Combining Interest Point and Invariant Moment for

JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 25, 499-515 (2009)

Combining Interest Point and Invariant Moment for Geometrically Robust Image Watermarking* LEI-DA LI, BAO-LONG GUO AND LEI GUO+ Institute of Intelligent Control and Image Engineering Xidian University Xi’an 710071, P.R. China + National Laboratory of Pattern Recognition, Institute of Automation Chinese Academy of Sciences Beijing 100080, P.R. China This paper presents a new robust image watermarking scheme for resisting both traditional and geometric attacks. A watermark synchronization scheme is first presented using image features. Harris interest points are first extracted from the scale normalized image and the locally most stable points are employed to generate some non-overlapped circular regions. Watermark synchronization is achieved using these local circular regions. Thereafter, the rotation invariant pseudo-Zernike moments (PZMs) are computed over each circular region and the watermark signal is composed of the PZM vectors extracted from all the local regions. Then the PZM vectors are modified and reconstructed, producing some error images. The watermark is embedded by adding the error images into the corresponding local circular regions in spatial domain directly. During watermark detection, local circular regions are first extracted from the distorted image and PZMs are computed over each local region. A minimum distance decoder is proposed to detect the watermark blindly. Simulation results on Stirmark 4.0 show that the watermark is robust against traditional signal processing attacks, rotation, scaling, flipping, Stirmark random bending as well as combined attacks. Keywords: image watermark, geometric attack, watermark synchronization, feature extraction, pseudo-Zernike moment, Stirmark

1. INTRODUCTION The prevalence of computer networks has made it much easier to share and distribute digital multimedia data. However, how to protect the copyright of these products is still an open problem. Digital watermarking is a promising way to protect the copyright of digital contents [1-3]. In this paper, we address the robust image watermarking technique for copyright protection. Extensive schemes have been proposed for image watermarking. However, many of them are vulnerable to geometric attacks, such as rotation, scaling and translation (RST). Geometric attacks can defeat many watermarking schemes in that they introduce synchronization error between the original and the embedded watermark and therefore mislead the watermark detector. This problem is most pronounced when the original image is not available in watermark detection [4]. Watermark robustness to geometric attacks has attracted much attention recently [5, 6]. Zheng et al. [6] reviewed the most common types of RST invariant image waterReceived May 17, 2007; revised July 20, August 16 & October 9, 2007; accepted November 12, 2007. Communicated by Tong-Yee Lee. * This paper was partially supported by the National Natural Science Foundation of China (60572152 and 60802077) and Ph.D. Programs Foundation of Ministry of Education of China (20060701004).

499

500

LEI-DA LI, BAO-LONG GUO AND LEI GUO

marking algorithms and pointed out their advantages and disadvantages. Current countermeasures can be classified as template based embedding, invariant domain embedding, and feature based synchronization. Template based embedding usually embeds a template at predetermined locations in addition to the watermark [7, 8]. The template is commonly composed of local peaks. Before watermark detection, the template is first detected and used to estimate the parameters of the distortions that the image has undergone. Then the watermark can be detected after inverting the distortions. Template based schemes are usually subject to template-removal attacks as anyone can access the local peaks and eliminate them. Invariant domain embedding has been extensively explored [9-15]. O’Ruanaidh et al. [9] first reported the RST invariant image watermarking in Fourier-Mellin domain. The Discrete Fourier Transform (DFT) of the original image is first computed and the log-polar mapping (LPM) is applied on the DFT magnitude spectrum. Then a second DFT is conducted on the new coordinate system and the watermark is embedded in the magnitudes of this DFT. This method suffers severe implementation difficulty which is mainly due to the LPM and inverse LPM. Lin et al. [10] embed the watermark into a one-dimensional signal obtained by taking the Fourier transform of the image, resampling the Fourier magnitudes into log-polar coordinates, and then summing a function of those magnitudes along the log-radius axis. Zheng et al. [11] embed the watermark in the LPMs of the Fourier magnitude spectrum of an original image, and use the phase correlation between the LPM of the original image and the LPM of the watermarked image to calculate the displacement of watermark positions in the LPM domain. This approach preserves the image quality by avoiding computing the inverse LPM. However, it is not a blind scheme. Another kind of invariant domain schemes embed the watermark using Zernike or pseudo-Zernike moments [12-15]. Kim et al. [12] embedded the watermark by modifying Zernike moments with orders less than 5. Rotation invariance is achieved by using the magnitude of the Zernike moments while scaling and translation invariance are achieved by image normalization. While their experimental results presented a high Peak Signal to Noise Ratio (PSNR) value (36dB), according to our experiments, the watermarked images show a great ring effect along the inscribed circle of the image. Xin et al. [13-15] embed the watermark using Zernike/pseudo-Zernike moments by dither modulation. The watermark capacity is much higher than that of Lee’s scheme. This scheme can resist rotation, scaling, flipping and so on. However in case of scaling, the distorted image has to be scaled back to its original size manually before watermark detection. Feature based synchronization has become a new direction for robust image watermarking recently [16-21]. Bas et al. [16] use an image’s feature points to construct a triangular tessellation that they use to embed the watermark. After a probable attack, the scheme detects the feature points, letting it reconstruct the original tessellation and detect the watermark by correlation. The drawback of this scheme is that they extract large numbers of feature points, and many of the points from the original image and distorted images are not matched. As a result, the sets of triangles during watermark insertion and extraction are different. Tang et al. [17] adopt the Mexican Hat wavelet scale interaction to extract feature points. Local patches are generated based on the feature points. Two sub-blocks are further extracted inside the initial patch and a 16-bit watermark is embedded into the sub-blocks in DFT domain. The watermark can resist rotation and crop-

