AN SVD ORIENTED WATERMARK EMBEDDING ... - CiteSeerX

International Journal of Innovative Computing, Information and Control Volume 3, Number 3, June 2007

c ICIC International °2007 ISSN 1349-4198 pp. 609—620

AN SVD ORIENTED WATERMARK EMBEDDING SCHEME WITH HIGH QUALITIES FOR THE RESTORED IMAGES Chin-Chen Chang1,2 1

Department of Information Engineering and Computer Science Feng Chia University Taichung 40724, Taiwan [email protected]

Chia-Chen Lin Department of Computer Science and Information Management Providence University 200, Chung-chi Rd., Taichung 43301, Taiwan [email protected]

Yih-Shin Hu 2

Department of Computer Science and Information Engineering National Chung Cheng University 160, San-Hsing, Min-Hsiung, Chiayi 621, Taiwan

Received August 2006; revised December 2006 Abstract. Considering Chang et al.’s SVD-based watermarking scheme, which successfully embeds watermarks into images, and its hidden watermarks can resist various attacks. In this paper, we further extend their idea so that the hidden watermarks can be removed to provide authorized users better image quality for later usage after the ownership of purchased images has been verified. To achieve our objective, we modify their embedding strategy, and the extra information required for later restoration is embedded into the least important non-zero coefficients of the S matrices in the image. Experimental results confirm that our scheme not only provides good image quality of watermarked images but also successfully restores images with high restoration quality. Keywords: Watermark, Singular value decomposition, Intellectual property rights, Removable watermarking, Restored images

1. Introduction. Owing to the progress in information technologies and the growth of the Internet, vast amounts of data such as text and images have been digitized for easy storage, processing and transmission over the Internet. To prevent the transmitted data from being tampered with or grabbed from the Internet, two approaches have been proposed over the past decade. One is legislation that forces violators to pay stiffer penalties for illegal cribs and manipulations. The other one is based on information technologies such as watermarking, copy detection or digital signatures. By using watermarking, the original owners of digital media can embed their own logos such as portraits or trademarks or even secret information into their works. Later, the embedded logos or secret information can be easily extracted by the real owners or authorized users who have the necessary confidential data, also called keys, to prove ownership. 609

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Basically, watermarking schemes are classified into two categories: one is in the spatial domain [10,13-15,17]. The other is in the frequency domain [2,5,8,9,11,19]. Watermarking schemes, which are designed in the spatial domain, directly modify digital data to hide watermarks. The advantage of this scheme is low computational complexity. However, hidden watermarks were easily damaged by various types of signal processing. As for watermarks designed in the frequency domain, they must transform digital data into the frequency domain first by using various transformations; for example, Fast Fourier Transformation or Discrete Cosine Transformation or Discrete Wavelet Transformation. Later, the coefficients are modified to hide the watermarks. Finally, the modified coefficients must be inversely transformed into the spatial domain to generate the watermarked images. Although frequency-domain watermarks can resist various types of digital signal processing, the computation cost is higher than with spatial-domain watermarking. In past years, several SVD-(Singular Value Decomposition) based watermarking schemes have been proposed [1,16]. In 2007, Chang et al. proposed a novel SVD watermarking scheme [3]. Their embedding strategy is simple and the experimental results confirm that their scheme not only resists various digital signal processes but also provide acceptable image quality of watermarked images and high bit correction ratio (BCR) of the extracted watermarks. Considering that the authorized users may require higher image quality for later usage after they verify the ownership of their purchased images, in this paper we improve on Chang et al.’s scheme [3] so that the hidden watermarks can be removed and high image quality can be provided in restored images. The experimental results further prove that the proposed scheme also works well after the watermarked images are compressed by JPEG. The rest of this paper is organized as follows. In Section 2, we briefly describe Chang et al.’s SVD-based watermarking scheme [3]. The proposed embedding scheme is presented in Section 3. Several experimental results are illustrated and discussed in Section 4. Finally, concluding remarks are stated in Section 5. 2. Related Works. In this section, the SVD and Chang et al.’s SVD watermarking scheme [3] are briefly reviewed. 2.1. SVD. SVD is a linear algebra scheme developed for a variety of applications, particularly in least-squares problems [6]. Recently, it also has been used in image processing applications that include image compression [21], image hiding [4], noise reduction [7,12], and image watermarking [1,16] because the singular values of an image do not change greatly when a small interference is added to an image. Assume the rank of an image matrix A whose size is N × N and r ≤ N . The SVD of A is defined as ⎡ ⎤ s1 0 · · · 0 ⎢ 0 s2 · · · 0 ⎥ ⎥ A = U SV T = [u1 , u2 , ..., uN ] × ⎢ ⎣ 0 0 ... 0 ⎦ (1) 0 0 · · · sN r P × [v1 , v2 , ..., vN ]T = si ui viT i=1

