Thesis Organization

In the remainder of this thesis, the proposed method for copyright protection by watermarking for color images against rotation and scaling attacks is described in Chapter 2. In Chapter 3, the proposed method for copyright protection by watermarking for color images against rotation and cropping attacks is described. And in Chapter 4, the proposed method for copyright protection by watermarking for color images against print-and-scan operations is described. In Chapter 5, the proposed method for copyright protection by watermarking for color images against scaling and line-removal attacks using an image rescaling technique is described. In Chapter 6, the proposed method for tampering detection in color images by signature-free authentication via DCT-coefficient relationship comparison is described. Finally, in Chapter 7, we give some conclusions and briefly point out some possible directions for future research works.

Authentication signals Cover image

Stego-image Embed authentication

signals

IDCT DCT

Key

Figure 1.5 Flowchart of proposed method for temper detection.

Chapter 2

Copyright Protection by

Watermarking for Color Images

against Rotation and Scaling Attacks Using Peak Detection and

Synchronization in DFT Domain

The proposed method for copyright protection of color images against rotation and scaling attacks is described in this chapter. The main idea is to embed a watermark as coefficient-value peaks in the DFT domain of an input image. Then, by detecting the peaks in the DFT domain, the embedded watermark can be extracted.

2.1 Introduction

Digital watermarking is a technique for embedding a watermark into an image to protect the owner’s copyright of the image. The embedded watermark must be robust.

The stego-image may be rotated or scaled by illicit users. It is desirable that after applying these operations on the stego-image, the watermark is not fully destroyed and can be extracted to verify the copyright of the image.

The remainder of this chapter is organized as follows. In Section 2.2, the idea of the proposed method will be described. By certain properties of the DFT coefficients, we can embed a watermark in the DFT domain with robustness against rotation and

scaling attacks. In Section 2.3, the proposed watermark embedding process is presented. In Section 2.4, the proposed watermark extraction process is described. In Section 2.5, some experimental results are illustrated. Finally, in Section 2.6 some discussions and a summary are given.

2.2 Idea of Proposed Method

2.2.1 Properties of Coefficients in DFT Domain

After applying a discrete Fourier transformation (DFT) to an input image, the DFT coefficients in the frequency domain can be obtained. The DFT of an image

of size )

, (x y

f M×Ncan be described by the equation described below:

∑

The Fourier transform is a complex function of the real frequency variables. It has several properties, and some of them are described in the following.

A. Symmetry property

If a 2D signal is real, then the Fourier transform has a symmetry property, as shown by the following equation [27]:

)

The symbol (^∗) indicates complex conjugation. Because the Fourier transform of an image can be complex, we can divide it into two functions. One is the magnitude function or spectrum |F(u,v)|=[R²(u,v)+I²(u,v)]²¹ , and the other the phase

imaginary parts of F( vu, ). And for real signals, Equation (2.2) leads to:

It means that the magnitude value of a coefficient (or simply a coefficient value) and its symmetric version are equal. In addition, both the magnitude and the phase functions are necessary for complete reconstruction of an image from its Fourier transform. But the magnitude part is less important than the phase part. The magnitude-only image is unrecognizable. On the contrary, the phase-only image is barely recognizable [24]. Therefore, we may calculate and adjust the magnitude values of the DFT coefficients to embed information without causing significant loss of image quality.

B. Invariant properties of rotation and scaling

After we apply some image processing operations like rotation and scaling to an image, the coordinates and magnitude values of the DFT coefficients of the image will be altered, too. Changes of the DFT coefficients after scaling and rotation operations in the discrete image domain are listed in Table 2.1 [28]. The scaling operation has almost no effect on the DFT coefficients. It means that when an image is scaled, each DFT coefficient is the same as the original one except only with some noise. On the other hand, after rotating an image in the spatial domain, the locations of the DFT coefficient values will have the same rotation in the DFT domain. Figures 2.1(a) and (b) show an original image and a rotated version of it. And the corresponding Fourier spectrum images, in which each pixel value is equal to the magnitude value of the DFT coefficient, are shown in Figures 2.1(c) and (d), respectively. Note that the Fourier spectrum image in Figure 2.1(d) has the same rotation like Figure 2.1(b).