IMAGE WATERMARKING USING INTEREST POINT AND INVARIANT MOMENT

501

ping attacks. However, it is fragile to scaling attacks, even slightly. In our analysis, this is due to the feature selection strategy. In this scheme, a feature point has a higher priority for watermark embedding if it has more neighboring feature points inside its disk. This can produce feature points that locate at high textured areas while not obtaining the points with the best robustness. As a result, the feature points used for embedding and extraction cannot be matched. In Qi’s scheme [18], the image content is represented by important feature points obtained by the adaptive Harris corner detector. An imagecontent-based adaptive embedding scheme is applied in DFT domain of each perceptually high textured subimage. This scheme can resist more general geometric attacks. The shortcoming of this scheme is that the positions of the important feature points have to be saved for watermark detection. Lee et al. [19] develop a scale-invariant feature transform (SIFT) based watermarking scheme. They extract image feature points by SIFT and use them to generate a number of patches. The watermark is embedded into multiple patches additively in spatial domain. This scheme performs well, but the watermark similarities are all lower than 0.7. We also propose a feature based watermarking scheme using SIFT [20]. Watermark synchronization is achieved using SIFT keypoints and the watermark is embedded in Zernike domain. This scheme is robust to both RST attacks and traditional attacks, but it is not a blind scheme. In this paper, we present a new robust image watermarking scheme which can be classified as feature based synchronization. A new watermark synchronization scheme is first proposed using locally most stable Harris feature points. Local circular regions are extracted for watermark embedding and extraction. The watermark signal is composed of rotation invariant pseudo-Zernike moments (PZMs) and it is embedded by modifying PZMs. A minimum distance decoder is designed to detect the watermark blindly. Unlike Xin’s schemes, our scheme can detect the watermark without any manual assistance. Localized embedding achieves better watermark invisibility and PZM based embedding enhanced watermark robustness. Experimental results using Stirmark 4.0 show that the proposed scheme is robust to rotation, scaling, flipping, Stirmark random bending as well as traditional image processing attacks.

2. WATERMARK SYNCHRONIZATION SCHEME Geometric attacks can mislead the watermark detector because the position of the watermark has changed. As a result, watermark synchronization is necessary before watermark detection. In our scheme, watermark synchronization is achieved using local circular regions that can be generated using Harris feature points. Fig. 1 shows the diagram of the proposed synchronization scheme. In Fig. 1, the image is first scale normalized, because Harris interest points are sensitive to image scale change. Scale normalization is carried out using the method in [22].

Fig. 1. Diagram of the proposed synchronization scheme.

LEI-DA LI, BAO-LONG GUO AND LEI GUO

502

Given an image f(x, y), the geometric moment m00 is first computed using

m p , q = ∑ ∑ x p y q f ( x, y ) x

(1)

y

where mp,q is the (p + q)th order moment of f(x, y). Scale normalization is achieved by transforming f(x, y) into a new image f(x/a, y/a), with a = β /m00 , where β is a predetermined value. Once the image has been normalized, the next step is to extract the Harris feature points. Harris detector extracts feature points from the second-moment matrix of the original image [23]. Given an image f(x, y), the gradient images are first computed. ⎧⎪ X = f ( x, y ) ∗ (− 1, 0, 1) = ∂f/∂x ⎨ T ⎪⎩Y = f ( x, y ) * (− 1, 0, 1) = ∂f/∂y

(2)

Then the second-moment matrix is constructed. ⎡ Ax , y M =⎢ ⎣ Cx, y

⎧ Ax , y = X 2 ∗ w ⎪⎪ C x, y ⎤ with ⎨ Bx , y = Y 2 ∗ w ⎥ Bx , y ⎦ ⎪ ⎪⎩ C x , y = ( XY ) ∗ w

(3)

where *denotes for convolution and w = exp(− (x2 + y2)/2σ2) is the Gaussian smoothing function. Then the determinant and trace of M is calculated. 2 ⎪⎧ Det ( M ) = Ax , y Bx, y − Cx , y ⎨ ⎪⎩Trace( M ) = Ax , y + Bx, y

(4)

Finally, the detector response is calculated. RH = Det(M) − k ⋅ Trace2(M)

