Robust image watermarking using local Zernike moments

J. Vis. Commun. Image R. 20 (2009) 408–419

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Robust image watermarking using local Zernike moments Nitin Singhal a, Young-Yoon Lee a, Chang-Su Kim b,*, Sang-Uk Lee c a b c

Samsung Electronics Co. Ltd., Suwon, Republic of Korea School of Electrical Engineering, Korea University, Seoul, Republic of Korea Signal Processing Laboratory, School of Electrical Engineering and INMC, Seoul National University, Republic of Korea

a r t i c l e

i n f o

Article history: Received 8 December 2008 Accepted 22 April 2009 Available online 3 May 2009 Keywords: Digital image watermarking Digital right management Local Zernike moments Feature point detection Image normalization Content-based synchronization Salient region parameters Geometric distortions

a b s t r a c t In this work, we propose a robust image watermarking algorithm using local Zernike moments, which are computed over circular patches around feature points. The proposed algorithm locally computes Zernike moments and modifies them to embed watermarks, achieving robustness against cropping and local geometric attacks. Moreover, to deal with scaling attacks, the proposed algorithm extracts salient region parameters, which consist of an invariant centroid and a salient scale, and transmits them to the decoder. The parameters are used at the decoder to normalize a suspect image and detect watermarks. Extensive simulation results show that the proposed algorithm detects watermarks with low error rates, even if watermarked images are distorted by various geometric attacks as well as signal processing attacks. Ó 2009 Elsevier Inc. All rights reserved.

1. Introduction Digital images can be easily duplicated without any loss. This feature facilitates the illegal use of copyrighted materials, e.g., unrestricted duplication and dissemination via the Internet. As a result, the piracy makes service providers hesitate to offer services in digital form, in spite of digital imaging equipments replacing analog ones. To overcome this reluctancy and possible copyright issues, the intellectual property rights of digital images should be protected. To protect copyrighted images, many approaches, including authentication, encryption, and digital watermarking, have been proposed. Encryption methods may guarantee secure transmission of data to authenticated users through unsecured channels. However, once decrypted, the data are identical to the original and their piracy cannot be restricted. Digital watermarking is an alternative approach to deal with these unlawful acts. It hides invisible marks or copyright information in digital contents and claims the copyrights. The marks should be robust enough to survive various attacks. It is also desirable that illegal attempts should cause the degradation of image quality without erasing the watermarks. With the development of watermarking technologies, attacks against watermarking systems also have become more sophisticated. Those attacks can be classified into signal processing attacks and geometric attacks. Signal processing operations, such as lossy compression, denoising, noise addition, and filtering, reduce the * Corresponding author. E-mail address: [email protected] (C.-S. Kim). 1047-3203/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.jvcir.2009.04.002

energy of watermarks, while geometric attacks induce synchronization errors between the original and the watermarked images and therefore can mislead the watermark decoder. Most previous watermarking methods provide robustness against signal processing attacks, but only a few specialized methods address geometric attacks. Watermarking schemes to combat geometric attacks can be classified into non-blind schemes, semi-blind schemes, invariant domain embedding, template-based synchronization, and content-based synchronization. Section 2 will review these watermarking schemes. In this paper, we propose a novel robust image watermarking algorithm. Although there are techniques that deal with geometric attacks, random bending, cropping, and non-isotropic scaling still remain to be difficult attacks. The proposed algorithm embeds watermarks by modifying local Zernike moments (LZMs), which are defined over circular patches around feature points. Unlike the conventional algorithms using moments [1,2], we compute Zernike moments locally to achieve resilience against cropping. Moreover, to make the proposed algorithm robust against scaling attacks, we extract salient region parameters and transmit them to the decoder. The decoder uses the parameters to normalize a suspect image and detect watermarks. Simulation results demonstrate that the proposed algorithm provides robust performance in various attack scenarios. We presented some of our preliminary results in [3]. In this work, we extend the work in [3] by evaluating the performance of the proposed algorithm more extensively in multiple application scenarios. Moreover, we analyze the false alarm rate of the proposed watermarking algorithm.

N. Singhal et al. / J. Vis. Commun. Image R. 20 (2009) 408–419

The paper is organized as follows. Section 2 reviews conventional synchronization techniques. Section 3 introduces local Zernike moments and a feature point detection scheme. Section 4 describes the proposed watermarking system. Section 5 proposes an image normalization scheme using salient region parameters. Section 6 evaluates the performance of the proposed algorithm. Section 7 concludes the paper. 2. Conventional synchronization techniques In this section, we review synchronization techniques in conventional watermarking methods to deal with geometric attacks or distortions. 2.1. Non-blind schemes Non-blind schemes use the original image to identify geometric distortions. For example, Dong et al. [4] used a deformable mesh model to correct geometric distortions. It is effective in the case of local distortions, but the extension to global affine distortions is computationally demanding. 2.2. Semi-blind schemes Semi-blind schemes use side information instead of the original image to extract watermarks. Lu et al. [5] proposed a watermarking scheme, which embeds two complementary watermarks into the wavelet coefficients of the original image. In their scheme, the positions of the watermarks are necessary for the watermark extraction and thus are transmitted to the decoder as the side information. Shieh et al. [6] proposed a semi-blind scheme based on singular value decomposition. Their scheme divides the original image and the watermark image into blocks. Then, it replaces the singular values of each block in the watermark image with those of a similar block in the original image to generate a secret image. The secret image and the mapping between watermark blocks and original blocks are used as the side information for the watermark detection. In [7], an object-based watermarking algorithm using the scale-invariant feature transform (SIFT) was proposed. It selects an object region in the original image to embed a watermark, and transmits the SIFT features of the object region as the side information. At the decoder, those features are used to identify the object region and then to extract the watermark. These semiblind schemes provide robustness at the expense of a large amount of side information. 2.3. Invariant domain embedding The watermarking schemes in this category embed watermarks into features, which are invariant to geometric distortions. O’Ruanaidh and Pun [8] derived a feature domain that is invariant to rotation, scaling, and translation attacks using the Fourier–Mellin transform (FMT). The method in [9] is also based on the properties of FMT and uses a translation and scale invariant domain, while resisting rotation attacks by an exhaustive search. However, these FMT-based schemes fail to distinguish the size change due to scaling from one due to cropping. Hence, they are vulnerable to cropping attacks.

