# A Robust Image Watermarking in the Joint Time-Frequency Domain

- Mahmut Öztürk
^{1}Email author, - Aydın Akan
^{1}Email author and - Yalçın Çekiç
^{2}

**2010**:509757

https://doi.org/10.1155/2010/509757

© Mahmut Öztürk et al. 2010

**Received: **4 February 2010

**Accepted: **15 April 2010

**Published: **24 May 2010

## Abstract

With the rapid development of computers and internet applications, copyright protection of multimedia data has become an important problem. Watermarking techniques are proposed as a solution to copyright protection of digital media files. In this paper, a new, robust, and high-capacity watermarking method that is based on spatiofrequency (SF) representation is presented. We use the discrete evolutionary transform (DET) calculated by the Gabor expansion to represent an image in the joint SF domain. The watermark is embedded onto selected coefficients in the joint SF domain. Hence, by combining the advantages of spatial and spectral domain watermarking methods, a robust, invisible, secure, and high-capacity watermarking method is presented. A correlation-based detector is also proposed to detect and extract any possible watermarks on an image. The proposed watermarking method was tested on some commonly used test images under different signal processing attacks like additive noise, Wiener and Median filtering, JPEG compression, rotation, and cropping. Simulation results show that our method is robust against all of the attacks.

## Keywords

## 1. Introduction

Recently, the production, distribution, and use of digital media has become very popular. Although these products have the advantages of high quality, ease of modification, and quality duplication, they introduce the problems of copyright protection issues because they can be easily copied and altered. Watermarking techniques are proposed as a solution to copyright protection problems of digital media files. The basic idea in watermarking is embedding a secret data into a multimedia file. In recent research, new methods are proposed to watermark audio, image, and video files.

In digital watermarking, a specific information called watermark is embedded in a multimedia file in such a way that it can be detected or extracted when necessary. The watermark may contain information about the digital object as well as information about the user or owner. As for image and video files, the watermark can be another image or signature logo. The watermark may be embedded so that it is either visible or invisible.

The principle of watermarking is to embed a digital code (watermark) within the host multimedia document, and to use such a code to prove ownership, to prevent illegal copying, to give some indications about the watermarked data or to enable the access to enhanced versions of the content or to additional services. The watermark code is embedded by making imperceptible modifications to the original data.

A watermarking algorithm in general consists of three basic components: (i) watermark, (ii) encoder (watermarking algorithm), and (iii) decoder (detection or extraction algorithm). To be useful a digital watermarking system must satisfy some basic requirements. First of all, the embedded watermark should be perceptually invisible. In other words, its presence should not affect the image quality. Moreover, the embedded watermark should be robust against the common signal processing manipulations like additive or multiplicative noise (Gaussian or salt and pepper (SP) noise), filtering, JPEG Compression, and rotation.

Image watermarking algorithms are mainly concentrated on spatial or spectral domains. Although successful methods have been presented using both approaches, they also have limitations and weaknesses. In the spatial domain, the image area where watermark is embedded is chosen based on the texture of the original image [1, 2]. In the spectral approach, watermark is embedded in a transform domain using discrete cosine transform, discrete wavelet transform, and so forth. For an invisible and robust watermarking, the watermark is embedded into middle frequencies range [3–5]. Watermarking in the frequency domain has advantages in terms of robustness, but there are limitations like invisible embedding may be difficult. Some new techniques are introduced by combining the advantages of both spatial and spectral domains for robust and invisible watermarking. This can be done using joint SF representations of images [6, 7]. Watermarking in the joint SF domain provides flexibility in terms of how much watermark will be embedded in which image region, and in what frequency band.

A new spatiofrequency- (SF-) based image watermarking algorithm which uses Discrete Evolutionary Transform (DET) has been presented in our past works [8]. In this paper, a new approach is presented for embedding watermark into SF representation of the image. By using this approach, more robust, invisible, secure and high capacity watermarking algorithm is obtained.

The rest of the paper is organized as follows: In Section 2, we give a brief introduction to DET calculated by a multiwindow Gabor expansion as a linear time-frequency representation method. Then we present our SF domain image watermarking technique based on DET in Section 3. Watermark extraction algorithm with correlation detector is given in Section 4. Embedding and extraction performance tests are given in Section 5, followed by conclusions and discussion of the results in Section 6.

