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With the development of information security, the traditional encryption algorithm for image has been far from ensuring the security of image in the transmission. This paper presents a new image watermarking scheme based on Arnold Transform (AT) and Fuzzy Smooth Support Vector Machine (FSSVM). First of all, improved AT (IAT) is obtained by adding variables and expanding transformation space, and FSSVM is proposed by introducing fuzzy membership degree. The embedding positions of watermark are obtained from IAT, and the pixel values are embedded in carrier image by quantization embedding rules. Then, the watermark can be embedded in carrier image. In order to realize blind extraction of watermark, FSSVM model is used to find the embedding positions of watermark, and the pixel values are extracted by using quantization extraction rules. Through using improved Arnold inverse transformation for embedding positions, the watermark coordinates can be calculated, and the extraction of watermark is carried out. Compared with other watermarking techniques, the presented scheme can promote the security by adding more secret keys, and the imperceptibility of watermark is improved by introducing quantization rules. The experimental results show that the proposed method outperforms many existing methods against various types of attacks.

Application and popularization of multimedia technologies and computer networks have made duplication and distribution much easier for multimedia contents [

Recently, attacks against image watermarking systems have become more sophisticated [

In this paper, embedding and extraction models of watermark based on AT and FSSVM are proposed with corresponding algorithms. The watermark image is first processed by IAT, and the pixel values are embedded by using quantization embedding rules. The watermarked carrier image can be obtained. Then the embedding method is presented by increasing secret keys to enhance the security degree. The quantization embedding rules can improve imperceptibility of watermark well. FSSVM model is constructed by training some embedding positions to find out positions embedded with watermark in the extraction process. The pixel values of watermark are extracted by introducing quantization extraction rules. FSSVM model not only enhances the training speed and precision of image characteristic values, but also realizes the blind extraction of watermark with the help of quantization extraction rules. The watermark coordinates are calculated by improving Arnold inverse transformation for embedding positions. The original watermark image is extracted, and the processing does not need original carrier image. Moreover, the combination of spatial domain and SVM can balance imperceptibility and robustness of watermark well.

The rest of this paper is organized as follows. In Section

In practical applications, AT not only scrambles the pixel position by encoding the iterative number of the process, but also reduces the key spaces of storage and transmission. Although there are many ways for scrambling, here we will discuss only the AT in [

Since the transformation is an iterative process, if the location (

SVM has been successfully applied to classification and function estimation problems introduced by Vapnik within the context of statistical learning theory and structural risk minimization [

In order to obtain the last two parameters

To solve the above convex optimization problem, the core idea is to transform the optimization question into dual form by using Lagrange multiplier method as follows:

In order to improve the efficiency and precision of prediction, SVM is introduced, and through combining with fuzzy mathematics and transforming the problem into unconstrained optimization problem, one can optimize the object function and transform the risk function into fuzzy dual extreme problems. Then, it can effectively reduce the errors between the predicted pixel values and the actual pixel values in the carrier image. The FSSVM model is used to train the specific pixels in some positions and find the embedding positions of watermark in carrier image, which is constructed in detail as follows.

Select

Take each position coordinate

Calculate the corresponding eigenvalues of the image block in the carrier image for each position coordinate

Let each feature vector

Use the principle of structural risk minimization to determine the parameters (

The watermark embedding procedure, participating in the optimization flow chart of Figure

Process of watermark embedding.

Input a carrier image

Expand the pixel matrix of binary image into square matrix for making

In the above conversion formulas, independent parameters

Let

Determine the pixel value

If the watermark pixel value

If the watermark pixel value

If the watermark pixel value

If the watermark pixel value

Replace the original pixel values in the carrier image with those of the calculated

The watermark extraction procedures are illustrated with the help of block diagrams in Figure

Process of watermark extraction.

Denote the watermarked carrier image by

Test

The eigenvalue selection refers to one-order moment and second-order moment of the probability statistics. In fact, one can also increase the type of eigenvalue, such as the third-order moment, which is beneficial for improving the prediction accuracy. Here, the

Compare the pixel values

Compute the corresponding pixel values in the watermark, when the position coordinates (

Suppose that

Restore the pixel values of original watermark image according to the values of

For the experimental purposes, specific software has been developed to implement the proposed methods using MATLAB. Figure

(a) Original carrier image; (b) original watermark image; (c) the watermarked image; (d) the extracted watermark without attack.

