## Image watermarking using block site selection and DCT domain constraints

Optics Express, Vol. 3, Issue 12, pp. 512-523 (1998)

http://dx.doi.org/10.1364/OE.3.000512

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### Abstract

In this paper we propose an image watermarking algorithm based on constraints in the Discrete Cosine Transform (DCT) domain. An image watermarking algorithm has two stages: signature casting (embedding) and signature detection. In the first stage it embeds an identifying label in the image. This is recognized in the second stage. The proposed algorithm has two processing steps. In the first step certain pixel blocks are selected using a set of parameters while in the second step a DCT coefficient constraint is embedded in the selected blocks. Two different constraint rules are suggested for the parametric modification of the DCT frequency coefficients. The first one embeds a linear constraint among certain selected DCT coefficients and the second defines circular detection regions according to the given parameters. The watermarks cast by the proposed algorithm are resistant to JPEG compression and filtering.

© Optical Society of America

## 1. Introduction

5. M. Barni, F. Bartolini, V. Capellini, and A. Piva, “A DCT-domain system for robust image watermarking,” Signal Processing **vol. 66**, no. 3, pp. 357–372, 1998. [CrossRef]

5. M. Barni, F. Bartolini, V. Capellini, and A. Piva, “A DCT-domain system for robust image watermarking,” Signal Processing **vol. 66**, no. 3, pp. 357–372, 1998. [CrossRef]

8. I. J. Cox, J. Kilian, T. Leighton, and T. Shamoon, “Secure Spread Spectrum Watermarking for Multimedia, IEEE Trans. on Image Processing , **vol. 6**, no. 12, pp. 1673–1687, Dec. 1997. [CrossRef]

8. I. J. Cox, J. Kilian, T. Leighton, and T. Shamoon, “Secure Spread Spectrum Watermarking for Multimedia, IEEE Trans. on Image Processing , **vol. 6**, no. 12, pp. 1673–1687, Dec. 1997. [CrossRef]

10. S. A. Kassam, *Signal detection in Non-Gaussian Noise*, Springer-Verlag, 1988. [CrossRef]

11. G. K. Wallace, “The JPEG still picture compression standard,” IEEE Trans. on Consumer Electronics , **vol. 38**, no. 1, pp. 18–34, Feb. 1992. [CrossRef]

11. G. K. Wallace, “The JPEG still picture compression standard,” IEEE Trans. on Consumer Electronics , **vol. 38**, no. 1, pp. 18–34, Feb. 1992. [CrossRef]

## 2. Block site selection

*k*is the owner identifier,

**S**

_{k}denotes the watermarking vector,

**L**

_{k}the component vector used for identifying the sites and

**C**

_{k}the parameter vector for embedding the DCT coefficient constraint.

11. G. K. Wallace, “The JPEG still picture compression standard,” IEEE Trans. on Consumer Electronics , **vol. 38**, no. 1, pp. 18–34, Feb. 1992. [CrossRef]

*x*

_{j}is the difference between two consecutive chosen sites (measured by number of blocks) for the last

*j*= 1,…,

*N*sites,

*L*is the number of Gaussian functions,

*G*() is the output of the network.

*λ*

_{i},

*w*

_{i,j},

*r*

_{i,j},

*N*,

*L*∊

**L**

_{k}are the Gaussian parameters provided by the watermarking code. In the following we consider a row-column scanning order for chosing the appropriate blocks. The condition of selecting a block site is that the Gaussian network output is above a chosen threshold

*α*∊ (0,1):

*G*(x) is given in (2). This condition is fulfilled for a certain data range. The proces of selecting the block sites is illustrated in Figure 2.

*λ*

_{i}= 1 for

*i*= 1,…,

*L*. We consider that a Gaussian function is activated if its output is above a certain threshold. Providing the distances between the chosen block sites, we consider the simplifying model where each Gaussian function is activated, in a certain order, only one at the time. In order to fulfill this condition, the parameters of the Gaussian network must form a circulant matrix :

*i*= 1,…,

*L*and

*j*= 2,…,

*N*, where mod

*L*denotes the operation modulo

*L*. The number of distinct network parameters is 2

*L*. After the

*L*-th Gaussian unit is activated, the process continues with the first unit.

