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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 8 — Apr. 16, 2007
  • pp: 4804–4813
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A dual Fourier-wavelet domain authentication-identification watermark

Farid Ahmed  »View Author Affiliations

Optics Express, Vol. 15, Issue 8, pp. 4804-4813 (2007)

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A dual Fourier-Wavelet domain watermarking technique for authentication and identity verification is proposed. Discrete wavelet transform (DWT) domain spread spectrum is used for embedding identity (such as registration number, transaction ID etc.) information. While a blind detector detects an ID, it is important to validate with other ancillary data. To satisfy that requirement, we embed a robust signature and hide it in a mid-band wavelet subband using Fourier domain bit-embedding algorithm. Results are furnished to show the compression tolerance of the method.

© 2007 Optical Society of America

1. Introduction

As an example of the premise of this paper, let us consider an attack where classified information can be changed and then leaked. The solution paradigm should, in this case, address the issue of identifying the leaker as well as whether any tampering was done on the leaked image. Our proposed solution is to add dual watermark for this dual purpose. A robust watermark is to be used to embed identity information into the image, while a semi-robust authentication watermark is expected to determine whether tampering was done.

We employ transform-domain watermark, which is generally shown to be more robust than its spatial-domain counterpart. In particular, the authentication part of the current work is based on the Fourier phase-based watermark called ‘Phasemark’ [3

3. F. Ahmed and I. S. Moskowitz, “Correlation-based watermarking method for image authentication applications,” Opt. Eng. 431833–1838 (2004). [CrossRef]

]. In Ref. [4

4. F. Ahmed and I. S. Moskowitz, “Phase Signature-based Image Authentication watermark robust to compression and coding,” Proc. SPIE 5561, 133–144 (2004). [CrossRef]

] the authors showed how Phasemark can be used in wavelet domain for better compression tolerance. In this work we extend that further to have a better compression tolerance while maintaining the quality of the image to an acceptable level. The primary advantage of using wavelet domain for watermarking stems from the flexibility of sub-band decomposition and a predictable compression tolerance [5

5. P. Meerwald and A. Uhl, “A survey of wavelet domain watermarking algorithms,” Proc. SPIE 4314, 505–516 (2001). [CrossRef]


2. Proposed Fourier-Wavelet domain watermark

The proposed method is based on the Fourier transform of the selected subbands of the wavelet decomposition of an image. Using wavelets, an image can be decomposed into a low-resolution smooth image and a number of detailed images [6

6. S. Mallat, A Wavelet Tour of Signal Processing (Academic Press, NY, 1998).

]. Figure 1 shows the sub bands resulting from a two-level decomposition.

Fig. 1. Level 2 decomposition showing the sub bands.

With one-level decomposition, we denote the smooth sub band as A1 (‘A’ stands for the approximate image and 1 is for level 1 decomposition). The detailed part has three components depending upon the directional vector used in the decomposition. These are horizontal (H1), vertical (V1), and diagonal (D1). With a second level of decomposition, the A1 sub band can be further decomposed into an even smoother version (A2) and three more detailed sub bands (H2, V2, and D2). The decomposition can go on for more levels of resolution.

Figure 2 shows the flowchart of the watermark embedding process using 1 level of decomposition. Among the 4 sub bands, the A1 and D1 sub bands are unaffected with the watermarking process. Since perceptual quality is mostly affected by A1, this is good for image quality preservation. In addition, since compression will most likely affect D1 sub band more, watermark signal will be less affected by compression. Note that A1 is used for computing the image hash, or the authentication signature, which is subsequently embedded in the H1 or V1 subband. The identity information is embedded in the other subband. If we use two level decompositions, then we choose A2 as the signature subband, H2 and V2 for authentication and identity embedding. Looking at Fig. 2, it might be tempting to use only Fourier transform, avoiding wavelet transform altogether, since the DFT-only method would be more efficient. But there appear to be two problems associated with this. First, the ‘conjugate symmetry’ of the transform domain coefficients is necessary to transform the image back to the spatial domain. With the DFT-only method, while the complete full-image transform coefficients satisfy the conjugate symmetry condition, the one-fourth shares representing the approximate, horizontal, vertical and diagonal detail components by themselves do not satisfy. On the other hand, with the proposed DWT-DFT method since individual subbands of the original image are independently Fourier transformed, the symmetry is maintained, admittedly with more calculations necessary. The second aspect is that the DWT-DFT gives the flexibility of wide range of robustness and perceptual quality.