409

template-based schemes address the synchronization after local and global geometric attacks, templates can be easily detected and removed since they usually represent peaks in the transform domain. 2.5. Content-based synchronization Content-based synchronization schemes [11] locate watermarks using image semantics. Moment normalization [12], Radon transformation [13], and Zernike moments [1,2] have been extensively used to achieve rotation invariance. Moreover, to realize scale and translation invariance, these schemes adopt the global image normalization technique [14], which uses the image centroid and the central moments. Their main limitation is the inability to resist cropping attacks, since missing contents can lead to incorrect centroid and central moments. The advances in content-based synchronization have resulted in a class of algorithms known as region-based watermarking [15– 18]. Feature points in the host image are used to locate regions for watermark embedding. At the receiver side, the feature points are expected to be robustly detected even after geometric distortions. Bas et al. [15] presented an overview of different feature point detectors and a benchmark system to select a robust detector. They concluded that the Harris corner detector [19] is the most robust one. They also proposed a watermark embedding algorithm based on the triangular mesh decomposition, where each triangle is formed from three detected feature points. Although their algorithm provides a certain degree of robustness, thorough robustness evaluation through a standard benchmark, such as Stirmark [20,21], is missing. Tang and Hang’s algorithm [17] uses the Mexican-Hat wavelet scale integration to extract feature points. It employs a local image warping scheme to realize resilience against geometric distortions. Although it provides robustness against cropping, it does not take scaling attacks into account and yields poor results against shearing and rotation attacks. More recently, in [18], the scale-space theory was employed for feature point detection, where feature points are determined through the automatic scale selection and the local extreme detection. 2.6. Summary After surveying the existing methods that deal with geometric distortions, we have the following observations: (i) the semi-blind watermarking schemes require a large amount of side information; (ii) the invariant domain embedding is vulnerable to cropping attacks; (iii) template signals for distortion parameter recovery are easily removed; (iv) the content-based synchronization using the moment normalization, Radon transformations, or Zernike moments are very sensitive to cropping and local geometric distortions; and (v) the robust extraction of feature points plays a key role in the region-based watermarking schemes. In this work, we propose a watermarking algorithm in the category of the content-based synchronization. We combine the advantages of region-based watermarking and Zernike moments to resist various geometric attacks as well as signal processing attacks. Also, it is noted that the proposed algorithm requires side information similarly to the semi-blind schemes [5–7]. However, the proposed algorithm requires a significantly lower amount of side information than these schemes.

2.4. Template-based synchronization 3. Preliminaries Template-based schemes identify the geometric transformations by retrieving artificially embedded references, called templates. In [10], templates are inserted into the discrete Fourier transform (DFT) domain as local peaks at predefined positions. Geometric attacks are recovered using the template distortions. Although the

3.1. Local Zernike moments Zernike [22] introduced a set of complex orthogonal functions with a simple rotational property, which form an orthogonal basis

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for the class of square integrable functions. Since Teague [23] pioneered the use of Zernike moments in image analysis, Zernike moments have been frequently utilized for various image processing and computer vision tasks [24,25]. The Zernike basis function is defined as

ð1Þ

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where a ¼ x2 þ y2 ; h ¼ arctanðy=xÞ; n is a non-negative integer,    and m 2 Dn ¼ 0; 2; . . . ; 2 n2 . bxc denotes the greatest integer less than or equal to x. The radial Zernike polynomial r nm ðaÞ is a polynomial in a of degree n, defined as

r nm ðaÞ ¼

s¼0

ð1Þs ðn  sÞ!an2s    : s! nþjmj  s ! njmj s ! 2 2

ð2Þ

Note that rnm ðaÞ ¼ r n;m ðaÞ. The basis functions are orthogonal, satisfying

nþ1

Z Z

v nm ðx; yÞv pq ðx; yÞdxdy ¼

p



1; if n ¼ p and m ¼ q; 0;

otherwise:

x2 þy2 61

ð3Þ The completeness and orthogonality of v nm ðx; yÞ allow us to represent any square integrable function f ðx; yÞ on the unit disk as a series.

f ðx; yÞ ¼

1 X X

gðx; cÞ ¼

1 jxj2 =2c e : 2pc

ð8Þ

Then, the scale-space representation of f ðxÞ is given by

v nm ðx; yÞ ¼ rnm ðaÞejmh ;

ðnjmjÞ=2 X

coordinate x ¼ ðx; yÞ, and let gðx; cÞ denote a 2D Gaussian kernel with scale c.

znm v nm ðx; yÞ;

ð4Þ

f ðx; cÞ ¼ gðx; cÞ  f ðxÞ;

ð9Þ

where  denotes the linear convolution operator. The second order derivative matrix UðxÞ is defined as

"

# f xx ðx; cÞ f xy ðx; cÞ ; UðxÞ ¼ s  gðx; sÞ  f yx ðx; cÞ f yy ðx; cÞ 2

ð10Þ

where f x denotes the partial derivative of f with respect to x. In this work, s ¼ 4 and c ¼ 2. The matrix UðxÞ in (10) describes the distributions of the second order derivatives in a local neighborhood of x. The local derivatives are computed with pre-Gaussian smoothing with scale c. Then, the derivatives are averaged in the neighborhood of x with a Gaussian window of scale s. The eigenvalues of this matrix represent two principal signal changes in the neighborhood of x. This property enables the extraction of corner or junction points, at which curvatures are significant in orthogonal directions. Specifically, a point x is declared to be a feature point if the matrix UðxÞ has two significant eigenvalues. To reduce the complexity of explicit eigenvalue computation, the Harris corner measure (HCM) [26] is defined as

n¼0 m2Dn

where znm is the Zenike moment of order n with repetition m, given by

znm ¼

nþ1

Z Z

p

f ðx; yÞv nm ðx; yÞdxdy:

ð5Þ

x2 þy2 61

Zernike moments are rotationally invariant. Specifically, if the image f ðx; yÞ is rotated by an angle /, then the Zernike moments are modified by

~znm ¼ znm ejm/ :

ð6Þ

hðx; sÞ ¼ k1  k2  0:04ðk1 þ k2 Þ2 ; ¼ detfUðxÞg  0:04  ðtracefUðxÞgÞ2 ;

ð11Þ ð12Þ

where k1 and k2 are the eigenvalues of UðxÞ. If a point has a locally maximal HCM, it is detected as a feature point. Fig. 1 illustrates the robustness of the corner point detection against geometric distortions. Fig. 1(a) shows the detected corner points in the original image. Fig. 1(b) shows non-overlapping circular patches centered around the corner points. Fig. 1(c)–(e) shows non-overlapping circular patches obtained after scaling, cropping, and rotation attacks, respectively.