(5)

where k is a constant. Finally, interest points can be extracted by comparing the responses with a threshold, which we denote by THarris in this paper. In our implementation, the window size of the Gaussian kernel is 3 × 3, k = 0.04 and THarris is set to be 2000. As many feature points can be detected initially, we only employ the locally most stable ones in order to achieve better robustness. These locally most stable points (LMSPs) are generated as follows. For each detected interest point, search within a circular region. If the detector response at the central point achieves local maximum, this interest point is selected, otherwise, dismiss it. These LMSPs are denoted by the set Ω1, then Ω1 = {(x, y) | RH(x, y) > RH(s, t), ∀(s, t) ∈ Ux,y}

(6)

where Ux,y is the circular region. Note that the radius of the circular region, which we denote by Rregion here, is determined by the image owner. Fig. 2 (a) shows an example of

IMAGE WATERMARKING USING INTEREST POINT AND INVARIANT MOMENT

503

(a) (b) (c) (d) Fig. 2. (a) Locally most stable points; (b) Circular regions generated using (a); (c) Finally selected points; (d) Circular regions generated using (c).

LMSPs detected from image Lena and Fig. 2 (b) shows the corresponding circular regions determined by these LMSPs. The feature point centered at each circular region is the LMSP. In Fig. 2 (b), some of the circular regions overlap with others. In order to obtain non-overlapped circular regions, some of the interest points must be dismissed. As a result, the LMSPs are optimized by the following operations to generate the finally selected points and the non-overlapped circular regions. Step 1: Choose, from Ω1, the feature point with the biggest response, say P0; Step 2: Dismiss the points whose corresponding regions overlap with that of P0; Step 3: Update Ω1 by dismissing P0; Step 4: If the circular regions generated using the updated points in Ω1 still overlap with others, repeat steps 1-3, otherwise go to step 5; Step 5: Generate non-overlapped regions using the reserved feature points.

Fig. 2 (c) shows the finally selected points and Fig. 2 (d) shows their corresponding local circular regions. These regions have some desirable properties, such as rotation and scale invariance, which will be shown in the experiments. In our scheme, watermark embedding and extraction are implemented in these local circular regions.

3. WATERMARKING SCHEME 3.1 Pseudo-Zernike Moments and Watermark Generation

In order to embed the watermark into the circular regions, the embedding scheme should be designed in a rotation invariant pattern, because the orientations of the local regions are different when the image is rotated. In this paper, we employ the pseudoZernike moment (PZM) to design the watermark, because the magnitude of PZM is rotation invariant. Although the Zernike moment (ZM) can also be used here, PZM performs better than ZM in regard of noise insensitiveness [24]. We will first introduce the basic theory of PZM and then present the watermark generation process. Pseudo-Zernike basis is a set of orthogonal and complete polynomials defined on the unit circle x2 + y2 ≤ 1 [13]. The polynomial is defined as follows: Vnm(x, y) = Vnm(ρ, θ) = Rnm(ρ)ejmθ

(7)

LEI-DA LI, BAO-LONG GUO AND LEI GUO

504

where ρ = x 2 + y 2 , θ = tan-1(y/x). Here n (order) is a nonnegative integer while m (repetition) is an integer subject to the constraint that n − |m| ≥ 0. Rnm(ρ) is the radial polynomial defined as

Rnm ( ρ ) =

n −|m|

∑

s =0

(−1) s (2n + 1 − s ) ! ρ n − s . s !(n + |m| + 1 − s) !(n − |m| − s) !

(8)

These polynomials are orthogonal and satisfy

∫∫

Vn*m ( x, y )V p q ( x, y )dxdy =

x 2 + y 2 ≤1

π n +1

⎧1 a = b . ⎩0 a ≠ b

δ n pδ m q with δ ab = ⎨

(9)

Given an image f(x, y) with size N × N, the PZMs can be computed by Anm =

n +1

π

∫∫ x + y ≤1 f ( x, y)Vn m ( x, y)dxdy. *

2 i

2 j

(10)

For a digital image with size N × N, Eq. (10) can be approximated by Anm =

n +1

π

N

N

∑ ∑ f ( xi , y j )Vnm* ( xi , y j )ΔxΔy

(11)

i =1 j =1

where xi2 + y 2j ≤ 1, and Δx = Δy = 2/N. Given all PZMs with the maximum order Nmax, the image can be reconstructed as f ( x, y ) =

N max

n

∑ ∑

AnmVnm ( x, y ).

(12)

n = 0 m =− n

As the proposed synchronization method extracts circular regions from the original image, a PZM vector can be directly computed over each extracted region. In this paper, the watermark signal is composed of all the PZM vectors. Suppose that we extract K local circular regions from the original image and the order of the PZMs computed is n, then the watermark signal consists of K PZM vectors.