where U and V are N × N orthogonal matrices, S is an N × N diagonal matrix, ui and vi are U ’s and V ’s column vectors, respectively, and si ’s are singular values satisfying

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s1 ≥ s2 ≥ · · · ≥ sr = sr+1 = · · · = sN = 0. Furthermore, the columns of U are called left-singular vectors, and the columns of V are called right-singular vectors.

2.2. Chang et al.’s SVD watermarking scheme. Chang et al.’s SVD watermarking is designed to work on binary logos [3]. For an image of N ×N pixels and a binary watermark of P × P pixels, they first divide the image into (N/4) × (N/4) non-overlapping blocks whose size is 4 × 4 pixels. Then, they apply a one-way hash function [9], which is based on Rabin’s scheme [18] to decide the positions of the embedded blocks for each watermark bit. The watermarking embedding procedure of Chang et al.’s is shown in Figure 1.

Figure 1. Flowchart of Chang et al.’s watermark embedding procedure

To achieve high robustness, every binary value of a watermark is embedded into three separate blocks. Therefore, the bit stream of the watermark is copied three times to generate P × P × 3 bit streams, and the bit streams are sequentially embedded into the non-zero coefficients in S matrices, which are obtained by using SVD computing on P × P × 3 different blocks of the image. For each generated Sj matrix of each block Bj , where 1 ≤ j ≤ (N/4) × (N/4), as below, they let s3 be equal to s2 and set s2 be equal to s2 + σ × Wi for embedding the binary value of the watermark, where σ is a constant and Wi is the watermark bit. If s1 < s2 + σ × Wi , they let s1 = s2 + σ × Wi . Each Sj matrix of a block Bj contains one binary value of the watermark only. After embedding one watermark bit into the Sj matrix of a block Bj , the embedded block Bj0 is obtained

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by inversing its corresponding U , V and the embedded Sj0 matrices. ⎡ ⎤ s1 0 0 0 ⎢ 0 s2 0 0 ⎥ ⎥ Sj = ⎢ ⎣ 0 0 s3 0 ⎦ 0 0 0 s4 j

(2)

In the extraction procedure, the hidden watermark W Ti can be extracted from the watermarked image by Equation (3), where 1 ≤ i ≤ P × P . The experimental results show Chang et al.’s scheme can resist JPEG, sharpening, blurring, cropping and noisy attacks. Although their scheme successfully resists various attacks and provides high BCR of the extracted watermarks, the watermarked images can not be restored with higher quality for later usage. Considering users may need higher image quality of their purchase images for other applications after verifying ownership, we try to extend Chang et al.’s concept to achieve removability of watermark and provide high restoration image quality after watermarked images have been verified. ⎧ ⎨ 1, if s2 − s3 > σ/2, (3) W Ti = ⎩ 0, otherwise.

3. The Proposed Scheme. Our proposed scheme for binary logos is also based on the SVD of image blocks, for an image and a binary watermark of N × N pixels and P × P pixels, respectively. In our scheme, the image is first divided into (N/4) × (N/4) non-overlapping blocks whose size is 4 × 4 pixels. To maintain the robustness of the hidden watermark, each binary value of the P × P binary image will be embedded into three separate blocks in the image. However, the extra information which will be used for recovering is embedded into the last non-zero coefficient in the S matrix of block Bj during the watermark embedding procedure to make sure the watermarked image can be restored with higher image quality, where 1 ≤ j ≤ (N/4) × (N/4). The proposed watermarking scheme can be broken into two procedures: embedding, and extracting and restoring. The following subsections give detailed descriptions of both proposed procedures. 3.1. Embedding procedure. To provide robustness of the hidden watermark and maintain the image quality of the watermarked image, each binary value of the watermark is embedded into the second non-zero coefficients of the S matrices in the image. Later, the extra information required for recovering image is embedded into the fourth non-zero coefficients of the S matrices in the image. To make sure the order of non-zero coefficients in each S will not be changed and the hidden watermark can be successfully extracted in the extracting and restoring procedure, different modification principles are designed for various conditions. The proposed embedding algorithm is presented below in detail. [The Embedding Algorithm] Input: coordinate (xi , yi ), block Bj , and watermark bit Wi Output: a watermarked image Step 1: Let i = 1.