Table 2.1 Changes of DFT coefficients after operations in discrete spatial domain.

Operations Scaling Rotation

Changes of DFT coefficients Almost no effect Rotation

(a) (c)

(b) (d) Figure 2.1 Input images, and Fourier spectrum images of G channel. (a) Image

“Lena”. (b) Image “Lena” after rotation. (c) Fourier spectrum image of image “Lena” (d) Fourier spectrum image with the same rotation angle of (b).

2.2.2 Properties of Color Channels

A full-color image has three color channels, namely, red (R), green (G), and blue (B). Generally speaking, we can embed watermark information into all of these three

channels. However, human eyes are less sensitive to the frequency of blue color. And its greatest sensitivity is distributed over the region of the yellow/green frequency [25].

In addition, according to experiments, a watermark can be embedded into both red and blue channels in the DFT domain without creating perceivable effects. On the contrary, hiding information in the green channel is too sensitive to human vision. If we embed the watermark in the DFT domain of the green channel, the stego-image will appear to include obvious reticular effects.

2.2.3 Proposed Technique of Using DFT Peaks for Watermarking

In the proposed watermarking method, after the zero frequency point F(0,0) is shifted to the center of the DFT domain, a watermark is embedded in a ring region which covers a middle band, denoted as B subsequently, in the frequency domain between two circles with two pre-selected radii R1 and R2 where R1 < R2, as shown in Fig. 2.2. The middle band of the frequency domain is divided into n equally-spaced concentric circles with radii r₁, r₂, …, r_n, and into m angle ranges with starting angles θ1, θ2, …, θm, as seen in Fig. 2.3. Then, n×m embeddable positions p₁, p₂,…, p_n×m are selected in this study to be located at (u_k, v_k) in the frequency domain described by:

pk = (uk, vk) = (ricosθj, risinθj), (2.4) where 1 ≤ i ≤ n, 1 ≤ j ≤ m and 1 ≤ k ≤ n×m, and at each embeddable position pk, the coefficient value is adjusted to be a local peak in the frequency domain.

More specifically, let W be a watermark to be embedded, which is taken to be a serial number in this study in the form of a bit stream, and let M(uk, vk) be the DFT coefficient value at an embeddable position p_k = (u_k, v_k). Then, we embed a watermark

bit w_i at p_k in the frequency domain in this study by modifying M(u_k, v_k) to be a local peak M’(uk, vk) by the following equation:

M’(uk, vk) = M(uk, vk) + c×wi (2.5) where c is a pre-selected parameter that determines the strength of the embedded watermark signal.

It is noted that, when conducting watermarking in the above way of changing the DFT coefficient value at an embeddable position pk = (uk, vk) for the amount of δ = c×wi, we must preserve the positive symmetry property of the DFT [26] by changing the corresponding coefficient value at pk’= (−uk, −vk) for the same amount δ. Otherwise, the peak created at pk will be counteracted by the symmetric coefficient value at p_k’ after applying the inverse DFT. That is, we must perform, as is done in this study, the following operation

M’(−u_k, −v_k) = M(−u_k, −v_k) + δ (2.6) in addition to Eq.(2.5) each time we embed a watermark bit wi at an embeddable position p_k = (u_k, v_k).

R₁

R₂

Figure 2.2 A ring region of middle frequency band.

R A ^{(xk, yk)}

Figure 2.3 The ring region divided into concentric circles and into angular sectors.

2.2.4 Proposed Technique for Synchronizing Peak Locations for Protection against Rotation and Scaling Attacks

In order to deal with rotation and scaling attacks, an extra local peak P_sync, called synchronization peak, is created in the DFT domain to serve as a signal for synchronizing the peak locations p₁, p₂, …, p_n×m mentioned previously in a way described later. Psync is embedded into the previously-mentioned middle frequency band B at a location p_sync described by:

p_sync = (u_sync, v_sync)

= (rsynccosθsync, rsyncsinθsync) (2.7) where rsync is selected to be larger than R2 and θsync is a pre-selected angle value. We adjust the DCT value M of Psyn to be a peak value M’ = M + c where c is the constant value mentioned previously.