*N*- 1 block site locations

*x*

_{j}=

*d*

_{j}for

*j*= 1,…,

*N*- 1. In the signature embedding stage we have to find the location of next block site that fulfills the condition (2). From (2) and (3), after assuming that only one Gaussian function is activated at the time and after applying the function In, we obtain the following range of distances expressed through the number of blocks :

*T*

_{i,N}given by (7) provide an interval from where to chose the next site. The sites that fulfill the condition (3) alternate with those which do not fulfill it. We impose the condition that only one Gaussian function is activated for a chosen block location. In order to fulfill this we impose :

*M*×

*R*is the image size and

*T*

_{i,N}are the distances recursively calculated in (7) for

*i*= 1,…,

*L*- 1.

*L*-th ) function from the Gaussian network. We evaluate the bounds for the number of pixels contained in such a region :

*s*

_{k}is the number of pixels from a signed region

*n*is the total number of block sites,

*T*

_{i,N}is provided in (7) and 64 is the number of block pixels. This region represents the area from the image where the watermark can be identified without the need of knowing the rest of the image. After embedding the watermark in a certain region, the process is repeated until the entire image is watermarked.

## 3. The DCT coefficient constraint

**vol. 38**, no. 1, pp. 18–34, Feb. 1992. [CrossRef]

**vol. 38**, no. 1, pp. 18–34, Feb. 1992. [CrossRef]

*f*

_{j}(

*k*,

*l*) are the image pixel values from the

*j*-th block, and

*F*

_{j}(

*u*,

*v*) are the transform coefficients.

*K*of frequency pairs used for embedding the given constraint is provided by the watermark vector (1).

*F*is the vector of the modified DCT frequency coefficients,

*∊*

**Q***is the weighting vector provided by the watermark (1). The vector*

**C**_{k}*is characteristic to a watermark and contains the parameters corresponding to the selected DCT frequencies. In order not to produce significant distortions in the image these parameters must not be in a big ratio with respect to each other. This constraint is embedded in all the block sites which fulfill (2,3). The DCT frequency coefficients*

**Q***F*are modified based on a least mean squares approach [15] such that we obtain a minimal distortion in the image, in order to fulfill (13). The relationship (13) is essentially a linear and time invariant system in the DCT domain [14].

*H*, the number of circular regions. For a selected block site, we evaluate the Euclidean distance between its DCT coefficient vector and that of the watermark. The chosen DCT coefficients are changed to the value of the closest watermark parameter vector :

*for*

**Q**_{i}*i*= 1,…,

*H*is the set of coefficient vectors provided by the watermark and ∥.∥ denotes the Euclidean distance. This approach is similar to the DCT vector quantization where the vector size is

*K*.

**vol. 38**, no. 1, pp. 18–34, Feb. 1992. [CrossRef]

*must be from the same range. The chosen watermark parameter which make up the signature code should be chosen such that after embedding the constraint (13) or (14) we do not have large distortions in the image. After modifying the DCT coefficient values, the image is reconstructed based on the inverse DCT transform:*

**Q**_{i}*g*

_{j}(

*k*,

*l*) are the pixel values of the

*j*-th block from the watermarked image.

*b*denotes the location of the last chosen block site by (2, 3),

*T*

_{j,N}is provided in (7) and k is the selected block.

## 4. Watermark detection

*x*the random variable associated to the block site location, by

*y*the random variable associated to the DCT constraint given by either (13) or (14) and by

*P*(

*x*,

*y*|

*g*,

*) the probability of jointly estimating these random variables when providing the watermark code*

**S**_{k}*and the signed image*

**S**_{k}*g*. In our approach it is not necessary to have available the original image for detecting the watermark. The probability

*P*(

*x*,

*y*|

*g*,

*) can be decomposed, based on the Bayes rule, in :*

**S**_{k}*P*(

*y*|

*g*,

*) is the probability of detecting the DCT coefficient constraint and*

**C**_{k}*P*(

*x*|

*y*,

*g*,

**L**

_{k}) is the probability of detecting the location constraint, provided that the respective blocks already fulfill the first constraint, in the DCT coefficient domain. The probability

*P*(

*x*,

*y*) depends only on the image and has been neglected in (17).

