Geometrically Invariant Watermarking Scheme Based on Local Feature Points

JOURNAL OF MULTIMEDIA, VOL. 7, NO. 3, JUNE 0 3 Geometrcally Invarant Watermarkng Scheme Based on Local Feature Ponts L Jng School of Computer and Informaton Engneerng, Henan Unversty of Economcs and Law, Zhengzhou, Chna Emal: jngl776@6.com Xaowen Zhang Department of Computer Scence, Unversty College Cork, College Road, Cork, Ireland Emal: skyof45 @yahoo.com.cn Abstract Based on local nvarant feature ponts and cross rato prncple, ths paper presents a feature-pont-based mage watermarkng scheme. It s robust to geometrc attacks and some sgnal processes. It extracts local nvarant feature ponts from the mage usng the mproved scale nvarant feature transform algorthm. Utlzng these ponts as vertexes t constructs some quadrlaterals to be as local feature regons. Watermark s nserted these local feature regons repeatedly. In order to get stable local regons t adjusts the number and dstrbuton of extracted feature ponts. In every chosen local feature regon t decdes locatons to embed watermark bts based on the cross rato of four collnear ponts, the cross rato s nvarant to projectve transformaton. Watermark bts are embedded by quantzaton modulaton, n whch the quantzaton step value s computed wth the gven PSNR. Expermental results show that the proposed can strongly fght more geometrcal attacks and the compound attacks of geometrcal ones. Index Terms dgtal watermark, nvarant feature ponts, the cross rato of four collnear ponts, geometrcal attacks, quantzaton modulaton I. INTRODUCTION Geometrc attacks means watermarked mage s transformed by some geometrcal dstortons, such as rotaton, scalng, translaton (RST), random bend attack (RBA), and shearng etc. Geometrc attacks nduce synchronzaton errors between the orgnal and the extracted watermark durng the detecton process, and the nserted watermark can not be detected correctly although t s stll present n watermarked mage. Up to now a few algorthms have presented the topc of how to acheve robustness aganst geometrc attacks, whch can be approxmately classfed nto the followng categores: watermarkng based on nvarant transform[,], watermarkng based on synchronzaton templates[3,4], watermarkng based on nvarant moments[5,6], and watermarkng based on feature ponts[7,8,9,0]. Compared wth other knds of algorthms, watermarkng based on feature ponts has better performance aganst geometrc attacks. It s not only robust to RST attack and local geometrc attacks (for example RBA and croppng), but also to combnaton of more geometrc attacks. For ths reason watermarkng based on feature ponts has been a researchng focus n recent years. Feature-pont-based watermarkng uses local nvarant feature ponts to decded local feature regons, watermark s nserted these local regons repeatedly. The watermark nserted postons combned wth these nvarant feature ponts, n ths way keepng watermarkng synchronzaton. The stablty of feature ponts to geometrc transform and sgnal processes decdes the robustness of watermarkng system. Bas et al. [7] used Harrs corner detectng to extract feature ponts from mage. Tang and Hang [8] extract feature ponts by Mexcan hat wavelet scale nteracton. Wang et al. [9] use Harrs-Laplace and Lee et al.[0] use Scale Invarant Feature Transform (SIFT). The stablty of extracted feature ponts by these s s very dfferent. Harrs corner ponts are robust to rotaton, but not to scalng and affne transform. Feature ponts extracted by Mexcan hat wavelet scale nteracton are robust to sgnal processes, but not to geometrc transform. Compared to these s, feature ponts from Harrs-Laplace and SIFT have better robustness []. Other mportant factors of Feature-pont-based watermarkng are the selecton of local feature regons and the watermark nsertng and extractng. Many algorthms [9, 0] choose crcle patches centerng local feature ponts to nsert watermark. They are robust to rotaton and scalng, but not to shearng of affne transform. When the watermarked mage s transformed by shearng, part of nserted watermark bts wll beyond the detected crcle patches and watermark can not be extracted correctly. Tang and Hang [8] used normalzed crcle patches to resst affne transform. However, the normalzaton s senstve to the mage contents used, so the robustness of these patches wll decrease when the mage s dstorted. Up to now these algorthms only do:0.4304/jmm.7.3.3-38

