A DWT Based Blind Watermarking Method with High Robustness and Forgery Detection Capability A. Shahroudy and M. Jamzad Department of Computer Engineering Sharif University of Technology Azadi Ave, Tehran, Iran

Phone: (98) 21-6616 4618 Fax: (98) 21-6601 9246 E-mail: [email protected], [email protected] Keywords: Robust Digital Watermarking, DWT, Forgery Detection Abstract – In this paper, a new watermarking method in discrete wavelet transform (DWT) domain is proposed. We insert the bits of a binary logo redundantly in LL subband of wavelet transform of host image to improve the watermark robustness. Watermark extraction is done using a fuzzy decision making method. In order to detect any forgery in the watermarked image we used the bits of the same logo to embed a semi-fragile watermark in detail subbands. Experimental results of this method presented PSNR values above 40db in watermarked image and acceptable robustness against attacks like JPEG compression and cropping. In addition, by implementing another fuzzy decision making method on the same watermarked image, we could detect any forgery in any location of the watermarked image.

1. INTRODUCTION With the advancement of technology, different products became digitized and presented in web and internet. In recent years, a serious problem with digital producers is illegal copying, malicious forgery and redistributions. One of the best solutions for these problems is to watermark digital products. Reference [1] is a good review of history, applications and ideas about state of the art in digital watermarking. Some early works on watermarking were based on special domain [2]. But many methods on transform domain such as DFT that hides the watermark pattern in phase coefficients [3] and DCT that uses spread spectrum techniques [4, 5] are available. In addition there are many methods based on DWT that embed the watermark based on human visual perception model. DWT [6, 7] in each level divides the image in 4 subbands named LL (an approximation of the image), HL, LH and HH that are image details in vertical, horizontal and diagonal directions, respectively. The watermarking methods in DWT, depending on their purpose, embed the watermark in different subbands and levels. Since the coefficients in higher levels are more robust with respect to usual attacks such as compression and additive noise, therefore to improve the robustness, the watermark pattern is embedded in LL [8] or detail subbands of higher levels of DWT [9]. In addition in [10] a method for detecting forgery on watermarked image is presented that embeds the watermark pattern in detail subbands. Generally, DWT techniques can be divided in two categories, first, those that modify the coefficients in a subband by adding a sequence of randomly generated noise values to coefficients [4], and second, quantizing the

values of subband coefficients to embed a predefined binary watermark pattern [8]. In this paper, we propose a new method for embedding a predefined binary watermark pattern in LL3, LH3 and HL3 subbands. The embedding in LL3 is done by dividing this subband into 4 blocks and insert a copy of entire watermark pattern in each block. This redundancy in embedding is performed for increasing robustness. We also insert a semi-fragile watermark for forgery detection in HL3 and LH3 subbands. Since we shall assume that the watermarked image should have gone through some attacks, therefore, multiple embedding of watermark pattern, guided us to use fussy logic to determine the correctness certainty of extracted bits of watermark. The rest of paper is organized as follows, in section 2 we give a brief description of image decomposition, in section 3 the embedding techniques are discussed, in section 4 we introduce how to detect watermark and forgery, the experimental results are given in section 5. Finally we provide our conclusion in section 6.

2. IMAGE DECOMPOSITION IN DWT In this method we used CDF9/7 wavelets [11] for analyzing the host image. We applied a three level decomposition on the host image. Fig.1. shows an example of three level decomposition of Lena. In the proposed method, we embed a binary watermark pattern in LL3 subband. To detect forgery the same watermark pattern is embedded in LH3 and HL3 subbands.

3. HOW TO EMBED THE WATERMARK 3.1 Watermark embedding in LL3 In this method the LL3 subband is divided into 4 equal size blocks. In each block the entire watermark pattern is embedded once. This will increase the robustness with respect to attacks such as cropping and compression. For simplicity, the method of embedding is described only for the upper left block. In each step, 4 pixels of a 2×2 window are selected to embed one bit of watermark. Therefore, the first bit of watermark is embedded in first 2×2 window, the second bit in second 2×2 window and so on.