Thus, the magnitudes of Zernike moments can be used as rotationally invariant image features. The rotational invariance of Zernike moments is valid, provided that one uses a true analog image function. In the case of digital images, however, the integration in (5) cannot be applied directly. Instead, its approximate version should be used. In this work, we compute local Zernike moments over a circular image patch pðx; yÞ of radius R by

^znm ¼

n þ 1 XX

pR2

v nm ðx; yÞpðx; yÞ:

ð7Þ

x2 þy2 6R2

We shall simply use znm to denote the approximated ^znm . 3.2. Feature point detection Feature point detection is an approach in computer vision to extract features to infer the contents of an image. Especially, corner detection is often used in motion detection, tracking, image mosaicing, panorama stitching, 3D modeling, and object recognition. A corner can be defined as a point around which there are two dominant and different edge directions. Corner points are robust against image distortions, and thus they can be used to locate patches for robust watermark embedding. We employ the Harris corner detector [19,26] as a feature point detector. Let f ðxÞ denote the original image brightness at a spatial

Fig. 1. Illustration of the corner point detection: (a) Harris corner points in the original image. (b) Non-overlapping circular patches around the corner points. Nonoverlapping circular patches detected after (c) scaling, (d) cropping, and (e) rotation attacks.

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4. Proposed algorithm As shown in Fig. 2, we consider two application scenarios. In scenario I, we focus on the robust watermarking scheme against non-scaling attacks. In scenario II, we extract salient region parameters and transmit them to the decoder as side information. The decoder uses the parameters to normalize a suspect image and detect watermarks, when a watermarked image passes through scaling attacks as well as non-scaling attacks. This section describes the proposed watermark embedding and extraction procedures, which are used for both scenarios I and II. The next section will describe the salient region parameters and the image normalization scheme for scenario II. 4.1. Watermark embedding Fig. 3 outlines the watermark embedding procedure. We first extract feature points from an input image as described in Section 3.2. Then, each feature point is associated with a circular patch of radius R. A feature point with a small HCM has a low probability of being re-detected, since it disappears easily when image contents are modified. The distribution of feature points also affects the performance of the watermarking system. If the distances between adjacent feature points are too small, the patches overlap in large areas. On the other hand, if the distances are too large, only a small number of patches are available, reducing the watermark strength. To control the distribution of feature points and to obtain non-overlapping patches, we first select the feature point p1 with the highest HCM. Then, the second feature point p2 is selected such that it has the highest HCM, subject to the constraint dðp1 ; p2 Þ P 2R. Similarly, the nth feature point pn is selected such that it has the highest HCM, subject to the constraint

min dðpk ; pn Þ P 2R:

ð13Þ

16k6n1

Let Nf denote the number of feature points extracted, and Np the number of non-overlapping patches. In this work, Nf is fixed for every image, but N p varies. We consider two factors in the selection of local Zernike moments (LZMs) for watermark embedding. First, the moments with orders higher than a certain threshold nmax cannot be computed reliably. Second, the moments with repetitions m ¼ 4i ði 2 ZÞ cannot be computed accurately [1]. Therefore, these moments are not used for embedding. Let S ¼ fznm : n 6 nmax ; m P 0; m–4ig be the set of candidate LZMs for watermark embedding. In this work, we set nmax ¼ 12.

We modify LZMs using the dither modulation, which is a special form of quantization index modulation for data hiding [27]. Let b ¼ ðb1 ; . . . ; bL Þ denote a bit sequence of length L, which is to be embedded into a circular patch pðx; yÞ. Using a key, we pseudo-randomly choose L LZMs from S to form a Zernike moment vector z ¼ ðzn1 m1 ; . . . ; znL mL Þ. The magnitude of each zni mi is quantized using the dither modulation, producing a new vector ~ z ¼ ð~zn1 m1 ; . . . ; ~znL mL Þ. Specifically, ~zni mi is given by

j~zni mi j ¼ qðjzni mi j  di ðbi ÞÞ þ di ðbi Þ;

~zni mi ¼

j~zni mi j  zni m i ; jzni mi j

i ¼ 1; . . . ; L:

ð15Þ

Note that, in quantizing each zni mi , its conjugate zni ;mi should also be quantized to have the same magnitude, so that the reconstructed patch is real. Due to the limitations of high-order LZMs and digitization errors, the reconstruction from LZMs is not perfect. To resolve this issue, we adopt the approach in [1], where the watermark pattern is generated from quantization errors and then added to the original patch. Specifically, let eni mi ¼ ~zni mi  zni mi and eni ;mi ¼ ~zni ;mi  zni ;mi denote the quantization errors of zni mi and zni ;mi , respectively. We construct the watermark pattern wðxÞ from the quantization errors of the selected LZMs by

wðxÞ ¼

L X ½eni mi v ni mi ðxÞ þ eni ;mi v ni ;mi ðxÞ:

~ðxÞ by adding the original Then, we obtain the watermarked patch p patch pðxÞ and the watermark pattern wðxÞ, i.e.,

~ðxÞ ¼ pðxÞ þ wðxÞ: p

ð17Þ

4.2. Watermark extraction Fig. 4 shows the block diagram of the proposed watermark extractor. Similarly to the embedding procedure, we extract feature points from a suspect image using the Harris corner detector. Around each feature point, we define a circular patch of radius R. Using the same key as the embedder, the extractor pseudo-randomly selects L LZMs of the patch, forming a Zernike moment

Distortion classification

Normalized image

Feature point extraction

Embedding

Message

Scenario I

ð16Þ

i¼1

Salient region parameters

Feature point extraction

ð14Þ

where qðÞ is the quantizer with step size D, and di ðÞ is the dither function for the ith quantizer satisfying di ð1Þ ¼ D2 þ di ð0Þ. The dither variable di ð0Þ is uniformly distributed over ½0; D and is randomly generated. The modified LZMs are then calculated as

Salient region parameters

Original image

i ¼ 1; . . . ; L;

Scenario II

Fig. 2. Two application scenarios.