Fig. 2. DWT-DFT Domain Dual Watermark Embedding using level 1 decomposition

Now we shall show how the actual embedding process works, in terms of level 1 decomposition without any loss of generality.

2.1 Embedding authentication signature

A number of different image hashes are reported in literature [7

7. J. Fridrich and M. Goljan, “Robust hash functions for digital watermarking,” IEEE Proc. Int. Conf. on Information Technology: Coding and Computing,” 178 – 183 (2000).

]. In Ref. [3

3. F. Ahmed and I. S. Moskowitz, “Correlation-based watermarking method for image authentication applications,” Opt. Eng. 431833–1838 (2004). [CrossRef]

], we have shown binary-phase-only-filter (BPOF) [8

8. J. L. Horner and J. R. Leger, “Pattern recognition with Binary phase-only filters,” Appl. Opt. 24, 609–611 (1985). [CrossRef] [PubMed]

] signature to be an effective image authenticator. In the present work, since the BPOF is extracted from an approximate sub band, like A1 or A2 instead of the original image, the resulting signature is expectedly even more robust. In Ref. [4

4. F. Ahmed and I. S. Moskowitz, “Phase Signature-based Image Authentication watermark robust to compression and coding,” Proc. SPIE 5561, 133–144 (2004). [CrossRef]

] we used the same sub band for signature and embedding. That had the undesirable effect of changing the signature domain, so that even in absence of any kind of degradation, the computed signature and the extracted signature from the watermarked image will not be the same. We eliminate that problem by not embedding the signature in the same signature sub band. In this work, these two spaces are separate, as we use the A1 as the signature space and the H1 (or V1) as the signature hiding space for authentication verification.

Since the signature and the bit-plane embedding uses Fourier transform, it is instructive to look at the magnitude and phase of discrete Fourier transform (DFT) of an arbitrary image x(m,n). During the signature generation phase x(m,n) represents the A1 image. The DFT of x(m,n) can be represented in polar form with its magnitude and phase as following,


Where, X(u,v) is the magnitude part of the frequency component given by |H(u,v)|, and ϕ(u,v) is the phase part of frequency H(u,v) given by


2.2 Embedding Identity info

As mentioned above, the subband with the higher energy in the mid-frequency range in wavelet decomposition is used for the spread spectrum watermarking of the identity information, m. This could be a unique identification number of an image, or a registration or serial number, or any other tracking number.

The identity is first encoded using source coding and optionally with the help of error correction and detection coding, and finally spreading, represented as Wm, which is made the same size as the subband under consideration. The key, k is used as a seed in pseudorandom number generator, to come up with the pattern Wk, which is also the same size as the subband image. These two binary patterns (Wk and Wm) are then combined, which can take as simple as an XOR operation as follows.


2.3 Detection: authentication and identification

The detector in turn does the reverse operations of performing the authentication test and then extracting the identity information. Note that since the two processes in the embedder were done independently, the order of these two operations in the detector does not make any difference. Also note that the detector is a blind one which does not need the original image, but it makes use of the knowledge of the keys used in the embedder as well as the wavelet parameters used. It however does not need to know the specific subband used.

The detector performs the desired wavelet decomposition and identifies the authentication and identification subbands from the measurement of entropy (expressed as the energy content, in terms of L2 norm, in this paper). Specifically, our selection is based on the fact that, authentication is a 1-bit decision, while identification involves the extraction of multiple bits of embedded information. Hence, identification needs a better embeddable subband. And we argue that the subband with more energy (or entropy in this case) will be better embeddable.