*P*(

*y*|

*g*,

*C*

_{k}), the algorithm should take into account the likelihood that the signal is distorted. For example, after applying the JPEG compression algorithm on a watermarked image, the constraints (13) or (14) imposed onto the DCT coefficients are likely to be modified. The spread of the DCT coefficients with respect to the embedded values is large for small JPEG quality factors (large compression ratios). This accounts for a certain distortion in the image. Such distortions should be taken into account in the embedding stage.

*D*

_{L}and

*D*

_{C}depend on the assumed level of watermark corruption due to compression. A large value for

*D*

_{C}or

*D*

_{L}should be assumed when the watermarked image is going to be heavily compressed ( low quality factor ). By assuming a certain level of watermark distortion, (18, 19) instead of (13, 14) are considered in the detection stage.

*D*

_{L}or

*D*

_{C}, some of these blocks undesirably fulfill the given constraint, their DCT coefficients are modified forward the opposite. The detection region size parameters,

*D*

_{L}and

*D*

_{C}are associated to the image distortion produced by the watermark. The same parameter

*D*

_{L}or

*D*

_{C}embedded in images with different DCT frequency distributions is likely to cause different distortions.

*H*

_{0}for a certain signature

*is taken based on the detection ratio defined as follows :*

**S**_{k}*q*(

*x*,

*y*|

*) is a normalizing probability,*

**S**_{k}*s*

_{i}is the region size, measured in pixels where the watermark was successfully identified,

*p*represents the number of regions and

*c*∊ [0,1]. The bounds of the region size where the watermark can be successfully identified are given in (10). If the watermark is detected in the entire image then the above expression has a value equal to one. The expression (20) has a value zero in the case when the image was not signed with the respective watermark. If various distortions occur in the image than the expression (20) has an output in the interval [0,1] depending on the image corruption. Therefore, we consider a detection threshold of

## 5. Simulation results

*N*= 2 and

*L*= 3. The watermark characteristic DCT frequencies are F(2,1), F(1,2), and F(2,2). In order to measure the distortion produced in the image by the watermark we use the signal-to-noise ratio (

*SNR*) between the watermarked and original image, where

*SNR*expressed in dB is defined as :

*f*,

*g*are the original and the watermarked image. The watermarked images from Figures 4 (a) and (b) have a

*SNR*of 31.1 dB and 31.3 dB when compared to the original image. In order to find the watermark resistance to JPEG, we compress the watermarked images at various compression ratios and we detect the watermark in the compressed images according to (20). For the images represented in Figures 4 (a) and (b) the watermark was correctly identified after they were compressed at 13:1 and 18:1, respectively. The block sites that were chosen to embed the DCT coefficient constraint are displayed in Figure 3 (b). No periodicity with respect to their location in the image can be visually identified. The watermarked images shown in Figures 4 (a) and (b) contain some textured areas, slightly visible.

*SNR*ratio provided near each curve denotes the embedding level

*D*

_{C}or

*D*

_{L}for the respective watermark. It is clear from these plots that the watermark embedded in an image based on a certain embedding level is able to resist up to a certain compression ratio. For example a watermarked image having high

*SNR*of about 38dB (i.e., the signature is almost invisible ), can resist to compression ratios up to 8:1 for the scheme given by (18) and up to 11:1 for the scheme given by (19) as it can be seen in Figures 5 (a) and (b). The algorithm which defines circular detection regions in the DCT coefficient domain (19) provides better detection capabilities when compared to the linear type DCT coefficient constraint algorithm (18). If the watermarks are not designed to resist at big compression ratios, the image distortions will not be significant. The image quality degrades if the watermarks are intended to resist at higher compression ratios. However, in these cases, after compressing the image, the distortions introduced by JPEG are significant as well.

*SNR*< 23dB for the linear constraint and to

*SNR*< 31dB for a circular detection region.

