A Desynchronization Resilient Watermarking Scheme

Transcription

1 A Desynchronzaton Reslent Watermarkng Scheme Xaojun Q and J Q Department of Computer Scence, Utah State Unversty, Logan, UT Xaojun.Q@usu.edu, jq79@gmal.com Abstract. Ths paper presents a content-based desynchronzaton resstant dgtal mage watermarkng scheme. The mage content s represented by strong mportant feature ponts obtaned by our robust and mproved Harrs corner detector. These feature ponts are more resstant to geometrc attacks and are therefore used by the Delaunay trangle matchng and mage restoraton method to reduce synchronzaton errors. The spread-spectrum-based blnd watermark embeddng and retreval scheme s appled n the Fourer doman of each perceptually hghly textured submage. The multplcatve scheme s then used to embed the same copy of the watermark at hghly secure md-frequency postons generated by one-way hash functons wth dfferent secret keys. The watermark detecton decson s based on the number of matched bts between the recovered and embedded watermarks n embeddng submages. Expermental results demonstrate that our scheme s more robust to desynchronzaton attacks (.e., geometrc and common mage processng attacks) than other peer featurebased approaches. Keywords: Desynchronzaton reslent dgtal watermarkng, mportant feature ponts, spread-spectrum-based blnd watermarkng, Delaunay trangle matchng. 1 Introducton Wth the rapd growth of multmeda data dstrbuton, many dgtal watermarkng schemes have been proposed for copyrght protecton. The robustness of the watermark to common mage processng and geometrc attacks s essental n many applcatons [1]. However, these desynchronzaton attacks are dffcult to tackle due to nduced synchronzaton errors n watermark detecton and decodng. Several watermarkng schemes, ncludng template-based, nvarant-doman-based, moment-based, and feature-based, have been developed to counterattack desynchronzaton dstortons. Template-based watermarkng algorthms [2], [3], [4] embed mage ndependent templates to assst synchronzaton n watermark detecton process. However, these template features can be exploted [5] to destroy the synchronzaton pattern. Invarant-doman-based watermarkng algorthms [6], [7], [8], [9] generally provde a RST (Rotaton, Scalng, and Translaton) nvarant doman to mantan synchronzaton under affne transforms. The Fourer-Melln transform and log-polar resamplng are two typcal examples. However, the nterpolaton accuracy and alasng n the resamplng and ntegraton may cause problems n synchronzaton. Moment-based watermarkng Y.Q. Sh (Ed.): Transactons on DHMS IV, LNCS 5510, pp , Sprnger-Verlag Berln Hedelberg 2009

2 30 X. Q and J. Q algorthms utlze ordnary geometrc moments [10], [11], [12] or Zernke moments [13], [14] to solve the geometrc nvarance problem. However, perfect nvarance cannot be acheved due to the dscretzaton errors. Feature-based watermarkng algorthms [15], [16], [17], [18], [19], [20] use mage dependent feature ponts to represent nvarant reference ponts for both embeddng and detecton. They generally are the best approaches to resstng desynchronzaton dstortons snce feature ponts provde stable references for both watermark embeddng and detecton. Several related, representatve schemes are brefly revewed here. Bas et al. [15] used the Harrs corner detector for feature extracton. These feature ponts were mxed wth a Delaunay tessellaton to mark each trangle for embeddng the watermark. The orgnal watermark trangles were then warped durng the detecton to correlate wth the correspondng marked trangles. Smlarly, Seo and Yoo [16], [17] extracted feature ponts usng the Harrs-Laplace detector and decomposed the mage nto dsjonted local crcular or ellptcal regons for watermark embeddng and extracton. Lee et al. [18] proposed to use the SIFT (Scale-Invarant Feature Transform) to determne the local crcular regons for watermarkng. The smulaton results from all of the above methods show that the robustness of each scheme depends on the capacty for preservng feature ponts after geometrc transformaton, especally on mages wth more texture and mages wth less texture and large homogeneous areas. Moreover, these methods embed the watermark n the spatal doman after geometrc normalzaton accordng to the shapes of the regon. Consequently, watermark robustness to common mage processng s not satsfactory and the feature ponts-based transformaton doman watermarkng schemes were proposed. Tang and Hang [19] adopted the Mexcan hat wavelet scale nteracton method to extract feature ponts. They embedded and extracted the watermark n the normalzed dsks centered at the extracted feature ponts. Wang et al. [20] mproved Tang s method by usng the scale nvarant Harrs-Laplace detector to fnd the radus of each crcular regon. However, Tang s scheme performs well under only mld geometrc dstorton and certan common mage processng attacks. The watermark capacty of both schemes s only 16 bts, whch may restrct ther practcal applcatons. In ths paper, we develop a desynchronzaton reslent watermarkng scheme. Ths scheme combnes the advantages of mportant feature extracton, perceptual analyss, one-way hash functons, and spread-spectrum-based blnd watermark embeddng and retreval to reduce the watermark synchronzaton problem and resst dfferent attacks. Secton 2 descrbes the proposed robust feature extracton method. Secton 3 brefly presents our varants of two mportant technques used n the proposed scheme. Secton 4 covers the detals of the watermark embeddng and detecton procedure. Secton 5 compares our scheme wth three feature-based approaches n terms of robustness aganst both geometrc dstortons and common mage processng attacks. In addton, we also demonstrate the performance of our proposed scheme on 105 mages of varous textures under dfferent Strmark attacks. Secton 6 concludes ths presentaton. 2 Feature Ponts Extracton Extractng feature ponts s the most mportant step n the proposed dgtal mage watermarkng scheme. In order to detect watermarks wthout access to the orgnal mages, we look for feature ponts that are perceptually sgnfcant and can thus resst

