Robust localized image watermarking based on invariant regions

Digital Signal Processing 22 (2012) 170–180

Contents lists available at SciVerse ScienceDirect

Digital Signal Processing www.elsevier.com/locate/dsp

Robust localized image watermarking based on invariant regions Yanwei Yu a,c , Hefei Ling b,∗ , Fuhao Zou b , Zhengding Lu b , Liyun Wang b a b c

School of Software Engineering, University of Science and Technology of China, Hefei 230027, China School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China Suzhou Institute for Advanced Study, University of Science and Technology of China, Suzhou 215123, China

a r t i c l e

i n f o

a b s t r a c t

Article history: Available online 10 September 2011

The robustness of the localized watermarking methods mainly depends on the robustness of the feature locating the watermark. Based on the mean luminance of the disk, a rotation and scale invariant feature extraction algorithm is proposed. A theoretical verification of the rotation and scale invariance of extracted feature points in the continuous image is further performed. The extracted feature points are used to construct rotation and scale invariant circular regions, where the watermark is embedded after affine normalization. Experimental results show that the constructed regions fit the watermarking applications much better than those in previous feature-based watermarking schemes from the aspect of robustness against common attacks including filtering, JPEG compression, cropping, rotation and scaling, and the proposed localized image watermarking scheme has better robustness than previous featurebased watermarking schemes against common signal process and geometrical attacks while maintaining imperceptibility. © 2011 Elsevier Inc. All rights reserved.

Keywords: Watermarking Geometrical attack Rotation and scale invariant feature Content-based synchronization

1. Introduction Digital watermarking has been an important technique to resolve copyright protection by embedding the copyright information into the digital product [1]. Although the research of digital watermarking has made a great progress, the geometric attack is still a threat to the watermarking applications. The geometric distortions desynchronize the watermark information while preserving the visual quality, and therefore they can disable most of previous robust image watermarking detectors. Moreover, watermark synchronization is more difficult to handle in the applications of the blind watermarking detection. The paper focuses on the robustness against geometric distortions in the image blind watermarking. Nowadays, the robustness research against geometric distortions in the image blind watermarking has been a hot. The existing robust image blind watermarking methods resilient to geometric distortions can be classified into three categories: (1) geometric recovery methods [2–5], (2) geometric invariant [6–15], (3) featurebased method [16–23]. In the first category, the parameters of geometrical distortions can be estimated, and thus the detected image is inversely geometrical transformed before the watermark detection. Typically, the parameters of geometrical distortions can be estimated by three ways, including exhaustive search [2], the use of a template [3], and inserting a periodic watermark pattern [4,5]. The computation of exhaustive search is large and its

*

Corresponding author. E-mail address: [email protected] (H. Ling).

1051-2004/$ – see front matter doi:10.1016/j.dsp.2011.09.005

© 2011

Elsevier Inc. All rights reserved.

applicability is limited because of the variety of geometric distortions. Moreover, the method of exhaustive search may increase the false alarm probability [24]. The template and periodic watermark pattern are easily removed [25] so that both methods are not practical. The geometric invariants, including Fourier–Mellin transformation domain [6–8], log-polar domain [9], generalized Radon transformation domain [10], ordinary moments [11–13] and Zernike moments [14,15], are utilized to embed the watermark and maintain synchronization under geometric transforms. In spite of the robustness against rotation and scaling attacks, the methods embedding the watermark into geometric invariant may typically be highly vulnerable against cropping attacks and locally-varying geometric transformations. The feature-based method is a contentbased localized watermarking scheme. It locates the watermark by using the stable feature points of the image, at each of which the watermark is embedded into the corresponding local regions independently [16]. Thus, the feature-based method can resist local geometric distortions involving cropping attacks so that it is a promising method to resolve the robustness against geometric distortions in the blind watermarking. Bas et al. [17] extracted feature points of the image by Harris detector and performed a Delaunay tessellation on the set of points. The watermark was then embedded inside each triangle of the tessellation. However, the Harris points were sensitive to scaling [26] so that the method is not robust against scaling. Tang and Hang [18] adopted a feature extraction method called Mexican Hat wavelet scale interaction. Image normalization was separately applied to unoverlapping image disks with center at the extracted feature points and the fixed radius. Two 32 × 32 blocks in each

Y. Yu et al. / Digital Signal Processing 22 (2012) 170–180

image disk were chosen for watermark embedding. Although the scheme experimentally shows the robustness against most attacks, it is vulnerable to scaling attacks because these attacks can result in the content changes of two blocks in the image disks with a fixed radius. Li and Guo [19] detected the Harris feature points from the scale normalized image and embed the watermark inside each cirque region with center at the locally most stable Harris points and fixed radius. The proposed scheme can resist global geometric distortions including rotation, scaling and moderate translation. However, the proposed method cannot resist cropping since scale normalization may be vulnerable to cropping in nature. In recent years, researchers turn to resynchronize the watermark by using the scale invariant feature based on the scale-space idea in the pattern recognition, such as scale invariant feature transform (shortly named SIFT) [20], Harris–Laplace [21]. In [20], the SIFT feature is used to generate the circular patches as the embedding units. The rectangular watermark is considered to be a polar-mapped watermark and inversely polar-mapped to assign embedding units before embedding. The watermark correlation detection is done by circular convolution. Rotation invariance of the watermark is achieved using the translation property of the polarmapped circular patches. In [21], Harris–Laplace method is used to detect the scale invariant feature points based on the scale selection at Harris corner points. At each feature point, the watermark is embedded after affine normalization according to the local characteristic scale. The characteristic scale is the scale at which the normalized scale-space representation of an image attains a maximum value, and the characteristic orientation is the angle of the principal axis of an image. The robustness of the localized watermarking methods mainly depends on the robustness of the feature locating the watermark. Nowadays, existing feature-based watermarking methods directly use the feature in the pattern recognition to synchronize the watermark. However, the requirement of the watermarking application is partially different from the pattern recognition field, so the requirements of feature in both circumstances are partially different. First, the types of attacks involved in both circumstances are not entirely the same, and thus the feature extracted for the purpose of pattern recognition may be sensitive to some malicious attacks in the watermarking application. Next, the local requirement of the feature in the pattern recognition field is much stricter than the watermarking application because the feature in the watermarking application is used to locate the local region, which should be large enough to embed/detect the watermark. Finally, the feature in the watermarking application requires having much higher accuracy of repeatability than that in the pattern recognition field. In the pattern recognition field, the feature is considered to be robust if the overlap error between the regions in the reference image and the regions in the distorted image located by the feature is smaller than the threshold (typically 40% [27]). In the watermarking application, the feature is considered to be robust if the shift between the predicted region and computed region located by the feature is smaller than the threshold. For example, the circularly symmetric watermark shows vulnerability to geometric distortions more than ±2 pixels translation and ±5% scaling by experiment. Thus, the feature in the pattern recognition field is not necessary to fit the watermarking application. It is urgent to develop a feature extraction method fit for the watermarking application. Based on the mean luminance of the disk, a rotation and scale invariant feature (briefly named DRSIF) extraction algorithm used for the watermarking applications is proposed in this paper. Moreover, a theoretical verification of the rotation and scale invariance of DRSIF points in the continuous image is performed. A complete localized image watermarking scheme is further proposed based on invariant regions constructed by using DRSIF. Centered at each