We now describe how we use the synchronization peak P_sync in the proposed watermark extraction process to calculate the rotation angle of a tampered stego-image which suffered possibly from a rotation attack. Because of the DFT properties mentioned previously and illustrated by Fig. 1, if a stego-image is rotated, the location of P_sync will also be changed with the same rotation angle. We may calculate first the new angle θ’_sync of P_sync and take the difference ∆θ between θ’_sync and θsync to decide whether the stego-image has been rotated: if ∆θ ≠ 0, then rotated;

else, not. If rotated, then we find the angles θ’_k of the remaining local peaks, and compute their original angles θ"_k by

θ"_k = θ’_k − ∆θ. (2.8)

On the other hand, as mentioned previously, if a stego-image is rescaled, the DFT coefficient values are almost unaffected. It means that the radii of the local peaks will not be changed.

2.3 Watermark Embedding Process

As mentioned previously, a watermark used for image ownership protection is assumed to be a serial number in this study, and the watermark is transformed into a watermark bit stream. In this section, the process of embedding a watermark bit stream in a color image will be described.

2.3.1 Embedding of Watermarks

In the proposed watermark embedding process, we use the two channels of red and blue to embed a watermark bit stream in the DFT domain according to the idea described in Section 2.2.2. And the middle band area of the Fourier spectrum is

divided into several concentric circles. Then, the watermark bit stream is embedded in the region of the concentric circles.

Furthermore, the watermark bit stream is divided into two halves to be embedded in the red and blue color channels, respectively. For either channel, the spatial domain is transformed into the frequency domain by the DFT. In the middle band of the DFT domain, locations that can be use to create peaks are decided according to the scheme described in Section 2.2.3. Then, we can get pairs of locations (uk, vk) and (−uk, −vk).

Using the watermark bit stream W, if a bit wk of W equals “1,” coefficient values of the corresponding embeddable positions (uk, vk) and (−uk, −vk) are adjusted to be peaks by Eqs. (2.5) and (2.6) to embed a watermark bit. On the contrary, if wk equals

“0”, the corresponding coefficient values are not changed. In addition, a synchronization peak is also embedded into the middle frequencies according to the scheme described in Section 2.2.4.

2.3.2 Detailed Algorithm

The inputs to the proposed watermark embedding process are a color image C and a watermark W. The output is a stego-image S. The process can be briefly expressed as an algorithm as follows. Figure 2.4 shows a flowchart of the process.

Algorithm 1: Watermark embedding process.

Input: A given color image C and a watermark W.

Output: A stego-image S.

Steps.

1. Transform the red and blue channels of C into the frequency domain by the DFT to get C’red and C’blue.

2. Divide W into two parts Wred = w1w2…w_l and Wblue = w_l+1w_l+2…w2_l.

3. Embed W_red and W_blue into C’_red and C’_blue, respectively, by performing the following operations.

3.1 Decide n radiuses R = {r₁, r₂,…, r_n} of equally-spaced concentric circles in the middle band between two circles with radiuses R1 and R2, with R1< R2.

3.2 Decide m angles Θ = {θ₁, θ₂,…, θ_m} equally distributed in the range from ^0° to ^180°. Also, take l to be ^m×n.

3.3 Obtain l positions P = {p¹, p2,…, p_l} with pk (k = 1, 2, …, l) located at (r_icosθ_j, r_isinθ_j ) with k = (i − 1)×m + j, and their l symmetric positions Q = {q1, q2,…, q_l} with qk located at the symmetric location of pk , where 1≤i≤n, and 1≤ j≤m.

3.4 If watermark bit wk equals 1, then adjust the pair of the coefficient values located at p_k and q_k to be local peaks by Eqs. (2.5) and (2.6), where 1 ≤ k ≤ l for C’red or l + 1 ≤ k ≤ 2l for C’^blue.

3.5 Add a synchronization peak P_sync according to the scheme described in Section 2.2.4.

4. Transform the C’_red and C’_blue back into the spacial domain by the inverse DFT.

5. Take the final result as the desired stego-image S.

Transform into

Figure 2.4 Flowchart of the embedding process.