3 A Desynchronzaton Reslent Watermarkng Scheme 31 varous types of desynchronzaton dstortons. These mage-content-bounded feature ponts can be further used as synchronzaton markers (.e., anchor ponts) n watermark detecton. To ths end, we propose a robust and mproved Harrs corner detector to fnd relatvely strong IFPs (Important Feature Ponts) to reduce the synchronzaton errors n watermark detecton. Our two major contrbutons are: Improve the Harrs corner detector [21] to reduce nose effect and regulate the densty of IFPs based on the dmenson and texture of the mage. Strengthen the mproved Harrs corner detector to dscard some non-stable IFPs. These two mprovements can also be appled to other detectors to acheve better performance. The algorthmc flow of our mproved Harrs corner detector s summarzed as follows: 1. Apply a rotatonally symmetrc 3 3 Gaussan low-pass flter wth the standard devaton of 0.5 to blur the orgnal mage to ncrease the nose resstance. 2. Compute three dervatve mages, A, B, and C, by convolvng the blurred mage wth the horzontal, vertcal, and dagonal edge flters, respectvely. 3. Apply the same Gaussan low-pass flter to blur three dervatve mages (e.g., A, B, and C) to further ncrease the nose tolerance. 4. Calculate the corner response functon R as defned n [21],.e., R = (AB-C) 2-0.4(A+B) 2, wthn a crcular wndow, whch s at the mage center and covers the largest area of the orgnal mage. The resultng functon reduces the effect of mage center based rotaton attacks and removes the corner ponts near the mage border. 5. Search for IFPs whose corner response value R(x,y) s are larger than a threshold T and are the local maxma wthn a crcular neghborhood centered at (x, y). We choose the crcular neghborhood wndow to avod the ncreasng detector ansotropy and to obtan a homogeneous dstrbuton of feature ponts n the mage. It s also mportant to determne the approprate wndow sze snce a small wndow makes the feature ponts concentrate on textured areas and a large wndow tends to solate the feature ponts. Fg. 1 llustrates the effect of dfferent wndow szes on the resultant feature ponts. We can easly observe that the smaller wndow yelds more feature ponts. However, these extra feature ponts wll requre more computatonal cost n the detecton process. The larger wndow yelds fewer feature ponts and requres fewer computatonal cost n the detecton process. However, the possblty of losng some IFPs s also ncreased. In order to make a compromse between the number of feature ponts and the computatonal cost n watermark detecton, we determne a sutable wndow sze based on the dmenson and texture of the mage. We roughly classfy mage textures as hgh, medum, and low, based on the rato of the feature ponts to the total number of pxels n an mage, wheren the feature ponts are obtaned by usng our mproved Harrs corner detector wth a fxed 3 3 neghborhood wndow. That s: hgh texture f rato 0.01 mage has medum texture f rato (1) low texture f rato

4 32 X. Q and J. Q The dameter of the crcular wndow s calculated: wh D = (2) np where ntegers w and h respectvely represent the wdth and heght of the mage; nteger p s an emprcal value (.e., p = 5) for obtanng a reasonable number of feature ponts for mages wth large homogeneous areas; and nteger n s the wndow sze quantzer, whch depends on the texture of the mage. It s set to be 2, 2.5, and 3 for mages wth hgh, medum, and low textures, respectvely. (a) Fg. 1. The effect of dfferent wndow szes on the feature ponts. (a) (b) Our mproved Harrs corner detector ensures to extract IFPs n a nosy mage. However, these IFPs may not be robust under certan geometrc or common mage processng attacks. Fg. 2 demonstrates ths observaton by dsplayng the IFPs of two attacked Lena mages. We can clearly see that some IFPs are present n both attacked mages whle others are only present n one attacked mage. (b) Fg. 2. The non-robustness of IFPs under attacks. (a) IFPs after rotaton. (b) IFPs after reszng. In order to keep the strong IFPs whch resst geometrc attacks, we further enhance the mproved Harrs detector by quanttatvely evaluatng ts capacty for preservng the IFPs when the mage undergoes certan attacks. Ths evaluaton functon s computed as: Numkept ( Numnew + Numloss ) Numkept ( Numnew + Numloss ) Score = = (3) Num + Num Num kept (a) loss (b) or