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Step 2: Perform SVD operation on block Bj which is located in ⎡ the coordinate (x ⎤ i , yi ) s1 0 0 0 ⎢ 0 s2 0 0 ⎥ ⎥ to generate its corresponding Uj , Sj , and Vj matrices. Let Sj = ⎢ ⎣ 0 0 s3 0 ⎦ . 0 0 0 s4 j Step 3: If s1 > s2 , then this block is embeddable and go to Step 4; otherwise, let i = i + 1 and go to Step 2. Step 4: Let s4 be equal to |s2 − s3 | if |s2 − s3 | will not change the order of the non-zero coefficients. Otherwise, let s4 be equal to −|s2 − s3 |, so that matrix Sj0 is generated as ⎤ s1 0 0 0 ⎢ 0 s2 0 0 ⎥ ⎥ ⎢ ⎣ 0 0 s3 0 ⎦ . 0 0 0 s4 j ⎡

Step 5: Let s2 be equal to s2 + σ × Wi so that matrix Sj0 is changed to ⎤ s1 0 0 0 ⎢ 0 s2 0 0 ⎥ ⎥ ⎢ ⎣ 0 0 s3 0 ⎦ . 0 0 0 s4 j ⎡

Step 6: Perform SVD inverse operation on Uj , Sj0 , and Vj matrices to reconstruct the watermarked block, BWj , which is equal to Uj × Sj0 × VjT . Step 7: Let i = i + 1. Go to Step 2 until all binary values of watermark have been embedded into the image. Figure 2 presents an example that demonstrates the proposed watermark embedding algorithm. This example shows that the embedded block is very similar to its original block.

3.2. Extracting and restoring procedure. In the extracting and restoring procedure, not only the hidden watermark must be extracted correctly from the watermarked image, but the watermarked image must also be restored with high image quality after the hidden bits are extracted. Because the watermark has been embedded three times into the image, the extracted watermark can be simply determined by these three extracted watermarks by using a majority voting strategy. Therefore, the correction rate of the extracted watermark will be promoted. The algorithm for watermark extraction is depicted as follows. [The Extracting Algorithm] Input: coordinate (xi , yi ) and embedded block BWj0 Output: the extracted watermark Step 1: Let i = 1.

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Figure 2. Example of our proposed watermark embedding procedure Step 2: Perform SVD operation on block BWj0 which is located in (xi , yi ) to generate its corresponding U Wj , SWj , and V Wj matrices. Let ⎡ ⎤ s1 0 0 0 ⎢ 0 s2 0 0 ⎥ ⎥ SWj = ⎢ ⎣ 0 0 s3 0 ⎦ 0 0 0 s4 j

Step 3: If s1 ≤ s2 then this block has nothing embedded, i = i + 1 and go to Step 2; otherwise, go to Step 4. Step 4: Extract the hidden watermark by Equation (4). ⎧ ⎨ 1, if s2 − s3 > σ/2, W Ti = (4) ⎩ 0, otherwise. Step 5: Step 6: Step 7: Step 8:

Let i = i + 1. Go to Step 2 until P × P × 3 watermark bits have been extracted. Let i = 1. If W Ti + W Ti+p×p + W Ti+p×p×2 ≥ 2, let Wi0 = 1. Otherwise, let Wi0 = 0. Let i = i + 1. Go to Step 6 until i = P × P .

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Because our embedding algorithm is extended from Chang et al.’s scheme, our proposed scheme certainly inherits the robustness of Chang et al.’s scheme. The removability of the hidden watermark and the recovery of the image with high quality are the major features of the proposed scheme; therefore, we intend to prove that the proposed scheme can achieve our objective in the next section. 4. Experimental Results. Seven gray-level images whose size is 512 × 512 pixels and two binary watermark images whose size is 64 × 64 pixels, as shown in Figure 3, served as test images in the following experiments. To prove performance in image quality of restored images, we implemented the proposed scheme by using Java. The simulation platform is Microsoft Windows XP, Pentium III with 1 GHz memory.