171

point of the image, a series of concentric rings are generated when the ratio of the outer radius to the inner radius of each ring is fixed and the inner radius of the rings comes from a discrete geometric progression. For each ring, the absolute difference between the mean luminance of the inner ring and the mean luminance of the outer ring is computed. For the observed point, the maximum of absolute mean luminance difference sequence is taken as its response value, and the inner radius of the ring which attains the maximum of absolute mean luminance difference sequence is taken as its characteristic radius. Finally, the points whose response value attains the local maximum are selected as DRSIF points. At each DRSIF point, a rotation and scale invariant circular region is constructed according to its characteristic radius and orientation and used as the watermark embedding region, where the watermark is embedded after affine normalization. The characteristic orientation can be determined by the moment of region. In order to rapidly locate the watermark in the watermark detection process, a partitioning strategy is proposed. Through experiments, the robustness of the watermark embedding regions and the performances of proposed localized image watermarking scheme are verified respectively. Experimental results show that the regions constructed based on DRSIF fit the watermarking applications much better than those in other feature-based watermarking schemes, and the proposed localized image watermarking scheme outperforms other feature-based watermarking schemes. This paper is organized as follows. Section 2 introduces the DRSIF point involving a theoretical verification of its rotation and scale invariance, and its extraction algorithm. Section 3 describes how to construct the watermark embedding/detection regions respectively. Section 4 describes the proposed localized watermarking scheme. Section 5 evaluates the performance of the embedding regions and proposed localized image watermarking scheme in comparison with other literature. Section 6 concludes. 2. DRSIF extraction algorithm 2.1. Basic principle Given an image I , its rotated and scaled version is denoted as ˜I. Assume the point located at position (x, y ) in the image I and the point at (˜x, y˜ ) in the image ˜I are the same. Then the relationship can be written as follows:

⎧ ⎪ ⎨ I x, y (ρ , θ) = ˜I x˜ , y˜ (ρ˜ , θ˜ ) ρ˜ = s · ρ ⎪ ⎩˜ θ =θ +ϕ

(1)

where the rotation and scaling parameters are ϕ and s respectively. Let I x, y (ρ , θ) denote the luminance of the image I at polar coordinate point (ρ , θ), which is corresponding to the Cartesian ˜ denote the luminance of the coordinate point (x, y ). Let ˜I x˜ , y˜ (ρ˜ , θ)

image ˜I. In polar coordinates, the point (ρ˜ , θ˜ ) of image ˜I is distorted version of the point (ρ , θ). For a circular ring CR(x, y ; r ; t ) with center (x, y ), inner radius r and outer radius r · t (t > 1) in the image I , there exists the same ring CR(˜x, y˜ ; s · r ; t ) with center at (˜x, y˜ ), inner radius s · r and outer radius s · r · t (t > 1) in the transformed image ˜I , where the point (˜x, y˜ ) of image ˜I is transformed version of the point (x, y ) of image I . For the ring CR(x, y ; r ; t ) in the image I , the absolute mean luminance difference MD(x, y ; r ; t ) is computed as follows:





MD(x, y ; r ; t ) =  M (x, y ; r · t ) − M (x, y ; r )

(2)

where M (x, y ; r ) denotes the mean luminance of disk D (x, y ; r ) with center (x, y ) and radius r in the image I ,

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M (x, y ; r ) =

 r2π

1

F (˜x, y˜ ) I x, y (ρ , θ)ρ dθ dρ

π r2

(3)

0 0

For the point at (x, y ) in the image I of size M × N, its response value F (x, y ) is defined as the maximum of the absolute mean luminance difference of the ring with center at (x, y ) and the fixed ratio t of the outer radius to the inner radius,

F (x, y )

 = max MD(x, y ; r ; t )  0 < r < min{ M − y , y , N − x, x} 

(4)

and its characteristic radius R (x, y ) is defined as the minimum of the inner radius of the ring with center at (x, y ) at which the response value is attained,





R (x, y ) = min 0 < r < min{ M − y , y , N − x, x}  MD(x, y ; r ; t )

= F (x, y )

(5)

Then, the points whose response value attains the local maximum in the circular neighborhood with radius 1 are selected as DRSIF points. Theorem 1. After an image is rotated and scaled, the absolute difference between the mean luminance of the inner and the outer of the ring in the transformed image is equal to that of the same ring in the original image. Proof. For a disk D (x, y ; r ) with center (x, y ) and radius r in the D (˜x, y˜ ; s · r ) with center at image I , there exists the same disk

(˜x, y˜ ) and radius s · r in the transformed image ˜I. From Eqs. (1)

(˜x, y˜ ; s · r ) of the disk

D (˜x, y˜ ; s · r ) and (3), the mean luminance M in the transformed image ˜I can be computed as follows:

(˜x, y˜ ; s · r ) = M

=

1

π (s · r )2 1

π (s

· r )2

s·r 2π 0

˜I x˜ , y˜ (ρ˜ , θ˜ )ρ˜ dθ˜ dρ˜

0

 r2π





I x, y (ρ , θ) s2 · ρ dθ dρ 0 0

= M ( xu , y u ; r )

(6)

(˜x, y˜ ; s · r ; t ) Further, the absolute mean luminance difference MD

(˜x, y˜ ; s · r ; t ) in the transformed image ˜I can be comof the ring CR puted as follows:

= F (x, y )

(8)

Eq. (8) shows that the response value is rotation and scale invariant. From the definition of the response value and characteristic radius, Theorem 1 and Eq. (8), it can be derived that,



x˜ , y˜ ;

MD R (˜x, y˜ ); t



=

F (˜x, y˜ ) = F (x, y )  

x˜ , y˜ ; s · R (x, y ); t = MD x, y ; R (x, y ); t = MD ⇒

R (˜x, y˜ )  s · R (x, y )

(9)

In the same way, it can be derived that,

R (x, y ) 

R (˜x, y˜ )/s

(10)

From the above two inequalities, it can be obviously derived that

R (˜x, y˜ ) = s · R (x, y ). In other words, the characteristic radius is rotation and scale invariant. The repeatability rate R ε of points is introduced to measure the stability of DRSIF points [28],

Rε =

C (I1, I2) min(m1 , m2 )

× 100%

(11)

where C ( I 1 , I 2 ) denotes the number of point-to-point correspondences in the original image and distorted image, and m1 and m2 denote the number of feature points in the original image and distorted image. The larger the repeatability rate, the higher the stability of the feature points. Because the response value is rotation and scale invariant, in the transformed image after rotation and larger scaling, the points corresponding to the DRSIF points in the original image are still DRSIF points. From Eq. (11), it is easily concluded that the repeatability rate is 100% after rotation and scaling. Namely, DRSIF points are rotation and scale invariant. 2.2. DRSIF points extraction algorithm

 

(˜x, y˜ ; s · r ; t ) = 

(˜x, y˜ ; s · r ) MD M (˜x, y˜ ; s · r · t ) − M   =  M (x, y ; r · t ) − M (x, y ; r ) = MD(x, y ; r ; t )