5 A Desynchronzaton Reslent Watermarkng Scheme 33 where Num or denotes the number of IFPs present n the orgnal mage; Num new, Num loss, and Num represent the number of IFPs that have been created, destroyed, and preserved after certan attacks, respectvely. The preservaton, creaton, kept or loss status of these feature ponts s evaluated by performng an nverse transformaton, whch restores the attacked mage to be algned wth the orgnal mage, on the IFPs obtaned from the attacked mage. Ths evaluaton functon yelds the maxmal value of 1 when the detector precsely fnds the IFPs under a certan attack,.e., Num new= Numloss = 0. In general, the larger the Score, the more capacty of the detector to preserve the IFPs under attacks. Fg. 3 llustrates the block dagram of fndng the relatvely strong IFPs. Varous mage rotaton and scalng attacks have been performed on the orgnal mage to fnd several attacks that preserve most of the strong IFPs n the orgnal mage. Our extensve expermental results show that random attacks can roughly estmate all possble rotatons and scalng factors. The best attacks that acheve the hghest Score values wll be further used to ndvdually pre-attack the orgnal mage to fnd the IFPs n ts correspondng attacked mages. Choosng these pre-attacks ensures that a decent number of strong IFPs can be obtaned to reduce the synchronzaton errors. The strong IFPs are obtaned by: where IFP strong I n or =1 { Algn( IFP )} = IFP (4) Attack IFP or represents the IFPs n the orgnal mage; IFPAttack represents the IFPs after the th best attack, whch can be ether a rotaton or a scalng attack; and () Algn s an algnment operator to regster the orgnal and attacked mages; and n s the number of the best attacks and s adaptvely chosen based on the mage texture. In our system, we set n to be 6 for hgh textured mages, 4 for medum textured mages, and 2 for low textured mages. Fg. 4 llustrates the effect of dfferent pre-attacks on the resultng IFPs and shows the relatvely strong IFPs obtaned by ntersectng IFPs of the orgnal and ts preattacked mages. We can easly observe the senstvty of the IFPs to dfferent attacks. That s, some IFPs may dsappear or show up or shft a bt after attacks. Consequently, t s mpossble to locate the robust IFPs whch can survve varous attacks n the real world. To address ths challengng ssue, we select a few best pre-attacks to extract the strong IFPs that are lkely preserved under dfferent attacks. Such a choce keeps the balance between the robustness and the number of strong IFPs. Specfcally, the ntersecton operaton ncreases the robustness of the extracted strong IFPs and keeps enough IFPs to regan the synchronzaton (.e., algn the watermarked mage wth the orgnal mage). In other words, a robust resynchronzaton can be acheved by usng a few best pre-attacks for a compromse between the robustness and the number of strong IFPs. The ratonale for choosng the best pre-attacks s based on the followng observatons: 1. Most IFPs survvng a rotaton or scalng attack can survve any combned RST attacks or any mage processng attacks f the mage s not cropped. The followng ntutve proofs support ths observaton: a) Croppng may result n substantal loss of the IFPs and therefore wll not be consdered as a pre-attack. b) A feature pont,

6 34 X. Q and J. Q major characterstc n an mage, must be dfferentated from ts neghbors no matter what knds of the attacks are performed on the mage. c) Any rotaton or scalng attack, lke any combned RST attack, requres an nterpolaton operaton to modfy the ntensty of each pxel. The mage processng attacks wll modfy the ntensty of each pxel n another way. However, these modfcatons should not make the dfferentaton between the feature pont and ts neghbors dsappear. That s, most feature ponts should stll stand out when compared to ther neghbors after geometrc and mage processng attacks. As a result, we can always use a rotaton or scalng attack to fnd potental IFPs. Orgnal Image Yes One of Varous Image Attacks Improved Harrs Corner Detector Capacty Score Calculaton Another Attack? No Capacty Score Sortng No One of Selected Image Attacks Improved Harrs Corner Detector Feature Ponts Restoraton Fnsh Attacks? Yes Improved Harrs Corner Detector I n = 1 Attacks wth Top Scores Strong Important Feature Ponts Fg. 3. Block dagram of extractng strong IFPs 2. The IFPs whch are preserved after several pre-attacks are more robust aganst attacks than the other IFPs whch are destroyed or created after the pre-attacks. 3. The best pre-attacks usually yeld more IFPs than any other pre-attacks (e.g., random attacks, worst attacks, or mage processng attacks). Ths leads to more anchor ponts for synchronzaton and therefore ncreases the possbltes for fndng the geometrc transformaton n watermark detecton. 4. The IFPs obtaned from the best pre-attacks always ntersect wth majorty IFPs obtaned from an attacked mage. Ths ndcates that we can always fnd enough IFPs to perform synchronzaton.

7 A Desynchronzaton Reslent Watermarkng Scheme 35 a: (a.1) (a.2) (a.3) (a.4) (a.5) (a.6) (a.7) b: (b.1) (b.2) (b.3) (b.4) (b.5) (b.6) (b.7) c: (c.1) (c.2) (c.3) (c.4) (c.5) (c.6) (c.7) d: (d.1) (d.2) (d.3) (d.4) (d.5) (d.6) (d.7) Fg. 4. The effect of dfferent pre-attacks on the resultant strong IFPs. (a) IFPs obtaned from 6 best pre-attacks. (a.1) R180º (a.2) R250º (a.3) R265º (a.4) R280º (a.5) R60º (a.6) S0.95 (a.7) Fnal strong IFPs by ntersectng the orgnal and ts 6 best pre-attacked mages. (b) IFPs obtaned from 6 worst pre-attacks. (b.1) R145º (b.2) R235º (b.3) R220º (b.4) R320º (b.5) R190º (b.6) S0.90 (b.7) Fnal strong IFPs by ntersectng the orgnal and ts 6 worst pre-attacked mages. (c) IFPs obtaned from 6 random pre-attacks. (c.1) R16º (c.2) R145º + S0.95 (c.3) R240º + S0.87 (c.4) R110º + S T[5, 5] (c.5) R68º + S T[10, 10] (c.6) S0.8 +T[10, 10] (c.7) Fnal strong IFPs by ntersectng the orgnal and ts 6 random pre-attacked mages. (d) IFPs obtaned from 6 common mage processng pre-attacks. (d.1) Medan flterng 2 2 (d.2) Medan flterng 3 3 (d.3) Mean flterng JPEG90% (d.4) Sharpenng (d.5) Gaussan flterng (d.6) Hstogram equalzaton (d.7) Fnal strong IFPs after ntersectng the orgnal and ts 6 common mage processng pre-attacked mages. Here, R denotes rotaton, S denotes scalng, and T denotes translaton. 5. The IFPs obtaned from the worst pre-attacks seem to be the most stable ones. However, some IFP may not be preserved under certan attacks due to the senstvty of the IFPs to dfferent attacks. In addton, these IFPs may not possess suffcent anchor ponts for the synchronzaton n the detecton process. Fg. 5 demonstrates the fnal preserved strong IFPs by applyng our proposed robust and mproved Harrs corner detector on four mages wth dfferent textures. That s, random rotaton and scalng operatons are respectvely appled on each mage to fnd ts best pre-attacks. The mproved Harrs detector s then appled to fnd the IFPs for each orgnal mage and ts correspondng best pre-attacked mages. The ntersecton of all IFPs yelds strong IFPs to be saved for the detecton process. As shown n Fg. 5, the proposed approach effectvely elmnates some unrelable feature ponts whch fal to be detected after certan geometrc attacks.