Extraction

Extracted Message

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N. Singhal et al. / J. Vis. Commun. Image R. 20 (2009) 408–419

Circular patch p( x ) Original image

Feature point detection

z

Local Zernike moments

Dither modulation

Watermark pattern e

+

+

reconstruction

+

Watermark pattern w(x)

Watermarked ~ patch p(x)

Key Message b

Fig. 3. The block diagram of the watermark embedder.

Suspect image

Circular patch ~ p( x ) Feature point Local Zernike detection moments

z’

^ Extracted b message

Dither modulation

Key Fig. 4. The block diagram of the watermark extractor. 0

ðz0n1 m1 ; . . . ; z0nL mL Þ,

vector z ¼ which possibly carries the watermark information. Next, we generate dither variables di ð0Þ and di ð1Þ. We then quantize the magnitude of each z0ni mi with the corresponding two dithers by







0



zni mi ¼ qð z0ni mi  di ðjÞÞ þ di ðjÞ; j

j ¼ 0 or 1:

ð18Þ





By comparing the distance between z0ni mi and its two quantized versions, we estimate the bit embedded into jzni mi j via

^ ¼ arg min b i

j2f0;1g





2

0 0

zni mi  zni mi ; j

ð19Þ

^i , which is the minimum distance decoder rule [27]. These bits b ^ where i ¼ 1; . . . ; L, form the extracted message b. In this work, we use the codewords of a BCH code [28] as watermark messages. A patch is declared to carry a watermark message ^ satisfies b, if the extracted message b

^ 6 t; dH ðb; bÞ

ð20Þ

where dH is the Hamming distance function, and t is the error correcting capability of the BCH code. Finally, the image is authenticated to be marked with a watermark b, if b is detected from a majority of circular patches within the image. 5. Image normalization using salient region parameters As shown in Fig. 2, in scenario II, we employ salient region parameters, which are composed of an invariant centroid and a salient scale, to deal with scaling attacks. At the extractor, we first classify geometric distortions of a suspect image, using the salient region parameters, and normalize the suspect image to invert possible scaling attacks. Then, the watermarks are extracted using the method in Section 4.2. 5.1. Salient region parameters In the global image normalization [14], an attacked image is matched to the original image using the image centroid and the central moments. However, if an image is cropped or its pixel values are changed, its centroid and central moments are also modified from those of the original image. As a result, the attacked image may not be normalized reliably, causing watermark detection failures. Kim et al. [29] used invariant circular regions with symmetrically distributed intensity values for image normalization. Their

scheme is robust against rotation, translation, and cropping attacks, but it is not clear how they handle scaling attacks. Their scheme fixes the radius of an invariant circular region, but it should be covariant with the image scale. If the image scale factor is not known in advance, it is impossible to determine the radius at the decoder side. To overcome this shortcoming, Yang et al. [30] proposed to use the notion of salient region. Their algorithm first normalizes a suspect image to the original image size and obtains the intensity difference map. Then, at different scales, it extracts invariant circular regions on the map. It then computes the 2nd Hu moment [31] over the region at each scale. The region with the minimum moment is called the salient region. However, we observed that the 2nd Hu moments at different scales do not yield the discriminating minimum in many cases. Also, the interpolation noises in the case of down-scaling attacks degrade the intensity difference map and consequently the accuracy of the estimated salient scale. In this work, we combine the concepts of the invariant centroid in [29] and the salient scale in [30] to normalize a suspect image robustly in the decoder. In contrast to [30], however, we use the 1st Hu moment to determine the salient scale. To make the determination of the salient scale more robust against scaling attacks, we use image intensity values directly, instead of intensity differences. Also, we estimate the centroid and the scale of a suspect image without normalizing it to a predefined size. We call the invariant centroid and the salient scale as the salient region parameters. The salient region parameters are estimated as follows. For each scale r 2 ½rmin ; rmax , (1) Compute the initial centroid c0 ¼ ðx0 ; y0 Þ of the entire image after performing the Gaussian low-pass filtering to reduce the effects of waveform attacks.

x0 ¼

Z

xf ðx; yÞdx; y0 ¼

X

Z

yf ðx; yÞdy;

ð21Þ

X

where f denotes the Gaussian filtered image, and X denotes the set of pixel coordinates of the entire image. (2) Compute iteratively the ith centroid ci of the circular region that has radius r and center ci1 , until the centroid converges to Þ. cðrÞ ¼ ð x; y (3) Compute the 1st Hu moment m1 ðrÞ over the circular region with radius r and center cðrÞ, given by

m1 ðrÞ ¼

l20 þ l02 ; ðl00 Þ2

where the central moment

ð22Þ

lpq is given by

N. Singhal et al. / J. Vis. Commun. Image R. 20 (2009) 408–419

XX

lpq ¼

2

Þ ðxxÞ þðyy

2

Þq f ðx; yÞ: ðx  xÞp ðy  y

413

ð23Þ

6r 2

The 1st Hu moment m1 measures the symmetry of the energy distribution. For example, m1 is zero, if the intensity values are symmetrically distributed. Then, we obtain the salient scale q by

q ¼ arg min m1 ðrÞ:

ð24Þ

r2½r min ;r max 

and the invariant centroid c by

c ¼ cðqÞ:

ð25Þ

Fig. 6 compares the robustness of the proposed salient region selection method with that of the Yang et al.’s algorithm [30]. We see that the proposed algorithm extracts the centroids and the scales with high accuracy even after scaling, cropping, and rotating attacks, whereas the Yang et al.’s algorithm locates the salient regions unreliably with inaccurate scales. Fig. 5 compares the success rates of the proposed salient region selection method and the Yang et al.’s algorithm after scaling, rotation, and cropping attacks. Hundred randomly chosen images from the Corel image database [32] are used in this test. The salient region parameters are declared to be successfully detected when the centroid coordinates and the scale are recovered within one pixel error. A success rate is defined as the ratio between the number of images whose salient region parameters are successfully detected and the number of test images. 5.2. Image normalization We carry out the image normalization in two steps. First, we detect the change in the sampling rate of the suspect image. Second, we normalize the image to the original sampling rate. We assume that the size and the salient region parameters of the original image are available at the decoder. However, the proposed algorithm does not require the original image itself. The watermark embedder registers the side information, i.e., the size and the salient region parameters of the original image, to a trusted third party. The authenticator or the watermark extractor requests the side information from the trusted party to carry out image normalization prior to the watermark extraction. It is noted that the amount of the side information is negligible, and thus the side information can be transmitted in a raw file without compression from the embedder to the trusted third party or from the trusted third party to the extractor.

