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We propose a new image watermarking scheme based on the real SVD and Arnold scrambling to embed a color watermarking image into a color host image. Before embedding watermark, the color watermark image

Security and copyright protection are important issues in multimedia applications and services. Among the protection techniques, digital watermarking is considered a powerful method, which is a technique that hides the secret information in a host image without affecting its normal usage. The watermark can be extracted and used for authentication and verification of ownership. Digital watermarking has been concerned since it has been proposed in [

Compared with the binary and greyscale image, the color image can greatly improve the capacity and fidelity of the information. First, the color image can hide a great amount of data. Second, the color perception relies not only on the luminance but also on the chrominance. Color image can be broken into multiple prime color channels, so the color image watermarking is more challenging compared to single channel greyscale images. There are various breakup techniques available in the literature for color image like YIQ, YCbCr, RGB, and HSI, out of which RGB is apparently the most popular space, because this channel format is a natural scheme for representing real world color, and each of the three channels is highly correlated with the other two.

The typical algorithms for color image watermarking can be summarized as follows.

An effective watermarking algorithm should meet certain requirements, including transparency, robustness, adequate information capacity, and low computational complexity.

Watermarking algorithms utilizing the Singular Value Decomposition (SVD) have become popular during the last ten years [

In this paper, we propose a new image watermarking scheme based on the real SVD and Arnold scrambling to embed a color watermarking image into a color host image. Before embedding the watermark, the color watermark image

The remainder of this paper is organised as follows. In Section

The SVD [

The SVD of an

Scrambling is a pretreatment stage of watermarking, which transforms the meaningful image into another meaningless one and provides security in watermarking scheme. Even if the aggressors obtain the embedded watermarking image, they cannot extract the watermark without the knowledge of the scrambling algorithm.

In the proposed watermarking scheme, the 2D Arnold scrambling transformation [

Arnold scrambling.

A quaternion

In [

For a quaternion matrix

For any quaternion matrix

Let

From (

From this notation and Theorem

Let

In addition, we have the following results about the SVD of a quaternion matrix and its real representation.

Let

Therefore, if we want to compute the SVD of an

Suppose that

From Theorems

Suppose that

This kind of Householder based transformation is

After the bidiagonal matrix

On the other hand, we can extract the three imaginary parts

Not only is the computation time related to the number of floating points arithmetics, but also it has a lot to do with the assignment number. In Table

Computation amounts and assignment numbers for real SVD and quaternion SVD.

Real flops | Assignment number | |
---|---|---|

Real SVD | | |

Quaternion SVD | | |

We now provide a numerical example to compare the efficiencies of the three algorithms mentioned above. All these computations are performed on an Intel Core i5@ 2.20 GHz/8 GB computer using Matlab R2013a.

For

In [

Comparison of the SVD algorithms.

From the above discussion and Figure

In this section, we describe our color image watermarking algorithm, in which a color watermark image is embedded as copyright message into a color host image.

Assume that an original host image

We shuffle the color watermark image

The original RGB host color image

The R, G, and B color components of

Perform the SVD for

Form

The watermark is extracted as follows.

Both the original host image

The R, G, and B color components of

Perform the SVD for

Extract the watermarks. Set

The inverse Arnold scrambling is applied to

To verify the effectiveness of the proposed algorithm, a series of experiments were conducted where different host images are adopted. We carried out our experiments in Matlab R2013a environment on a laptop with Intel i5 processor rated at 2.5 GHz.

In the first experiment, color image Pepper of size

Original host image

Original watermark

Scrambling watermark

Watermarked host image

Extracted watermark

Recovery watermark

In the second experiment, we use

Original host image

Original watermark

Scrambling watermark

Watermarked host image

Extracted watermark

Recovery watermark

In the third experiment, the watermark is the same as in the above two experiments. We use

Original host image

Original watermark

Scrambling watermark

Watermarked host image

Extracted watermark

Recovery watermark

The visual fidelity can be measured by calculating a parameter known as peak signal-to-noise ratio (PSNR) and the structured similarity index (MSSIM) between the original host image

The mean structured similarity index (MSSIM) [

In order to measure the quality of the embedded and extracted watermark, the Normalized Correlation (NC) is calculated between the original watermark

In Table

PSNR, MSSIM, and NC values and CPU times.

Host image | N | ST | SF | PSNR | MSSIM | NC | CPU (second) |
---|---|---|---|---|---|---|---|

Lena | | 0 | 0.28 | 26.5018 | 0.8942 | 0.9998 | 0.3346 |

Lena | | 1 | 0.28 | 26.1693 | 0.8892 | 0.9998 | 0.3363 |

Lena | | 5 | 0.28 | 26.2047 | 0.8840 | 0.9998 | 0.3380 |

Pepper | | 0 | 0.14 | 42.1996 | 0.9946 | 0.9995 | 0.5012 |

Pepper | | 1 | 0.14 | 42.1940 | 0.9949 | 0.9994 | 0.5075 |

Pepper | | 5 | 0.14 | 42.0375 | 0.9947 | 0.9995 | 0.5110 |

Butterfly | | 0 | 0.14 | 44.3700 | 0.9954 | 0.9995 | 1.4372 |

Butterfly | | 1 | 0.14 | 44.3636 | 0.9949 | 0.9995 | 1.4226 |

Butterfly | | 5 | 0.14 | 44.3654 | 0.9949 | 0.9995 | 1.4257 |

In this paper, we have proposed a new double RGB color image watermarking algorithm based on the real SVD and Arnold scrambling. First, the color watermark image is scrambled by Arnold transformation to obtain a meaningless image. Then, the original host image is divided into nonoverlapping pixel blocks. We form a real matrix with the red, green, and blue components in each pixel block and perform the SVD of the real matrices. We then replace the three smallest singular values of each real matrix by the red, green, and blue values of corresponding pixel of the scrambled watermark with scaling factor, to form a new watermarked host image. With the reserve procedure, we can extract the watermark from the watermarked host image.

The experimental results show that the proposed algorithm achieves high PSNR, high MSIIM of the watermarked image, and high NC of the extracted watermark. In addition, in the process of the algorithm, we only need to perform real number algebra operations, which have very low computational complexity and therefore are more effective than the one using the quaternion SVD of color image, which costs a large amount of quaternion operations.

The idea described in this paper can also be applied to other kinds of methods concerning double color image watermarking problems.

The authors declare that they have no competing interests.

This research is supported by the National Natural Science Foundation of China under Grants 11171226 and 11301247, the Natural Science Foundation of Shandong under Grant ZR2012FQ005, Science and Technology Project of Department of Education, Shandong Province (J15LI10), and the Science Foundation of Liaocheng University under Grants 31805 and 318011318.