Therefore, C3 and C2 are changed according to (4). C 2′ = C 2 −

d′ − d ⋅Δ 2

C3′ = C3 +

d′ − d ⋅Δ 2

(4)

Since for redundant saving of the same watermark pattern in LL3, it was divided into 4 blocks, the order of scanning each block for embedding purpose is shown in Fig.3. Fig.1. Result of DWT decomposition of Lena using CDF 9/7.

These windows are non-overlapped. The scanning mechanism is from left to right and top to bottom as visualized in Fig. 2. Now, if the host image size is 2 n × 2 n so the LL3 subband will be 2 n −3 × 2 n−3 and each of the 4 blocks will be 2 n−4 × 2 n−4 . Since one bit of watermark is embedded in 4 pixels, thus the watermark pattern size can be maximum 2 n−5 × 2 n−5 bits. For example in a 512×512 image, we can embed maximum 16×16 bits of watermark. In the following we describe how to embed one bit in a window of 2×2 in LL3. Let Bi,j be the 4 coefficients in 2×2 above mentioned window. We sort |Bi,j| in increasing order. Assume Ci , i=1...4, are these sorted values. We quantize the distance of C2 and C3 according to the distance from C1 and C4. We define ∆ as (1). Δ=

C4 − C1 ×α 2

C3 − C2 Δ

(2)

We quantize d to its closest even or odd integer according the current watermark bit value as (3). ⎧⎪ ⎣d ⎦ d′ = ⎨ ⎪⎩ ⎣d ⎦ + 1

if ( ⎣d ⎦ is even) xnor ( w j = 0) if ( ⎣d ⎦ is even) xor ( w j = 0)

(3)

In (3) wj is the value of current bit of watermark. To modify the value of C3 – C2, both C3 and C2 are changed by the same amount. In case of increasing the distance between C3 and C2, we increase C3 and decrease C2. To decrease C3 – C2 we perform the opposite. This ensures no alternation in contrast in the corresponding region of watermarked image.

Fig. 2. Location of 2×2 window and the scanning method.

For forgery detection, we embed semi-fragile watermark in LH3 and HL3. The watermark pattern is exactly the same used in LL3. The difference is in scanning order of embedding and also in how we quantize C2 and C3. Since HL3 contains the vertical details of the 3rd level of wavelet decomposition, therefore instead of using a 2×2 window, we use a 4×1 window. The scanning order is shown in Fig.4. But in LH3 the window is 1×4, the scanning order is horizontal and the movement is from left to right. In this step, one bit of watermark is saved in 4 coefficients as shown in Fig.4., We sort Bi,j in increasing order. For simplicity we assume Ci , i=1…4 are these sorted values in increasing order. In this step, we adjust the values of C2 - C1, and C4 - C3 according to the distance between C1 and C4. Thus ∆ is defined by (5).

(1)

In (1) α is the strength of watermark. Higher values for α increase the robustness of watermark, while it decreases the image quality. In practical implementation we set α = 0.5. Let define d as (2).

d=

3.2 Watermark embedding in LH3 and HL3

Δ=

C4 − C1 ×β 2

(5)

Where β is the strength coefficient for fragile watermark. Higher values of β results in higher robustness but it results in more degradation in watermarked image. In practical implementation we set β = 0.2. In this step, if the calculated ∆ is within the highest 30% of its largest values, then we embed a watermark bit in this 4×1 window, otherwise we skip this window (and also this bit of watermark) and test the next window in the order given in Fig.4. In order to be able to implement this condition on ∆, at first we need to calculate all ∆s for both LH3 and LH3 subbands and then, sort them separately. In fact, the windows that have small ∆ can not resist attacks such as compression. For this reason we do not embed any bit in the coefficients of this window and therefore, we prevent the decrease of PSNR of watermarked image. We define d2 and d3 as (6): (6) C4 − C3 C2 − C1 d2 =

Δ

d3 =

Δ

Now, we modify d2 and d3 according to (7) in such a way that an odd d2 and even d3 shows a zero watermark bit and an even d2 and odd d3 represents a one bit.