8 36 X. Q and J. Q Fg. 5. Relatvely strong and mportant feature ponts 3 Our Varants of Related Technques 3.1 The PN-Sequence and One-Way Hash Functons We use the PN (Pseudo-Nose) sequence based spread spectrum method n our system due to ts robustness aganst nose and ts capablty to acheve error free transmsson near or at the lmts set by Shannon s nosy channel codng theorem [22]. Ths sequence combned wth the watermark s adaptvely embedded nto md-frequency postons n the DFT doman snce hgh-frequency watermark can be easly elmnated by lossy compresson and low-frequency watermark s usually notceable. We mprove the one-way hash functon [23], whch s easy to compute and dffcult to nvert, to generate the hghly secure md-frequency postons by the followng seven steps: 1. Save all mddle frequency postons nto vector V. 2. Randomly choose two large prme numbers p and q, and compute the secret key n=pq. 3. Obtan two seeds X and Y usng the encpher process : n K 2 X = m mod n; Y = X mod (5) where m s the orgnal mage dentfcaton number (.e., a numercal seral number for regsterng the mage) and K s the second secret key. 4. Calculate an ndex l by: 2 Y = Y mod n l = ( Y mod n) mod length( V (6) 5. Choose the lth tem n V as the embeddng poston. 6. Remove the lth tem from V so no duplcated postons are produced and no collson occurs. 7. Repeat steps 4-6 untl the total number of embeddng postons s reached. These hghly secure embeddng postons can be easly reproduced gven the same secret keys n and K. In the meantme, the reproducton of these postons s computatonally nfeasble wthout knowng n and K. To ensure the attackers cannot fnd out the watermark embeddng postons by comparng several watermarked copes, dfferent secret keys are used to generate embeddng postons for each embeddng submage. )

9 A Desynchronzaton Reslent Watermarkng Scheme Blnd Embeddng and Retreval A watermarkng system should be secure and relable. It s also desrable to extract the watermark ndependent of the orgnal mage. In our system, we adopt the blnd retreval scheme of MPEG vdeo watermark [24], [25] to elmnate the need of storng values at embeddng postons of each host submage. We employ ths blnd retreval scheme n the DFT doman nstead of ther proposed DCT doman. The multplcatve nstead of addtve embeddng s also appled n our modfed scheme. That s: where FIˆ = FI + FI G W p, = 1,..., N (7) FI s the orgnal md-frequency DFT sequence wth length N, Fˆ I s the watermarked DFT sequence, G s the embeddng strength, p s the bpolar PN sequence generated by a secret key, and W s the blnd watermark bt sequence obtaned by repeatng the bpolar watermark message w by a spreadng factor s such that W = w j for js < ( j +1) s. The blnd retreval can be acheved by de-spreadng the blnd watermarked bt sequence usng the correlaton detector. The same embeddng PN-sequence p s used to multply the possbly watermarked sequence: W ' = p FIˆ (8) The W s further grouped nto blocks of sze s where each block s computed: ( j+ 1) s = js+ 1 ( j+ 1) s S1 ( j+ 1) s 2 p ˆ FI = pfi + G p FI W = js+ 1 = js S 2 (9) where j = 0,..., n 1 and n s the length of w. For a large s, FI s statstcally uncorrelated wth p. As a result, S 2 >>S 1 and Eq. (9) s smplfed: ( j+ 1) s = js+ 1 ( j+ 1) s 2 p ˆ FI G p FI W = js S 2 ( j+ 1) s = G FI W = js Snce FI and G are postve, the embedded bpolar watermark bt w j s therefore smlar to the sgn of the correlaton sum ŵ. That s: j S 2 (10) ( j 1) s w wˆ sgn p FIˆ j j = +, j = = js+ 1 0,..., n-1 (11) 4 Watermark Embeddng and Detecton Scheme 4.1 Watermark Embeddng Scheme Our watermark s desgned for copyrght protecton. We vew all possble embeddng submages as ndependent communcaton channels. To mprove the robustness of the