120 [30] Proposed

Success rate (%)

100 80 60

Fig. 6. Comparison of the salient region selection methods: (a)–(d) are obtained by the Yang et al.’s algorithm [30], while (e)–(h) are obtained by the proposed algorithm. (b) and (f) are the scaled versions of the original images (a) and (e), respectively. (c) and (g) are the cropped versions, and (d) and (h) are the rotated versions. Note that [30] resizes a suspect image to the original image size before the salient region selection, while we estimate the salient region directly on the suspect image.

Let co ¼ ðxo ; yo Þ and qo denote the invariant centroid and the salient scale of the original image, respectively. Given these salient region parameters, the decoder also computes the invariant centroid cs ¼ ðxs ; ys Þ and the salient scale qs of the suspect image with the constraint 12 6 qs =qo 6 2. In this work, we use both the invariant centroid and the salient scale to classify the geometric distortions of the suspect image, whereas the Yang et al.’s [30] scheme uses the scale information only. Let S ¼ kðxo ; yo Þk=kðxs ; ys Þk, where k  k denotes the L2 norm. We classify geometric attacks into five categories:

40 20 0 Scale (0.5,0.5)

Rotation (30°)

Centered cropping (25%)

Fig. 5. The comparison of the success rates of the proposed salient region selection method and the Yang et al.’s algorithm [30] after scaling, rotation, and cropping attacks.

 xs ¼ xo and ys ¼ yo ) (I) Symmetric Cropping  xs ¼ xo or ys ¼ yo ) (II) Aspect Ratio Change or Small Shearing or Translation  xs – xo and ys – yo – S ¼ 1 ) (III) Rotation-Only or Rotation-Crop – S–1 qs – qo )(IV) Scaling or Upscaling-Crop or Non-Isotropic Scaling qs ¼ qo )(V) Translation

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(V) Translation: In this category, the invariant centroid is shifted by a translation attack, but the salient scale remains the same. No normalization is performed, since this is a nonscaling attack.

Fig. 7 illustrates how an invariant centroid is shifted after cropping, scaling, aspect ratio change, rotation, and translation attacks. After the classification, within each category, we further differentiate scaling attacks, which changes the image sampling rate, from non-scaling attacks. Then, we normalize the suspect image in the case of scaling attacks as follows.

After the normalization, we estimate the watermark message in the suspect image using the method in Section 4.2.

(I) Symmetric Cropping: No normalization is performed, since cropping is a non-scaling attack. (II) Aspect Ratio Change or Small Shearing or Translation: This category includes both scaling and non-scaling attacks. We investigate border pixels to discriminate aspect ratio change, which is a scaling attack, from small shearing and translation. In the case of small shearing and translation, some border pixels are missing or zero padded, while no pixel padding occurs in aspect ratio change. The suspect image with an aspect ratio change attack is normalized by resizing it to the original image size. (III) Rotation-Only or Rotation-Crop: After a rotation attack, the invariant centroid is also rotated by the same angle, but the distance of the invariant centroid from the image center remains the same, S ¼ 1. Since rotation attacks are non-scaling ones, no normalization is performed. (IV) Scaling or Upscaling-Crop or Non-Isotropic Scaling: This category includes scaling attacks only. We first compute the directional scale factors Sx ¼j xo j = j xs j and Sy ¼j yo j = j ys j. Then, we normalize the suspect image by the scale factors Sx and Sy in the x and y directions, respectively.

6. Experimental results We first analyze the false alarm rate of the proposed watermarking algorithm. We then compare the performance of the proposed algorithm with that of the conventional algorithms against non-scaling attacks in scenario I. It is unfair to compare them against scaling attacks, since the conventional algorithms do not employ the scheme for normalizing spatial sampling rates. Finally, we evaluate the robustness of the proposed algorithm against scaling as well as non-scaling attacks in scenario II, in which the salient region parameters are transmitted to the decoder for image normalization. 6.1. False alarm analysis The encoder extracts N f feature points, and selects N p non-overlapping circular patches centered around the feature points. In this work, N f ¼ 50; N p varies according to the feature point distribution, and each circular patch has radius R ¼ 21. Then, the encoder generates a 31-bit watermark message ðL ¼ 31Þ using the BCH code

XS

XO

XO

XO=XS

YO=YS

YS

YO

YO=YS

(b) Scaling

(a) Cropping

XS

(c) Aspect ratio change

XS XO XO

YS

(e) Translation

(d) Rotation

Original image

YO

YO

YS

XS

Attacked image

Fig. 7. Shifts of an invariant centroid after (a) cropping, (b) scaling, (c) aspect ratio change, (d) rotation, and (e) translation attacks.

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Pimage ¼

Nf  X Nf P ipatch ð1  Ppatch ÞNf i ; i i¼Nv

0

10

−5

10

P image

[28], and embeds the same 31-bit watermark message into each of the N p circular patches repeatedly. When computing the invariant centroid of the input image, the radius q is selected within [2,30]. The decoder selects N f circular patches, which may overlap, and checks whether each patch contains the watermark. If the watermark is detected from more than N v circular patches, the image is authenticated to be marked with the watermark. Let us analyze the false alarm rate to determine the error correcting capability t of the BCH code. The false alarm rate is the probability to declare an un-watermarked image as watermarked, which is given by

−10

10

Nv = 1

−15

ð26Þ

10

Nv = 2 N =3 v

where Ppatch is the false alarm rate of a circular patch. The decoder should locate a patch with an error less than 0.75 pixels to extract LZMs reliably. The Harris corner detection cannot yield such a high accuracy in digital images. To compensate for small displacement errors after watermark embedding, we perform the minimum distance detection K ¼ 49 times by translating each circular patch from 0:75 pixels to 0.75 pixels with step size 0.25 pixels in the x and y directions, respectively. The bilinear interpolation is used to execute quarter pixel shifts. If the watermark is detected from at least one out of the K positions, the patch is claimed to be watermarked. Therefore, the false alarm rate of a circular patch is given by

Table 1 The error correcting capabilities t, the corresponding BCH codes, and the resultant false alarm rates Pimage for three different values of N v , which are used in the simulations.