Fig. 3. The method of scanning 4 blocks of LL3.

4.2 Detection of possible forgery in watermarked image

Fig.4. Location of 4 coefficients and scanning order in HL3. ⎧ ⎣d 2 ⎦ d 2′ = ⎨ ⎩ ⎣d 2 ⎦ + 1

⎧ ⎣d 3 ⎦ d3′ = ⎨ ⎩ ⎣d 3 ⎦ + 1

if ( ⎣d 2 ⎦ is even) xor ( wi = 0) if ( ⎣d 2 ⎦ is even) xnor (wi = 0)

if ( ⎣d 3 ⎦ is even) xor ( wi = 0) if ( ⎣d 3 ⎦ is even) xnor ( wi = 0)

(7)

In (7) wi is the watermark bit that we want to embed in 4 coefficients. Now to modify C2 - C1 we only change C2 and to modify C4 - C3 we change C3 according to (8). C2′ = C 2 + (d 2′ − d 2 ) ⋅ Δ

C3′ = C3 − (d 3′ − d 3 ) ⋅ Δ

(8)

We shall note that in each of HL3 and LH3 subbands, the capacity of embedding watermark bits is 4 times of the maximum watermark pattern size as described in section 3.1. Therefore, in each subband, we embed the same watermark pattern 4 times. In this case, the purpose for this redundancy is not to increase the robustness of watermark, but the aim is to embed a fragile pattern in all important parts of the subband in order to be able to detect the possible forgery imposed on the watermarked image.

4. WATERMARK DETECTION ALGORITHM Watermark detection is done in two categories: Detection of watermark pattern itself and Detection of possible forgery in watermarked image. 4.1 Detection of watermark pattern In this step we must have the same method of calculation for ∆ and d as described in section 3.1. That is, we calculate the closest integer to d and according to its value to be odd or even, we can verify the watermark bit to be 1 or 0, respectively. But since each watermark bit is embedded into different locations in 4 blocks of LL3, therefore we shall propose an algorithm to decide on the true value of the current bit of watermark (wj) from 4 detected bits from 4 blocks (b1, b2, b3, b4). For this purpose we use the fuzzy mean of b1, b2, b3, b4. A belief value is calculated for each bi according to (9) and the final value of wj is calculated from (10) ~ (12). belief i = 1 − 2 × d i − round (d i ) ⎧− 1 votei = ⎨ ⎩+ 1

if round ( d i ) is even

(9) (10)

if round ( d i ) is odd

σ = ∑ (votei × belief i )

(11)

if σ < 0 if σ > 0

(12)