## 6. Conclusions

## References

1. | B. M. Macq and J.-J Quisquater, “ Cryptology for Digital TV Broadcasting,” Proc. of the IEEE , |

2. | W. Bender, D. Gruhl, and N. Morimoto, “Techniques for data hiding,” MIT Media Lab., Technical Report 1995. |

3. | E. Koch and J. Zhao, “Towards robust and hidden image copyright labeling,” |

4. | O. Bruyndonckx, J.-J Quisquater, and B. Macq, “Spatial method for copyright labeling of digital images,” |

5. | M. Barni, F. Bartolini, V. Capellini, and A. Piva, “A DCT-domain system for robust image watermarking,” Signal Processing |

6. | I. Pitas and T. H. Kaskalis, “Applying signatures on digital images,” |

7. | A. G. Borş and I. Pitas, “Embedding parametric digital signatures in images,” |

8. | I. J. Cox, J. Kilian, T. Leighton, and T. Shamoon, “Secure Spread Spectrum Watermarking for Multimedia, IEEE Trans. on Image Processing , |

9. | A. Papoulis, |

10. | S. A. Kassam, |

11. | G. K. Wallace, “The JPEG still picture compression standard,” IEEE Trans. on Consumer Electronics , |

12. | A. K. Jain, |

13. | A. C. Hung, “PVRG-JPEG CODEC 1.1,” Stanford University, Technical Report, 1993. |

14. | A. V. Oppenheim and R. W. Schafer, |

15. | B. Widrow and S.D. Stearns, |

16. | E. S. Chng, S. Chen, and B. Mulgrew, “Gradient radial basis function networks for nonlinear and nonstationary time series prediction,” IEEE Trans. |

**OCIS Codes**

(100.0100) Image processing : Image processing

**ToC Category:**

Focus Issue: Digital watermarking

**History**

Original Manuscript: November 2, 1998

Published: December 7, 1998

**Citation**

Adrian Bors and Ioannis Pitas, "Image watermarking using block site selection and DCT
domain constraints," Opt. Express **3**, 512-523 (1998)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-3-12-512

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### References

- B. M. Macq, J.-J Quisquater, " Cryptology for Digital TV Broadcasting," Proc. of the IEEE, vol. 83, no. 6, pp. 944-957, June 1995. [CrossRef]
- W. Bender, D. Gruhl, N. Morimoto, "Techniques for data hiding," MIT Media Lab., Technical Report 1995.
- E. Koch, J. Zhao, "Towards robust and hidden image copyright labeling," Proc. of IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Greece, pp. 452-455, 20-22 June 1995.
- O. Bruyndonckx, J.-J Quisquater, B. Macq, "Spatial method for copyright labeling of digital images," Proc. of IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Greece, pp. 456-459, 20-22 June 1995.
- M. Barni, F. Bartolini, V. Capellini, A. Piva, "A DCT-domain system for robust image watermarking," Signal Processing, vol. 66, no. 3, pp. 357-372, 1998. [CrossRef]
- I. Pitas, T. H. Kaskalis, "Applying signatures on digital images," Proc. of IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Greece, pp. 460-463, 20-22 June 1995.
- A. G. Bors, I. Pitas, "Embedding parametric digital signatures in images," European Signal Processing Conference, EUSIPCO'96, Trieste, Italy, Sep. 10-13, pp. 1701-1704, 1996.
- I. J. Cox, J. Kilian, T. Leighton, T. Shamoon, "Secure Spread Spectrum Watermarking for Multimedia, IEEE Trans. on Image Processing, vol. 6, no. 12, pp. 1673-1687, Dec. 1997. [CrossRef]
- A. Papoulis, Probability and Statistics (Prentice Hall, 1990).
- S. A. Kassam, Signal detection in Non-Gaussian Noise (Springer-Verlag, 1988). [CrossRef]
- G. K. Wallace, "The JPEG still picture compression standard," IEEE Trans. on Consumer Electronics, vol. 38, no. 1, pp. 18-34, Feb. 1992. [CrossRef]
- A. K. Jain,Fundamentals of Digital Image Processing (Prentice Hall, 1989).
- A. C. Hung, "PVRG-JPEG CODEC 1.1," Stanford University, Technical Report, 1993.
- A. V. Oppenheim, R. W. Schafer,Discrete-Time Signal Processing (Prentice-Hall, 1989).
- B. Widrow, S.D. Stearns, Adaptive Signal Processing. (Prentice Hall, Englewood Cliffs, NJ, 1985).
- E. S. Chng, S. Chen, B. Mulgrew, "Gradient radial basis function networks for nonlinear and nonstationary time series prediction," IEEE Trans. on Neural Networks, vol. 7, no. 1, pp. 190- 194, Jan 1996.

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