ROBUST IMAGE WATERMARKING BASED ON LOCAL ZERNIKE MOMENTS Nitin Singhal† , Young-Yoon Lee† , Chang-Su Kim‡ , Sang-Uk Lee† †

Signal Processing Laboratory, School of Electrical Engineering and INMC, Seoul National University, Seoul, Korea ‡ School of Electrical Engineering, Korea University, Seoul, Korea ABSTRACT

Invariant image features can be used to carry watermarks so as to improve the robustness of the watermarks against geometric transformations. However, most previous watermarking algorithms using invariant features are still sensitive to cropping attacks and combinations of rotation, scaling, and translation (RST) attacks. To improve the resilience against these attacks, we propose a multi-bit image watermarking algorithm using local Zernike moments (LZMs). The magnitude of LZMs are dither-modulated to embed watermark bits. To achieve scale invariance, we restore the original sampling rate using invariant centroid and geometric moments. Simulation results demonstrate that the proposed watermarking algorithm is robust against various geometric attacks as well as signal processing attacks. Index Terms— digital image watermarking, digital right management, invariant image features, and local Zernike moments.

the image sampling rate before the watermark extraction. Simulation results show that the proposed algorithm provides significantly better robustness than the conventional algorithm [5]. The paper is organized as follows. Section 2 introduces Zernike moments and the Harris corner detector. Section 3 proposes a scale normalization scheme. Sections 4 and 5 describe the proposed watermark embedding and extraction algorithms, respectively. Section 6 show simulation results. Finally, Section 7 concludes this paper. 2. PRELIMINARIES 2.1. Zernike Polynomials and Zernike Moments The radial Zernike polynomial Rnm (ρ) is defined as (n−|m|)/2

Rnm (ρ) =



s=0

1. INTRODUCTION With the development of watermark technologies, attacks against watermarking systems also have become more sophisticated. Those attacks can be classified into signal processing attacks and geometric attacks. Most previous watermarking methods have shown robustness against signal processing attacks, but only a few specialized methods have addressed geometric attacks. In general, geometric attacks are dealt with in three ways. First, a registration pattern is inserted into the host signal along with a watermark. Second, the host signal is normalized before the watermark detection. Third, watermarks are inserted into invariant image features. For invariant feature selection, moments and invariant functions of moments have been extensively studied. Hu [1] derived seven functions of moments that are invariant to RST. Farzam et al. [2] first reported Zernike moments as robust image features and used them to achieve the robustness against rotation, additive noise and lossy compression. Recently, Xin et al. [3] embedded watermarks by modifying Zernike moment vectors, and realized RST invariance via image normalization. The normalization scheme in [4] also uses invariant geometric moments to normalize the size of a suspect image. However, most algorithms based on geometric moments and image normalization are highly sensitive to cropping attacks and combinations of RST attacks. In this paper, we propose a novel robust image watermarking algorithm based on local Zernike moments (LZMs). We compute LZMs over the circular regions around feature points, and modify the moments to embed watermarks. Unlike other methods using Zernike moments, we compute the moments locally and achieve the robustness against cropping. Moreover, to achieve scale invariance, we develop a classification scheme for geometric distortions to normalize

1-4244-1274-9/07/$25.00 ©2007 IEEE

401

s!



(−1)s (n − s)!ρn−2s    . − s ! n−|m| −s ! 2

n+|m| 2

(1)

Then, the Zernike basis [3] is a set of complete and orthogonal functions on the unit disk, given by Vnm (x, y) = Rnm (ρ)ejmθ ,

(2)



y 2 , θ = arctan(y/x), where ρ = x2 +   n is non-negative integer, and m ∈ Dn = 0, ±2, ..., ±2 n2  . x denotes the greatest integer less than or equal to x. In this work, we adopt the following formula, which is most commonly used in literature to compute LZMs of an image f (x, y) over a circular patch with radius R. Znm =

n+1   ∗ Vnm (x, y)f (x, y)Δx Δy , π 2 2 2

(3)

x +y ≤R

where V ∗ denotes the complex conjugate of V , and Δx = Δy = 1/R. Similar to other orthogonal and complete basis, the Zernike basis can be used to decompose an image f (x, y) =

∞  

Znm Vnm (x, y).

