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Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 3, Iss. 12 — Dec. 7, 1998
  • pp: 491–496
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Wavelet-based digital image watermarking

Houng-Jyh Mike Wang, Po-Chyi Su, and C.-C. Jay Kuo  »View Author Affiliations


Optics Express, Vol. 3, Issue 12, pp. 491-496 (1998)
http://dx.doi.org/10.1364/OE.3.000491


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Abstract

A wavelet-based watermark casting scheme and a blind watermark retrieval technique are investigated in this research. An adaptive watermark casting method is developed to first determine significant wavelet subbands and then select a couple of significant wavelet coefficients in these subbands to embed watermarks. A blind watermark retrieval technique that can detect the embedded watermark without the help from the original image is proposed. Experimental results show that the embedded watermark is robust against various signal processing and compression attacks.

© Optical Society of America

1. Introduction

We can classify digital watermarking into two classes depending on the domain of watermark insertion, i.e. the spatial- and the frequency-domain watermarking. Spatial domain watermarking is easy to implement and requires no original image for watermark detection. However, it often fails under signal processing attacks such as filtering and compression. Besides, the fidelity of the original image data can be severely degraded since the watermark is directly applied on the pixel values. Frequency domain watermarking generally provides more protection under most of the signal processing attacks. But the existing frequency-domain watermark algrithms require the original image for comparison in the watermark retrieval process, which is not practical for a huge image database. Furthermore, the necessity of progressive transmission is one of the requirements for Internet distribution. The lack of progressive transmission property in existing spatial- and frequency-domain watermarking algorithms limits their Internet applications.

To solve the above problems associated with existing watermarking algorithms, we propose a new frequency-domain wavelet-based watermarking technique. The proposed method searches significant coefficients across subbands to embed the watermark. The watermark is adaptively weighted in different subbands to achieve robustness as well as high perceptual quality. Besides, a blind watermark retrieval algorithm (i.e. to retrieve watermark without the original image as a reference) can be applied. Experimental results show that the proposed algorithm can survive with various geometric, filtering, and compression attacks.

2. Significant coefficient search

After the wavelet transform, we assume that wavelet coefficients in each sub-band follow the Gaussian distribution. It was shown in [1

1. Houng-Jyh Wang and C.-C. Jay Kuo, “High fidelity image compression with multithreshold wavelet coding (MTWC),” SPIE’s Annual Meeting - Application of Digital Image Processing XX, San Diego, CA July 27 - August 1 (1997)

] that, for a Gaussian distribution with zero mean and variance σ 2, the simplified rate-distortion model becomes

D={T212σ2>T212,σ2,σ2>T212.
(1)

MTWC is a bit-plane coder. Each coefficient Cs (x,y) in subband s can be represented by

Cs(x,y)=sign×(a0T20+a1T21++abT2b+),
(2)

where “sign” is the sign value (e.g. +1 for positive sign or -1 for negative sign) of coefficient Cs (x, y), b is the bit-plane layer number (b = 0 indicates the most significant bit (MSB) plane layer), ab , is the binary bit at the bth bit plane and T is the initial threshold of subband s calculated via

T=Cmax,s2,
(3)

where C max,s is the maximum absolute coefficient value in subband s. The significant coefficient searching procedure can be summarized as follows.

  1. Set the initial threshold Ts of each subband to one half of its maximum absolute value of coefficients inside the subband. Set all coefficients un-selected.
  2. Select the subband (except the DC term) with the maximum value of βsTs , where βs is the weighting factor of subband s. For the selected subband, we examine all un-selected coefficients Cs (x, y) and choose coefficients greater than the current threshold Ts as significant coefficients. Cast the watermark in these selected significant coefficients.
  3. Update the new threshold in subband s via Tsnew = Ts /2.
  4. Repeat Step 2 to Step 3 until all watermark symbols are cast.

3. Adaptive watermark casting and retrieval

Figure 1. The blockdiagram of invisible watermark embedding and detection (a)embedding (b)detection.