3 JOURNAL OF MULTIMEDIA, VOL. 7, NO. 3, JUNE 0 concern affne transform attack, dot not nvolved projectve transform yet. Ths paper utlzes mproved SIFT algorthm and nvarance of cross-rato n projectve transform, proposed a watermarkng scheme. scheme belongs to feature-pont-based watermarkng, s robust to geometrc attack. It extracts stable feature ponts usng the mproved SIFT algorthm, and optmzes the dstrbuton of feature ponts. Then choose qualfed quadrlateral regons to nsert watermark. Every regon s decded by four feature ponts. The watermark s nserted nto every regon repeatedly. The locaton to nsert watermark bt s based on nvarance of cross-rato, and usng quantzaton modulaton to nsert. Expermental results show the proposed scheme s not only robust to general sgnal processes, but also to many geometrcal dstortons, such as affne transform, projectve transform, croppng and ther combnaton. The rest of ths paper s organzed as follows. Secton descrbes the feature ponts extractng and adjustng used n the proposed scheme. Secton 3 revews cross-rato theory of four collnear ponts and gven two lemmas, whch s the theory bass of watermark nsert. In Secton 4, we present watermark nsertng process. Secton 5 covers the detals of the watermark detecton procedure. Smulaton results n Secton 6 wll show the performance of our scheme. Fnally, Secton 7 concludes ths presentaton. II. EXTRACTING FEATURE POINTS AND OPTIMIZING THEIR DISTRIBUTION Ths paper utlzes SIFT algorthm to extract feature ponts. SIFT feature s extracted by consderng local mage propertes and s nvarant to rotaton, scalng, translaton, and partal llumnaton changng. And also robust to a substantal range of affne dstorton, change n 3D vewpont, addton of nose[]. The basc dea of the SIFT s to extract features through a staged flterng that dentfes stable ponts n the scale space. It frst selects canddates for features by searchng for peaks n the scale space of the dfferenceof-gaussans (DoG) functon, then localzes each feature usng measures of ts stablty. The canddate locatons that have a low contrast or are poorly localzed along edges are removed by measurng the stablty of each feature usng a Hessan matrx H as follows: Tr( H ) ( r + ) stablty = < Det( H ) r Dxx Dxy Where H = () Dxy Dyy Here r s the rato of the largest to the smallest egenvalue and s used to control stablty. They use r=0. The quanttes Dx Dxy, and Dyy are the dervatves of the scale space mages. The next work s to assgn orentatons based on local mage gradent drectons, at last gve a descrptor for every SIFT feature pont. Our scheme only use SIFT ponts to decde quadrlateral regons when nsertng and detectng watermark. So we abnegate constructng feature vector process and save computng tme. SIFT algorthm generates large numbers of features ponts that densely cover the mage. A typcal mage of sze 500 500 pxels wll gve rse to about 000 stable features ponts, and these feature ponts densely coverng structure complex regons of mage. And the feature ponts used n watermark nsertng and extractng should be stable and be dstrbuted equally. So we mproved SIFT algorthm to get stable feature ponts wth optmzed dstrbuton, removng those feature ponts that are susceptble to watermark attacks. Combned our work, we change the procedure of SIFT algorthm, and the followng s our mprovng measures. Usng a Gaussan flter to blur the orgnal mage before feature ponts extracton. By ths preprocess, t can reduce the nterference of nose and ncrease the robustness of extracted feature ponts. In SIFT algorthm we leave out the step of representng feature descrptor that s 8 element feature vector for each feature. Only reman feature ponts detector, whch reduces largely calculatng tme wthout destroyng our scheme. In order to mprove the robustness of feature ponts, properly ncrease the samplng frequency and depth n scale drecton at scale space. Wth shorter samplng dstance and larger samplng depth, the extracted feature ponts are more robust to scale changng. Set a threshold Th, when searchng local extremum n 3 3 3 regon of scale space, DoG functon D(y,σ) should meet the followng formula: { D ( y, σ ) D( y, σ ) > Th} () In our experences we set Th=0.05 The mprovng mentoned above can strengthen the robustness of extracted feature ponts, but ther dstrbuton s stll