(4)

n=0 m∈Dn

2.2. Harris Corner Detector We employ the Harris corner detector as a feature point detector. The Harris detector is based on the second moment matrix, which reflects the local distribution of gradients in the image [6]. Given a scale s, the uniform Gaussian scale-space representation I of an image f is defined by I(x;s) = g(x;s) ∗ f (x),

(5)

MMSP 2007

where x = (x, y) refers to a spatial coordinate, g(x;s) is the associated uniform Gaussian kernel with zero mean and standard deviation s, and ∗ denotes the linear convolution. The scale-normalized second moment matrix μ(x, s) is  Ix2 (x;t) Ix Iy (x;t) μ(x,s) = s2 · g(x;s) ∗ , (6) 2 Iy (x;t) Ix Iy (x;t) ∂ I(x;s) ∂x

and t is set to s/2. This matrix represents where Ix = the statistics of gradient directions in the neighborhood of x. The point x is declared to be a feature point if the matrix μ(x, s) has two significant eigenvalues. To this end, the scale normalized Harris corner strength (SHCS) is defined as U (x,s) = det{μ(x,s)} − 0.04 · (trace{μ(x,s)})2 .

Compute C o, r o LZM Selection

Feature Point Detection

LZM Computation Z Dither Modulation ~ + Z

Patch Reconstruction

If a point x has the local maxima of SHCS, it is detected as a feature point. 3. SCALE NORMALIZATION

1. Calculate the initial centroid C0 of the entire image after performing the Gaussian low pass filtering to reduce the effects of waveform attacks, such as lossy compression and noise addition. 2. Iteratively compute the ith centroid Ci from the circular region with radius ρ˜ and center point Ci−1 , until the centroid ˜ converges to C.

402

b K2

-

(7)

The normalization scheme in [4] normalizes the scale of an image by resizing the image to a predefined size. However, it is vulnerable to cropping and combinations of RST. Kim et al. [7] proposed the notion of invariant centroid to achieve the image normalization, which is robust to geometric attacks. In their method, the radius of the circular region is predefined to compute the invariant centroid, but it should be covariant with the image scale. Therefore, if the image scale factor is not known in advance, it is impossible to determine the radius. Yang et al. [8] used invariant circular region to select the salient scale of an image using the intensity difference map and the second order Hu moment [1]. Their method is claimed to be robust against cropping and RST, but the interpolation noises during down scaling operations significantly degrade the intensity difference map and consequently the estimation of the salient scale. In this work, we combine the concepts of the invariant centroid [7] and the Hu moments to achieve robust image normalization. We classify geometric distortions into two categories: resampling and non-resampling distortions. Distortions due to the change in spatial sampling rate belong to the first category, while all the other distortions belong to the second category. To aid the normalization of a resampled image, we send minimal information, i.e., the invariant centroid Co of the original image and the associated radius ρo to the decoder as the side information. By comparing the invariant centroids Co , Cs and the radii ρo , ρs of the original and suspect images, respectively, the scale is normalized prior to the watermark extraction in Section 5.1. To make the scale determination more robust against interpolation noises, we use image intensity values and estimate the invariant centroid of the suspect image without resizing it to a predefined size. To precisely determine small scale changes, we employ the first order Hu moment. We calculate invariant centroid and its corresponding radius as follows. For each radius ρ˜ ∈ [ρmin , ρmax ], we perform the following steps:

K1

+

f

+

~ f

Fig. 1. The proposed watermark embedder. 3. Compute the region descriptor I1 over the circular region with ˜ = (˜ radius ρ˜ and center C x, y˜). Specifically, the central moment μpq is defined as  (x − x ˜)p (y − y˜)q f (x, y). (8) μpq = x2 +y 2 ≤ρ ˜2

Then, the normalized central moment ηpq is given by μpq , γ = (p + q)/2 + 1. ηpq = (μ00 )γ

(9)

Finally, we get the first order Hu moment I1 , given by I1 = η20 + η02 .

(10)

Note that the first order Hu moment I1 is computed for each radius ρ˜ ∈ [ρmin , ρmax ]. Then, we find the radius ρ and the corresponding invariant centroid C at which I1 achieves minimum. 4. WATERMARK EMBEDDING Fig. 1 shows the main components of the proposed watermark embedder. The embedding is performed as follows: 1. Given the input image, the invariant centroid Co and the radius ρo are obtained by the normalization method in Section 3. Co , ρo , and the image size A × B are sent to the decoder as the side information. 2. Harris feature points are extracted from the image as described in Section 2.2. Then, to each feature point, a circular patch of radius R is associated. To select non-overlapping patches from the set of all patches, we assume that the feature point with a larger SHCS measure can be detected more reliably. Let N denote the number of feature points, and Tm the number of non-overlapping patches. N is fixed for every image, but Tm varies.