For the authentication test, we take the magnitude spectrum of the Fourier transform of the authentication subband and round the coefficients to represent them in a number of bit-planes. At this point, the detector should know which bit-plane is used for hiding the signature. This can be done either by a using an agreed-upon bit-plane between the embedder and detector or conceivably, the detector can select it by performing a correlation with all the bit-planes with the computed phase-only information as mentioned below. After this bit-plane selection, the encrypted embedded signature is extracted. Then we use the shared key to generate a Fourier-symmetric random matrix and XOR with the extracted encrypted signature to obtain the decrypted version S’(u,v).

From the phase information ϕA(u,v) , of the Fourier transform of the approximate subband (A1 or A2), we then compute phase-only-filter (POF) as



3. Simulation and results

3.1 Which Wavelet?

A small-tap wavelet like Haar filter is found to extract more detailed information, compared to a large-tap wavelet like dB6, as shown in Table 1. Since we are embedding in the two high-energy detailed subbands, we choose ‘Haar’ wavelet for the rest of the simulation.

Table 1. The energy of the subbands (using L2-norm)

View This Table

3.2 Image Database

We tested the algorithm using the SIPI [9] database images. Figure 3 shows the first level wavelet decomposition of the 256×256 image, ‘The Chemical Plant’. As shown in Table 1, the horizontal subband, H1 [shown in Fig. 3(b)] contains more energy compared to the vertical subband, V1 [shown in Fig. 3(c)]. Hence H1 is used to embed the identification information, while V1 is used to hide the authentication information. We just arbitrarily used a 9-digit number for the identification. We convert it to binary form and add some taint bits to result in a code of 32-bit. This is then replicated to make it equal to the size of subband, which is 128×128 for the level 1 and 64×64 for level 2 decomposition. Note that A1 [shown in Fig. 3(a)] is used to calculate the BPOF-based signature and D1 [shown in Fig. 3(d)], is not changed in the embedding process.

Fig. 3. 1-level decomposition of the ‘Chemical Plant’ with Haar Wavelet (a) Approximation, (b) Horizontal Detail, (c) Vertical, (d) Diagonal Detail

3.3 Detection metrics

We also investigated the use of a computationally less expensive ‘inner product’ metric to benchmark the authentication value. This is done by computing the inner product of the computed BPOF from the phase information [HA POF (u, v)] of the approximate band and the extracted BPOF. Figure 4(b) shows the result. While both metrics yield in similar performance, it turns out that the correlation-based metric offers better discrimination between a marked and unmarked image. For the rest of the simulation, we therefore use the PSR metric.

Fig. 4. Authentication Performance for a set of images at different strength a) PSR value, b) Inner product value

Now, it is clear from Fig. 4(a) that for the unmarked case, the PSR is close to zero. This means the highest peak and the second highest peak values are similar, indicating a bad correlation and thus unauthenticated image. To understand the authentication characteristics, we need to know the sources of error in this watermarking process. There are three error sources. First, the rounding of Fourier magnitude in the embedder introduces some errors. Second, the rounding of the image after the final inverse Wavelet transform in the embedder yields in some error. Third, the detector introduces error while rounding the Fourier magnitude. Since rounding error affects a lower order bit plane more adversely than a higher-order bit-plane, we see that, as we increase the watermark strength (by selecting a higher-order Fourier magnitude bit plane), the error decreases and saturates, and thus yielding better authentication. Finally, note also that it is possible to define a threshold of detection value, for example a value of 5dB (giving enough guard band) can differentiate the marked and unmarked image very well.

For an understanding of how well the identity verification works, we use the bit error rate (BER), which is defined as the ratio of the number of incorrectly identified bits to the total number of bits. Note that in real applications we don’t know the actual bits, so the identity number need to be validated by the authenticity metric and this is one of the interesting contributions of the present work.