10 38 X. Q and J. Q transmtted watermark bts, all channels carry the same copy of the chosen watermark. Durng the detecton process, we clam the exstence of watermark f one copy of the embedded watermark s correctly detected n one embeddng submage. The watermark embeddng process s detaled step by step as follows: 1. Image tessellaton: Evenly dvde the 8-bt grayscale mage nto 3 3 nonoverlappng submages. The last several nondvsble rows and columns are not used for embeddng. 2. Perceptual analyss: Apply the Harrs corner detector to fnd all feature ponts n the orgnal mage by usng a 3 3 wndow. Choose the submages that have a large number of feature ponts to be embeddng blocks. These blocks are perceptually hgh textured. 3. For each perceptually hgh textured submage SubA: 3.1 DFT: Apply global DFT to obtan FSubA. 3.2 Poston Generator: Generate hghly secure embeddng postons n the mdfrequences between f 1 and f 2 n the upper half plane of FSubA by usng our one-way hash functon. 3.3 operaton: Embed the spread bpolar watermark message bt W j nto each poston (x k, y k ) by usng the multplcatve formula [26]: ( xk, yk )' = FSubA( xk, yk ) + FSubA( xk, yk ) G W j p j (12) FSubA where p j {1, -1} (zero mean and unt varance) s the PN-sequence generated by a secret key. The same changes are carred out at center-based symmetrc postons due to the constrants n the DFT doman for obtanng a real mage. 3.4 IDFT (Inverse DFT): Apply the IDFT to FSubA to obtan the watermark embedded submage SubA, whch replaces the orgnal submage SubA. The proposed robust and mproved Harrs detector s fnally used to fnd strong IFPs n the watermarked mage. The poston of each strong IFP, the bpolar watermark message bt sequence W, the number of embeddng postons Len, two secret keys n and K for our one-way hash functon n each submage, two mddle frequency ratos, and the secret key for generatng the PN-sequence are saved for watermark detecton. Snce strong IFPs are obtaned va the ntersecton operaton, the number of IFPs s optmzed and the storage s mnmal compared to the cost of savng the mage tself. If all the nformaton s compressed, the storage cost wll be further mnmzed. 4.2 Watermark Detecton Scheme The watermark detecton procedure does not need the orgnal mage. The relatvely strong IFPs are frst extracted by ntersectng the IFPs obtaned by applyng our proposed mproved Harrs corner detector on the probe mage and a few randomly rotated probe mages. Two sets of Delaunay tessellaton-based trangles [27] are generated usng the strong IFPs found n the probe mage and the saved strong IFPs, respectvely. These two sets of trangles are then matched to determne the possble geometrc transformatons the probe mage has undergone. These geometrc transformatons are further utlzed to restore the probe mage so synchronzaton errors are mnmzed n the detecton.

11 A Desynchronzaton Reslent Watermarkng Scheme 39 The choce of Delaunay tessellaton s based on two attractve propertes: 1) Local property: If a vertex dsappears, the tessellaton s only modfed on connected trangles. 2) Stablty area: Each vertex s assocated wth a stablty area where the tessellaton pattern s not changed when the vertex s moved wthn ths area. That s, the tessellaton patterns of other trangles reman the same even though losng or shftng an IFP affects the trangle(s) connected to t. In addton, two propertes of the Delaunay tessellaton always ensure that an dentcal generaton of trangles can be obtaned f the relatve postons of the IFPs do not change. We mplemented the Qhull algorthm [28] to generate the IFPs-based trangles due to ts fast speed and less memory constrants. In our system, the angle radans are used to match Delaunay tessellaton-based trangles. That s, f two trangles have very smlar angle radans (.e., the angle dfference s less than 0.01 radan), they are clamed to be lkely matched. The possble geometrc transformatons are determned from the matched trangle pars snce the IFPs-based trangles undergo the same transformaton as the mage tself. The detaled steps are: 1. Calculate the scalng factor SF by reszng the probe trangle to the same sze as the target matched trangle. 2. Calculate the translaton factor TF by regsterng one of the vertces of the matched trangle par. 3. Calculate the rotaton factor RF by algnng the other two unregstered vertces of the matched trangle par. These factors form a 3-element tuple (SF, TF, RF) where SF measures the scalng rato up to a precson of 1/10, TF measures the translaton n pxel numbers, and RF measures the rotaton angle n an nteger degree. Snce an mage and the wthn trangles undergo exactly the same transformaton, we use the majorty of the dentcal 3-element tuples obtaned from all matched trangle pars to restore the probe mage. The same embeddng procedure s appled to the restored probe mage to obtan the watermark embedded DFT sequence FSubA for each potental embeddng submage. The blnd watermark retreval scheme s then appled to extract the bpolar watermark bt sequence W j, whch s compared wth the orgnal watermark bt sequence W j to determne the presence of the watermark. That s, the number of matched bts n a potental embeddng submage s compared wth a threshold to determne whether the watermark s present n the probe mage. Ths threshold s calculated based on the false-alarm probablty that may occur n watermark detecton. The Bernoull trals are used to model W j snce every watermark bt s an ndependent random varable. The probablty of a k-bt match between extracted and orgnal watermark bt sequences wth a length of n s calculated as: p n k k n k k = p ( 1 p) where p s the success probablty for the extracted bt to be matched wth the orgnal watermark bt. We further smplfy Eq. (13) by assumng p to be 1/2: (13)