 

(˜x, y˜ ; r˜; t )  0 < r˜ < min{ M − y , y , N − x, x} · s/t = max MD   = max MD(x, y ; r˜/s; t )  0 < r˜ < min{ M − y , y , N − x, x} · s/t   = max MD(x, y ; r ; t )  0 < r < min{ M − y , y , N − x, x}/t

(7)

Inference 1. The response value and characteristic radius of the same points in an image and its geometrically transformed image are rotation and scale invariant. Proof. Centered at a point (x, y ) in the continuous image I of size M × N, a series of concentric rings {CR(x, y ; r ; t )} can be generated when the ratio of the outer radius to the inner radius of each ring is fixed, where 0 < r < min{ M − y , y , N − x, x}/t. Assume the point (x, y ) in the image I and the point (˜x, y˜ ) in the rotated and scaled image ˜I are the same. Therefore, in the transformed image ˜I, there exists the same series of concentric rings {CR(˜x, y˜ ; r˜ ; t )}, where 0 < r˜ < min{ M − y , y , N − x, x} · s/t. Assume the response value and characteristic radius at the point (x, y ) in the image I exist. From the definition of the reF (˜x, y˜ ) of the sponse value and Theorem 1, the response value

transformed point (˜x, y˜ ) of image ˜I can be computed as follows:

Given an image I , its transformed version scaled by s is denoted as ˜I. For the two rings with the fixed ratio t of the outer radius to the inner radius in the image I , their inner radiuses are rm and rm+1 respectively. In the transformed image ˜I, there exist the same two rings with the fixed ratio t of the outer radius to the inner radius, of which the inner radiuses are rn and rn+1 respectively. Then,

rn = s · rm ,

r n +1 = s · r m +1

(12)

Further,

r m +1 rm

=

r n +1 rn

(13)

Eq. (13) shows that the ratio of the inner radius of the two neighbor rings is a fixed constant. Thus, let the inner radius r i of the rings come from a discrete geometric progression with common ratio k. Namely, r i = r0 · ki −1 , r0 > 0, k > 1, i ∈ N + . Centered at each point of the image, a series of concentric rings is generated when the ratio of the outer radius to the inner radius of each ring is fixed and the inner radius of the rings comes from

Y. Yu et al. / Digital Signal Processing 22 (2012) 170–180

distorted image, in order to guarantee the DRSIF reference points can be redetected in the distorted image, it should be satisfied,

Table 1 The DRSIF extraction algorithm. For each point located at (x, y ) in the image, do: • Centered at (x, y ), generate a series of concentric rings {CR(x, y ; ri ; t ) | i ∈ N + }, where the inner radius r i = r0 · ki −1 , r0 > 0, i ∈ N + and t is the fixed ratio of the outer radius to the inner radius of each ring. • Compute the absolute mean luminance difference of each ring in the series of ring {CR(x, y ; r i ; t ) | i ∈ N + } and generate a series of absolute mean luminance difference {MD(x, y ; r i ; t ) | i ∈ N + }. • Compute its response value and characteristic radius, and then judge whether it is a DRSIF point.

a discrete geometric progression. For each ring, the absolute difference between the mean luminance of the inner ring and the mean luminance of the outer ring is computed. For the observed point, the maximum of absolute mean luminance difference sequence is taken as its response value and the minimum inner radius of the ring which attains the maximum of absolute mean luminance difference sequence is taken as its characteristic radius. Finally, the points whose response value attains the local maximum in the 3 × 3 neighborhood are selected as DRSIF points. The DRSIF extraction algorithm is described in Table 1. In order to simplify the analysis of the scale invariance when the inner radius of ring comes from a discrete geometric progression with common ratio k, we will not consider the resampling error introduced by geometric distortions for the moment. Let I and ˜I denote an image and its scaled version with the parameter s respectively. For a circular ring CR(x, y ; rl ; t ) with center at (x, y ), inner radius rl and outer radius rl · t (t > 1) in the image I ,

(s · x, s · y ; rm ; t ) with center there exists the most similar ring CR (s · x, s · y ), inner radius rm and outer radius rm · t (t > 1) in the transformed image ˜I, where the point at (x, y ) in the image I and the point at (s · x, s · y ) in the image ˜I are the same. Then,

 |rm − s · rl |  min |rm+1 − s · rl |, |rm−1 − s · rl |

(14)

The relative error of the inner radiuses of these two rings having similar content is defined as follows:

εr (k, s) =

|rm − s · rl | s · rl

(15)

From Eqs. (14) and (15), further,

|rm − s · rl | εr (k, s) = s · rl s · rl − s · rl /k  2s · rl  (1 − 1/k)/2

173



s · ra  ra  rb  s · rb

(17)

ra  s · r u  s · r v  rb

The scale parameter s is unknown. Assume m  s  n. Then it is derived that,



n · ra  ra  rb  m · rb

(18)

ra /m  r u  r v  rb /n

Consider 0.5  s  2. Namely, m = 0.5 and n = 2. If the inner radius range is [ra , rb ] during the DRSIF detection in the original image, the DRSIF points with the characteristic radius in the range from 4ra to rb /4 are selected as the reference point to embed the watermark and the inner radius range is [2ra , rb /2] during the DRSIF detection in the distorted image so that the DRSIF points as the reference to embed the watermark are theoretically necessary to be redetected in the distorted image. In the real digital image application, the discrete radius, the resampling error introduced by geometrical distortions, and the noise introduced by signal process inevitably impact the stability of DRSIF points. Thus, the DRSIF points used to locate the watermark should be firstly selected. Because of the instability of the regions near the border of the image, we should avoid the DRSIF points whose distance to the border of an image is smaller than rb /2. In addition, in order to improve the robustness against rotation, the DRSIF points whose response value attains the maximum in its circular neighborhood are selected. Concretely, the DRSIF points satisfying the following conditions are selected as the reference points to embed watermark:

F (x, y ) > F (xa , ya ) ∀(xa , ya ) ∈ A (x, y )

(19)

where F (x, y ) and A (x, y ) denote the response value and circular neighborhood of the point at (x, y ) respectively. And, the radius of the neighborhood A (x, y ) depends on the characteristic radius R (x, y ) of point at (x, y ). Namely,







2

A (x, y ) = (xa , ya )  (xa − x)2 + ( ya − y )2  m · R (x, y )

(20)

where m is set at 1/8 to guarantee the radius of A (x, y ) is above 1 due to considering the range of R (x, y ) is [8, 48] during DRSIF detection in the distorted image in the later experiment section. At the point (xi , y i ), the circular region is constructed as follows:

(16)

Given the two rings with the fixed ratio of the outer radius to the inner radius and the same center in the digital image, they are considered same if the relative error of inner radiuses doesn’t exceed 0.05. Thus, when the resampling error introduced by geometric distortions is not considered for the moment, we consider the characteristic radius is still scale invariant if common ratio k of the geometric progression is smaller than 10/9 that can be derived from Eq. (16). 3. Invariant region based on DRSIF Assume the inner radius range of concentric rings is [ra , rb ] during the DRSIF detection in the original image and the DRSIF points with the characteristic radius in the range from r u to r v are selected as the reference point to embed the watermark. Assume the inner radius range is [ra , rb ] during the DRSIF detection in the distorted image. After the original image is scaled by s to obtain the