⎡ A01 ,0 , A11 , −1 , A11 ,0 , A11 ,1 , " , An1 , − n , " , An1 , n ⎤ ⎢ 2 ⎥ ⎢ A0 ,0 , A12, −1 , A12,0 , A12,1 , " , An2 , − n , " , An2 , n ⎥ ⎢ ⎥ Watermark signal: ⎢ A03 ,0 , A13, −1 , A13,0 , A13,1 , " , An3 , − n , " , An3 , n ⎥ ⎢ ⎥ " ⎢ ⎥ ⎢⎣ A0K,0 , A1K, −1 , A1K,0 , A1K,1 , " , AnK, − n , " , AnK, n ⎥⎦

(13)

In Eq. (13), each row is a PZM vector computed over one circular region. 3.2 Moment Modification and Watermark Insertion

In this paper, the watermark is embedded repeatedly into each local region by modi-

IMAGE WATERMARKING USING INTEREST POINT AND INVARIANT MOMENT

505

fying its PZM vectors. Therefore, we first introduce how to modify the moments and then present the watermark insertion process. Some of the followings are based on [12]. Given the PZM vector (denoted by A) of one local region R(x, y), we modify Anm by Δnm, and the modified moment is denoted by A′nm, then the image reconstructed from those modified moments is Rˆ ( x, y ) =

∞

∑∑

n =0 m

∞

′ Vnm ( x, y ) = ∑ ∑ ( Anm + Δ nm )Vnm ( x, y ) Anm n=0 m

∞

(14)

= R ( x, y ) + ∑ ∑ Δ nmVnm ( x, y ) = R( x, y ) + e( x, y ). n =0 m

The reconstructed image consists of two parts: the original image and an error image. If we only modify Ak,l by α, then the error signal e( x, y ) is ∞

e( x, y ) = Rˆ ( x, y ) − R( x, y ) = ∑ ∑ Δ nmVnm ( x, y ) n =0 m

(15)

= " + Δ k , −lVk , −l + " + Δ k , lVk , l + " = α (Vk , −l + Vk , l ). Note that because of the conjugate symmetry of PZMs, Ak,-l must also be modified accordingly to obtain a real image. l =0 ⎧α Vk , l Therefore, e( x, y ) = ⎨ ⎩α (Vk , l + Vk , −l ) otherwise

(16)

If we add e(x, y) into the original image in spatial domain, the PZMs will be different. Ideally, the added image e(x, y) only affects Ak,l, and A′k,l becomes A′k,l = Ak,l + α.

(17)

As an example, we modified the moment A21 of one circular region, and added the reconstructed error image to the original region. Then we computed PZMs of the modified region again, the magnitude differences are computed and shown in Fig. 3. In Fig. 3, obvious peaks can only be found where the PZMs have been modified. In fact, the above information indicates that we can modify the PZM vector in the original

Fig. 3. Magnitude difference at (2, − 1) and (2, 1).

LEI-DA LI, BAO-LONG GUO AND LEI GUO

506

Fig. 4. Diagram of watermark insertion.

watermark at predetermined order and repetition for watermark embedding. During watermark detection, we compute the PZM vector from a synchronized region and the magnitude difference between the original vector and the newly extracted one is computed. If peaks appear only at the same order and repetition, then we can claim the presence of the watermark, otherwise not. The diagram of the proposed watermark insertion scheme is shown in Fig. 4. The original image is first scale normalized and the non-overlapped circular regions are extracted using the method described in section 2. For each region, the PZM vector is first extracted as the watermark. The PZM vector is then modified at specialized order and repetition. An error image is then produced by reconstructing the modified vector. Then it is added into the original region under proper strength to obtain the watermarked region. Then the watermarked region is used to replace the original region. The above operation is done repeatedly until all local regions are watermarked. Finally, the whole image is inverse scale normalized to obtain the watermarked image. During watermark insertion, some owner-determined data are combined to generate a private key. The construction of the private key is shown in Fig. 5. β

THarris

Rregion

ORDPZM

ORDmod + REPmod

Fig. 5. Construction of the private key.

In Fig. 5, β is the scale normalization parameter, THarris is the threshold for Harris detector, Rregion is the radius of the circular region, ORDPZM is the order of computed PZM during watermark generation, ORDmod and REPmod are the order and repetition of the modified PZM during watermark insertion, respectively. It takes about 7 bytes to store the private key. For security purpose, the private key can be further encrypted. 3.3 Watermark Detection

Fig. 6 shows the diagram of watermark detection. In Fig. 6, the first several steps are exactly the same as those of watermark insertion. Non-overlapped circular regions

IMAGE WATERMARKING USING INTEREST POINT AND INVARIANT MOMENT

507

Fig. 6. Diagram of watermark detection.

are first extracted for synchronization using the private key. For each region, PZMs are first computed, and a minimum distance decoder is proposed to detect the watermark. The minimum distance decoder is designed as follows. Suppose that the PZM vector computed over one synchronized region is denoted by i i i ˆ [ A0,0 , Aˆ1,i −1 , Aˆ1,0 , Aˆ1,1 , " , Aˆ ni , − n , " , Aˆni , n ]. Then what the minimum distance decoder does is to find the PZM vector from the original watermark signal Eq. (13) that has the smallest distance with the extracted one. The distance is computed as follows: i − A j )2 + ( A ˆ i − A j ) 2 + ( Aˆ i − A j ) 2 + ( Aˆ i − A j ) 2 + " + ( Aˆ ni , n − Anj, n ) 2 Di , j = ( Aˆ0,0 0,0 1, −1 1, −1 1,0 1,0 1,1 1,1