12 40 X. Q and J. Q n 1 n! pk = (14) 2 k!( n k)! The false-alarm probablty for each embeddng submage s a cumulatve probablty of the cases that k T, where k and T respectvely represent the number of matchng bts and the threshold for each submage. It s computed as: n n 1 n! Pfalse alarm( ) =. (15) k = T 2 k!( n k )! Based on Eq. (15), the perfect match between the extracted and orgnal watermarks 5 n a sngle embeddng submage leads to a false alarm probablty of Ths s a low false alarm probablty so we can confdently clam the watermark exsts. In our system, we wll check the perfect match n any embeddng submage to ndcate the presence of the watermark. 5 Expermental Results To evaluate the performance of the proposed watermarkng scheme, we conducted experments on varous standard 8-bt grayscale mages and dfferent knds of attemptng attacks. We frst perform the watermark nvsblty test usng four bt gray-level mages. We then llustrate the effectveness of the proposed strong IFPs-based mage restoraton scheme, whch functons as a self-synchronzaton scheme to algn the possbly geometrcally dstorted watermarked mage wth the orgnal one. Next, we perform extensve comparsons wth three well desgned feature-based RST reslent watermarkng schemes proposed by Tang and Hang [19], Wang et al. [20], and Bas et al. [15]. Fnally, we summarze the performance of our proposed scheme under a varety of Strmark attacks on bt watermarked grayscale mages. 5.1 Watermark Invsblty Test We evaluate watermark nvsblty on four mages: Lena, Pepper, Arplane, and Baboon. These four mages correspond to several texture categores. For example, Baboon ncludes textured areas wth hgh frequency components; Lena and Arplane nclude large homogeneous areas whereas Lena has sharp edges; and Pepper falls n a low-textured category. The PSNRs of these four watermarked mages are 43.33, 44.06, 42.27, and 37.62, respectvely. These PSNR values are all greater than 35.00db, whch s the emprcal value for the mage wthout any percevable degradaton [29]. 5.2 Important Restoraton Test Image restoraton s an mportant step n the proposed watermarkng scheme. In general, we apply the Delaunay tessellaton on the strong IFPs to generate trangles, and use angle degrees to fnd the matched trangles between the orgnal and probe

13 A Desynchronzaton Reslent Watermarkng Scheme 41 mages. We further use these matched trangles to fnd the possble geometrc attacks. Table 1 lsts four mage texture dependent parameters and the number of strong IFPs determned by applyng our mage-texture-based mproved and robust Harrs corner detector on four mages wth dfferent textures. These four parameters are Rato (the factor for classfyng mage textures), Type (the texture decded by Eq. (1)), D (the dameter of the crcular wndow of the robust and mproved Harrs corner detector), and SNum (the number of embeddng submages determned by perceptual analyss). It clearly shows that dameter D s determned by the mage texture. That s, the more complcate the texture, the larger the dameter D. The value of SNum ndcates the dstrbuton of the perceptually hgh texture wthn an mage. These adaptve parameters are automatcally determned based on mage textures. They mprove the accuracy n fndng the mage-content-based strong IFPs and the robustness n resstng geometrc and common mage processng attacks on dfferent textured mages. We also observe that the number of IFPs s less than 35 for all the test mages wth dfferent textures. Ths observaton clearly demonstrates that our mproved and robust Harrs corner detector does regulate the number of IFPs. It also ndcates that the cost of savng IFPs for watermark synchronzaton s mnmal compared wth the cost of savng the host mage. Table 1 also lsts the ratos between the number of matched trangle pars for determnng the geometrc transformaton and the total number of matched trangle pars under four random geometrc attacks. All smulaton results yeld ratos of larger than 85%, whch ndcate a hgh accuracy n fndng the possble geometrc transformaton a probe mage may undergo. When comparng the results between the mages, t should be noted that the number of matched trangle pars s not lnearly related to the number of strong IFPs due to the senstvty of the IFPs to dfferent attacks. However, our mproved and robust Harrs corner detector generates relatvely strong IFPs to reduce the synchronzaton errors. In addton, two propertes of the Delaunay tessellaton always ensure that there are enough matched trangles, as ndcated by hgh ratos n Table 1, for restorng the probe mage. Table 1. Image adaptve parameters and ratos under dfferent attacks Images Images Robust Geometrc Attacks Adaptve Parameters IFPs Rato Type D SNum (a) (b) (c) (d) Lena Med /16 23/25 10/11 15/16 Baboon 0.01 Hgh /20 25/27 12/14 12/12 Pepper Low /22 17/18 13/15 16/17 Plane Med /18 24/26 10/10 15/ Comparson wth Feature-Based RST Robust Watermarkng Schemes We compare the proposed scheme wth three feature-based RST robust watermarkng schemes, namely Tang s scheme [19], Wang s scheme [20], and Bas s scheme [15] n Tables 2 through 4. Each gray cell ndcates that the correspondng method fals to detect the watermark under the correspondng dstorton. Table 2 summarzes the