(x − xi )2 + ( y − y i )2 = (σ · si )2

(21)

where σ is used to control the size of the region and si is the characteristic radius at the point (xi , y i ). In order not to reduce the watermark correlation value, the watermarked regions should not be overlapped. The rule that the more robust one of the overlapped regions survives is adopted in this paper. Assume the larger the response value of the region, the stronger the robustness of the region. When the two regions overlap, the one with larger response value survives, where the response value of a region is the response value of the point at its center. Fig. 1 shows the construction process of watermark embedding regions based on DRSIF points for Lena image of size 512 × 512. First, the DRSIF points with the inner radius in range [ra , rb ] are selected as shown in Fig. 1(a). Then, the DRSIF points with the characteristic radius in the range [4ra , rb /4] are selected as shown in Fig. 1(b). And then, after the DRSIF points near to the border of the image are discarded and the DRSIF points whose response value attains the maximum in its circular neighborhood are selected to construct the candidate regions as shown in Fig. 1(c).

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Y. Yu et al. / Digital Signal Processing 22 (2012) 170–180

Fig. 1. (a) DRSIF points with the inner radius in range [ra , rb ], (b) DRSIF points with the characteristic radius in the range [4ra , rb /4], (c) candidate regions, (d) watermark embedding regions.

Finally, according to the surviving rule, the unoverlapping regions fit to embed the watermark are selected as the final watermark embedding regions as shown in Fig. 1(d). Those regions whose entropy values are below 6 have less texture by experiment, and are considered to be unfit to embed watermark to keep watermark imperceptibility. 4. Proposed watermarking scheme 4.1. Watermark embedding

in spatial space. For the region f i with center at xoi and radius R i , the watermark embedding process is mathematically described as below:





x p y q I (x, y ) dx dy

m p ,q =

(22)

Γ

and its central moments



μ p,q can be defined as:

(x − x¯ ) p ( y − y¯ )q I (x, y ) dx dy

μ p,q =

(23)

Γ

where x¯ =

m 1, 0 , m0,0

y¯ =

m0,1 . m0,0

Then, define the characteristic orientation θci as follows:

⎧ μ +μ − arctan μ30,,30 +μ12,,21 , ⎪ ⎪ ⎨ θci = if −(μ3,0 + μ1,2 ) sin θci + (μ0,3 + μ2,1 ) cos θci  0 ⎪ ⎪ ⎩ π − arctan μ3,0 +μ1,2 , else μ0,3 +μ2,1

(24) A binary zero-mean pseudorandom sequence of length L is generated by a secure key and modulated to a circular watermark template W with radius M. For each watermark embedding region f i , the same circular watermark template is embedded after affine normalization according to its radius R i and characteristic orientation θci . In order to maintain perceptual transparency after watermarking, the noise visibility function (NVF) [29] is introduced. The watermark is adaptively embedded by an additive way





T

(25)

where α and β denote the watermark strength, W denotes the circular watermark template, and f i denotes the watermarked region. Typically, β = 3 [29] and α is adjusted to keep the PSNR and local mean PSNR both above 36. The geometrical transformation matrix H R ,θ i , i

As described in Section 3, based on DRSIF points extracted in the original image, the scale invariant watermark embedding regions are constructed. The characteristic orientation can be determined by the moment of region in order to obtain the resilience against rotation. At each watermark embedding region, the same watermark template is embedded after affine normalization according to its characteristic radius and orientation. The estimated angle in the image normalization technique is used as characteristic orientation to reflect the rotation parameter of suffered distortions. The details of the image normalization process can be found in [29]. Here, we only briefly describe its computational steps. The parameters below are computed once for each image disk. Given a region f i in an image I , f i = { I (x, y ) | (x, y ) ∈ Γ }, where Γ is the range of the region, its original moments m p ,q can be defined as:



f i = f i + (1 − NVF ) · α + NVF · β · W H R ,θ i x − xoi i c

c



cos θci M H R ,θ i = · i c Ri sin θci

− sin θci cos θci



(26)

where M is the radius of the circular watermark template. In all, the watermark embedding process is summed as below: Step 1. Construct the watermark embedding regions. Step 2. Embed the watermark into all the watermark embedding regions. Concretely, for each region, perform: • Compute the characteristic orientation. • Geometrically normalize the circular watermark template. • Embed the normalized watermark. 4.2. Watermark detection The watermark detection process can be deemed as the inverse process of the watermark embedding. Firstly, the watermark detection regions can be constructed based on DRSIF points. Then, at each watermark detection region, the watermark detection is blindly done. Theoretically, the construction of the watermark detection regions is the same as that of the watermark embedding regions. However, the image content may be slightly altered by the embedded watermark and the suffered distortions so that the extracted feature points in the distorted image may change slightly, and some points may even disappear. Thus, it is difficult to reconstruct the watermarked regions on the detected image. Fortunately, because of the redundancy between image pixels, the watermark can still be correctly detected when the deviation amount of the watermark detection region is not too large. It is natural that the watermark detection should be performed on all constructed regions based on DRSIF points in the detected image. However, it is necessary to result in a large computation price. Thus, the key problem is to improve the probability to hit the watermark embedding regions during the construction of the watermark detection regions. To resist scaling, the radius range of the candidate watermark detection regions is enlarged in the detected image. Detailed explanations can be seen in Section 3. Thus, the radius range of the candidate watermark detection regions is only a subzone of the radius range of the watermark embedding regions. To explore the

Y. Yu et al. / Digital Signal Processing 22 (2012) 170–180

real radius range of the watermark embedding regions, we should avoid the converged radius range during the watermark detection. Because of the unoverlapping and the robustness of the watermark embedding regions, we propose a partitioning strategy, which partitions the detected image into a series of watermark detection candidate regions according to their position and radius. Assume the radius range of the candidate watermark detection regions is [r s , rt ]. According to the space position, the detected image is first partitioned into four parts by matrix model. For each of four parts, it is further partitioned into three parts according to the radius, including the range [r s , 2r s ), the range [2r s , rt /2] and the range (rt /2, rt ]. In sum, the detected image is partitioned into 12 parts. From 12 parts, the candidate watermark detection region with the largest response value and larger entropy ( 5.5 by experiment) is selected in turn until a region is found to have been watermarked. If a watermarked region is newly found, all regions overlapping the watermarked region are deleted from the candidate watermark detection regions and the radius range of the candidate watermark detection regions is reduced. The partitioning strategy is then performed on the new set of the candidate watermark detection regions to locate the next watermarked regions. The above process is repeated until N ( N = 50) regions are detected. Thus, the watermark detection process can be considered as a repeated selection-detection process. Since the rotation transform is lossy, we do not directly compute the original watermark template and the estimated watermark template in the geometrically normalized watermark detection region. For each of scale normalized watermark detection region, the watermark template is estimated by using the Wiener filtering. Let W d denote the estimated watermark template for a 1 o T region with center at xoi and radius R i , W d = D ( H − R i ( x − xi ) ) where D is used to estimate the watermark by using the Wiener filtering. After the original watermark template is rotated according to the characteristic orientation, we compute the normalized correlation value between the estimated watermark template W d and the rotated watermark template W  as follows:





Corr W , W  = √

W  · Wd

( W  · W  )( W d · W d )

175

the optimal combined parameters including the inner radius range [ra , rb ] in the original image, the common ratio of the inner radius of two neighbor concentric rings k and the fixed ratio of the outer radius to the inner radius of each ring t are very important since they determine the robustness of the detected DRSIF points. If ra is too small, the DRSIF points are not robust enough. Otherwise, the locality of DRSIF points is weak and computation complexity has a sharp increase. rb mainly relies on the size of the image and computation complexity. By experiment, we set the inner radius range [ra , rb ] to be [4, 96] during the DRSIF detection in the original image, and thus it can be derived that those DRSIF points with the characteristic radius in the range from 16 to 24 are selected as the reference to embed the watermark and the inner radius range is [8, 48] during the DRSIF detection in the distorted image according to Section 3. To determine k and t, we compute the mean repeatability rate of the 150 most robust DRSIF points in 8 test images under different combined parameters and various attacks, and choose the optimal combined parameters which attain the maximum of the mean repeatability rate under various attacks. We set k = 1.03 and t = 1.2 by experiment. Although these parameters are set by experiment, they are independent of the choice of test image set. Considering size of test images and characteristic radius, we set the magnification factor controlling the radius of the watermark embedding/detection region σ = 2.5. 5.1. Robustness of the watermark embedding regions Let T denote the suffered distortions for test images with the scaling parameter s. Let R ori (x, y ) denote the radius of the watermark embedding region centered at (x, y ) from test images. Let R pre (x, y ) and R dis (x, y ) denote the predicted radius and computed radius of the watermark embedding region centered at (x, y ) from distorted test images. Assume the point at (x, y ) in the test image and the point (˜x, y˜ ) in the distorted test image are the same. Then the relationship exists as below:

(˜x, y˜ ) = T (x, y ) R pre (˜x, y˜ ) = s · R ori (˜x, y˜ )

(27)

where W  = W ( H θ i (x − xoi ) T ). c If the normalized correlation value exceeds the watermark detection threshold, the region is claimed to have been watermarked. An image is claimed to have been watermarked if at least μ regions are found watermarked. The watermark detection threshold differs with different μ. How to determine the watermark detection threshold by the analysis of false alarm will be elaborately discussed in Section 5.2. The watermark detection process can be summed as below: Step 1. Construct the candidate watermark detection regions. Step 2. Select a watermark detection region out of the candidate watermark detection regions as the current region according to the partitioning strategy and discard the region from the candidate set. Step 3. Detect the watermark on the current region and update the set of the candidate watermark detection regions. Step 4. Repeat Steps 2–3, until the image is claimed to be watermarked or N regions have been detected. 5. Experimental results We took two kinds of test to verify the robustness of the watermark embedding regions and the performance of proposed watermarking scheme respectively. In whole experiments, the choice of

(28)

To assess the robustness of the watermark embedding regions based on DRSIF points, the repeatability rate of regions is introduced. The repeatability rate of the watermark embedding regions R f p indicates the ratio of N p to N total , where N p and N total are the number of the hit watermark embedding regions during the construction of the watermark detection regions and the number of the watermark embedding regions respectively. A watermark embedding region with center at (x, y ) and radius R ori (x, y ) is claimed hit if there is at least one watermark detection region whose deviation from the predicted region does not exceed the amount of ±2 pixels of the location and ±0.05 of the characteristic radius. The larger the repeatability rate R f p of the watermark embedding regions, the higher the stability of the watermark embedding regions. The repeatability rate of the watermark embedding regions R f p can be computed as follows:

R fp =



Np N total



=

#{(x, y ) | C 1 ∩ C 2 } N total



C 1 = dist (˜x, y˜ ), T (x, y )  2



C2 =



| R dis (˜x, y˜ ) − s · R ori (x, y )|  0.05 s · R ori (x, y )

 (29)

where #{·} denotes the size of the set, and dist{ A , B } indicates the distance between point A and point B. In the experiment, we selected the standard images with a size of 512 × 512 from USC-SIPI Image Database, including Airplane, Couple, Fishingboat, Lena, Peppers, Watch, Bridge, and Baboon, as

176

Y. Yu et al. / Digital Signal Processing 22 (2012) 170–180

Fig. 2. Test images: (a) Airplane; (b) Couple; (c) Fishingboat; (d) Lena; (e) Peppers; (f) Watch; (g) Bridge; (h) Baboon. Table 2 Numbers of regions for images. Method

Airplane

Bridge

Couple

Watch

Fishingboat

Baboon

Peppers

Lena

Average number

DRSIF Harris–Laplace SIFT

8 19 12

13 21 18

14 14 12

14 19 15

16 16 17

13 12 17

13 19 20

13 13 15

13 16.625 15.75

test images. The chosen set of test images is shown in Fig. 2. Among them, Bridge and Baboon are highly-textured images. As described in Section 3, the watermark embedding regions based on DRSIF points are constructed for test images. To verify the robustness of the watermark embedding region, we attacked the test images by using Stirmark 3.1, including common signal process and geometrical attacks, such as median filter, sharpening filter, Gaussian filter, JPEG compression, cropping, rotation, scaling and so on. For each test image, the numbers of the watermark embedding region based on DRSIF, Harris–Laplace, SIFT are shown in Table 2. Under each attack, the average repeatability rate of the watermark embedding regions for all test images are computed and further compared with that based on SIFT [20] and Harris– Laplace [21] as shown in Table 3. From the above two tables, it can be found that, the watermark embedding regions based on DRSIF are more robust than those based on SIFT and Harris–Laplace against geometric attacks, and slightly worse than those based on Harris–Laplace against some signal processing attacks. However, we can improve the robustness against signal processing attacks by increasing the watermark embedding strength. 5.2. Performance of proposed watermarking scheme Four standard images with a size of 512 × 512 from USC-SIPI Image Database, including Airplane, Lena, Peppers, Baboon, are chosen as test images in this experiment as shown in Fig. 2. Among them, the image Baboon is a highly-textured image. In the experiment, the watermark capability is set to be 1024 bits which is the same as that in [21] and can satisfy the payload requirement of most copyright protection applications. A 1024-length watermark sequence (L = 1024) is used and the radius of the watermark template is 37 (M = 37). In order to compare with the method in [21] conveniently, the local search process is similarly used during the

Table 3 Average repeatability rate of regions after various attacks. Attacks

DRSIF (%)

Harris–Laplace (%)

SIFT (%)

Median filter 2 × 2 Median filter 3 × 3 Median filter 4 × 4 Sharpening filter 3 × 3 FMLR Gaussian filter 3 × 3 JPEG (Q = 40%) JPEG (Q = 50%) JPEG (Q = 60%) JPEG (Q = 70%) JPEG (Q = 80%) JPEG (Q = 90%) Cropping 5% off Cropping 10% off Cropping 15% off Cropping 20% off Cropping 25% off Rotation 0.25◦ Rotation 0.50◦ Rotation 1◦ Rotation 5◦ Rotation 10◦ Rotation 30◦ Scaling 50% Scaling 75% Scaling 90% Scaling 110% Scaling 130% Scaling 150% Scaling 200%