(18) where j = 0, 1, 2, …, K. Note that in Eq. (18), the moment that was previously modified for watermark insertion should be excluded in computation. For example, if we modify i − A j ) 2 and ( A ˆi − the moments A3,1 and A3,-1 to insert the watermark, then terms ( Aˆ3,1 3, −1 3,1 j 2 A3, −1 ) should not appear in Eq. (18). Then, the minimum distance between the extracted PZM vector and the watermark is: Dmin(i) = min(Di,1, Di,2, Di,3, …, Di,k).

(19)

Upon obtaining the minimum distance Dmin(i), say Dmin(i) = Di,m, the absolute difi , A ˆ i , Aˆ i , Aˆ i , " , Aˆ ni , − n , " , Aˆni , n ] and [ Am , Am , Am , Am , " , ference between [ Aˆ0,0 0,0 1, −1 1,0 1,1 1, −1 1,0 1,1 m m An, − n , " , An, n ] is then computed as: i − Am |, |A ˆ i − Am |, |Aˆ i − Am |, |Aˆ i − Am |, " , |Aˆ ni , n − Anm, n |]. Ediff = [|Aˆ0,0 0,0 1, −1 1, −1 1,0 1,0 1,1 1,1

(20)

Ideally, peaks can only be found at (ORDmod, − REPmod) and (ORDmod, REPmod) of Ediff, where the moments were previously modified to embed the watermark. The shape of the detected watermark is shown in Fig. 6. In implementation, we set a threshold (T) to enhance watermark robustness. If for any s ≠ ORDmod, t ≠ ± REPmod, the following relation always holds.

LEI-DA LI, BAO-LONG GUO AND LEI GUO

508

i m |AˆORD | − |Aˆ si ,t − Asm,t | > T . − AORD mod , ± REPmod mod , ± REPmod

(21)

Then we can claim that the watermark has been successfully detected. In this paper, the threshold T is set to be 0.002, which is determined experimentally.

4. EXPERIMENTAL RESULTS AND DISCUSSIONS In this section, three experiments have been conducted to evaluate the performance of the proposed scheme, namely watermark synchronization, watermark invisibility and watermark robustness. In experiments, gray images with size 512 × 512 are used as the original images, including Lena, Peppers, Boat, Girl, Barbara, Baboon and House etc. The radius of the circular regions (Rregion) is 40 pixels, and the order of PZM used for watermark generation (ORDPZM) is 5. The moments (3, 1) and (3, − 1) are modified to insert the watermark, i.e. ORDmod = 3 and the REPmod = 1. The scale normalization parameters (β) are 3.6 × 107, 3.0 × 107, 3.4 × 107 and 3.4 × 107, respectively for Lena, Peppers, Baboon and House. 4.1 Watermark Synchronization

In our scheme, both watermark embedding and extraction are implemented in the local circular regions. As a result, the redetection of these regions is crucial. To evaluate the performance of watermark synchronization, we extract the local regions from both the original images and the distorted images, and compare their locations to determine whether they are matched. Fig. 7 shows an example of watermark synchronization on image Lena, where the matched regions are marked with the same color.

(a)

(b)

(c)

(d)

(e) (f) (g) (h) Fig 7. Local regions extracted from: (a) The original image; (b) The median-filtered image; (c) The added-Gaussian noise image; (d) The 20% JPEG image; (e) The 0.8× scaled image; (f) The 10-deg-rotated image; (g) The horizontally flipped image; (h) The vertically flipped image.

IMAGE WATERMARKING USING INTEREST POINT AND INVARIANT MOMENT

509

It is observed from Figs. 7 (c) and (f) that new regions may appear due to distortions, such as added noise and image rotation. However, most of the regions detected in the original image can be redetected from the distorted images. Table 1 lists the simulation results on other test images, where the denominator denotes the number of original regions and the numerator denotes the number of redetected regions. It can be seen from both Fig. 7 and Table 1 that the performance of the watermark synchronization scheme is satisfactory, regardless of traditional attacks or geometric attacks. This also provides a strong basis for robust watermark embedding and extraction. Table 1. Redetected regions compared to the original regions. Type of attack No attack Rotation 10 deg Scaling 0.8 Rotation 10 deg + Scaling 0.8 Flip horizontally Flip vertically Median filter (3 × 3) Added Gaussian noise JPEG compression 50

Peppers 7 6/7 5/7 6/7 6/7 7/7 5/7 7/7 6/7

Boat 9 9/9 6/9 7/9 8/9 9/9 6/9 7/9 7/9

Girl 8 8/8 6/8 5/8 8/8 8/8 5/8 6/8 8/8

Barbara 7 5/7 6/7 5/7 7/7 6/7 6/7 7/7 7/7

Baboon 8 8/8 6/8 8/8 8/8 8/8 2/8 7/8 5/8

House 9 7/9 7/9 6/9 9/9 8/9 5/9 8/9 7/9

4.2 Watermark Invisibility

Watermark invisibility is another criteria for image watermarking. Fig. 8 shows an example of watermark embedding. The original images and the watermarked images are shown in Figs. 8 (a) and (b), respectively. Fig. 8 (c) shows the corresponding residual images between Figs. 8 (a) and (b), which are magnified 40 times for better display.