Ppatch ¼ 1  ð1  PD ÞK ;

Nv

t

BCH code

P image

1 2 3

2 3 5

(31,21,2) (31,16,3) (31,11,5)

105:5 105:9 103:7

ð27Þ

where PD is the probability of detecting a watermark from a nonwatermarked circular patch, given by

PD ¼

t  X L i pe ð1  pe ÞLi ; i i¼0

P image = 10−5

−20

10

0

5

10

15

20

25

30

35

t Fig. 8. The false alarm rate P image (in log scale) in terms of the error correcting capability t of the BCH code, when the watermark should be detected from at least N v patches in order to declare an image as watermarked.

ð28Þ

where pe is the probability that a detected bit is erroneous. Note that, when there are less than t bit errors, they are corrected by the BCH code and the watermark is falsely detected. To estimate P D , various un-watermarked images, chosen from the Corel image database [32], are used as the input images to the watermark detection procedure. For each patch, we compute

erroneous bits by comparing a pre-determined watermark message and the detected message. Then, we obtain P D from the cumulative distribution of erroneous bits using (28). Fig. 8 plots the false alarm rate P image in terms of the error correcting capability t for three values of N v . It is observed that Pimage increases as t gets larger. Also, for a fixed t, increasing N v reduces

Table 2 The comparison of detection ratios, when the watermarks are corrupted by various attacks. Note that autocrop refers to cropping to the original size after rotation. The numbers in the parentheses refer to the numbers of watermarked patches (N p ). The detection ratios of [17] and [18] are excerpted from the corresponding papers. Attack

Parameters

Detection ratio (%) Lenna Proposed (12)

Baboon [18] (14)

[17] (8)

Proposed (11)

Pepper [18] (22)

[17] (11)

Proposed (12)

[18] (14)

[17] (4)

Linear geometric transform

H1 H2 H3

75.0 75.0 91.6

— — —

50.0 50.0 62.5

81.8 81.8 72.7

— — —

45.4 36.4 36.4

91.6 83.3 91.6

— — —

0.0 25.0 25.0

Rotation + cropping

1° 2° 5°

100.0 100.0 91.6

— — —

37.5 0.0 0.0

90.9 63.6 45.4

— — —

27.3 9.1 0.0

83.3 66.6 25.0

— — —

50.0 25.0 0.0

Rotation Rotation + autocrop Shearing Cropping

45° 45° x  1% y  1% 5% 10% 15% 25%

91.6 16.6 83.3 83.3 66.6 50.0 50.0

42.8 35.7 — — — 42.8 21.4

— — 50.0 25.0 25.0 — —

63.6 27.7 81.8 72.7 72.7 72.7 36.4

4.5 9.1 — — — 27.3 22.7

— — 45.4 18.2 18.2 — —

66.6 25.0 91.6 50.0 50.0 33.3 25.0

71.4 28.6 — — — 21.4 14.3

— — 25.0 50.0 50.0 — —

Gaussian filter Median filter Additive noise JPEG compression

r ¼ 1; 3  3

91.6 58.3 25.0 91.6 83.3 33.3

— — 35.7 57.1 35.7 50.0

62.5 12.5 62.5 62.5 25.0 —

90.9 9.1 54.5 81.8 72.7 45.4

— — 4.5 22.7 4.5 4.5

72.7 18.2 54.5 63.6 36.4 —

91.6 66.6 41.6 91.6 75.0 33.3

— — 28.5 85.7 35.7 35.7

25.0 25.0 100.0 75.0 0.0 —

Stirmark attacks

33 r ¼ 10 50 30

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N. Singhal et al. / J. Vis. Commun. Image R. 20 (2009) 408–419

Table 3 The average PSNRs of the watermarked images and the average detection ratios in terms of the dither quantizer step size D, when N v = 1.

D

Average PSNR (dB)

1 2 3 4 5 6 7 8

55.3 49.2 45.6 43.3 41.1 39.6 38.3 37.2

Average detection ratio (%) No attack

Scaling (0.75,0.75)

Rotation (30°)

Centered cropping (25%)

JPEG (30)

92.9 92.9 98.6 100 100 100 100 100

0 0 11.4 43.8 55.3 67.9 69.3 69.3

0 52.8 74.2 77.0 77.0 77.0 77.0 77.0

41.3 41.3 44.2 44.2 44.2 44.2 44.2 44.2

0 8.6 44.3 87.2 90.0 91.4 91.4 91.4

the false alarm rate. Table 1 summarizes the error correcting capabilities t, the corresponding BCH codes [28], and the resultant false alarm rates P image for three values of N v , which are used in the following simulations.

dither quantizer step size D affects the robustness and the water-

6.2. Robustness test: scenario I We compare the proposed algorithm with the characteristic scale embedding algorithm in [18] and Tang and Hang’s algorithm in [17]. Table 2 shows the detection ratios for scenario I attacks on the ‘‘Lenna,” ‘‘Baboon,” and ‘‘Pepper” images, when N v is set to 1. The detection ratio is defined as

Rdetection ¼

Dp ; Np

ð29Þ

where Dp is the number of circular patches where the watermark is successfully detected, and Np is the number of watermarked patches in the original image. We use the peak signal-to-noise ratio (PSNR) to measure the quality of a watermarked image, defined as

PSNR ¼ 10log10

! 2552 ; MSE

ð30Þ

where MSE denotes the mean squared error between the original and the watermarked images. In the proposed algorithm, the PSNR of a watermarked image is determined by the quantization step size D of the dither modulation in (14). A larger D leads to stronger watermarks and better robustness, but results in a lower PSNR. We choose the dither quantizer step size D, such that the PSNRs of watermarked images are close to or higher than 40 dB and the watermarks are almost imperceptible. More specifically, the PSNRs for the ‘‘Lena,” ‘‘Baboon,” and ‘‘Pepper” are 43.16, 39.79, and 43.07 dB in the proposed algorithm, while they are 49.42, 45.70, and 56.60 dB in the Tang and Hang’s algorithm [17], respectively. Also, in the characteristic scale embedding algorithm [18], it was reported that the PSNRs of the watermarked images were between 38 and 45 dB. Therefore, the Tang and Hang’s algorithm [17] provides better watermark image qualities than the proposed algorithm or the characteristic scale embedding algorithm [18]. Also, note that the image quality performance of the proposed algorithm is comparable to that of [18]. In the next subsection, we will discuss how the

Table 4 The PSNR qualities of the watermarked images.