## 2. Time-Frequency Analysis by DET

In the following, we briefly explain the Discrete Evolutionary Transform (DET) as a tool for the time-frequency representation of image sequences.

where is, in general, a time and frequency dependent window.The DET can be seen as a generalization of the short-time Fourier transform, where the windows are constant. The windows can be obtained from either the Gabor representation that uses nonorthogonal frames, or the Malvar wavelet representation that uses orthogonal bases. Details of how the windows can be obtained for the Gabor and Malvar representations are given in [11]. Here, for the representation of image pixel sequences in spatiofrequency domain, we consider DET calculated by multiwindow Gabor frames.

We should mention that above evolutionary spectral estimate is always nonnegative, and normalizing to unit energy, the total energy of the signal is preserved, thus justifying the use of as a TF energy density for . Furthermore, DET provides a linear signal representation where the sequence may be obtained from the TF representation much easier than it is with the bilinear TF representations such as Wigner distribution [13]. Hence DET is appropriate for watermarking applications in the SF domain where embedding and extracting a watermark will be easily implemented using linear operations.

## 3. Watermark Embedding in the Joint SF Domain

In our SF-based watermarking approach, the rows of the image to be watermarked are considered as one dimensional sequences and transformed into the joint SF domain. Watermark is embedded onto coefficients which are selected from these SF representation matrices. Therefore, it is possible to increase the length of the watermark to high values. Thus, we can embed more information to image.

Although it is possible to embed the watermark to all rows of the image, it is embedded only to chosen rows because of the security reasons. Also the watermark is embedded to chosen coefficients of the DET matrices. So, two different keys have to be used. One of them is used for the chosen rows, and the other one is for the chosen coefficients. Therefore, a more secure watermarking method is obtained.

There are methods to represent two dimensional images in the SF domain, but computational complexity and the dimensionality problems make them difficult to use in watermarking applications [6]. Recently new methods are presented where TF distributions (TFDs), usually the Wigner distribution, of each row of an image is used for embedding a watermark in the joint TF domain [7, 14]. However, synthesis of a sequence from its modified bilinear TFD is generally a difficult problem. Hence, we propose a new SF domain watermarking where we use the linear DET explained above to embed the watermark into any row of the image. Then the watermarked rows are easily obtained by the inverse transformation. We used multiwindow Gabor expansion based DET in our approach. However, other linear time-frequency representations may be used instead. For instance, the short-time Fourier transform (STFT) may be employed as well which is a special case of the DET where the window function is constant. Multiwindow Gabor-based DET is compared and shown to perform better than the STFT in many applications in previous studies [8, 12].

, is obtained. The window is obtained by using Gabor representation. Watermark sequence, , is the copyright or some other necessary information. M is the length of the watermark sequence. In this paper, normally distributed random sequences that have zero mean and unity variance are used. The lengths of the sequences are chosen as 512.

*x*th row, in chosen space and frequency band. Then, the watermark is embedded to these coefficients as follows [15]:

Here, , , represents the chosen DET coefficients. is the watermark sequence. If it is needed to decrease the power of the watermark, a weighting constant can be used.

Here, is the watermark embedded DET matrix, and is the watermarked image matrix.

## 4. Watermark Extraction

In digital watermarking studies, methods have been presented for detection and extraction of the watermark by assuming that some information used in the embedding is known to the detector [14]. However, there are many works where blind detection is achieved without using any extra information. In practical applications such as copyright protection, the most important goal is the detection of watermark existence even after the watermarked image is attacked. In our study, we assume that we have the original and the watermarked images and try to extract the watermark.

In this paper, a correlation based detection method is used. First of all, the DET of the watermarked image row is calculated by using the key which shows the watermarked rows of the image. With the help of the second key, watermarked coefficients are chosen from the DET matrix, and they are saved as a sequence, . contains watermarked and probably attacked coefficients. After that, the DET of the original image's same row is calculated and sequence is obtained again.

In our simulations, we take , , and . takes the highest value when the original and the extracted watermarks are same. So, we take the variance of the original watermark as variance of .

## 5. Simulations

PSNR Values of the watermarked images.

Image | Lena | Baboon | Boats | Barbara |
---|---|---|---|---|

PSNR (dB) (25 rows watermarked) | 63.0542 | 59.0494 | 62.4428 | 63.0009 |

PSNR (dB) (All rows watermarked) | 49.2935 | 46.5275 | 48.4713 | 49.9196 |

Correlations between the original and the extracted watermarks under Noise and Filtering attacks.