(a) (b) (c) Fig. 8. (a) Original images; (b) Watermarked images; (c) Magnified residual images.

510

LEI-DA LI, BAO-LONG GUO AND LEI GUO

It is easily seen from Figs. 8 (a) and (b) that we insert the watermark so as not to be visible to the naked eyes. The PSNR values are 45.5dB and 46.9dB, respectively for Lena and House. In implementation, the PSNR values for all test images are higher than 40dB. The numbers of extracted regions for watermarking are 6 and 9, respectively for Lena and House. Our scheme achieves comparable image quality with that of [17], while both are than that of [19]. The reason is that the method in [19] embeds the watermark by modifying the pixels in spatial domain directly, while [17] and our scheme embed the watermark using transform domain techniques. 4.3 Watermark Robustness

In this subsection, we employ Stirmark 4.0 to test the robustness of our scheme [25]. Stirmark 4.0 attacks include traditional attacks and geometric attacks, such as JPEG compression, median filtering, added noise, image rotation, scaling etc. We also test the watermark robustness under flipping attacks, which have been reported by Xin et al. [1315]. Figs. 9 to 15 show some distorted images and the detected watermark. As ORDPZM is 5 and the (3, ± 1)th moments are modified to embed the watermark, it produces (5 + 1)2 = 36 PZMs and the detected watermark is located at index 12 and index 14, respectively. Table 2 lists the simulation results on different attacks included in Stirmark 4.0. The table shows the number of regions from which the watermark can be successfully detected and the number of original regions used for watermark insertion.

Fig. 9. Watermarked image and the detected watermark.

Fig. 10. 20% JPEG compressed image and the detected watermark.

Fig. 11. Added-noise image and the detected watermark.

IMAGE WATERMARKING USING INTEREST POINT AND INVARIANT MOMENT

511

Fig. 12. Rotated image and the detected watermark.

Fig. 13. 0.75 × scaled image and the detected watermark.

Fig. 14. Horizontally flipped image and the detected watermark.

Fig. 15. Vertically flipped image and the detected watermark.

It can be seen from Table 2 that our scheme can extract the watermark accurately when no attack occurs. For JPEG compression, median filtering and added Gaussian noise, the watermark can be readily detected. The above results are comparable with that of [17], while both are better than those of [16] and [19]. The reason is that in [16] and [19], the watermarks are embedded in spatial domain additively, somewhat like added noise. As a result, they are more likely to be affected by signal processing attacks. Rotation and scaling are two types of geometric attacks that can be easily implemented without causing visible degradations. Our scheme is robust to these attacks. Scale invariance is achieved by normalizing the original image to a uniform scale before feature detection. Bas’ scheme [16] and Tang’s scheme [17] are theoretically not robust to scaling attack, because the feature detection methods are scale sensitive. Lee’s scheme [19] can resist image scale change, but all the watermark similarities are smaller than 0.7. Rotation robustness of our scheme is achieved using pseudo-Zernike moments. The three schemes

512

LEI-DA LI, BAO-LONG GUO AND LEI GUO

Table 2. Simulation results on Stirmark 4.0 attacks. Type of Attack No attack JPEG compression 60 JPEG compression 70 JPEG compression 80 JPEG compression 90 Median filter 3 × 3 Median filter 5 × 5 Added uniform noise Rotation 5 degree Rotation 10 degree Rotation 15 degree Rotation 30 degree Rotation 45 degree Rotation 90 degree Scaling 0.75 × Scaling 0.90 × Scaling 1.1 × Scaling 1.5 × Rotation 0.50 degree + scaling Rotation 1 degree + scaling Rotation 2 degree + scaling Random distortion 0.95 Flip horizontally Flip vertically

Lena 6 4/6 5/6 5/6 5/6 5/6 5/6 2/6 4/6 4/6 5/6 4/6 4/6 4/6 6/6 5/6 4/6 5/6 4/6 4/6 4/6 5/6 4/6 5/6

Baboon 8 3/8 3/8 3/8 3/8 2/8 2/8 3/8 3/8 2/8 1/8 1/8 2/8 2/8 2/8 3/8 2/8 3/8 2/8 2/8 3/8 2/8 3/8 2/8

Peppers 7 4/7 3/7 3/7 4/7 3/7 2/7 1/7 4/7 4/7 3/7 5/7 3/7 2/7 4/7 5/7 5/7 4/7 4/7 7/7 6/7 7/7 7/7 6/7

House 9 4/9 5/9 4/9 4/9 1/9 1/9 2/9 4/9 4/9 4/9 3/9 2/9 2/9 3/9 4/9 4/9 4/9 3/9 4/9 4/9 4/9 4/9 4/9

in [16], [17] and [19] can all resist image rotation. However, rotation invariance can only be achieved at small angles, typically 10 degree in [16], 5 degree in [17] and 10 degree in [19]. Our scheme can resist large rotations, such as 90 degree or even an obtuse angle. Our scheme is also robust to combined attacks, such as rotation plus scaling.