Suspect Image

3. The watermark information is embedded into each selected non-overlapping circular patch as follows. (a) Orders of LZMs: The moments cannot satisfy the required invariance properties, if they have orders higher than a threshold ηmax . In this work, we extract only the LZMs whose orders are less than or equal to ηmax = 12. (b) Modification of LZMs: Let L denote the length of a watermark message b. We select L LZMs randomly to form a Zernike moment vector Z = (Zn1 m1 , ..., ZnL mL ). To embed a watermark bit bi , the magnitude of Zni mi is quantized into Z˜ni mi using the binary dither mod˜ = ulation [3]. Thus, we construct a new vector Z (Z˜n1 m1 , ..., Z˜nL mL ). Note that, in quantizing each Zni mi , its conjugate Zni ,−mi also should be quantized to ensure that they have the same magnitude and thus the reconstructed image is real. (c) Watermarked patch: Let eni mi = Z˜ni mi − Zni mi and eni ,−mi = Z˜ni ,−mi − Zni ,−mi denote the quantization noise signals of Zni mi and Zni ,−mi respectively. The watermark signal w(x) can be constructed from the quantization noises of the selected LZMs via w(x) =

L 

[eni mi Vni mi (x) + eni ,−mi Vni ,−mi (x)].

C o, r o, A x B Scale Normalization

Compute C s, r s

Feature Point Detection

LZM Selection

K1

LZM Computation Z' Dither Modulation

K2

Minimum distance decoder ^

b

Fig. 2. The proposed watermark extractor.

i=1

(11) As a result, the reconstructed watermarked patch is obtained by f˜(x) = f (x) + w(x), (12) where f˜(x) is the watermarked patch and f (x) is the original patch. The circular patch around the feature point in the original image is replaced by the obtained watermarked patch. 5. DECODING 5.1. Scale Normalization The decoder receives the invariant centroid Co = (xo , yo ) of the original image, the associated radius ρo , and the size A × B of the original image as the side information. Then, the decoder estimates the invariant centroid Cs = (xs , ys ) and the radius ρs of the suspect image with the constraint 12 ≤ ρs /ρo ≤ 2 . The decoder classifies geometric distortions to achieve the scale normalization. Let S = (xo ,yo ) , where · is the L2 norm. (xs ,ys )

5.2. Watermark Extraction The process of the proposed watermark extraction is shown in Fig. 2. First, the scale of the suspect image is normalized as described in Section 5.1 to make the watermark robust to image scaling and to guarantee an acceptable level of accuracy in the Zernike moment computation. Then, feature points are detected on the normalized image using the Harris detector. We select N invariant feature points based on SHCS measure. Around each feature point, the circular patch of radius R is extracted, and the LZMs of orders less than or equal to ηmax = 12 are computed. We choose L LZMs, forming a Zernike moment vector Z = (Zn 1 m1 , ..., Zn L mL ). Then, we quantize the magnitude of each Zn i mi with the corresponding binary dither vectors using the dither modulation [3], and estimate ˆ using the minimum distance decoder. Small errors the watermark b of watermark can be corrected using error correcting codes. The suspect image is declared to be watermarked, if the watermark information is successfully extracted for one or more circular patches. 6. SIMULATION RESULTS

1. Cs = Co ⇒ Flipping and symmetric cropping (I) 2. Cs = Co (a) ys = yo or xs = xo ⇒ Aspect ratio change (II) (b) ys = yo and xs = xo i. S = 1 ⇒ Rotation (III) ii. S = 1 A. ρs = ρo ⇒ Scaling (IV) B. ρs = ρo ⇒ Translation (V) The suspect image in category (II) is normalized by resizing it to A × B. The image in category (IV) is scaled with the scale factor S to generate the normalized image.

403

We use BCH(31,11,5) code to generate a 31-bit watermark message. 50 circular patches (N = 50) in an image are selected during watermark embedding and extraction . The deviation s in (5) is set to 4. When calculating the invariant centroid of the original image, the radius ρo is selected within [2, 80]. The radius of a circular patch is R = 21. The extraction of LZMs is sensitive to geometric distortions, which involve more than 0.75 pixel translation. However, the feature point detector cannot have such a high accuracy since we are dealing with digital images. To resolve this issue, we perform the minimum distance detection multiple times by translating each circular patch from -0.75 pixels to 0.75 pixels with the step size 0.25 pixels.