2.4 Watermark Extraction Process

In the proposed watermark extraction process, no other information but the stego-image is needed as the input. The watermark can be extracted to verify the copyright. The processes of applying this technique will be described in this section.

And a detailed algorithm for the process will be given.

2.4.1 Extraction of Watermarks

In the proposed watermark extraction process, the red and blue channels of a stego-image are accessed. Each of these two channels is transformed into the DFT domain. Then, the local peaks in the middle frequency band of the DFT domain are detected using a pre-selected threshold value T: if any DFT coefficient value M is larger than T, it is judged to be a local peak. Because of the symmetry property of the DFT coefficient values specified in Eq. (2.3), we may only detect peaks within the range of the upper-half Fourier spectrum image. After collecting all the peaks, a detected peak with the largest radius r’sync and angle θ’_sync is taken to be the synchronization peak, which is then used to synchronize all the remaining peaks in a way described by Eq. (2.8). The result is a set of local peaks P’ = {p'1, p'2,…, p'h}.

Then, we calculate the new radius r’sync of Psync and take the ratio ρ between r’sync and rsync to decide R'1 = R1 × ρ and R'2 = R2 × ρ. Also, we divide the ring area of the middle frequency band B between the two circles with radii R'₁ and R'₂ into n equally-spaced concentric circles and into m angle ranges to make B become a set of l sectors D = {d1, d2,…, d_l} where l = m×n, as seen in Figure 2.5. Then, we compare P’ and D to decide the watermark bit stream W = w1w2…w_l by:

⎩⎨ integer number as the extracted watermark and complete the watermark extraction process. The detail of the process can be described as an algorithm as follows.

R’

₁

R’

₂

Figure 2.5 The middle frequency band is separated into concentric circles and into angular sectors.

2.4.2 Detailed Algorithm

The input to the proposed watermark extraction process includes just a stego-image S. The output is a watermark W that is a serial number embedded presumably in S. The extraction algorithm can be expressed as an algorithm as follows. Figure 2.6 illustrates the proposed process of watermark extraction.

Algorithm 2: Watermark extraction process.

Input: A stego-image S.

Output: A watermark W.

Steps.

1. Transform the red and blue color channels of S into the DFT domain to get Fourier spectra S’red and S’blue.

2. Detect peaks within the upper halves of S’_red and S’_blue, respectively, by performing the following operations.

2.1 Use a threshold value T to detect peaks in the middle-frequency band. If a coefficient value is larger than T, it is considered as a peak.

2.2 Select the peak with the largest radius as the synchronization peak P_sync, and calculate its angle change ∆θ with respective to the original angle of the synchronization peak.

2.3 Reconstruct the angles of the remaining peaks by Eq. (2.8) to get their new locations P’ = {p'₁, p'₂,…, p'_h}.

2.4 Divide the middle frequency band between R'1 and R'2 into n equally-spaced concentric circles and into m sectors to make B become a set of l sectors D = {d¹, d2, …, d_l}, where l = m×n.

2.5 Compare P’ and D to decide the watermark bit stream according to the way specified by Eq. (2.9).

3. Concatenate the two watermark bit streams obtained from processing S’_red and S’blue sequentially, and transform the result into a serial number as the desired watermark W.

Decode watermark bit stream Decide a threshold

value T Get R and G

channels Stego-image

Watermark DFT

Detect peaks

Find synchronization

peak

Reconstruct angles of remaining peaks

Figure 2.6 Flowchart of the extraction process.

2.5 Experimental Results

Some experimental results of applying the proposed method are shown here. A serial number 877 is transformed into binary form to be a watermark bit stream. The factor c that determines the embedded watermark strength is assigned to be 1.5.

Figure 2.7 shows an input image with size 512×512. And Figure 2.8(a) shows the stego-image of Figure 2.7 after embedding the watermark. In addition, Figures 2.8(b) and (c) show the corresponding Fourier spectrum image and the detected locations of the peaks marked with red and green marks. The green mark is the synchronization peak. Figure 2.8(d) show a rotated image of Figure 2.8(a) and the corresponding Fourier spectrum image and the detected peak locations are shown in Figures 2.8(e) and (f), respectively. It shows that the Fourier spectrum image have the same angle of rotation with the tampered image. Figure 2.9(a) shows a scaled image of Figure 2.8(a) and the corresponding Fourier spectrum image with the detected peak locations are shown in Figure 2.9(b). The embedded peaks can be successfully detected in our experiments.