14 42 X. Q and J. Q detecton results compared wth the schemes of Tang [19] and Wang [20] aganst common mage processng attacks. Table 3 summarzes the detecton results compared wth the schemes of Tang [19] and Wang [20] aganst desynchronzaton attacks. These two tables show the rato between the number of correctly detected watermarked embeddng regons and the number of orgnal embedded watermarked embeddng regons. Here, we use the term detecton rate to denote t. Smlarly, the detecton rate n Tang s scheme refers to the fracton of correctly detected watermark embeddng dsks and the detecton rate n Wang s scheme refers to the fracton of correctly detected watermark embeddng LCR (Local Characterstc Regons). That s, the submages n our scheme correspond to the dsks n Tang s scheme and the LCRs n Wang s scheme, respectvely. Table 2. Comparson of the detecton rates (.e., the fracton of correctly detected watermark embeddng regons) under common mage processng attacks. (1) Medan flter (3 3). (2) Shapenng (3 3). (3) Gaussan nose. (4) JPEG 70%. (5) JPEG 50%. (6) JPEG 30%. (7) Medan flter (3 3) + JPEG 90%. (8) Sharpenng (3 3) + JPEG 90%. Lena Baboon Pepper Attacks Our Wang s Tang s Our Wang s Tang s Our Wang s Tang s Method Method Method Method Method Method Method Method Method (1) (2) (3) (4) (5) (6) (7) (8) Table 2 clearly shows that our scheme and Wang s scheme successfully pass all the tests whle Tang s scheme fals medan flterng, JPEG compresson 30%, and medan flterng wth JPEG compresson 90%. Our scheme shows better stablty than Wang s scheme due to the hgher detecton ratos under all the attacks. Our method also yelds almost equal performance on all three mages due to the regulaton of the number of strong IFPs on mages wth dfferent textures whereas Tang s method performs better on hgh textured mages such as Baboon. In summary, the performance of our scheme s much more stable under dfferent attacks n the comparson wth Tang s scheme and Wang s scheme. One reason s that our relatvely strong IFPs are more stable than those found by the Mexcan hat detector and the scale nvarant Harrs-Laplace detector. These robust IFPs ensure more accurate synchronzaton between the probe and orgnal watermarked mages. Another reason s that the watermark s embedded n the md-frequences, whch are n postons that are unlkely changed by common mage processng attacks. Table 3 clearly shows that our scheme performs the best n all the desynchronzaton attacks except the large croppng and local random bendng attacks. Specfcally,

15 A Desynchronzaton Reslent Watermarkng Scheme 43 our scheme can successfully resst several attacks Tang s scheme faled to tackle, namely, random relatvely large rotatons, scalng ratos, and any combnaton of RST attacks. Our scheme can handle large scalng attacks, whch Wang s scheme faled to handle. These successes are manly due to the followng three reasons: 1) Our proposed robust and mproved Harrs corner detector fnds relatvely strong IFPs whch are more resstant to desynchronzaton attacks. 2) The strong IFPs-based Delaunay trangle matchng and mage restoraton technque ensures enough matched trangles for accurate self-synchronzaton under a varety of RST and aspect rato changng attacks, whle the local characterstc regon derved from the scale-space theory s not geometrcally nvarant space, as explaned n Wang s scheme. 3) The DFT doman tself s robust to translaton and moderate croppng so t can accommodate the croppng attacks and further compensate the slghtly naccurate IFPs-based geometrc correcton. However, our scheme s more vulnerable to the local random bendng attacks than both Tang s and Wang s schemes, due to the possble naccurate mage restoraton resulted from the shfts of the bendng IFPs or the shfts of the embeddng pxels n a lmted number (usually less than 9) of the embeddng submages. A large amount of embeddng dsks n Tang s and Wang s schemes make t more robust to local bendng attacks snce bendng may not affect all the embeddng dsks and LCRs. Our scheme s also more vulnerable to large croppng attacks snce the potental embeddng regons may be removed. Tang s and Wang s schemes may survve large croppng attacks as long as a few dsks and the LCRs contanng the IFPs are not cropped. Table 3. Comparson of the detecton rate (.e., the fracton of correctly detected watermark embeddng regons) under geometrc attacks. (1) Removed 8 rows and 16 columns. (2) Croppng 55%. (3) Rotaton 5º. (4) Rotaton 15º. (5) Rotaton 30º. (6) Translaton x-10 and y- 19. (7) Scalng 0.6. (8) Scalng 0.9. (9) Scalng 1.4. (10) Local random benng. (11) Croppng 10% and JPEG 70%. (12)Rotaon 5º + Scalng 0.9. (13) Translaton x-10 and y-10 + Rotaton 5º + Scalng 0.9. Lena Baboon Pepper Attacks Our Wang s Tang s Our Wang s Tang s Our Wang s Tang s Method Method Method Method Method Method Method Method Method (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

16 44 X. Q and J. Q Table 4. The comparson between the proposed method and Bas s method [15] under dfferent processng and geometrc dstorton attacks Lena Arplane Car Attacks Our Bas s Our Bas s Our Bas s Method Method Method Method Method Method No Attack 8 8 Medan Flterng 3 3 Gaussan Flterng Shearng x-1%, y-1% Shearng x-0%, y-5% Shearng x-5%, y-5% Rotaton 10º Scalng 90% Scalng 80% JPEG 80% JPEG 45% JPEG 30% Strmark General Attacks Table 4 compares the proposed scheme wth Bas s scheme [15], whch s a featurebased spatal doman method, n terms of the robustness aganst dfferent attacks such as medan flterng, Gaussan flterng, shearng, rotaton, scalng, JPEG compresson, and Strmark general attacks. All these tests are performed on mages of Lena, Arplane, and Car for a far comparson. The comparson results upon varous common mage processng attacks and geometrc dstortons are lsted sde by sde n Table 4. Snce Bas s scheme dd not record the detecton rato, we use a to ndcate the method successfully detects the watermark after the attack and a to ndcate the method fals to detect the watermark. As shown n Table 4, both methods successfully pass the small shearng, rotaton, scalng, and Strmark general attacks. However, our method has advantages on common mage processng tests such as 8 8 medan flterng and 30% JPEG compresson due to the followng reasons: 1) Our method embeds the watermark nto the md-frequences whch are unlkely to be changed by common mage processng attacks, whle Bas s method ntroduces an nterpolaton problem when dong the watermark trangle wrappng n detecton. 2) Our method embeds the watermark n the DFT doman, whle Bas s scheme s sutable for drectly addng watermarks nto the spatal doman due to rregular shape of the embeddng area. Ths makes the method vulnerable to mage processng dstortons. 5.4 Comprehensve Smulaton Results under Strmark Attacks We performed a varety of attacks on bt watermarked grayscale mages of sze usng Strmark 3.1. These mages are evenly dstrbuted wth hgh, medum, and low textures accordng to Eq. (1). That s, the database contans 35 mages for each texture level. The overall average PSNR value for these 105 watermarked mages s 41.73db. Fg. 6 demonstrates the smulaton results of 15 knds of common attacks on the 105 watermarked mages. The smulated attacks are lsted on x-axs