i

⎧0 wj = ⎨ ⎩1

In this section we perform all necessary calculations to extract the watermark from HL3 and LH3. Since we are expecting that the watermarked image has been forged, thus it is possible that the semi-fragile watermark pattern is not detected correctly. But our tests showed that in spite of usual unintentional attacks the watermark pattern can be extracted completely. In this step, for watermark detection, we need to calculate ∆ and d. These parameters are calculated with the same method in section 3-2. However, only those ∆’s will be considered that are among the top 25% highest value of all ∆s. By evaluating these ∆s we can determine if the quantization to embed the watermark bit can still be recovered or not. Since in subbands HL3 and LH3 of watermarked image there is just one pixel corresponding to each block of size 8×8 in watermarked image, therefore detection of image forgery is performed on these 8×8 blocks. To carry on our calculations, we need a two dimensional array to represent the extracted watermark pattern. But for description simplicity, we assume only one index j for each element of this array. Now, for each index j we have 4 values that might be evaluated to determine our decision. Depending on the location of the block corresponding to bit j of watermark pattern, we have one pixel in LH3 and one in HL3. Each of these pixels was in horizontal and vertical quadruples when we have embedded the semi-fragile watermark. Each of these quadruples have two quantized values i.e. d2 and d3. Therefore to investigate if an 8×8 block has been modified, we have 4 evidences. If any of these 4 evidences were not among the quadruples with ∆ among the largest 25% of all ∆s, then we conclude that the bit has not been embedded in this block and so reject the vote for that evidence. It is obvious that in case of forgery in image, the values of ∆ for the forged blocks are among higher values of ∆. To determine if a block j is forged or not, we define a degree of belief for that block as (13). According (13) for each block j in watermarked image, we have two ∆’s one from HL3 and one from LH3 that are named ∆v and ∆h , respectively. In addition for each of these subbands we have two values for d. Therefore, totally we have 4 values of d as d2,h , d3,h , d2,v , d3,v. The belief of correctness for each evidence is given by (13). ⎧⎪ 1 − 2 × d i , s − round (d i ,s ) if Δ s ∈Top 25% of Δ k (13) belief i ,s = ⎨ ⎪⎩ 0 otherwise

In addition the vote of each evidence is calculated as (14). ⎧− 1 vote 2 , s = ⎨ ⎩+ 1 ⎧− 1 vote 3 , s = ⎨ ⎩+ 1

if round ( d 2 , s ) is odd if round ( d 2 , s ) is even

(14)

if round ( d 3 , s ) is odd if round ( d 3 , s ) is even

Now for each 16×16 block j of the watermarked image, we perform a fuzzy voting as given in (15) among the available votes using a weighted mean.

σ j = ∑ (votei , s × belief i , s )

(15)

i ,s

If σj became negative it indicates that there exists forgery in block j, and the magnitude of σj corresponds to the degree of this belief. In similar way, a positive σj is a proof for non-forgery in that block. Fig.5. Correlation of extracted watermark and the original one for JPEG compression and Cropping.

5. EXPERIMENTAL RESULTS We have implemented this method using MATLAB 7.1. We considered α = 0.5 and β = 0.2. The experiments are done in two categories: The ability of our method to detect the watermark itself, and its ability to determine if the watermarked image has been forged. We tested our algorithm on 4 standard images. In the first category, the robustness of our algorithm to detect watermark in case of attacking the watermarked image by mean and median filers, jpeg compression and cropping is evaluated. These results are shown in Table.1., Fig.5. and Fig.6.

Fig.6. Lena and Boat were forged. The small binary image on the right side shows the forgery locations.

6. CONCLUSION In this paper, we presented a watermarking algorithm based on DWT that is highly robust with respect to attacks such as jpeg compression, mean and median filtering, and cropping. The extraction procedure is based on a fuzzy method. Our algorithm has two main capabilities, first: it provides a high level of robustness by applying a new technique of modification in LL3 subband; and second, it uses a similar technique to modify HL3 and LH3 in order to detect forgery in watermarked image and also the locations of modification. Our experimental results provided satisfactory data compared with most resent works in this field. In our future work we plan to investigate the possibility of embedding similar semi-fragile watermarks in detail subbands of lower levels of DWT to provide more accurate forgery detection. In addition we believe that it is possible to make an adaptive method based on host image content for determining the strength of watermark parameters.

ACKNOWLEDGMENT We highly appreciate Iran Telecommunication Research Center for its financial support to this research that is part of an MSc thesis.

corr

PSNR Mean

Peppers

Lena

Boat

Baboon

43.275

41.434

43.746

45.414

0.973

0.973

0.982

0.963

1 0.991 0.981 0.916 Median Table 1: PSNR of original image and its watermarked version and the correlation between the original watermark pattern and the extracted one from mean and median filter attacks for 4 standard images.

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