Table 1. The comparison of detection ratios, when the watermarks are corrupted by various attacks. Note that autocrop refers to cropping to original size after rotation and autoscale refers to down scaling to original size after rotation. The numbers in the parentheses refer to the numbers of watermarked patches. Lenna (D) Attacks

Rotation

(b)

(c)

Fig. 3. (a) The original images, (b) the watermarked images, and (c) the magnified residuals for “Lenna” and “Baboon.” The peak signal to noise ratios (PSNRs) of the watermarked circular patches are between 35 and 40dB, when the dithered quantizer has the step size Δ = 4. The resulting PSNRs of the whole watermarked images are between 40 and 44 dB. Fig. 3 shows the original images, the watermarked images, and the magnified residuals between the original and the watermarked images. Note that the watermarks are not noticeable. Table 1. compares the robustness of the proposed algorithm against various attacks with that of the characteristic scale watermark embedding algorithm in [5]. The detection ratio D is defined as the ratio of the number of successfully detected patches to the number of watermarked patches. We see that the proposed algorithm provides significantly higher detection ratios than [5] for most attacks. 7. CONCLUSION In this work, we proposed a novel robust image watermarking algorithm based on LZMs. The proposed algorithm computes LZMs over the circular neighborhoods around invariant feature points to achieve the robustness against cropping and combinations of RST. Also, we proposed a classification scheme for geometric distortions to check whether the suspect image is corrupted by resizing or scaling attacks. Simulation results showed that the proposed algorithm is robust against various attacks, including cropping, affine transforms, and signal processing attacks. Future research issues include the improvement of the robustness and the extension of the algorithm to video watermarking. 8. ACKNOWLEDGMENT This work was supported by the Brain Korea 21 project in 2007. 9. REFERENCES [1] M. K. Hu, “Visual pattern recognition by moment invariants,” IRE Trans. Information Theory, vol. 8, pp. 179–187, June 1962. [2] M. Farzam and S. Shirani, “A robust multimedia watermarking technique using Zernike transform,” in IEEE Int. Workshop Multimedia Signal Processing, Feb. 2001, pp. 529–534.

404

[5]

Proposed

[5]

(12)

(14)

(11)

(22)

91.6%

42.8%

72.7%

4.5%

Rotation 45◦ +autocrop

66.6%

35.7%

63.6%

9.1%

45◦ +autoscale

Rotation

(a)

45◦

Baboon (D)

Proposed

66.6%

-

45.4%

-

Shearing x-5% y-5%

33.3%

35.7%

36.4%

4.5%

Scaling (0.75, 0.75)

83.3%

21.4%

63.6%

4.5%

Scaling (0.5, 0.5)

25.0%

21.4%

27.3%

4.5%

Scaling (1.0, 0.8)

100%

0.0%

90.9%

0.0%

Cropping (15% off)

58.3%

42.8%

72.7%

27.3%

Cropping (25% off)

58.3%

21.4%

36.4%

22.7%

Gaussian filter

75.0%

85.7%

90.9%

36.4%

Median filter

83.3%

64.3%

45.5%

13.6%

Add noise(σ = 15)

41.6%

-

36.7%

-

JPEG (Q = 50%)

100.0%

78.6%

100.0%

27.3%

JPEG (Q = 30%)

100.0%

57.1%

90.9%

13.6%

[3] Y. Xin, S. Liao, and M. Pawlak, “A multibit geometrically robust image watermark based on Zernike moments,” in IEEE Int. Conf. on Pattern Recognition, vol. 4, Aug. 2004, pp. 861–864. [4] M. Alghoniemy and A. H. Tewfik, “Geometric distortion correction through image normalization,” in IEEE Int. Conf. Multimedia and Expo, July 2000, pp. 1291–1294. [5] J. S. Seo and C. D. Yoo, “Image watermarking based on invariant regions of scale-space representation,” IEEE Trans. Signal Processing, vol. 54, no. 4, pp. 1537–1549, Apr. 2006. [6] K. Mikolajczyk and C. Schmid, “Scale and affine invariant interest point detector,” Int. J. Comput. Vis., vol. 60, no. 1, pp. 63–86, Oct. 2004. [7] B.-S. Kim, J.-G. Choi, and K.-H. Park, “Image normalization using invariant centroid for RST invariant digital image watermarking,” in IWDW 2002, LNCS 2613, 2003, pp. 202–211. [8] X. Yang, P. Xue, and Q. Tian, “Invariant salient region selection and scale normalization of image,” in IEEE Int. Workshop Multimedia Signal Processing, Oct. 2005, pp. 1–4.

Robust Image Watermarking Based on Local Zernike ...

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†The author is with the National Institute of Astro- physics, Optics and Electronics, Luis Enrique Erro No. 1. Sta. Maria Tonantzintla, Puebla, Mexico C.P. 72840 a) E-mail: [email protected] b) E-mail: [email protected] c) E-mail: jamartinez@inao