86.916 86.693 37.526 78.743 74.897 88.479 78.383 90.153 88.23 90.264 93.656 95.579 99.219 93.905 76.794 59.461 52.112 93.012 93.724 93.012 95.579 77.483 51.863 69.806 83.207 94.797 94.866 99.107 99.107 89.123

82.117 91.087 60.148 88.209 93.413 98.438 100 98.958 97.284 97.284 98.177 100 72.286 59.12 58.898 54.229 52.713 81.454 71.295 71.404 67.786 58.343 43.933 25.173 24.893 21.37 79.172 42.981 46.66 32.653

85.351 65.633 18.076 35.127 67.075 87.377 90.821 93.321 96.765 97.5 97.708 98.958 83.905 68.243 58.554 54.179 46.904 91.181 90.903 88.182 72.937 60.829 46.168 18.828 53.987 71.895 80.768 62.859 48.987 28.73

watermark detection process in the experiment. The content of distorted image change slightly so that the feature points of the image may slightly shift, and thus the location, characteristic orientation and radius of region may have a slight deviation. Thus,

Y. Yu et al. / Digital Signal Processing 22 (2012) 170–180

we search ±1 pixel of location in x or y direction, ±1.5◦ of characteristic orientation, and ±0.4 of characteristic radius. Then local search regions amount to 45 (five in x and y direction, three in angle and three in radius) for each watermark detection region. For each watermark detection region, the maximum normalized correlation value in its local search is used its final normalized correlation value. 5.2.1. False alarm analysis The watermark detection threshold can be determined by the probability of the false alarm P FA and the probability of the false rejection P FR , where P FA is the probability to declare an unwatermarked image as watermarked and P FR is the probability to declare a watermarked image as unwatermarked. The higher the watermark detection threshold, the lower the probability of the false alarm P FA and the higher the probability of the false rejection P FR . Thus, there is a tradeoff between the two probabilities in selecting the detection threshold. However, it is difficult to directly analyze the probability of the false rejection P FR since there are various kinds of unknown attacks. Thus, we select a threshold minimizing P FR with a fixed P FA as the detection threshold by the Neyman–Pearson criterion in hypothesis testing [30]. Assume that the watermark independent with the image has zero mean and unit variance. The mean C¯ and the standard deviation σC of the normalized correlation value [1] for unwatermarked local image regions are given by

C¯ = 0,

σC = √

(30)

L

where L denotes the length of the watermark. By the Gaussian assumption of the normalized correlation value, the probability of the false alarm in the local image region P FA-reg is given as follows:

∞  P FA-reg =



L 2π

exp −

x2 L



1

dx =

2

2

√ erfc

LThcorr

Thcorr

√

2

 (31)

where Thcorr denotes the threshold of watermark detection. Assume a local searching process involves at most V correlation computation. Then Eq. (31) can be rewritten:



∞ 

P FA-reg = 1 − 1 −



L 2π

Thcorr

1

= 1 − 1 − erfc 2

√

 2  V x L exp − dx 2

LThcorr

√

 V

2

(32)

An image is claimed watermarked if at least μ local regions are found to have been watermarked. Then, the probability of the false alarm for an image P FA can be computed as below:

P FA =

N    N i =μ

i

Table 4 Correlation detection threshold Thcorr (μ) for P FA with settings L = 1024, V = 45, N = 50. P FA = 10−4 P FA = 10−5 P FA = 10−6

i N −i P FA -reg (1 − P FA-reg )

(33)

where N denotes the number of the regions. From the above derived process, it can be found that the false alarm probability for an image P FA depends on not only the correlation detection threshold Thcorr (μ), but also L, V , N and μ. Set L = 1024, V = 45, N = 50. The correlation detection thresholds are denoted as Thcorr (1), Thcorr (2), and Thcorr (3) respectively when μ = 1, 2, 3. The watermark detection thresholds for different false alarm probability of the image P FA are shown in Table 4.

Thcorr (1)

Thcorr (2)

Thcorr (3)

0.1687 0.1814 0.1934

0.1377 0.1455 0.1529

0.1246 0.1304 0.1359

Table 5 Watermark embedding results. Image

Number of the watermark embedding regions

PSNR (dB)

LPSNR (dB)

Airplane Baboon Lena Peppers

8 13 13 13

41.668 35.159 39.927 39.112

36.173 31.817 36.471 36.103

5.2.2. Assessment of perceptual quality The perceptual quality of watermarked image can be assessed from two aspects, including global distortions and local distortions. The global distortions can be measured by PSNR between the watermarked image and the original image,

 PSNR = 10 × log10 MSE =

1

177

2552 MSE

M N  

1 M×N





2

I (x, y ) − I w (x, y )

(34)

x=1 y =1

where I (x, y ) and I w (x, y ) denote the original image and the watermarked image of size M × N respectively. Generally, the watermark is considered globally imperceptive if PSNR  36 dB. The local distortions can be measured by the mean PSNR between the watermarked image regions and the original image regions,

1 n

LPSNR =

n

PSNR(i )

(35)

i =1

where PSNR(i ) denotes the PSNR between the ith watermarked image region and the ith original image region, and n is the number of the watermark embedding regions. The computed perceptual quality results for the watermarked test images, including Airplane, Baboon, Lena and Peppers are shown in Table 5, where the second column indicates the number of the watermark embedding regions, the third column indicates PSNR, and the fourth column indicates the mean local PSNR LPSNR. Although the PSNR and LPSNR of watermarked image Baboon are both below 36 dB, it is still hard to find any quality degradation because the image Baboon is highly-textured. The results listed in Table 5 show that imperceptibility of the watermark is good for both local and global aspects. 5.2.3. Assessment of robustness In order to verify the robustness of the proposed localized watermarking scheme, the watermark detection is blindly done after attacking watermarked test images using Stirmark 3.1, including common signal processes and geometrical distortions. We compare the watermark detection results with those in [21]. In the experiment, V = 45, N = 50, and P FA = 10−5 . It is noted that the false alarm probability for an image P FA is a set at 10−4 in the literature [21]. Table 6 shows the compared results of resistance to common signal process, including median filtering, sharpening, Gaussian filtering, additive uniform noise, JPEG compression of different quality factor, and several combined signal process attacks. Table 7

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Y. Yu et al. / Digital Signal Processing 22 (2012) 170–180

Table 6 Watermark detection results under signal process. Attacks

Methods

Airplane

Baboon

Lena

Peppers

No attack

Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21]

2, 2, 3 (Yes) – 1, 2, 2 (Yes) 4, 5, 5 (Yes) 2, 6, 6 (Yes) 1, 1, 1 (Yes) 1, 2, 2 (Yes) 3, 4, 4 (Yes) 2, 2, 3 (Yes) 5, 7, 7 (Yes) 2, 2, 3 (Yes) 2, 2, 2 (Yes) 1, 2, 2 (Yes) 1, 1, 1 (Yes) 2, 2, 2 (Yes) 1, 2, 2 (Yes) 2, 2, 3 (Yes) 2, 3, 3 (Yes) 2, 2, 3 (Yes) 3, 3, 3 (Yes) 2, 2, 3 (Yes) 3, 4, 5 (Yes) 1, 2, 2 (Yes) 3, 3, 3 (Yes) 2, 6, 6 (Yes) 1, 1, 1 (Yes) 1, 2, 2 (Yes) 2, 4, 4 (Yes) 1, 2, 2 (Yes) 0, 0, 0 (No)