3.4 Quality of the watermarked image

We use the widely accepted objective metric PSNR (peak signal to noise ratio) as the quality indicator, which is defined as follows. The PSNR of a watermarked image Iw, with respect to the original image Io (both represented in 8-bit gray scale with peak intensity of 255), is given by,


In this work, quality of the watermarked image depends primarily on the selected subbands and the selected bitplane for Fourier magnitude embedding. For a given subband, higher strength of watermark is obtained by selecting higher-order bitplane. Specifically, in our implementation, we use the following relationship,

. BIT_POS=strength+6

We do this to represent the strength in a sliding scale of 1 to a desired maximum value. BIT_POS is the most significant bitplane of the Fourier magnitude that is used in embedding. The maximum strength of 6 used in simulation means, we have hidden the signature in bitplane number 12 of the Fourier magnitude. Typically, an increase of strength by 1 decreases the image quality by 6 dB in PSNR sense.

Fig. 5. Quality and Authentication Metric at a) Level 1 and b) Level 2 decomposition

Figure 5 shows a classical trade-off between the authentication and image quality metric for different watermark strength. As mentioned earlier, PSR is used as the metric for authentication and PSNR is used for measuring the quality of the watermarked image. The figure shows that a stronger watermark makes the authentication more robust, while degrading the quality of the image. As an example, strength of 4, results in the quality of more than 42 db. Figure 5 also shows that while the quality of the watermarked image remains similar for both 1-level and 2-level decomposition, authentication value decreases in level-2, which is primarily a correlation artifact. On the other hand, level-2 embedding is found to be more robust to compression as shown below.

3.5 Compression performance

After the watermark embedding, the image is compressed with different quality factor and then the detector is run. We used JPEG compression engine adopted by Matlab, and also used its definition of compression ‘quality factor’. Assuming a detection threshold of 5 dB, with a quality of 42 dB (strength 4), the method can tolerate compression quality factor up to 85, as shown in Fig. 6(a). As we increase the watermark strength from 4 to 5, it can tolerate a compression of approximately 60 quality factor. As we further increase the strength, the image can be compressed down to a quality of 40, with the authentication still working perfectly. If we compare the results with level 2 decomposition, as in Fig. 6(b), we see that the compression tolerance has significantly increased. For a strength of 5 (corresponding to PSNR 36 dB), it can now tolerate compression down to a quality factor of as low as 15.

A more important concern is how robust the embedded identity information is against compression. Figure 7 depicts the result. Our goal is to achieve BER of 0 for complete compression tolerance. Again, in general, level 2 embedding is found to be more compression tolerant. Specifically, if we look at the strength 5, level 1 can tolerate a quality factor of 75, while level 2 can go down to a quality of 30.

Fig. 6. Authentication Performance against Compression a) Level 1, b) Level 2.
Fig. 7. Identity verification Performance against Compression (BER vs compression QF) (a) Level 1, (b) Level 2.

Above results demonstrate the efficacy of the proposed dual DWT-DFT domain watermark that integrates the flexibility of embedding parameter selection offered by DWT, with the robustness of signature offered by DFT. While the authentication performances are found to be similar or better compared to some other contemporary transform domain watermarking techniques, our work introduces couple of unique contributions that were not reported in those works. These are i) tagging of authenticity and identity watermark; and ii) the energy-based selection of subbands for embedding authentication signature and the identification information. In addition, the mutual exclusivity of signature subband and embedding subband resulted in a signature robust to watermark itself. In our test with several images, it is also shown that even when we blackened out (replaced pixels with values of zero) up to an area of 100×100 pixel (out of 256×256), the authentication watermark still survived. On the other hand, since the authentication watermark is robust, it may not be very suitable for tamper-proof scenario, although modification in the busy area of the image can be still detected easily. Of course, the identification part is found to be more sensitive to malicious modification than the authentication part.

