Content Adaptive Image Watermarking Algorithm in Shearlet Transform Domain

With the rapid development of computer network technology, the digitization of information media has brought great convenience to information storage, transmission and copying. However, at the same time, how to implement effective copyright protection of digital products in a network environment has become a hot issue that needs to be solved in academia. How to solve the information security of communication systems in a network environment has also become an urgent issue. Digital watermarking, as an effective method to protect the information security of digital media, has attracted widespread attention and has become a new research hotspot in the field of information security [1-2].

Watermark embedding algorithms include spatial domain watermarking and frequency domain watermarking. Frequency domain watermarking includes DCT domain, Wavelet transform domain, Ridgelet transform domain, etc. [3-6]. Through research, it is found that the human eye is not sensitive to distortion of high-frequency information such as complex areas and areas with drastic grayscale changes, but is more sensitive to distortion of low-frequency information such as smooth areas. Therefore, while making full use of the frequency characteristics of human vision, considering the contrast masking effect of the image itself due to different background average brightness and the image texture masking effect, the image can provide a better visual masking mechanism for the watermark.

Jayant, Ran and others have shown that images are composed of three regions with different perceptual characteristics: smooth region, edge region and texture region, namely the three-component image model [7-8]. The human visual system (HVS) has different perceptual characteristics for these three regions. When recognizing the object in the image, the edge region plays an important role, while the smooth region and texture region play a secondary role. HVS is very sensitive to small changes in the smooth region, followed by the edge region, and least sensitive to changes in the texture region. Therefore, more watermark information can be embedded in the texture region of the image, followed by the edge region, and the least in the smooth region.

This paper proposes an adaptive digital watermarking algorithm based on HVS in Shearlet transform domain. The algorithm can embed watermark information with maximum strength under the condition of watermark invisibility, and has strong robustness against various attacks such as JPEG compression, noise addition, filtering and arbitrary cropping.

1 Shearlet Transform

The theoretical basis of Shearlet transform[9] is synthetic wavelet theory. Synthetic wavelet theory provides an effective method for geometric multiscale analysis through affine system. When the dimension n=2, the affine system with synthetic expansion is as follows:

2 Watermark Algorithm

2.1 Watermark Embedding

The location where the watermark is embedded directly affects the robustness of the watermark. Cox et al. proposed that the watermark should be embedded in the most important component of the human visual system (HVS). The important component is the main component of the image signal, carrying more signal energy. Even if the image is distorted to a certain extent, the main component can still be retained. In addition, the experimental results of Field et al. show that the receptive field characteristics of the visual cortex enable the human visual system to "capture" key information in natural scenes with only the least visual neurons. This is equivalent to the sparsest representation of natural scenes, or the "sparsest" encoding of natural scenes. Shearlet transform is a new image representation method proposed on this basis, which can accurately sparsely represent important information of the image. Based on the study of Shearlet transform, this paper proposes a content-based watermark embedding algorithm, which embeds the watermark information into the directional edge features with the highest energy in the image, thereby ensuring the robustness of the watermark.

Perform Shearlet transform on the carrier image f0(x,y) to obtain the low-pass sub-image fJ(x,y) and the band-pass sub-image (directional sub-image) Sj,l(x,y), where j represents the decomposition scale and l is the decomposition direction. In order to ensure the visual invisibility of the embedded watermark, the watermark information is only embedded in the intermediate frequency part of the band-pass sub-image. In this paper, the watermark is embedded in the directional sub-image with the largest energy. The larger the energy of the directional sub-image, the more important the sub-image is to the entire image. The calculation formula for the maximum directional sub-band energy is as follows:

Where, the values ​​of C0 and C1 correspond to the average standard deviation and average absolute mean of the ridgelet coefficients of each sub-block image, respectively; the selection of β is related to the image content.

Let Sj,l(x,y) be a high frequency coefficient of the image after Shearlet transformation,

Where, the threshold s is the standard deviation of the coefficient, let β = (μ-min(μ))/max(μ)-min(μ), where μ is the variance value of the high-frequency coefficient after binarization, max(·) is the maximum value function, and min(·) is the minimum value function.

Since the variance value μ can better divide the image content into texture, edge and smooth areas in turn, it can be seen from formula (11) that β is related to the attributes of the image content. The β value in the texture area is the largest, followed by the edge area, and the β value in the smooth area is smaller. Therefore, the maximum tolerable error β of the coefficient calculated by formula (10) is used as the watermark embedding strength factor. Since β is calculated based on the image content, the watermark embedding strength is adaptive, that is, in the texture area, the α value is larger, and the watermark embedding strength is larger; in the smooth area, the α value is smaller, and the watermark embedding strength is smaller; and the watermark embedding strength in the edge area is between the texture area and the smooth area.

2.3 Watermark Detection

The image protected by the watermark may be processed intentionally or unintentionally, so the image to be detected is damaged to a certain extent. The detection of watermark is similar to the weak signal detection at the receiving end during the communication process. This paper adopts the correlation detection method to detect the presence of watermark.

3 Experimental simulation

The experiment selected the Lena image of 512×512 size as the test image, randomly generated 1 000 zero-mean binary sequences that were evenly distributed and independent of each other in the interval [-1,1], selected the 500th sequence as the embedded watermark, and used the watermark attack software Stirmark to attack the embedded watermark image. In the experiment, the false alarm probability p=10 ^-8 .

Figure 1 (a) ~ (f) are the watermark information extracted from the image without attack, JPEG compression with quality factor 20, 3×3 median filter, Gaussian white noise with mean 0 and variance 60, salt and pepper noise with intensity 10%, and regular shearing of 3/4. It can be seen from the figure that the watermark can still be detected after the watermark image is attacked, which shows that the watermark algorithm in this paper is highly robust to JPEG compression attack, median and mean filter attack, and noise attack.

This paper proposes an adaptive image watermarking algorithm in Shearlet transform domain. Based on the sparse representation characteristics of Shearlet transform for high-dimensional data, a method for locating visually important information is determined. The robustness of the watermark is greatly improved by embedding the watermark on the visually important information. According to the different perceptions of the human eye on the smooth area, edge area and texture area of ​​the image, the strength of the embedded watermark is appropriately selected to solve the contradiction between robustness and visual invisibility. The effectiveness of the algorithm in this paper is proved through experiments.