Figures 2.10(a) and (b) show two other color images both with size 512×512.

And the corresponding stego-images after embedding the watermark are shown in Figures 2.10(c) and (d), respectively. The corresponding PSNR values are shown in Table 2.1, which show that the quality of each of the stego-images is still good. And the embedded watermark is imperceptible by human vision.

Finally, two rotated images are shown in Figures 2.11(a) and (b). And Figures 2.12(a) and (b) show two scaled images. The watermarks can be extracted successfully from each of these images by the proposed watermark extraction process in our experiments.

Figure 2.7 An input image “Lena”.

(a) (d)

(b) (e) Figure 2.8 An output stego-images with the watermark, the tampered image and

Fourier spectrum images. (a) Stego-Image “Lena”. (b) Fourier spectrum image of (a). (c) Peak locations of (c). (d) Tampered image after rotating 13 degree clockwise. (e) Fourier spectrum image of (d). (f) Peak locations of (e).

(c) (f) Figure 2.8 An output stego-images with the watermark, the tampered image and

Fourier spectrum images. (a) Stego-Image “Lena”. (b) Fourier spectrum image of (a). (c) Peak locations of (c). (d) Tampered image after rotating 13 degree clockwise. (e) Fourier spectrum image of (d). (f) Peak locations of (e) (continued).

(a) (b) Figure 2.9 The tampered image and the Fourier spectrum image. (a) Tampered image

after scaling to 90%. (b) Fourier spectrum image of (a) with peak locations.

(a) (c)

(b) (d) Figure 2.10 Input images, and output stego-images with the watermark. (a) Image

“Pepper”. (b) Image “Jet”. (c) and (d) Stego-images after embedding the watermark, respectively.

Table 2.2 The PSNR values of recovered images after embedding watermarks.

Lena Pepper Jet

PSNR 33.0 33.0 33.0

(a) (b) Figure 2.11 Some tampered images with different rotations. (a) Tampered image after

rotating 97 degree clockwise. (b) Tampered image after rotating 7 degree counterclockwise.

(a) (b) Figure 2.12 Some pered images with different scaling ratios. (a) Tampered image

In this chapter, we have proposed a method for embedding a watermark into a color im

tam

after scaling to 150%. (b) Tampered image after scaling to 90%.

2.6 Discussions and Summary

age by using peak detection and synchronization of coefficient-value peak locations in the DFT domain. Utilizing some properties of image coefficients in the

DFT domain, we can embed a watermark in the form of a binary stream by creating the peaks circularly and symmetrically in a middle frequency band in the transform domain. On the other hand, an extra synchronization peak is added to synchronize the peak locations. The embedded watermark was shown by the experimental results to be robust against rotation and scaling attacks, thus achieving the goal of image copyright protection.

However, the data hiding capability of the proposed watermark embedding method is not large and cannot accommodate a normal-sized logo image. It may be tried to solve this problem in the future.

Chapter 3

Copyright Protection by

Watermarking for Color Images against Rotation And Cropping Attacks Using Synchronization of Peak Locations in DFT Domain And DCT-Coefficient Relationship

Comparison

In this chapter, the proposed method for embedding a watermark in color images against rotation and cropping attacks is described. The idea is based on hiding information in two frequency domains, the DFT and DCT domains. In the DFT domain, a synchronization peak is embedded for the purpose of detecting if an image is suffered rotation attacks And in the DCT domain, multiple copies of watermarks and verification codes are embedded for the purpose of surviving cropping attacks.

The remainder of this chapter is organized as follows. In Section 3.1, an introduction is given first. In Section 3.2, several ideas behind the proposed methods are described. In Section 3.3, the proposed watermark embedding process is presented.

In Section 3.4, the proposed watermark extraction process is presented. Some

In Section 3.4, the proposed watermark extraction process is presented. Some

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