not equal. The dstrbuton of local feature ponts s related to the performance of watermarkng systems. In other words, the dstance between adjacent feature ponts should be determned carefully. In order to ft our work, ther number and dstrbuton need to be adjusted. The followng s adjustng. Detect feature ponts wth the mproved SIFT algorthm frstly. In the local crcle regons centered detected feature ponts wth the radus R, f the DoG fuucton D(y,σ) value of crcle center s the local extremum of the crcle regon, we keep the feature ponts, otherwse remove the ponts. In ths way, remaned feature pont s the most robust pont n the local crcle regon. The dstrbuton of remaned feature ponts s comparatvely even. And the dstance of two feature ponts can keep between R and R. Fg. (a) s the extracted feature ponts usng mproved SIFT algorthm, and Fg. (b) s the dstrbuton adjusted result by the above mentoned. The scale s of features pont s related to the scalng factor of the Gaussan functon n the scale space, and vares wth the local mage characterstc. So the local

JOURNAL OF MULTIMEDIA, VOL. 7, NO. 3, JUNE 0 33 crcle radus R s accordant wth the scale of the selected pont, namely R = r s. r s the adjustng parameter of the dstance between feature ponts. The value of r can be used to control the number of feature ponts. Wth lager r, the dstance between feature ponts s larger, the number of remaned feature ponts wll be smaller, and the local regon to nsert watermark wll be larger. On the contrary, r s smaller, the dstance between feature ponts wll be shorter, reman more feature ponts, and the local regon to nsert watermark wll be smaller. Smaller local regon to nsert watermark can be robust to local attacks, but can not contan more watermark bts. So settng the value of r should take nto account both robustness and watermark capactance. In our experence we set r=5. (a) extracted feature ponts (b) dstrbuton adjustng result Fgure. Extracted feature ponts and ther adjust result III. CROSS RATIO THEORY OF FOUR COLLINEAR POINTS As seen n Fg., A, B, C, D are four collnear ponts they all locate at lne m. Choose a drecton along the lne as the postve drecton (so that dstances measured n the opposte drecton are treated as negatve). The cross-rato r ABCD of these four ponts n the gven order s defned to be: r AC BD ABCD = (3) BC AD Where PQ denotes the sgned dstance between two ponts P and Q for some choce of orentaton. Fgure. The sketch map of cross-rato It s a standard result that the cross rato of four collnear ponts does not change under a transform. Affne transform s the specal form of projectve transform. The prncple of projectve transform s useful to affne transform, so the cross rato of four collnear ponts also keep nvarant under affne transform. The parallel lnes keep parallel after beng operated by affne transform, but do not keep parallel operated by projectve transform. And lne s stll lne after beng operated by projectve transform From cross rato s projectve nvarant, we can get the followng two lemmas: Lemma : Suppose three ponts of four collnear ones have been known, and the cross rato of the four collnear ponts s also gven, the forth pont s certan. Proof: Suppose A, B, C and D are dstnct collnear ponts, as shown n Fg.. Now know A, B, C are certan, and the cross rato CA DA r ABCD = : s also certan. If the CB DB forth pont D s not certan, then segment BD s not certan, from whch can deduce the cross rato CA DA r ABCD = : s not certan. That s n contradcton CB DB wth the known facts. So the forth pont D s certan. Lemma : Suppose four lnes a, b, c, d cross the same pont O, ntersect lne l at four ponts A, B, C, D, and ntersect lne l at four ponts A,B, C, D, as shown n Fg.. Accordng to the dualty prncple of projectve geometry, the followng equaton can be got. r = r = r (4) ABCD abcd A' B' C' D' Proof: Accordng to the dualty prncple of projectve geometry, f r ABCD s certan, then the cross rato rabcd of lne a, b, c and d s certan. The defnton of r abcd s followng: sn( ca) sn( da) r abcd = : (5) sn( cb) sn( db) Where sn(ca ) s the sne of the drected angle formed by lne c and a. The areas of trangle COA, COB, DOA and DOB can be calculated by the followng formula: S( COA) = h CA = OC OA sn( ca) (6) S( COB) = h CB = OC OB sn( cb) S( DOA) = h DA = OD OA sn( da) S( DOB) = h DB = OD OB sn( db) Where h s the hgh from pont O to lne l. From the above four area computng formula, the followng equaton can be deduced: CA DA sn( ca) OA sn( da) OA rabcd = : = : CB DB sn( cb) OB sn( db) OB (7) sn( ca) sn( ba) = : = rabcd sn( cb) sn( bd) Smlarly we can deduce So r = r = r ABCD abcd r = r A' B' C ' D' A B C D abcd Based on the Lemma and Lemma, we choose the watermark bts nsertng ponts n the local quadrlateral