(a) Lena

(b) F16

(c) Baboon

(d) Zelda

(e) Pepper

(f) Babara

(g) GoldHill

(h) logo of NCC university

(i) logo of FCU university

Figure 3. Seven gray scale 512 × 512 test images and two 64 × 64 binary logos To evaluate the image quality of the watermarked and restored images, the image quality is measured by P SN R(Peak Signal-to-Noise Ratio), which is defined in Equation

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(5). 2552 P SN R = 10 × log10 (5) M SE where 255 represents the maximum value of each pixel and the mean square error (M SE) for an image is defined in Equation (6). H

W

XX 1 (xij − x0ij )2 . M SE = ( ) H ×W i j

(6)

Here, the notations H and W represent the height and width of an image, xij is the pixel value of coordinate (x, y)in an original image, and x0ij is the pixel value after the watermark embedding procedure. In general, these values are acceptable and the difference between the original image and restored one is not sensitive to the human vision system once the P SN R of an image is greater than 30 dB. Furthermore, the BCR(Bit Correction Ratio) is defined in Equation (7) to measure the correction rate of the extracted watermark. PP ×P Wi ⊕ Wi0 BCR = i=1 × 100% (7) P ×P where Wi is the ith binary value of the original watermark, Wi0 is the ith binary value of the extracted watermark, and ⊕ denotes an operator of exclusive-OR. Note that a higher BCR implies that the extracted watermark is very similar to the original watermark. The logos in Figures 3(h) and 3(i) were embedded into seven gray-scale images by using the proposed scheme. According to the simulation results, the constant σ is set to 20 in the following experiments to achieve greater robustness of the hidden watermarks. Figure 4(a) presents the watermarked image of “Lena” and the extracted NCC logo is shown in Figure 4(b). Note that the proposed scheme can provide almost 100% BCR when no attack occurs. The P SN R of the watermarked image is about 34.33 dB. In other words, it is difficult to distinguish the difference between the watermarked image and the original image. The P SN R of the watermarked image is still 34.22 dB and the BCR of the extracted watermark is still up to 91.43 % when the watermarked image is compressed by JPEG, as shown in Figures 5(a) and 5(b).

(a) Watermarked image of “Lena” (P SN R = 34.33 dB)

(b) Extracted NCC watermark (BCR = 100%)

Figure 4. The watermarked image and the extracted watermark

AN SVD ORIENTED WATERMARK EMBEDDING SCHEME

(a) Watermarked image after JPEG encoding and decoding (P SN R = 34.22 dB)

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(b) Extracted NCC watermark (BCR = 91.43%)

Figure 5. The watermarked image after JPEG compressing when the quality is 90% and the extracted watermark Table 1 compares the performance of the proposed scheme on the P SN Rs of the watermarked image and the BCRs of the extracted watermark with those resulting from Chang et al.’s scheme when NCC logo is embedded into test images. From Table 1, we can see that although the P SN Rs of the watermarked images provided by the proposed scheme are lower than those of Chang et al.’s scheme, they are higher than 30 dB and the difference between ours and theirs is slight. Furthermore, the BCRs of the extracted watermarks are almost 100% for each test image with the proposed scheme, which are almost the same as those of Chang et al.’s scheme. Table 1. The comparisons between the proposed and Chang et al.’s schemes on P SN Rs and BCRs when NCC logo is embedded Results Proposed scheme Images P SN Rs BCRs Lena 34.33 dB 100% F16 33.92 dB 100% Baboon 31.67 dB 99.98% Pepper 34.73 dB 99.85% Babara 30.59 dB 100% GoldHill 34.04 dB 100%

Chang et al.’s scheme P SN Rs BCRs 35.37 dB 100% 35.44 dB 100% 31.34 dB 100% 35.94 dB 100% 32.19 dB 100% 35.50 dB 100%