The quality and perceptibility of digital image embedded with actual watermark are judged by using the value of peak signal-to-noise ratio (PSNR), which presents the damaged degree of embedded watermark information to carrier quality. The bigger the PSNR is, the smaller the damaged degree is. Then, PSNR is denoted by

The bit error rate (BER) between extracted watermark and original watermark is employed to evaluate the extracted watermark image objectively. The closer the distance between BER and 0 is, the higher the robustness of the watermark system is, and the stronger the antiattack capability is. Then, BER is denoted by

The objective evaluation of the test result of watermark can also use normalized correlation coefficient (NCC) to evaluate the similarity degree, which describes the change before and after embedding watermark in the carrier image. The greater the similarity degree is, the higher the robustness of watermark is. Then, NCC is denoted by

In order to further investigate the robustness of our proposed scheme, the watermarked image shown in Figure

Experimental results of watermark imperceptibility and robustness.

Attacks | PSNR | BER |
---|---|---|

Image brightening (+75) | 21.6031 | 0.0124 |

Image darkening (−50) | 12.5791 | 0.0074 |

Image histogram equalization | 15.9505 | 0.0088 |

Gaussian noise ( |
23.9825 | 0.0730 |

Median filter ( |
31.5116 | 0.0270 |

JPEG compression (10%) | 22.7442 | 0.0737 |

Geometric cutting (left 100 |
12.5184 | 0.0126 |

Geometric rotation |
22.0357 | 0.0142 |

(a) The extracted watermark after brightening (+75); (b) the extracted watermark after darkening (−50); (c) the extracted watermark after equalization; (d) the extracted watermark after adding Gaussian noise; (e) the extracted watermark after median filter; (f) the extracted watermark after compression; (g) the extracted watermark after cutting; (h) the extracted watermark after rotation.

The following part of our experiments continues testing the proposed algorithms in a new watermark image with size

Experimental results of watermark imperceptibility and robustness after changing watermark.

Attacks | AT + FSSVM | IAT + LSSVM | IAT + FSSVM | |||
---|---|---|---|---|---|---|

PSNR | BER | PSNR | BER | PSNR | BER | |

Image brightening (+75) | 15.6836 | 0.1706 | 21.5951 | 0.0024 | 21.5951 | 0.0041 |

Image darkening (−50) | 13.8697 | 0.1739 | 12.9168 | 0.0016 | 12.9168 | 0.0033 |

Image histogram equalization | 15.9308 | 0.1249 | 15.9258 | 0.0016 | 15.9258 | 0.0065 |

Gaussian noise ( |
24.0350 | 0.4710 | 23.9928 | 0.0155 | 23.9928 | 0.0122 |

Median filter ( |
31.4799 | 0.4531 | 31.4850 | 0.0155 | 31.4850 | 0.0123 |

JPEG compression (10%) | 22.7381 | 0.4702 | 22.7412 | 0.0073 | 22.7412 | 0.0059 |

Geometric cutting (left 100 |
31.5740 | 0.3045 | 11.6074 | 0.0049 | 11.6074 | 0.0080 |

Geometric rotation |
22.4917 | 0.3086 | 18.8479 | 0.0106 | 18.8479 | 0.0110 |

(a) The original changed watermark; (b) the extracted watermark without attack; (c) the extracted watermark after brightening (+75); (d) the extracted watermark after darkening (−50); (e) the extracted watermark after equalization; (f) the extracted watermark after adding Gaussian noise; (g) the extracted watermark after median filter; (h) the extracted watermark after compression; (i) the extracted watermark after cutting; (j) the extracted watermark after rotation.

The third part of our experiments is to test the proposed algorithms in a camera man image with size

Experimental results of watermark imperceptibility and robustness after changing carrier image.

Attacks | AT + FSSVM | IAT + LSSVM | IAT + FSSVM | |||
---|---|---|---|---|---|---|

PSNR | BER | PSNR | BER | PSNR | BER | |

Image brightening (+75) | 14.8985 | 0.0347 | 15.0029 | 0.0095 | 15.0029 | 0.0091 |

Image darkening (−50) | 16.5895 | 0.0158 | 16.4844 | 0.0039 | 16.4844 | 0.0084 |

Image histogram equalization | 21.9937 | 0.0439 | 21.9832 | 0.0101 | 21.9832 | 0.0067 |

Gaussian noise ( |
38.8298 | 0.0431 | 37.8283 | 0.0054 | 37.8283 | 0.0076 |

Median filter (9 |
33.0709 | 0.1410 | 34.5537 | 0.0381 | 34.5537 | 0.0277 |

JPEG compression (10%) | 36.1963 | 0.0379 | 34.7436 | 0.0131 | 34.7436 | 0.0135 |

Geometric cutting (left 100 |
23.6165 | 0.0193 | 12.8017 | 0.0049 | 12.8017 | 0.0106 |

Geometric rotation |
18.8558 | 0.0530 | 22.5508 | 0.0135 | 22.5508 | 0.0073 |

The original changed carrier image.