Attack | Lena | Baboon | Boats | Barbara |
---|---|---|---|---|

0.9126 | 0.8592 | 0.9443 | 0.9045 | |

0.9070 | 0.8705 | 0.9383 | 0.8740 | |

0.9251 | 0.9053 | 0.9165 | 0.8772 | |

0.8981 | 0.9040 | 0.8372 | 0.9219 | |

0.8655 | 0.8183 | 0.8875 | 0.8796 | |

0.9325 | 0.9354 | 0.9907 | 0.9689 | |

0.9189 | 0.9221 | 0.9063 | 0.9291 | |

0.8633 | 0.8721 | 0.8849 | 0.9139 | |

0.8834 | 0.8712 | 0.8295 | 0.8936 | |

0.8777 | 0.8616 | 0.8470 | 0.8737 | |

0.9834 | 0.9109 | 0.9923 | 0.9730 | |

0.9686 | 0.8851 | 0.9805 | 0.9532 | |

0.9687 | 0.8890 | 0.9815 | 0.9565 | |

0.9602 | 0.8168 | 0.9701 | 0.9154 | |

0.9813 | 0.8011 | 0.9940 | 0.9163 | |

0.3004 | 0.6862 | 0.3818 | 0.6111 | |

0.2580 | 0.3820 | 0.1761 | 0.5817 | |

0.4588 | 0.4429 | 0.3489 | 0.5800 | |

0.3975 | 0.4467 | 0.3215 | 0.5643 | |

0.4396 | 0.4498 | 0.3368 | 0.5773 |

Correlations between the original and the extracted watermarks under different attacks.

Attack | Lena | Baboon | Boats | Barbara |
---|---|---|---|---|

0.8909 | 0.8392 | 0.8414 | 0.8763 | |

0.9422 | 0.8783 | 0.9148 | 0.8798 | |

0.9480 | 0.8902 | 0.9133 | 0.9126 | |

0.9384 | 0.8579 | 0.9132 | 0.9356 | |

0.9543 | 0.8937 | 0.9114 | 0.9516 | |

Rotation (5°) | 0.5481 | 0.4119 | 0.7071 | 0.5505 |

Rotation (10°) | 0.5041 | 0.7318 | 0.5672 | 0.6447 |

Rotation (15°) | 0.5184 | 0.6140 | 0.5045 | 0.5467 |

Rotation (20°) | 0.4918 | 0.3878 | 0.4159 | 0.6098 |

Rotation (25°) | 0.3894 | 0.4957 | 0.4903 | 0.5161 |

Cropping (10 column) | 0.9873 | 0.9488 | 0.9726 | 0.9612 |

Cropping (25 column) | 0.9845 | 0.9351 | 0.9698 | 0.9550 |

Cropping (50 column) | 0.9354 | 0.9215 | 0.9655 | 0.9293 |

Cropping (75 column) | 0.9556 | 0.9000 | 0.9622 | 0.9423 |

Cropping (100 column) | 0.9614 | 0.8787 | 0.9688 | 0.9382 |

As we mention before, there are methods using TF techniques for watermark embedding in the literature. A two-dimensional (2D) SF based watermarking approach is presented in [6] where a special 2D chirp-type watermark is presented. The method differs from the watermarking technique we present in this paper in that the original image is added this 2D chirp signal, and 2D Radon-Wigner distribution is used for watermark extraction. Increased dimensions of the data makes this approach computationally demanding. Another method for embedding a one-dimensional watermark sequence into the rows of an image in the joint SF domain by using Wigner-Ville distribution is presented in [7]. We adopt this idea here, and use a linear SF representation which is efficiently implemented to embed and extract any type of watermark sequence into images.

## 6. Conclusions

In this work, a new watermarking algorithm that is based on a spatiofrequency transform is proposed. Discrete evolutionary transform is used for the SF representation of the rows of an image. Watermark embedding algorithm is developed to combine the advantages of both spatial and spectral domain watermarking techniques. Thus, a more successful method is proposed than methods that use only spatial or spectral domain embedding. At the detection end, the watermark can be extracted by using the original image. The performance of the method is tested under several attacks and observed that it is very successful against additive white Gaussian noise, salt and pepper noise, Wiener filtering, JPEG compression, and cropping. Furthermore, the proposed algorithm which is based on a linear representation is computationally simpler than other bilinear TFD-based methods [7, 14].

## Declarations

### Acknowledgment

This paper was partially supported by the Research Fund of the University of Istanbul project no 3898, UDP-3826/25052009, and T-928/06102006.

## Authors’ Affiliations

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