17 A Desynchronzaton Reslent Watermarkng Scheme 45 Average Detecton Rates Low Textured Images 0.1 Medum Textured Images Hgh Textured Images Attacks Fg. 6. The average successful detecton rates for three knds of textured mages under desynchronzaton attacks where all the numercally labeled attacks sequentally correspond to a category of dstortons ncludng no attacks, translaton, scalng, rotaton, croppng up to 5%, lnear geometrc transform, row and column removal wth a maxmum of 20 rows and columns removed, medan flterng, mean flterng, sharpenng, Gaussan flterng, hstogram equalzaton, and JPEG compressons wth qualty factors of 50%, 40%, and 30%. All the flterng operatons use the maxmum flter sze of 7 7. Each dstorton category (.e., numbers 2 to 12 on x-axs n Fg. 6) contans 3 random attacks. The y- axs summarzes the average detecton rates of all mages n each texture level under each dstorton category. Fg. 6 clearly demonstrates that our scheme acheves good robustness under both mage processng and geometrc dstortons and performs the worst for low and hgh textured mages under the lnear geometrc attacks. Specfcally, the average detecton rates for all smulated geometrc attacks are 94.89%, 89.75%, and 80.45% for medum, low, and hgh textured mages, respectvely. The average detecton rates for all smulated mage processng attacks are 100%, 100%, and 93.15% for medum, low, and hgh textured mages, respectvely. The average detecton rates for all smulated attacks are 97.45%, 94.88%, and 86.8% for medum, low, and hgh textured mages, respectvely. The overall average detecton rate for all mages under all smulated attacks s 93.04%. In summary, the all-around result of our proposed watermark scheme outperforms the peer feature-based schemes. It yelds postve detecton results for most mages wth low, medum, and hgh textures under dfferent desynchronzaton dstortons. It also works well on hghly textured mages due to the relatvely large number of strong IFPs for mage restoraton. Our proposed scheme acheves a good balance between nvsblty and robustness. Specfcally, the robust and mproved Harrs corner detector s capable of fndng the relatvely strong IFPs for dfferent textured mages. The Delaunay trangle matchng and mage restoraton scheme s able to effcently mnmze the synchronzaton errors and elmnate fake IFPs showed up n the hgh and extremely hgh textured mages n the matchng process. The spread spectrum

18 46 X. Q and J. Q embeddng and detecton makes our scheme more resstant to mage processng attacks. The perceptually hghly textured submage based embeddng scheme helps our system to survve some localzed mage attacks n Strmark. However, our scheme does not perform well on extremely low textured mages due to ts nsuffcent number of IFPs. It also fals the JPEG compresson wth a qualty factor of lower than 30% due to the mssng IFPs resulted from hgh compresson. 6 Conclusons In ths paper, we propose a novel and effectve content-based desynchronzaton reslent watermarkng scheme. The major contrbutons consst of: Robust and mproved Harrs corner detector: Ths detector s capable of fndng the relatvely strong IFPs n dfferent textured mages. These IFPs are more stable than the feature ponts extracted by Bas s, Tang s, and Wang s schemes due to the superor performance of the Harrs corner detector, the addtonal nose reducton, the regulaton of the densty of the IFPs based on the mage dmenson and texture, and the ntersecton of IFPs extracted from the pre-attacked mages. Consequently, they are more robust aganst desynchronzaton attacks. Perceptually hghly textured submage based watermark embeddng: These embeddng submages carry the same copy of the bpolar watermark bt sequence to mprove the robustness of transmtted watermark bts. They also ad the proposed watermark scheme n survvng some localzed mage attacks n Strmark. Spread-spectrum-based blnd watermark embeddng and retreval n the DFT doman: The spread spectrum scheme makes our scheme more resstant to common mage processng attacks. The DFT doman ensures more resstant to translaton and moderate croppng. The blnd retreval scheme does not requre the orgnal mage once the probe mage s algned wth the orgnal mage. Delaunay trangle matchng and mage restoraton: Ths scheme can effcently elmnate fake IFPs showed up n the hghly textured mages and accurately determne the possble transformaton a probe mage may undergo. The determned transformaton effectvely reduces the synchronzaton errors wthout ntroducng substantal nterpolaton errors as n Bas s, Tang s, and Wang s schemes, where the affne transform, nterpolaton, and the mage normalzaton are appled. The proposed method s robust aganst a wde varety of tests as ndcated n the expermental results. Partcularly, t s more robust aganst JPEG compresson and the combnaton of the geometrc dstortons wth large scalng ratos and rotatons than other feature-based watermarkng technques. It works successfully for mages wth low, medum, and hgh textures. It can be further mproved by developng a more relable feature extracton method under severe geometrc dstortons and a more effcent and accurate trangle matchng and mage restoraton method. The algorthm can be appled to color mages by embeddng watermark n the lumnance component of the color mage. In the real world, ths watermarkng technque can be appled to a lot of dfferent areas, such as photograph, audo, and vdeo.

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