34 JOURNAL OF MULTIMEDIA, VOL. 7, NO. 3, JUNE 0 regon decded by feature ponts, whch guarantees watermark s nvarant to projectve transformaton. IV. WATERMARK INSERTING The whole process of watermark nsertng can be seen n Fg. 3, frstly extract feature ponts from carrer mage wth the mproved SIFT algorthm gven n part II,and adjust the number and dstrbuton of feature ponts usng the n part II. Then choose the proper nvarance of cross rato. Suppose P P P 3 P 4 standng for a local feature regon, as shown n Fg. 4, lne P P 3 ntersects lne P P 4 at pont O If extremty ponts of two segments P, P, P 3, P 4 are nvarant to projectve transformaton, ther cross pont O keeps nvarance to projectve transformaton too. Because projectve transformaton s lnear transformaton n two dmensons space, lne transformed by projectve s stll lne. Two segment keep nvarance, and ther cross pont keep nvarance. Accordng to Fgure 4. The sketch map of choosng watermark bts nsertng locatons Fgure 3. Watermark nsertng process quadrlateral as local feature regons to nsert watermark and get watermarked mage. A. Choose Local Feature Regons Ths paper uses the local quadrlateral regons to nsert watermark, and the apexes of quadrlateral are the chosen feature ponts. Use the mproved SIFT algorthm to extract feature ponts, adjust the number and dstrbuton and get a set of feature ponts P = { p, =,, N}. And the local feature regons are decded by the feature ponts n set P. The to choose local feature regons s as the followng: regard feature ponts p, =,, N as center, n a round regon wth radum 4R searchng three feature ponts, and construct a quadrlateral wth pont p. The chosen quadrlateral should be convex quadrlateral that s close to square. To meet ths requrement, the nternal angle of chosen quadrlateral should be smaller than 00 degree, the length of two adjacent sdes should be smlar, and ther dfference can not be larger than 30 pxels. And the chosen quadrlateral regons maybe overlap each other. If two regons overlap (not nclude the two regons wth same pont and sde), choose the one approachng square, whch wll help watermark nsertng and detectng. B. Choose the Insertng Locatons for Watermark Bts In every local feature regon, decde the nsertng locaton for watermark bt based on the projectve Lemma n part III, gven three ponts of four collnear ponts and the cross rato of the four collnear ponts, the forth pont s certan. Gven n cross ratos n advance, locate n ponts n every segment, and control n/ ponts dstrbute one sde of cross pont O, another n/ ponts dstrbute the other sde, as shown n Fg. 4. In the tranglep P O, draw lnes between pont P and the ponts on segment P O, draw lnes between pont P and the ponts on segment P O. Accordng to Lemma n part III the cross ponts of these lnes keep nvarance to projectve transformaton. We choose the cross ponts (marked black dot n Fg. 4) as the nsertng locaton for watermark bts, whch wll be robust projectve transformaton. In order to keep the correct order of watermark bts when watermarked mage destroyed by geometrcal attacks, the watermark bt nsertng locaton should arrange n a certan order. We regulate arrangng the nsertng locaton from the orgnal sde along clockwse of the nternal angle at cross pont O. Arrangng order s along the arrowhead orentaton n Fg. 4. Use the same way to choose the watermark nsertng locaton n the other three trangles. C. Watermark Insertng Method We adopt quantzaton modulaton to modfy the pxel value at chosen watermark bt nsertng locaton. The pxel values at N watermark nsertng locatons are supposed to be I j ( j=,,,n, and watermark s a {0,}sequence, supposed to be W(j) j=,,,n. I j ( and W(j) are one to one correspondence. If W(j) correspondng I j ( s 0, modulate I j ( to center of even nterval; If W(j) correspondng I j ( s, modulate I j ( to center of odd nterval. Descrbe the quantzaton step as D, and the quantzaton nterval λ s defned as:

JOURNAL OF MULTIMEDIA, VOL. 7, NO. 3, JUNE 0 35 [ I ( / D] λ = (8) Where [] mean roundng a number to the nearest nteger. In order to nsert watermark bts, The pxel value of I j ( s modfed by (9) I I W W ( = ( λ 0.5) D f ( λ + W ( ))mod = ( = ( λ + 0.5) D f ( λ + W ( ))mod = 0 In order to strengthen the robustness of watermarkng system, the pxels n a 3 3 regon centered the chosen nsertng pont are also modfed. If the center nsertng pont s modfed to correspond 0, the 8 pxels around s modfed to correspond 0. If the center nsertng pont s modfed to correspond, the 8 pxels around t s also modfed to correspond. In modfyng the pxels wth (9), how to choose the quantzaton step D s a crucal problem. The step D s a key balance factor between robustness and mpercepton of watermark. If choose large value for step D, watermark wll have good robustness, but not guarantee mpercepton. If choose small value for step D, watermark wll have good mpercepton, but not guarantee robustness. In many former reported paper, the step D was adjusted through repeated expermentaton, to meet the requrement for Peak Sgnal-to-Nose (PSNR) of watermarked mage. In ths paper we deduce the quanttatve relaton between PSNR and step D. Based on the relaton, compute the step D wth PSNR drectly, not need repeated expermentaton. The followng s PSNR defnton. 55 PSNR( I, I ) = 0 log (0) 0 MSE N ' MSE = ( I ( I ( ) () M = Where MSE s mean square error, I s orgnal mage, I s watermarked mage. I( denotes the value of pxel (, M s pxel number n all local feature regon to nsert watermark, and N s pxel number used to nsert watermark bts. In many reported paper, M means the sze of mage and PSNR stands for the mpercepton of the whole mage. In ths paper watermark s nserted local feature regons, not the whole mage, f set N to be sze of the whole mage, PSNR wll be small even local regon changed largely. In ths case, watermark has been seen and PSNR can not express the qualty of watermarked mage. In local feature regon the watermark nsertng rato s ρ=n/m, the relaton of step D, nsertng rato ρ and mean square error MSE can be deduced. We can learn from (9) that quantzaton errors dstrbute the nterval [-D, D] equably. So the mathematcal expectaton of the square quantzaton errors s (). (D) D E ( I( I ( ) = = () 3 (9) And the mathematcal expectaton of the mean square error MSE s (3). N E( MSE) = E( I( I ( ) M = N D = = ρd (3) M 3 3 So we can deduce the relaton of step D, nsertng rato ρ and mean square error MSE 0.5 PSNR D = 55 ρ 0 0 (4) 3 V. WATERMARK DETECTING For nput mage I, frstly extract feature ponts wth the mproved SIFT algorthm, adjust the number and dstrbuton of feature ponts usng the presented n part II. Get a set of feature ponts Q = { q, =,, M}. Center feature ponts q, =,, M, n a round regon wth radum 4R searchng three feature ponts, and construct a quadrlateral wth pont q. Choose the protrudng quadrlaterals as watermark detectng regons. For every detectng regon, searchng watermark nsertng ponts wth the same as watermark nsertng, the cross ratos set s that used n watermark nsertng process. For pxel I ( extract watermark bt usng followng formula. f I '( / D mod = W '( ) = (5) 0 f I '( / D mod = 0 Where means round down, D s the same quantzaton step used n watermark nsertng. In every chosen local feature quadrlateral the two dagonal lnes dvde t nto four trangles, and watermark s nserted nto every trangle repeatedly. In any one trangle of any two local feature quadrlateral detect watermark sequence s W (). If the number of bts matched W () and orgnal watermark sequence W() s larger than the threshold T, we would judge mage I exst watermark. Determnng whether there are watermarks n mage I s concern to threshold T, whch decdes the error rate of watermark detector drectly. Two knds of errors are possble for detector: the falsealarm probablty and the mss probablty. The falsealarm probablty means no watermark nserted but detected whle the mss probablty means watermark nserted but detected havng none. There s a tradeoff between these two error probabltes n selectng detector parameters. Typcally, reducng one wll ncrease the other. The mss probablty depends on success detecton probablty. It s dffcult to evaluate the success detecton probablty of a watermarked bt. It depends on the attacks. So ths paper chooses the threshold T only dependng on the false-alarm probablty.