3.1 Invisible Watermark Casting

Figure 1(a) shows the blockdiagram of invisible watermark embedding. We perform watermark casting by using the spread spectrum technique. The watermark casting is performed as

Cs,k(x,y)=Cs(x,y)+αsβsTsWk,
(4)

where C′ is the coefficient of the watermarked image, C is the original coefficient, αs and βs are scaling factors, Ts is the current threshold of subband s in the jth bit plane, and Wk is the kth watermark element in a watermark sequence of length Nw . Wk takes value between 1 and -1. The value of αs is adjustable by users to increase (or decrease) the watermarked image fidelity and decrease (or increase) the security of watermark protection at the same time. It is chosen that αs ∊ (0.0,1.0]. The error introduced by watermark insertion is

Es,k(x,y)=αsβsTsWk,
(5)

Given |Wk | ≤ 1.0, the mean square error (MSE) introduced by the watermark can be computed as:

MSEΣs=1NsΣj=1NbitHsj(αsβsTs)2Height×Width,

where Hsj is the number of significant coefficients in subband s of the jth bit layer, Height and Width are the height and width parameters of the image, Ns is the total number of subbands (except for the lowest-frequency subband), Nbit is the total number of cast watermark bits per bit layer per subband. We would like to provide a watermarked image of high fidelity with a PSNR value greater than 35 dB. This implies that MSE should be less than 20.56 for an 8-bit gray level image. Thus, we have

MSENwHeight×Width(αmax)2(Tmax)2(βmax)220.56,
(6)

where Nw is the size of the watermark sequence, Tmax is the maximum value of Ts , α max is the maximum value of αs , and β max is the maximum value of βs . By using the fact that βmax = 1.0, we can obtain a constraint on αmax , i.e.

αmax1Tmax20.56×Height×WidthNw.
(7)

We see from (6) that a larger value of α will result in a watermarked image of lower fidelity.

3.2 Invisible Watermark Detection

When the watermarked image I′ is distributed to the public, it could go through various attacks to result in an attacked image I *. The difference between coefficient C * of I * and coefficient C of the original image I in the selected significant coefficient position (x, y) can be written as

Es,k*(x,y)=Cs,k*(x,y)Cs(x,y).

The similarity between C * and C is calculated as

SIM(I*,I)=NwΣk=1NwEs,k*(x,y)·Es,k(x,y)Es,k*(x,y)Es,k(x,y),
(8)

where Es,k (x,y) is the original watermark and Es,k*(x,y) is the attacked watermark with respect to wavelet coefficient Cs (x,y). The blockdiagram of watermark detection is given in Figure 1(b). As shown in (6), MSE between watermarked and original images is proportional to αmax2. Thus, the root mean square error (RMSE) is propotional to αmax . If the distortion of the watermarked image’s coefficient due to an attack is greater than RMSE, the watermark cannot be successfully retrieved via (8). Thus, robustness to attacks is highly dependent on αs .

3.3 Blind Watermark Detection

By blind watermark detection, we mean to retrieve the embedded watermark without any information from the original image. The most difficult problem associated with blind watermark detection in the frequency domain is to identify coefficients with the watermark inserted and the embedded watermark values. We develop a blind watermark detection algorithm by truncating selected significant coefficients to some specified value.

The main idea of blind watermarking comes from (2). Let Cs,b (x,y) be the selected significant coefficient in the bth bit plane of subband s, i.e. Ts,bC(x, y) ≤ T s,b-1, then the watermarked version of Cs,b (x,y) is:

Cs,b,k(x.y)=sign×Δp(Cs,b(x,y))×αsβsTs,bWk.
(9)

where sign is the sign value of Cs,b (x, y). The operation ∆p is defined as

Δp(Cs,b(x,y))=(1+2pαs)Ts,b,
(10)

where Ts,b is defined in (3) with subband number s and bit plane number b, and p is an integer between 1 and (2αs )-1. The distance DIS S,b,P(x,y) between ∆p(Cs,b (x,y)) and Cs,b ,(x,y) is defined as

DISs,b,p(x,y)=Δp(Cs,b(x,y))Cs,b(x,y).

Then, we can obtain p by

p=argminpDISs,b,p(x,y).

After p is selected, we have

DISs,b,p(x,y)2αsTs,b.

The blind watermark detection formula is basically the same as (8) with the replacement of Es,k (x, y) by Es,k* (x, y), which is

Es,k*(x,y)=Cs,b,k*(x,y)sign×ΔpCs,b,k*(x,y),
(16)

where Ts,b* is obtained from C *. Since Ts,b* comes from the largest coefficient in subband s, it is not easily attacked. Besides, no watermark is embedded, so Ts,b* should be very close to Ts,b .

Given the constraint βs ≤ 1.0, if the distortion on Cs,b,k(x, y) is less than αs Ts,b , then the watermark on Cs,b (x,y) can be perfectly detected. A larger αs could provide more robustness to attacks but a poorer PSNR performance in the watermarked image. In order to provide a watermarked image with PSNR greater than 35.0 dB, we have

MSENwHeight×Wight(2α)2(Tmax)2(β)220.56.
(11)

Thus, given that β ≤ 1.0, the value of αs is limited by

αmax14Tmax20.56×Height×WidthNw.
(12)

Compared with (7), we see that the performance of blind watermark detection is 4 times poorer than the watermark retrieval algorithm with the original image as a reference since the value of α is propotional to robustness against attacks.