4. Conclusion

We proposed a dual DWT-DFT domain watermark. Our contributions in this work are i) the choice of signature sub band and the mutual exclusivity of signature sub band and embedding sub band, resulting in a signature robust to watermark itself; ii) The tagging of authenticity and identity information; iii) the energy-based selection of sub bands for embedding authentication signature and the identification information; and iv) the compression-tolerant authentication and identity verification coming out from embedding in the Fourier magnitude of the selected wavelet sub band.

We furnished the results showing the discrimination ability of the authentication watermark and the compression tolerance of the authentication and identification watermark. Future work will focus on the security of the method in addition to the robustness.


The author greatly appreciates the constructive comments and suggestions by the anonymous reviewers.

References and links


I. Cox, J. Bloom, and M. Miller, Digital watermarking: Principles & Practice (Morgan Kauffman Publishers, 2001).


T. Liu and Z.-D. Qiu, “The survey of digital watermarking-based image authentication techniques,” 6th International Conference on Signal Processing, 21556 – 1559 (2002).


F. Ahmed and I. S. Moskowitz, “Correlation-based watermarking method for image authentication applications,” Opt. Eng. 431833–1838 (2004). [CrossRef]


F. Ahmed and I. S. Moskowitz, “Phase Signature-based Image Authentication watermark robust to compression and coding,” Proc. SPIE 5561, 133–144 (2004). [CrossRef]


P. Meerwald and A. Uhl, “A survey of wavelet domain watermarking algorithms,” Proc. SPIE 4314, 505–516 (2001). [CrossRef]


S. Mallat, A Wavelet Tour of Signal Processing (Academic Press, NY, 1998).


J. Fridrich and M. Goljan, “Robust hash functions for digital watermarking,” IEEE Proc. Int. Conf. on Information Technology: Coding and Computing,” 178 – 183 (2000).


J. L. Horner and J. R. Leger, “Pattern recognition with Binary phase-only filters,” Appl. Opt. 24, 609–611 (1985). [CrossRef] [PubMed]


USC-SIPI Image Database, http://sipi.usc.edu/services/database/Database.html

OCIS Codes
(070.4550) Fourier optics and signal processing : Correlators
(100.7410) Image processing : Wavelets

ToC Category:
Fourier Optics and Optical Signal Processing

Original Manuscript: January 2, 2007
Revised Manuscript: March 12, 2007
Manuscript Accepted: March 13, 2007
Published: April 5, 2007

Farid Ahmed, "A dual Fourier-wavelet domain authentication-identification watermark," Opt. Express 15, 4804-4813 (2007)

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  1. I. Cox, J. Bloom, and M. Miller, Digital watermarking: Principles & Practice (Morgan Kauffman Publishers, 2001).
  2. T. Liu and Z.-D. Qiu, "The survey of digital watermarking-based image authentication techniques," 6th International Conference on Signal Processing 2, 1556 - 1559 (2002).
  3. F. Ahmed and I. S. Moskowitz, "Correlation-based watermarking method for image authentication applications," Opt. Eng. 43, 1833-1838 (2004). [CrossRef]
  4. F. Ahmed and I. S. Moskowitz, "Phase Signature-based Image Authentication watermark robust to compression and coding," Proc. SPIE 5561, 133-144 (2004). [CrossRef]
  5. P. Meerwald and A. Uhl, "A survey of wavelet domain watermarking algorithms," Proc. SPIE 4314, 505-516 (2001). [CrossRef]
  6. S. Mallat, A Wavelet Tour of Signal Processing (Academic Press, NY, 1998).
  7. J. Fridrich and M. Goljan, "Robust hash functions for digital watermarking," IEEE Proc. Int. Conf. on Information Technology: Coding and Computing," 178 - 183 (2000).
  8. J. L. Horner and J. R. Leger, "Pattern recognition with Binary phase-only filters," Appl. Opt. 24, 609-611 (1985). [CrossRef] [PubMed]
  9. USC-SIPI Image Database, http://sipi.usc.edu/services/database/Database.html

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