36 JOURNAL OF MULTIMEDIA, VOL. 7, NO. 3, JUNE 0 For an unwatermarked mage, the extracted (0.) bts are assumed to be ndependent random varables, from whch we learn the success probablty of every bt s 0.5 Based on Bernoull trals, match the watermark sequence W () detected from trangle regon wth orgnal watermark sequence, f there are k bts matched successfully, the false-alarm probablty to detect watermark from one trangle can be computed wth the followng formula. (a)watermarked Lena (b) watermarked Baboon (c) watermarked Pepper Fgure 5. Watermarked mages N tr = k T P (0.5) N N! k! ( N k)! (6) Where N s the length of watermark sequence, k s the number of bt matched successfully. T s watermark detectng threshold. Four trangles n a local feature regon are all nserted watermark, f detect watermark from one trangle successfully, we judge exstng watermark n the local feature regon. The false-alarm probablty to detect watermark from one local feature regon can be computed from the followng formula. P qua 4 4 4! = ( Ptr ) ( Ptr ) (7)! (4 )! = If detect watermark from two local feature regon successfully, we judge exstng watermark n mage I. Suppose nsertng watermark n m local feature regon, the false-alarm probablty to detect watermark from mage I can be computed wth the followng formula. P false m m m! = ( Pqua ) ( Pqua ) (8)! ( m )! = Suppose the length of watermark sequence N=5, there are 0 local feature quadrlateral nsertng watermark, detect threshold T=0. From the above analyss we can learn the false-alarm probablty P false.8 0-3. VI. EXPERIMENTATION RESULT AND ANALYSIS We choose three gray mages Lena, Pepper and Baboon to test our scheme, ther sze s 5 5. These mages have dfferent texture. In expermentaton, the dstance adjustng parameter r=5, the length of watermark sequence N=5, quantzaton step D=5, detect threshold T=0. There are 7 local feature regons nsertng watermark n mage Lena, there are 4 local feature regons nsertng watermark n mage Baboon, and there are 9 local feature regons nsertng watermark n mage Pepper. A. The Vsual Qualty of Watermarked Image Fg. 5 ncludes the watermarked Lena, Baboon and Pepper. Fg. 6 s the dfference value mages between orgnal mages and watermarked ones (the dfference value s 30 tmes of orgnal one). The qualty of watermarked mage s descrbed by PSNR. If only concern the MSE of local feature regons, the PSNRs of watermarked Lena, Baboon and Pepper are 39.85, (a) Lena (b) Baboon (c) Pepper Fgure 6. Dfference value mages between orgnal mages and watermarked ones 39.59, and 39.345 respectvely. If concern the MSE of the whole mage, the PSNRs of watermarked Lena, Baboon and Pepper are 46.455, 46.455 and 46.455 respectvely. For our scheme, the fst PSNR computng way s proper. The PSNR n ths paper s computed wth the fst. PSNR of watermarked mage s related to quantzaton step D and watermark nsertng rato ρ. The lager value of D and ρ wll make watermark more robust, but the qualty of watermarked mage wll fall off, and get smaller PSNR. In secton IV part C we have analyzed the relaton of quantzaton step D, watermark nsertng rato ρ and PSNR, and deduce the relaton formula (4). Fg. 7 s the result value computed from theory and the experence, and gvng ther relaton curve. The theory value s computed from formula (4) and the experence value s come from three test mage. As can be seen n Fg. 7, wth the watermark nsertng rato ρ ncreasng, PSNR decrease; and wth the quantzaton step D ncreasng, PSNR decrease. The experence value and theory value ft better. But ρ= and ρ=0.5, the experence value and theory value have lttle Fgure 7. The relaton of PSNR, quantzaton step D and watermark nsertng rato ρ