4. Experimental results

Figure 2. Watermark retrieval from the watermarked 512 × 512 gray-level Lena image after (a) the 6 × 6 block mosaic attack, (b)the 50% uniform random noise attack, (c) the JPEG compression attack with 5% quality factor setting, and (d) the 512:1 compression attack with SPIHT.

We performed watermark protection on the Lena image of size 512 × 512 with Nw = 8,192 and α = 1.0. The PSNR between the original image and the watermarked image is 37.20 dB. Watermark retrieval results after the attack of 6 by 6 block mosaic lowpass filtering and 50% uniform random noise attack were shown in Figures. 2 (a) and (b), respectively. We see clearly that the embedded watermark with ID number 450 is retrieved successfully. It is worthwhile to point out that most existing spatial domain watermark algorithms cannot survive under even a 4 by 4 block mosaic filtering attack. The proposed algorithm can survive well under a DCT-based JPEG compression attack. The result after the JPEG compression with the quality factor set to 5% is shown in Figure. 2(c). Moreover, Figure. 2(d) shows that our algorithm can survive even under a 512:1 compression attack by using a wavelet-based compression codec known as SPIHT[2

2. A. Said and W. A. Pearlman, “A new, fast, and efficient image codec based on set partitioning in hierarchical trees,” IEEE Trans. on Circuits and Systems for Video Technology, pp. 243–250, June (1996)

].

Figure 3. Blind watermark retrieval for the gray-level Lena image of size 512×512 after (a) no attack, (b) soften filter attack, (c) JPEG compression attack and (d) 64:1 compression ratio attack by SPIHT.

Figure. 3(a) shows the blind watermark retrieval result of a watermarked Lena image without any attack, where the weighting factor α was set to 0.125. The watermark was retrieved successfully without any information from the original image. The PSNR value between the original image and the watermarked image is 46.18dB. Figures. 3 (b), (c) and (d) show the watermark retrieval results after soften, default JPEG compression and SPIHT 64:1 compression attacks. As shown in these figures, the embedded watermark with ID number 450 was retrieved successfully under these attacks.

5. Conclusion

In this work, we developed a perceptual watermark casting scheme which searches the perceptually significant wavelet coefficients. The watermark sequence is cast into selected significant coefficients to provide a higher tolerance to various attacks. Moreover, the fidelity of the watermarked image can be adjusted by using the weighting factor α of the cast watermark energy. A blind watermark retrieval technique was also proposed and analyzed. It was demonstrated by experiments that the proposed algorithm can provide an excellent protection under various attacks.

References

1.

Houng-Jyh Wang and C.-C. Jay Kuo, “High fidelity image compression with multithreshold wavelet coding (MTWC),” SPIE’s Annual Meeting - Application of Digital Image Processing XX, San Diego, CA July 27 - August 1 (1997)

2.

A. Said and W. A. Pearlman, “A new, fast, and efficient image codec based on set partitioning in hierarchical trees,” IEEE Trans. on Circuits and Systems for Video Technology, pp. 243–250, June (1996)

3.

Xiang Gen Xia, Charles G. Boncelet, and Gonzalo. R. Arce, “A multisolution watermark for digital images,” International Conference on Image Processing, IEEE Signal Processing Society, Santa Barbara, CA, July (1997)

OCIS Codes
(100.0100) Image processing : Image processing
(100.2000) Image processing : Digital image processing

ToC Category:
Focus Issue: Digital watermarking

History
Original Manuscript: October 30, 1998
Published: December 7, 1998

Citation
Houng-jyh Wang, Po-Chyi Su, and C.-C. Jay Kuo, "Wavelet-based digital image watermarking," Opt. Express 3, 491-496 (1998)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-3-12-491


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References

  1. Houng-Jyh Wang and C.-C. Jay Kuo, "High fidelity image compression with multithreshold wavelet coding (MTWC)," SPIE's Annual Meeting - Application of Digital Image Processing XX, San Diego, CA July 27 - August 1 (1997)
  2. A. Said and W. A. Pearlman, "A new, fast, and efficient image codec based on set partitioning in hierarchical trees," IEEE Trans. on Circuits and Systems for Video Technology, pp. 243-250, June (1996)
  3. Xiang Gen Xia, Charles G. Boncelet and Gonzalo. R. Arce, "A multisolution watermark for digital images," International Conference on Image Processing, IEEE Signal Processing Society, Santa Barbara, CA, July (1997)

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