7, 7, 8 (Yes) – 6, 6, 6 (Yes) 1, 2, 2 (Yes) 3, 4, 4 (Yes) 0, 0, 0 (No) 8, 8, 9 (Yes) 1, 1, 1 (Yes) 7, 7, 8 (Yes) 3, 4, 4 (Yes) 7, 7, 8 (Yes) 3, 4, 5 (Yes) 5, 5, 5 (Yes) 0, 1, 1 (No) 6, 7, 7 (Yes) 1, 1, 2 (Yes) 6, 7, 7 (Yes) 1, 2, 3 (Yes) 5, 5, 5 (Yes) 1, 2, 2 (Yes) 7, 7, 8 (Yes) 1, 2, 4 (Yes) 9, 10, 11 (Yes) 0, 1, 1 (No) 3, 4, 4 (Yes) 0, 0, 0 (No) 6, 6, 6 (Yes) 0, 1, 2 (No) 6, 7, 7 (Yes) 4, 6, 6 (Yes)

6, 7, 7 (Yes) – 4, 5, 6 (Yes) 5, 6, 6 (Yes) 6, 6, 6 (Yes) 1, 1, 2 (Yes) 4, 5, 6 (Yes) 3, 4, 5 (Yes) 6, 7, 7 (Yes) 5, 5, 5 (Yes) 6, 7, 7 (Yes) 1, 2, 2 (Yes) 5, 7, 7 (Yes) 0, 0, 0 (No) 6, 7, 8 (Yes) 1, 2, 2 (Yes) 6, 7, 7 (Yes) 1, 2, 3 (Yes) 4, 6, 6 (Yes) 3, 4, 4 (Yes) 7, 8, 8 (Yes) 3, 3, 4 (Yes) 4, 5, 6 (Yes) 2, 4, 4 (Yes) 6, 6, 6 (Yes) 1, 1, 1 (Yes) 4, 5, 6 (Yes) 5, 5, 5 (Yes) 3, 4, 5 (Yes) 1, 3, 4 (Yes)

4, 7, 7 (Yes) – 2, 6, 6 (Yes) 4, 4, 4 (Yes) 2, 2, 3 (Yes) 5, 5, 5 (Yes) 2, 5, 5 (Yes) 5, 5, 5 (Yes) 3, 6, 6 (Yes) 6, 6, 6 (Yes) 3, 6, 6 (Yes) 5, 5, 6 (Yes) 2, 4, 6 (Yes) 4, 4, 4 (Yes) 1, 3, 3 (Yes) 4, 5, 5 (Yes) 3, 6, 6 (Yes) 4, 6, 6 (Yes) 3, 7, 7 (Yes) 6, 6, 7 (Yes) 6, 8, 9 (Yes) 7, 7, 7 (Yes) 2, 5, 5 (Yes) 5, 5, 5 (Yes) 2, 2, 3 (Yes) 5, 5, 5 (Yes) 2, 5, 5 (Yes) 2, 4, 4 (Yes) 0, 1, 3 (Yes) 0, 1, 3 (Yes)

Median filter 4 × 4 Sharpening 3 × 3 Gaussian filter 3 × 3 Additive uniform noise (scale = 0.1) Additive uniform noise (scale = 0.2) JPEG (Q = 30%) JPEG (Q = 40%) JPEG (Q = 50%) JPEG (Q = 60%) JPEG (Q = 70%) Gaussian filter + JPEG (Q = 90%) Sharpening + JPEG (Q = 90%) Median filter + JPEG (Q = 90%) FMLR

Table 7 Watermark detection results under geometrical attacks. Attacks

Methods

Airplane

Baboon

Lena

Peppers

Cropping 15% off

Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21] Our method Seo et al. [21]

2, 3, 3 (Yes) 5, 5, 5 (Yes) 1, 1, 2 (Yes) 5, 5, 5 (Yes) 1, 2, 3 (Yes) 3, 5, 5 (Yes) 0, 2, 3 (Yes) 5, 5, 5 (Yes) 1, 1, 2 (Yes) – 0, 1, 3 (Yes) – 1, 2, 2 (Yes) 1, 1, 1 (Yes) 1, 2, 3 (Yes) 3, 3, 3 (Yes) 1, 2, 2 (Yes) 1, 2, 2 (Yes) 2, 2, 3 (Yes) – 2, 2, 4 (Yes) – 1, 2, 3 (Yes) 3, 4, 4 (Yes) 2, 2, 2 (Yes) 4, 4, 4 (Yes) 1, 2, 4 (Yes) 5, 5, 5 (Yes) 2, 2, 2 (Yes) 3, 3, 3 (Yes) 1, 2, 2 (Yes) 2, 2, 2 (Yes) 1, 2, 2 (Yes) 4, 4, 4 (Yes) 2, 2, 2 (Yes) 0, 0, 1 (No)

2, 2, 3 (Yes) 4, 4, 4 (Yes) 1, 1, 2 (Yes) 1, 2, 2 (Yes) 2, 3, 4 (Yes) 1, 3, 3 (Yes) 0, 2, 3 (Yes) 1, 1, 1 (Yes) 2, 3, 3 (Yes) – 1, 2, 3 (Yes) – 5, 8, 9 (Yes) 0, 0, 0 (No) 8, 10, 11 (Yes) 0, 2, 2 (Yes) 6, 7, 9 (Yes) 2, 3, 4 (Yes) 5, 6, 7 (Yes) – 6, 6, 7 (Yes) – 10, 10, 10 (Yes) 3, 3, 3 (Yes) 7, 8, 8 (Yes) 1, 5, 5 (Yes) 8, 9, 9 (Yes) 0, 3, 3 (Yes) 6, 8, 8 (Yes) 1, 2, 2 (Yes) 7, 8, 9 (Yes) 0, 2, 3 (Yes) 8, 8, 8 (Yes) 2, 3, 4 (Yes) 7, 8, 8 (Yes) 0, 0, 0 (No)

5, 5, 5 (Yes) 6, 6, 6 (Yes) 5, 5, 6 (Yes) 4, 4, 4 (Yes) 4, 5, 5 (Yes) 5, 5, 5 (Yes) 1, 2, 2 (Yes) 2, 2, 3 (Yes) 4, 5, 5 (Yes) – 2, 2, 2 (Yes) – 4, 5, 6 (Yes) 2, 2, 2 (Yes) 4, 6, 7 (Yes) 3, 4, 4 (Yes) 5, 7, 7 (Yes) 4, 5, 5 (Yes) 5, 7, 7 (Yes) – 3, 6, 6 (Yes) – 5, 7, 7 (Yes) 6, 6, 6 (Yes) 3, 4, 6 (Yes) 7, 7, 7 (Yes) 4, 5, 6 (Yes) 7, 7, 7 (Yes) 3, 5, 7 (Yes) 5, 6, 6 (Yes) 5, 6, 6 (Yes) 4, 5, 5 (Yes) 4, 7, 7 (Yes) 5, 5, 5 (Yes) 4, 5, 5 (Yes) 1, 1, 1 (Yes)