5. CONCLUSIONS The main contribution of this paper is that we presented a new watermark synchronization scheme which is based on robust interest points. Interest points are first extracted from the scale normalized image and the locally most stable points are employed to generate some non-overlapped circular regions. These regions are used for synchronization purpose. Based on the proposed synchronization method, a new image watermarking scheme is proposed using rotation invariant pseudo-Zernike moments. A minimum distance decoder is also presented to detect the watermark blindly. Experimental results on Stirmark 4.0 show that the proposed synchronization scheme works well and the watermark is robust to both traditional attacks and geometric attacks.

IMAGE WATERMARKING USING INTEREST POINT AND INVARIANT MOMENT

513

REFERENCES 1. I. J. Cox, M. L. Miller, and J. A. Bloom, Digital Watermarking, Morgan Kaufmann Publishers, 2002. 2. J. S. Pan, H. C. Huang, and L. C. Jain, Intelligent Watermarking Techniques, World Scientific Publishing Company, Singapore, 2004. 3. J. S. Pan, H. C. Huang, L. C. Jain, and W. C. Fang, Intelligent Multimedia Data Hiding, Vol. 58, Studies in Computational Intelligence, Springer, 2007. 4. F. A. P. Petitcolas, R. J. Anderson, and M. G. Kuhn, “Attacks on copyright marking systems,” in Proceedings of the 2d Workshop on Information Hiding, Vol. 1525, 1998, pp. 219-239. 5. V. Licks and R. Jordan, “Geometric attacks on image watermarking systems,” IEEE Multimedia, Vol. 12, 2005, pp. 68-78. 6. D. Zheng, Y. Liu, J. Zhao, and A. El-Saddik, “A survey of RST invariant image watermarking algorithms,” ACM Computing Surveys, Vol. 39, 2007, pp. 1-89. 7. S. Pereira and T. Pun, “Robust template matching for affine resistant image watermarks,” IEEE Transactions on Image Processing, Vol. 9, 2000, pp. 1123-1129. 8. W. Lu, H. T. Lu, and F. L. Chung, “Feature based watermarking using watermark template match,” Applied Mathematics and Computation, Vol. 177, 2006, pp. 377386. 9. J. J. K. O’Ruanaidh and T. Pun, “Rotation, scale and translation in Variant spread spectrum digital image watermarking,” Signal Processing, Vol. 66, 1998, pp. 303317. 10. C. Y. Lin, M. Wu, J. A. Bloom, I. J. Cox, M. L. Miller, and Y. M. Lui, “Rotation, scale, and translation resilient watermarking of images,” IEEE Transactions on Image Processing, Vol. 10, 2001, pp. 767-782. 11. D. Zheng, J. Zhao, and A. El-Saddik, “RST-invariant digital image watermarking based on log-polar mapping and phase correlation,” IEEE Transactions on Circuits and Systems for Video Technology, Vol. 13, 2003, pp. 753-765. 12. H. S. Kim and H. K. Lee, “Invariant image watermark using Zernike moments,” IEEE Transactions on Circuits and Systems for Video Technology, Vol. 13, 2003, pp. 766-775. 13. Y. Xin, S. Liao, and M. Pawlak, “Geometrically robust image watermarking via pseudo-Zernike moments,” in Proceedings of Canadian Conference on Electrical and Computer Engineering, Vol. 2, 2004, pp. 939-942. 14. Y. Xin, S. Liao, and M. Pawlak, “Robust data hiding with image invariants,” in Proceedings of IEEE Canadian Conference on Electrical and Computer Engineering, 2005, pp. 963-966. 15. Y. Xin, S. Liao, and M. Pawlak, “Geometrically robust image watermarking on a circular domain,” http://www.ee.umanitoba.ca/~pawlak/papers/Imaging/Watermarking.pdf. 16. P. Bas, J. M. Chassery, and B. Macq, “Geometrically invariant watermarking using feature points,” IEEE Transactions on Image Processing, Vol. 11, 2002, pp. 10141028. 17. C. W. Tang and H. M. Hang, “A feature-based robust digital image watermarking scheme,” IEEE Transactions on Signal Processing, Vol. 51, 2003, pp. 950-959.