Tables 2 and 3 list the P SN Rs of watermarked images, the P SN Rs of restored images and the BCRs of the extracted watermarks when NCC and FCU are embedded, respectively, and no attack occurs. Note that logos may affect the P SN Rs of watermarked images and restored images but the caused difference is slight. Tables 4, 5 and 6 list the P SN Rs of watermarked images, restored images and BCRs of the extracted watermarks with FCU logo and a JPEG compression quality of 90, 80 and 70, respectively. From Tables 4, 5, and 6, we can see that the average P SN R of the restored image is up to 32 dB and the average BCR of the extracted watermark is up to 89% when the

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Table 2. P SN Rs and BCRs of the proposed scheme when NCC logo is embedded Images

Results P SN Rs of the watermarked image Lena 34.33 dB F16 33.92 dB Baboon 31.67 dB Pepper 34.73 dB Babara 30.59 dB GoldHill 34.04 dB

P SN Rs of the restored image 38.57 dB 38.02 dB 33.63 dB 40.40 dB 32.04 dB 38.34 dB

BCRs of the watermark 100% 100% 99.98% 99.85% 100% 100%

Table 3. P SN Rs and BCRs of the proposed scheme when FCU logo is embedded Results P SN Rs of the waImages termarked image Lena 35.09 dB F16 34.83 dB Baboon 32.19 dB Pepper 35.83 dB Babara 30.99 dB GoldHill 34.99 dB

P SN Rs of the restored image 38.59 dB 38.02 dB 33.63 dB 40.41 dB 32.03 dB 38.35 dB

BCRs of the watermark 100% 100% 99.88% 99.78% 100% 100%

Table 4. P SN Rs of watermarked images, restored images and BCRs of extracted watermarks with a JPEG compression quality of 90 and FCU logo Images

Results P SN Rs of the watermarked image Lena 33.34 dB F16 33.10 dB Baboon 30.69 dB Pepper 33.75 dB Babara 29.54 dB GoldHill 32.72 dB

P SN Rs of the restored image 36.58 dB 36.16 dB 32.34 dB 37.51 dB 30.76 dB 35.78 dB

BCRs of the watermark 97.07 % 96.77 % 96.46 % 96.77 % 96.46 % 96.29 %

FCU logo is embedded into test images. In other words, experimental results confirm that the proposed scheme not only can provide acceptable image quality for watermarked images but also can restore images with high quality after the hidden watermarks have been verified. 5. Conclusions. In this paper, we extend Chang et al.’s concept to provide a removable watermarking scheme for binary logos. To make sure the watermarked images can be

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Table 5. P SN Rs of watermarked images, restored images and BCRs of extracted watermarks with a JPEG compression quality of 80 and FCU logo Images

Results P SN Rs of the watermarked image Lena 33.65 dB F16 33.42 dB Baboon 29.81 dB Pepper 34.10 dB Babara 29.23 dB GoldHill 32.40 dB

P SN Rs of the restored image 36.14 dB 35.74 dB 31.12 dB 36.75 dB 30.23 dB 34.66 dB

BCRs of the watermark 91.91% 91.69% 90.50% 92.50% 91.11% 90.60%

Table 6. P SN Rs of watermarked images, restored images and BCRs of extracted watermarks with a JPEG compression quality of 70 and FCU logo Results PSNRs of the waImages termarked image Lena 33.92 dB F16 33.95 dB Baboon 29.35 dB Pepper 34.55 dB Babara 29.03 dB GoldHill 32.41 dB

P SN Rs of the restored image 35.90 dB 35.84 dB 30.47 dB 35.45 dB 29.94 dB 34.21 dB

BCRs of the watermark 90.55% 90.03% 89.28% 91.45% 89.67% 89.94%

restored with high image quality to support different application requirements by authorized users; the proposed scheme not only modifies the embedding strategy of Chang et al.’s scheme but also hides extra information in the fourth non-zero coefficients of the S matrices in the image during the watermark embedding procedure. Because the proposed scheme improves on Chang et al.’s scheme, it inherits the robustness of their scheme. Furthermore, according to the experimental results, our proposed scheme has been proved to maintain acceptable image quality in watermarked images and good BCRs in extracted watermarks. Even for the compressed images under parameter 70, the average P SN Rs of watermarked images and restored images are still up to 30 dB and 32 dB, respectively. The average BCR is also up to 89%. In other words, authorized users can always restore images with high image quality for later usage after they verify ownership of their purchased images. Therefore, the proposed watermarking scheme is very suitable for the protection of rightful ownership of digital images and for on-line image purchasing.

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