(a) The extracted watermark without attack; (b) the extracted watermark after brightening (+75); (c) the extracted watermark after darkening (−50); (d) the extracted watermark after equalization; (e) the extracted watermark after adding Gaussian noise; (f) the extracted watermark after median filter; (g) the extracted watermark after compression; (h) the extracted watermark after cutting; (i) the extracted watermark after rotation.

From Tables

The fourth part of our experiments is to give more details and justifications of our scheme by taking six carrier images against thirteen kinds of attacks. The watermark is still Figure

The BER for six carrier images against thirteen attacks.

The last part of our experiments is to compare our proposed scheme with the other state-of-the-art watermarking methods based on SVM, which are Peng’s method [

The BER of four watermarking schemes for Boat against ten attacks.

From the above experimental results, the comparative analysis of our scheme with other schemes and the advantages of our algorithms are further summarized as follows.

(1) The embedding method presented in this paper is realized by using IAT and quantization rules, and more parameters (

(2) Compared with the existing SVM-based watermarking techniques, the FSSVM model proposed in this paper introduces the concept of fuzzy membership degree and combines the fuzzy mathematics with smooth SVM to simulate the visual features of the human eyes for the watermarked carrier image instead of the standard SVM. The application method not only provides a new solution for digital image watermark technique, but also quickens the training speed and improves the efficiency of image characteristic value. The predicted pixel results of test sample are closer to the actual values than the standard SVM. Thus, the extracted watermark is very close to the original watermark.

(3) Based on IAT, the proposed watermarking scheme has implemented mutual conversion of coordinates from watermarked carrier and original watermark, and then it makes full use of the chaotic scrambling feature of AT to distribute the watermark into the carrier image. In the combination of the new space domain transformation and FSSVM, the watermarked carrier image still can remember the relationship among the local pixels after experiencing various attacks and realize the correct extraction of watermark. Therefore, the embedding and extraction methods have strong robustness to all kinds of conventional image attacks, and they also balance imperceptibility and robustness of watermark well.

In this paper, a detailed investigation of image watermarking process by handling it as an optimization procedure based on IAT and FSSVM is presented. The watermarking technique of spatial domain by using IAT is introduced to determine the positions embedded with watermark. Then, one can make full use of the scrambling feature of IAT to evenly distribute the watermark into the whole space of carrier image. Through increasing the secret key parameters, the security degree is improved efficiently. By using quantization and round methods in mathematics to change the pixels of embedding positions, it not only realizes the imperceptibility of watermark, but also deduces the quantitative extraction rules reversely. So the process realizes the blind extraction of watermark without depending on the original carrier image. Furthermore, FSSVM model is constructed to predict the original pixel values of watermarked carrier when the watermark is extracted. Through comparing the predictable values with the actual pixel values of the watermarked carrier image, the positions embedded with watermark can be found out easily. It makes full use of spatial domain features of the image and improves the accuracy and efficiency in predicting outcomes. What is more, the combination of spatial domain and SVM not only efficiently improves the robustness of watermark obviously, but also realizes the blind extraction of watermark. Thus, it achieves the efficacy of advantageous complementarities. Hence, the proposed scheme in this paper is different from the traditional watermark embedding and extraction methods. Theoretical analysis and computer simulations indicate the feasibility of our proposed algorithms. Therefore, our proposed scheme has satisfied the blind extraction, robustness, imperceptibility, and security requirements. In addition, to extend the proposed idea to color video watermarking is another future work.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported by the National Natural Science Foundation of China (nos. 61370169, 61402153, and 61472042), the Key Project of Science and Technology Department of Henan Province (no. 142102210056), the Science and Technology Research Key Project of Educational Department of Henan Province (nos. 13A520529, 12A520027), and the Education Fund for Youth Key Teachers of Henan Normal University.