LEI-DA LI, BAO-LONG GUO AND LEI GUO

514

18. X. Qi and J. Qi, “A robust content-based digital image watermarking scheme,” Signal Processing, Vol. 87, 2007, pp. 1264-1280. 19. H. Y. Lee, H. S. Kim, and H. K. Lee, “Robust image watermarking using local invariant features,” Optical Engineering, Vol. 45, 2006, pp. 1-10. 20. L. D. Li, B. L. Guo, and K. Shao, “Geometrically robust image watermarking using scale-invariant feature transform and Zernike moments,” Chinese Optics Letters, Vol. 5, 2007, pp. 332-335. 21. C. Jin and S. Wang, “Robust watermark algorithm using genetic algorithm,” Journal of Information Science and Engineering, Vol. 23, 2007, pp. 661-670. 22. M. Alghoniemy and A. H. Tewfik, “Geometric invariance in image watermarking,” IEEE Transactions on Image Processing, Vol. 13, 2004, pp. 145-153. 23. C. Harris and M. Stephens, “A combined corner and edge detector,” in Proceedings of the 4th Alvey Vision Conference, 1988, pp. 147-151. 24. C. H. Teh and C. H. Chin, “On image analysis by the methods of moments,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 10, 1988, pp. 496513. 25. Stirmark 4.0, http://www.cl.cam.ac.uk/~fapp2/watermarking/Stirmark/.

APPENDIX: PROOF OF EQUATION (17) Proof: Suppose that the original PZM with order k and repetition l of a circular region R(x, y) is Ak,l, the reconstructed error image is e(x, y), we add the error image into the original region in spatial domain. Then the new PZM of the modified region can be computed as: Ak′ ,l = =

k +1

π

*

2

k +1

π

∫∫ x + y ≤1[ R( x, y) + e( x, y)]Vk ,l ( ρ ,θ )dxdy 2

∫∫ x + y ≤1 R( x, y)Vk ,l ( ρ ,θ )dxdy + *

2

= Ak ,l +

k +1

π

2

k +1

π

∫∫ x + y ≤1 e( x, y)Vk ,l ( ρ ,θ )dxdy *

2

2

∫∫ x + y ≤1 e( x, y)Vk ,l ( ρ ,θ )dxdy. *

2

2

Case 1: l ≠ 0 According to Eq. (16), e(x, y) = (Vk,l + Vk,l), then k +1

α (Vk ,−l + Vk ,l )Vk*,l ( ρ ,θ )dxdy π ∫∫ x2 + y 2 ≤1 α (k + 1) ⎡ V V * ( ρ , θ )dxdy + ∫∫ 2 2 Vk ,−lVk*,l ( ρ ,θ )dxdy ⎤ . = Ak ,l + x + y ≤1 ⎣⎢ ∫∫ x 2 + y 2 ≤1 k , l k ,l ⎦⎥ π

Ak′ ,l = A k ,l +

According to Eq. (9), we have:

π

π

∫∫ x + y ≤1Vk ,lVk ,l ( ρ ,θ )dxdy = k + 1 δ kk δ ll = k + 1 . *

2

2

Similarly:

π

∫∫ x + y ≤1Vk ,−l Vk ,l ( ρ ,θ )dxdy k + 1 δ kk δ −ll = 0. *

2

2

IMAGE WATERMARKING USING INTEREST POINT AND INVARIANT MOMENT

Then Ak′ , l = Ak , l +

515

α (k + 1) ⎡ π ⎤ + 0 ⎥ = Ak , l + α . ⎢ π ⎣ k +1 ⎦

Case 2: l = 0 According to Eq. (16), e(x, y) = α Vk,l, then k +1

α Vk ,lVk*,l ( ρ ,θ )dxdy π ∫∫ x 2 + y 2 ≤1 α (k + 1) * = Ak ,l + ∫∫ x2 + y2 ≤1Vk ,lVk ,l ( ρ ,θ )dxdy π α (k + 1) π δ kk δ ll = Ak ,l + α . = Ak ,l + π k +1

Ak′ ,l = Ak ,l +

Finally, we acquire that Ak′ , l = Ak , l + α . Lei-Da Li (李雷达) received his B.S. degree from Xidian University, at Xi’an, P.R. China, in 2004. Currently, he is pursuing the Ph.D. degree with the Institute of Intelligent Control and Image Engineering (ICIE), Xidian University. His research interests include pattern recognition, multimedia digital watermarking and multimedia digital signal processing.

Bao-Long Guo (郭宝龙) received his B.S., M.S. and Ph.D. degrees from Xidian University in 1984, 1988 and 1995, respectively, all in Communication and Electronic System. From 1998 to 1999, he was a visiting scientist at Doshisha University, Japan. He is currently a full professor with the Institute of Intelligent Control & Image Engineering (ICIE) at Xidian University. His research interests include neural networks, pattern recognition, intelligent information processing, image processing and image communication.

Lei Guo (郭磊) graduated for the Ph.D. from Institute of Intelligent Control and Image Engineering, Xidian University at Xi’an, P.R. China, in 2005, and he is now a postdoctor in National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences at Beijing, P.R. China. His research interests include information security, image steganography and digital watermarking.