Lenna Man Barbara Baboon Bridge Pepper

Average patch PSNR (dB)

Overall PSNR (dB)

34.7368 30.3185 33.5053 29.0137 28.8764 34.2658

43.1636 39.6812 43.5254 39.7928 39.4978 43.0707

Fig. 9. From top to bottom ‘‘Lenna,” ‘‘Man,” ‘‘Barbara,” ‘‘Baboon,” ‘‘Bridge,” and ‘‘Pepper.” (a) Original images, (b) watermarked images, and (c) magnified differences.

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Table 5 The number of circular patches, where the watermark is successfully detected, for the Lenna image. In this test, the watermark is inserted into 12 circular patches in the original image. Autocrop refers to cropping to the original size after rotation, and autoscale refers to down-scaling to the original size after rotation. x denotes the period of removed lines. Attacks

Median filtering

Gaussian filtering Additive uniform noise JPEG compression

Line removal

Centered cropping

Shearing

Parameters

22 33 44 r ¼ 1; 3  3 r ¼ 15 15 20 30 40 50 60 70 80 90 x ¼ 10 x ¼ 20 x ¼ 30 5% 10% 15% 20% 25% x 1% y 0% x 0% y 1% x 1% y 1% x 5% y 0% x 0% y 5% x 5% y 5%

Nv 1

2

3

12 7 1 3 0 0 2 10 10 11 11 11 12 12 0 4 4 10 8 6 6 6 11 12 10 9 6 0

12 7 2 5 2 3 3 10 10 11 11 11 12 12 2 5 6 10 8 6 6 6 11 12 12 9 9 1

12 10 4 9 4 8 11 12 12 12 11 12 12 12 5 8 9 11 8 7 7 7 12 12 12 10 10 4

mark image quality in detail. In Table 2, we use the following three linear geometric transformations.



 1:013 0:008 1:010 0:013 H1 ¼ ; H2 ¼ ; 0:011 1:008 0:009 1:011

 1:007 0:010 : H3 ¼ 0:010 1:012

ð31Þ

We see that the proposed algorithm provides significantly higher detection ratios than the conventional algorithms for most signal processing and geometric attacks. For example, the proposed algorithm survives centered-cropping attacks up to 25% cropping, while the algorithm in [17] can survive up to 10% cropping only. For rotation attacks, [17] yields poor results, since its filtering scheme is sensitive to rotations. The proposed algorithm and [18] can survive most non-scaling attacks in Stirmark 4.0 [20,21]. 6.3. Robustness test: scenario II In this section, we evaluate the performance of the proposed algorithm in scenario II on six test images of size 256  256: ‘‘Lenna,” ‘‘Man,” ‘‘Barbara,” ‘‘Baboon,” ‘‘Bridge,” and ‘‘Pepper.” Table 3 shows how the dither quantizer step size D affects the average PSNR of the six watermarked images and the average detection ratios. In this test, the watermarked images are corrupted by scaling, rotation, centered cropping, and JPEG compression attacks. As D increases, the embedded watermarks become stronger and the detection ratios improve, but the PSNRs become lower. However, note that the detection ratios saturate when D P 4. In the following tests, we choose 4 6 D 6 6, so that the PSNRs of the watermarked images are higher than 39 dB. Specifically, we choose D ¼ 6 for highly textured images ‘‘Baboon,” ‘‘Bridge,” and ‘‘Man,” while D ¼ 4 for ‘‘Lenna,” ‘‘Pepper,” and ‘‘Barbara.”

Attacks

Parameters

Nv 1

2

3

Rotation + autoscale

1° 2° 1° 2° 5° 1° 2° 5° 10° 15° 30° 45° 90° H1 H2 H3

10 3 12 12 11 11 12 12 11 10 11 11 12 9 9 11 3 0 7 9 10 11 11 7 11 10 6 5

10 4 12 12 12 12 12 12 11 10 11 11 12 9 9 11 6 1 9 10 11 12 11 8 11 12 8 6

11 7 12 12 12 12 12 12 11 11 11 11 12 12 11 12 8 3 10 10 12 12 12 10 12 12 11 8

Rotation + autocrop

Rotation

Linear transform

Random bending Scaling

(0.5,0.5) (0.75,0.75) (0.9,0.9) (1.1,1.1) (1.5,1.5) (1,0.8) (0.8,1) (1,1.2) (1.2,1) (0.7,0.9) (0.9,0.7)

Watermarks are inserted into non-overlapping circular patches only. In Table 4, we list the patch PSNRs as well as the PSNRs over the whole images. In the ‘‘Baboon” and ‘‘Bridge” images, the average patch PSNRs are relatively low. However, the watermark noises are imperceptible in such highly textured images. Fig. 9 shows the original images, the watermarked images, and the magnified differences between the original and the watermarked images. Note that the watermarks are not noticeable. We apply most of the attacks listed in Stirmark 4.0 [20,21]: JPEG compression, signal enhancement, additive uniform noise, linear geometric transformation, line removal, centered cropping, rotation, scaling, rotation + autoscale, rotation + autocrop, shearing, and aspect ratio change. The signal enhancement attacks include the Gaussian low-pass filtering and the median filtering. Table 5 shows the watermark detection results on the ‘‘Lenna” image. It shows the number of patches, where the watermarks are successfully detected. Recall that N v denotes the number of successfully detected patches, which are required to declare an image as watermarked. As N v increases, the proposed algorithm detects the watermarks from a larger number of patches, since we use a stronger BCH code as summarized in Table 1. However, a stronger BCH code corresponds to a smaller watermark capacity. Specifically, the capacity is 21, 16, and 11 bits, when N v is 1, 2, and 3, respectively. Thus, N v should be selected by considering the tradeoff between robustness and capacity. Figs. 10–15 summarize the average detection ratios on the six test images. For most attacks, the proposed algorithm can detect the watermark from a considerable number of circular patches. By using the salient region parameters, which require a negligible number of additive bits, the watermark is successfully detected in down-scaling and up-scaling attacks with high detection ratios. The proposed algorithm can survive non-isotropic scaling attacks as well, since it inverts the changes in the spatial sampling rate. Since we embed watermarks locally, the proposed algorithm can survive cropping attacks up to 25% cropping. As Zernike moments

