index of ech pixel, nd levels of the originl nd the processed pixels. 108 X i nd X ' i re the gry The performnce of the proposed scheme under geometric distortions is shown in Tble 6.. Our scheme survives row nd column removl, 10% centered cropping, nd up to 5% shering in x or y direction. Combintion of smll rottions with cropping does not cuse our scheme to fil. But, it is still sensitive to globl imge spect rtio chnges due to the feture loction shifts. It cn lso survive combined geometric nd high qulity JPEG compression ttcks, s shown in Tble 6.. In fct, the correctness of wtermrk detection under geometric distortions strongly depends on the disk loctions. For exmple, if the reference point of n imge disk is locted t the border of n imge, this point might be removed due to cropping ttcks. As result, this

23 disk loction cnnot be correctly identified. Rottion with cropping cn hve to similr effect. The Bboon imge hs deeper nd lrger textured res thn Len nd Peppers. In the cse of Bboon, mny fke reference points (feture points) my show up, nd the true reference points my shift quite significntly fter ttcks. On the other hnd, Peppers hs less texture. Its true feture points my dispper following ttcks. In ddition to the geometric distortions in StirMrk 3.1, we hve pplied locl wrping on the eyes nd mouth of Len, s shown in Fig. 6.13(). The extrcted disks t detector re shown in Fig. 6.13(b). Since locl vritions generlly ffect only few feture points extrcted by the Mexicn Ht wvelet scle interction scheme, the feture points cn still be correctly extrcted for wtermrk detection. The wtermrk cn still be detected quite relibly. 109

24 () (b) (c) () (b) (c) Fig The difference imge between the originl imge nd the wtermrked imge. The mgnitudes in disply re mplified by fctor of 30. () Len, (b) Bboon, nd (c) Peppers. f y f x Fig The wtermrked coefficients re chosen from the shded re. 110

25 () (b) Fig () Locl wrping is pplied to wtermrked imge Len, in the eyes nd mouth re (b) Wtermrk detection result for (). Seven wtermrked disks re correctly detected mong the originl eight. Tble 6.1. Frction of correctly detected wtermrk disks under common signl processing ttcks. Attcks Len Bboon Pepper Wtermrked imge 7/8 10/11 4/4 Medin filter 1/8 6/11 1/4 Medin filter 3 3 1/8 /11 1/4 Shrpening 3 3 4/8 4/11 4/4 Color quntiztion 7/8 4/11 1/4 Gussin filtering 3 3 5/8 8/11 1/4 Additive uniform noise (scle=0.1) 5/8 6/11 4/4 Additive uniform noise (scle=0.15) 4/8 4/11 /4 Additive uniform noise (scle=0.) 1/8 5/11 1/4 JPEG 80 6/8 9/11 3/4 JPEG 70 7/8 11/11 3/4 JPEG 60 6/8 7/11 1/4 JPEG 50 5/8 7/11 3/4 JPEG 40 3/8 5/11 1/4 JPEG 30 /8 4/11 0/4 Medin filter + JPEG90 /8 6/11 0/4 Medin filter JPEG90 1/8 1/11 1/4 Shrpening JPEG90 4/8 /11 4/4 Gussin filtering JPEG90 5/8 8/11 /4 111

26 Tble 6.. Frction of correctly detected wtermrk disks under geometric distortion ttcks. Attcks Len Bboon Pepper Removed 1 row nd 5 columns 3/8 6/11 3/4 Removed 5 rows nd 17 columns 0/8 3/11 1/4 Centered cropping 5% off /8 /11 /4 Centered cropping 10% off /8 /11 /4 Shering-x-1%-y-1% 4/8 5/11 1/4 Shering-x-0%-y-5% /8 3/11 1/4 Shering-x-5%-y-5% 1/8 /11 0/4 Rottion 1+Cropping+Scle 0/8 4/11 /4 Rottion 1+Cropping 3/8 3/11 /4 Rottion +Cropping 0/8 1/11 1/4 Rottion 5+Cropping 0/8 0/11 0/4 Liner geometric trnsform 5/8 4/11 1/4 (1.007,0.01,0.01,1.01) Liner geometric trnsform 4/8 4/11 1/4 (1.010,0.013,0.009,1.011) Liner geometric trnsform 4/8 5/11 0/4 (1.013,0.008,0.011,1.008) Removed 1 rows 5 columns + JPEG70 4/8 6/11 3/4 Removed 5 rows 17 columns + JPEG70 1/8 3/11 1/4 Centered cropping 5% + JPEG70 /8 /11 /4 Centered cropping 10% + JPEG70 3/8 /11 /4 Shering-x-1%-y-1%+JPEG70 /8 4/11 1/4 Shering-x-0%-y-5%+JPEG70 /8 3/11 0/4 Shering-x-5%-y-5%+JPEG70 1/8 0/11 0/4 Rottion 1+Cropping+Scle+JPEG70 0/8 4/11 0/4 Rottion 1+Cropping+JPEG70 4/8 3/11 1/4 Rottion +Cropping+JPEG70 1/8 1/11 1/4 Rottion 5+Cropping+JPEG70 1/8 0/11 0/4 Liner geometric trnsform 4/8 3/11 1/4 (1.007,0.01,0.01,1.01) +JPEG70 Liner geometric trnsform 4/8 5/11 3/4 (1.010,0.013,0.009,1.011) +JPEG70 Liner geometric trnsform (1.013,0.008,0.011,1.008) +JPEG70 3/8 5/11 0/4 11

27 Tble 6.3. PSNR vlues. Attcks Len Bboon Pepper Medin filter Medin filter Shrpening Color quntiztion Gussin filtering Additive uniform noise (scle=0.1) Additive uniform noise (scle=0.15) Additive uniform noise (scle=0.) JPEG JPEG JPEG JPEG JPEG JPEG (noise = difference between the wtermrked imge nd the ttcked imges) 6.7 Summry In this chpter, digitl imge wtermrking scheme ws designed to survive both geometric distortion nd signl processing ttcks. There re three key elements in our scheme: relible imge feture points, imge normliztion, nd DFT domin bits embedding. No reference imges re needed t the detector. Geometric synchroniztion problem between the wtermrk embedding nd detection is overcome by using visully significnt points s reference points. In ddition, the invrince properties of the imge normliztion technique cn gretly reduce the wtermrk serch spce. The simultion results show tht the proposed wtermrking scheme performs well under mild geometric distortion nd common signl processing ttcks. Furthermore, the embedded wtermrk cn resist composite ttcks of high qulity JPEG compression together with geometric distortions/signl processing. 113

28 The performnce of our scheme could be further improved if the feture points were even more robust. Thus, one direction of future reserch cn be the serch of more stble feture points nd/or more relible extrction lgorithms under severe geometric distortions. 114