JOURNAL OF MULTIMEDIA, VOL. 7, NO. 3, JUNE 0 37 dfference. The man reason s the watermark nsert locaton overlap wth the nsertng rato ρ ncreasng. These experences valdate the formula () s correct. When nsertng watermark, set nsertng rate based on the area of chosen regons, and the quantzaton step D s decded by PSNR of watermarked mage. Set PSNR=40dB to guarantee the qualty of watermarked mage. B. Test and Analyze the Robustness of Watermark In order to test the robustness of the proposed scheme, we carred three knd experments for watermarked mage. We manpulated the watermarked mage wth no attack, general sgnal attacks and geometrc attacks respectvely, and then detected watermark from the attached mage. Detectng results lsted n Table and Table, and compared wth Tang s [8]. In table and, a n a/b stands for the number of regons that detect watermark successfully, and b stands for the number of regons nserted watermark. means falng to detect watermark. As can be seen n table, when there no attack to the watermarked mages, the proposed scheme can detect all local feature regons nserted watermark, and the detected watermark bts matched the nserted watermark bts entrely. Watermark detected results from attacked mages by general sgnal process are also shown n table. From the experments results n table we can see the proposed TABLE I. THE EXPERIMENT RESULT UNSER NO ATTACK AND GENERAL SIGNAL PROCESS Watermarked Lena Watermarked Baboon Watermarked Pepper Attacks Tang Tang Tang No attack 7/7 7/8 4/4 0/ 8/9 4/4 Jpeg 80 6/7 7/8 0/4 9/ 8/9 3/4 Jpeg 70 4/7 7/8 3/4 / 4/9 3/4 Jpeg 50 /7 7/8 7/ /9 3/4 Jpeg 40 5/8 5/ /4 Medan flter (3 3) 6/7 /4 / 8/9 Gaussan flter (3 3) /7 5/8 0/4 8/ 9/9 /4 Addtve nose (d=0.) 5/8 6/ /9 4/4 Gaussan flter (3 3) +Jpeg90 /7 5/8 0/4 8/ 9/9 /4 TABLE II. THE EXPERIMENT RESULT UNSER GEOMETRIC ATTACKS Watermarked Lena Watermarked Baboon Watermarked Pepper Attacks Tang Tang Tang Remove 5 rows and 7 columns 5/7 /4 3/ 7/9 Remove 8 rows and 0 columns 4/7 /4 6/7 Croppng 0% /7 /8 0/4 / 6/7 /4 Croppng 0% /7 8/4 4/7 Shearng-x-5%-y-5% 5/7 /4 / 6/7 Shearng-x-0%-y-0% 3/7 9/4 4/7 Rotatng + Croppng 6/7 3/8 /4 3/ 5/7 /4 Rotatng 30 + Croppng 5/7 8/4 5/7 Rotatng 90 7/7 4/4 7/7 Scalng 0.5 5/7 /4 6/7 Scalng. 6/7 /4 7/7 Lnear geometrc transformaton 7/7 4/8 /4 5/ 5/7 (.0,0.03,0.009,.0) Project transformaton [0.05 0.0;. 0; ; 0.05] 6/7 /4 5/7 Project transformaton [0. 0.;.0 0; ; 0 0.9] 5/7 0/4 4/7 Rotatng 30 +Scalng 0.8+Jpeg 90 5/7 7/4 5/7

38 JOURNAL OF MULTIMEDIA, VOL. 7, NO. 3, JUNE 0 s robust to Jpeg compresson, medan flter and Gaussan flter, but faled to addtve nose and Jpeg compresson wth lager compresson rate. For 3 3 medan flter attack, the proposed shows more robust than Tang s. The man reason s that SIFT algorthm s more robust to medan flter than Mexcan hat wavelet scale nteracton algorthm. Watermark bt s nserted n 3 3 regon around the chosen pont, whch also strengthens the stablty to medan flter. For the addtve nose wth ntenson 0., expect the watermarked Pepper (detect watermark n two local feature regons n watermarked Pepper), the other two mages faled to detect watermark. The man reason s that SIFT feature ponts are senstve to nose. We also seen the proposed fals to Jpeg compresson wth qualty factor less than 70. The man