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100 Nv = 1 Nv = 2

Average detection ratio (%)

80

Nv = 3

70 60 50 40 30

Nv = 1

Average detection ratio (%)

90

100

Nv = 2 Nv = 3

80 60 40 20

20

0

10

(x 1% y 0%)

(x 0% y 1%)

(x 1% y 1%)

(x 5% y 0%)

(x 0% y 5%)

(x 5% y 5%)

Shearing

0 Median f iltering (2x2)

Median f iltering (3x3)

Median f iltering (4x4)

Gaussian f iltering s=1,3x3

Additive unif orm noise s = 15

Fig. 13. Average detection ratios after shearing attacks.

Fig. 10. Average detection ratios after filtering attacks. 120

Average detection ratio (%)

Nv = 1

120 Nv = 1 Nv = 2 Nv = 3 80

60

Nv = 3

80 60 40 20

40

o

o

o

o

o

o

2

5

10

15

30

45

au

90

o

o

1

p

p

ro toc

ro toc

2

5

+

au +

o

le

ro

ca

toc +

o

au

tos au

1

o

le ca tos +

2

1

o

+

au

20

p

0

o

Average detection ratio (%)

100

Nv = 2

100

Rotation

0 15

20

30

40

50

60

70

80

90

Fig. 14. Average detection ratios after rotation attacks.

JPEG compression (Quality) Fig. 11. Average detection ratios after JPEG compression attacks. 120

90

Nv=1

Average detection ratio (%)

80

Nv = 2 Nv = 3

70 60 50 40 30 20

Average detection ratio (%)

Nv = 1

Nv=2

100

Nv=3 80 60 40 20

10

0

Fig. 12. Average detection ratios after centered cropping attacks.

are insensitive to compression attacks and image noises, the proposed algorithm can survive JPEG compression with quality factor as low as 15 and additive noises with r ¼ 15. 7. Conclusions An image watermarking algorithm, which is robust against geometric and signal processing attacks, was proposed in this work. The proposed algorithm embeds watermarks locally into LZMs to

) 0.7 .9,

(0

(0

.7,

0.9

1.0

)

)

) .2, (1

(1

.0,

1.0

1.2

)

) .8, (0

(1

.0,

0.8

1.5 .5, (1

.1,

1.1

)

)

) 0.9 (1

,0

.9, (0

30%

.75

20%

.5,

15%

Centeredcropping

(0

10%

(0

5%

0.5

)

.75

)

0

Scaling Fig. 15. Average detection ratios after scaling attacks.

achieve the robustness against cropping and local geometric attacks. The proposed algorithm extracts salient region parameters and transmits them to the decoder. The parameters are used to normalize a suspect image and detect watermarks at the decoder. Simulation results demonstrated that the proposed algorithm provides robust performance in various attack scenarios. Future research issues include the elimination of the additive bits for

N. Singhal et al. / J. Vis. Commun. Image R. 20 (2009) 408–419

salient region parameters and the extension of the proposed algorithm to video watermarking. Acknowledgments This work was supported partly by the Ministry of Knowledge Economy, Korea, under the Information Technology Research Center support program supervised by the Institute of Information Technology Advancement (Grant No. IITA-2009-C1090-09020017) and partly by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MEST) (No. R012008-000-20292-0). References [1] Y. Xin, S. Liao, M. Pawlak, A multibit geometrically robust image watermark based on Zernike moments, in: IEEE Int. Conf. Pattern Recognit., vol. 4, 2004, pp. 861–864. [2] H.S. Kim, H.K. Lee, Invariant image watermark using Zernike moments, IEEE Trans. Circuits Syst. Video Technol. 13 (8) (2003) 766–775. [3] N. Singhal, Y.-Y. Lee, C.-S. Kim, S.-U. Lee, Robust image watermarking based on local Zernike moments, in: IEEE Int. Workshop Multimedia Signal Process., 2007, pp. 401–404. [4] P. Dong, J. Brankov, N. Galatsanos, Y. Yang, Geometric robust watermarking based on a new mesh model correction approach, in: Proc. IEEE Int. Conf. Image Process., vol. 3, 2002, pp. 493–496. [5] C. Lu, S. Huang, C. Sze, H.Y. Liao, Cocktail watermarking for digital image protection, IEEE Trans. Multimedia 2 (4) (2000) 209–224. [6] J. Shieh, D. Lou, M. Chang, A semi-blind digital watermarking scheme based on singular value decomposition, Computer Standards & Interfaces 28 (4) (2006) 428–440. [7] V.Q. Pham, T. Miyaki, T. Yamasaki, K. Aizawa, Geometrically invariant objectbased watermarking using SIFT feature, in: Proc. IEEE Int. Conf. Image Process., vol. 5, 2007, pp. 473–476. [8] J. O’Ruanaidh, T. Pun, Rotation, scale and translation invariant spread spectrum digital image watermarking, Signal Process. 66 (8) (1998) 303–317. [9] C.-Y. Lin, M. Wu, J. Bloom, M. Miller, I. Cox, Y.-M. Lui, Rotation, scale, and translation resilient public watermarking for images, IEEE Trans. Image Process. 10 (5) (2001) 767–782. [10] S. Pereira, T. Pun, Robust template matching for affine resistant image watermarks, IEEE Trans. Image Process. 9 (6) (2000) 1123–1129. [11] M. Kutter, S.K. Bhattacharjee, T. Ebrahimi, Towards second generation watermarking schemes, in: Proc. IEEE Int. Conf. Image Process., vol. 1, 1999, pp. 320–323.

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