2, 2, 2 (Yes) 2, 2, 2 (Yes) 1, 2, 2 (Yes) 2, 2, 2 (Yes) 2, 3, 4 (Yes) 3, 4, 4 (Yes) 1, 2, 2 (Yes) 1, 1, 1 (Yes) 4, 4, 4 (Yes) – 2, 2, 2 (Yes) – 1, 2, 3 (Yes) 2, 3, 3 (Yes) 3, 5, 7 (Yes) 6, 6, 6 (Yes) 4, 6, 7 (Yes) 6, 6, 6 (Yes) 3, 4, 6 (Yes) – 4, 6, 8 (Yes) – 3, 5, 6 (Yes) 5, 5, 5 (Yes) 2, 3, 4 (Yes) 7, 7, 7 (Yes) 2, 4, 6 (Yes) 5, 5, 5 (Yes) 2, 4, 7 (Yes) 5, 5, 5 (Yes) 2, 4, 5 (Yes) 3, 3, 3 (Yes) 5, 7, 8 (Yes) 4, 4, 4 (Yes) 2, 4, 5 (Yes) 0, 1, 1 (No)

Cropping 25% off Rotation 20◦ + autocrop Rotation 45◦ + autocrop Rotation 20◦ + scaling + autocrop Rotation 45◦ + scaling + autocrop Scaling 50% Scaling 75% Scaling 90% Scaling 150% Scaling 200% Linear geometric transform [1.007, 0.010, 0.010, 1.012] Linear geometric transform [1.010, 0.013, 0.009, 1.011] Linear geometric transform [1.013, 0.008, 0.011, 1.008] 17 column 5 row removed Random bending attack Shearing (1%) Shearing (5%)

shows the compared results of resistance to geometrical attacks, including cropping, scaling, rotation, linear geometric transform, row/column removed, random bending attack, shearing, and sev-

eral combined geometrical attacks. In a similar way as [21], the three numbers indicate the number of the regions found to have been watermarked with the three values of threshold (obtained

Y. Yu et al. / Digital Signal Processing 22 (2012) 170–180

from Table 4 for P FA = 10−5 ) in Tables 6 and 7. It is noted that an image is claimed watermarked if at least μ image regions are found to have been watermarked. Further, the sign “Yes” or “No” is added after those three numbers to indicate whether the image is watermarked. From Table 6, it can be seen that our method can extract the watermark perfectly when no attacks occur. From the results in the above two tables, it can be observed that our method has good robustness against the attacks listed in the tables and outperforms that in [21]. In both tables, the robustness for image Baboon in [21] is obviously worse than other image. It may be because Harris– Laplace points used to synchronize the watermark in [21] at the textured regions is unstable. Because the locality of DRSIF points is worse than Harris–Laplace points, DRSIF points are more stable than Harris–Laplace points on textured regions so that our method is also robust for textured images. In addition, the method in [21] has poor robustness against shearing (5%) that may also be due to the same reason. To show the robustness of our proposed scheme against scaling, we specially tested the scaling with various parameters and rotation combined with scaling. The experimental results show that our proposed scheme has good robustness against scaling so that the strong robustness of DRSIF points against scaling is verified again. 6. Conclusion The robustness against geometric distortions, especially local geometric distortions with cropping, has been an obstacle in the image blind watermarking technique. The localized watermarking scheme using feature points is a promising technique to overcome such problems. We developed a rotation and scale invariant feature (DRSIF) extraction algorithm based on the mean luminance of the disk. Furthermore, we proposed a localized watermarking scheme based on invariant regions constructed using DRSIF points. The invariant regions not only resist basic RST attacks, they also survive common image processing. Under perceptual imperceptibility, the watermarking scheme is also robust against combination of these attacks. Because the response value and characteristic radius are computed at each point of the image during DRSIF points extraction, a certain amount of computation is involved. One future work is to how to decrease the computation of DRSIF point. In addition, we try to apply the DRSIF points to other fields, such as pattern recognition. Acknowledgments This work is supported by the NSF of China under Grant Nos. 60873226 and 60803112, the Fundamental Research Funds for the Central Universities, Wuhan Youth Science and Technology Chenguang Program, and the Perspective Research Foundation of Production Study and Research Alliance of Jiangsu Province of China under Grant No. BY128. References [1] I.J. Cox, M.L. Miller, J.A. Bloom, in: E. Fox (Ed.), Digital Watermarking, first ed., Morgan Kaufmann, 2001. [2] S. Baudry, P. Nguyen, H. Maitre, Estimation of geometric distortions in digital watermarking, in: Proceedings of IEEE International Conference on Image Processing, vol. 2, Rochester, NY, United States, 2002, pp. 885–888. [3] S. Pereira, T. Pun, Robust template matching for affine resistant image watermarks, IEEE Trans. Image Process. 9 (6) (2000) 1123–1129. [4] D. Delannay, B. Macq, Generalized 2-D cyclic patterns for secret watermark generation, in: Proceedings of IEEE International Conference on Image Processing, Vancouver, Canada, 2000, pp. 72–79. [5] Hefei Ling, Zhengding Lu, Fuhao Zou, A geometrically robust watermarking scheme based on self-recognition watermark pattern, in: Proceedings of IEEE International Conference on Multimedia and Expo, 2006, pp. 1601–1604.

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Yanwei Yu received a B.S. degree in computer application from Air Force Radar Academy, Wuhan, China, in 2002, and Ph.D. degree in computer application from Huazhong University of Science and Technology (HUST), Wuhan, China, in 2008. She is currently a teacher at School of Software Engineering, University of Science and Technology of China, China. Her research interests include digital watermarking, image processing and digital rights management.

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Hefei Ling received a B.E. degree in power engineering from Huazhong University of Science and Technology with a lot of honors, Wuhan, China, in 1999, and the Ph.D. degree in computer application from Huazhong University of Science and Technology in 2005. He is currently an associate professor of the School of Computer Science and Technology at Huazhong University of Science and Technology. His research interests include watermarking, copy detection and image processing. Fuhao Zou received a B.S. degree in computer science from Central China Normal University, Wuhan, China, in 1998, and Ph.D. degree in computer application from Huazhong University of Science and Technology (HUST), Wuhan, China, in 2006. He is currently a teacher at School of Computer Science and Technology, HUST. His current research interests mainly focus on digital watermarking, digital rights management, and copy detection.

Zhengding Lu was born in 1944, he is currently a Professor, Ph.D. tutor and Director of the School of Computer Science and Technology at Huazhong University of Science and Technology. His research interests are distributed system and software, and Internet/Intranet. He has published over 160 technical papers and is the author of 9 books. Liyun Wang received a B.E. degree in Computer Science and Technology from the Huazhong University of Science and Technology (HUST), Wuhan, China, in 2005. Currently, she is a Ph.D. student at the School of Computer Science and Technology, Huazhong University of Science and Technology (HUST), China. Her research interests include digital watermarking, image processing and digital rights management.