reason s that the proposed nserts watermark nto space doman and Tang s nto DFT doman. The low frequency coeffcent n frequency doman s more stable to Jpeg compresson than pxel n space doman. The geometrc attack nclude rotaton, scalng, translate, croppng, remove column and row, shearng, lnear geometrc transformaton, projectve transformaton and ther combnaton. Part experment results are shown n table. Compared wth Tang s the proposed s robust to wder range of geometrc attacks. For rotaton, Tang s only ressts the rotaton under 5, whle the proposed can resst rotaton wth arbtrary angle. For projectve transformaton, Tang s s no useful, but the proposed can resst a certan degree projectve transformaton. From table we can see the proposed has better performance than Tang s n resstng geometrc attacks. There are two man reasons: () SIFT feature s more stable to geometrc transformaton than Mexcan hat wavelet scale nteracton feature. () the proposed choose watermark nsertng locaton based on cross rato, whch s nvarance to projectve transformaton, makng watermark robust to projectve transform. VII. CONCLUSION Utlzng two knd of nvarance, namely feature ponts extracted by mproved SIFT algorthm and cross rato of collnear ponts, ths paper presents a watermarkng to resstng geometrc attack. The holds the mert of feature-pont-based watermarkng, and compared wth Tang s, a classcal feature-pontbased watermarkng, t has stronger ablty to resst geometrc attack. The man contrbuton of ths paper nclude: () combne the watermarkng system, mproved SIFT algorthm and get faster computng speed and more stable feature ponts. () Based on the cross rato nvarance to projectve transformaton, t choose the locaton of watermark bt, whch guarantees watermark nsertng and nsertng locaton synchronzaton. (3) For quantzaton modulaton embeddng, analyze the relaton between quantzaton step and PSNR, and deduce ther relaton formula, whch help decde the quantzaton step drectly accordng to the gven PSNR. ACKNOWLEDGMENT Ths work was supported n part by a grant from Scence Technology Project of Henan, Chna (No. 0646009) and Natonal Natural Scence Foundaton of Chna (No.0903063 and 08400400) REFERENCES [] D. Zhang, J. Zhao, and A. Saddk. RST-nvarant dgtal mage watermarkng based on log-polar mappng and phase correlaton. IEEE Trans Crcuts Syst Vdeo Technol, 003, 3 (8): 753-765. [] CY. Ln, M. Wu, and J A. Bloom. Rotaton, scale, and translaton reslent watermarkng for mages. IEEE Trans Image Process, 00,0 (5): 767 78. [3] S. Perera, PUNT. Robust Template Matchng for Affne Resstant Image Watermarks. IEEE Trans on IP, 000, 9(6): 3-9. [4] XG. Kang, JW. Huang, and Y. Ln. Spread-Spectrum Watermarkng Ressts to Affne Transformaton. Acta Electronc Snca, 004, 3(): 8-. (n Chnese) [5] P. Dong, JG. Brankoy, and NP. Galatsanos. Dgtal watermarkng robust to geometrc dstortons. IEEE Trans on Image Process, 005, 4(): 40 50. [6] MD. Sang, Y. zhao. 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L Jng, receved her PH.D. degree n computer software theory from Informaton Engneerng Unversty, Zhengzhou, Chna n 009. Now she s an ASSOCIATE PROFESSOR of School of Computer and Informaton Engneerng, Henan Unversty of Economcs and Law, Zhengzhou, Henan Provnce, Chna. Hs research felds nclude artfcal neural network,, data mnng and mage process, etc. Dr. Jng s also a member of Chna Computer Federaton. Xaowen Zhang, s a postgraduate n the department of computer scence, Unversty College Cork, Ireland.