CN102147912A - Adaptive difference expansion-based reversible image watermarking method - Google Patents

Abstract

A reversible image watermarking method based on adaptive difference extension, including watermark embedding process, watermark extraction process and image restoration process; before watermark embedding, the original image needs to be preprocessed, including alternate division, difference calculation, calculation Image complexity and set parameters; in the embedding process, use adaptive expansion to embed the corresponding watermark; then embed additional information, and in certain cases the watermark data will be mixed with additional information; in the extraction process, first perform additional information Extraction, difference calculation; then carry out the inverse operation of adaptive difference expansion, extract watermark data and restore the original difference; finally restore the image through the restored difference; the present invention has reversibility and can provide more Large embedding capacity and better image quality, especially when embedding a large amount of watermark data.

Description

A Reversible Image Watermarking Method Based on Adaptive Difference Extension

technical field

The invention relates to a method for embedding and extracting a reversible image watermark, in particular to a reversible image watermark method based on adaptive difference expansion.

Background technique

The digital information revolution has brought profound changes to human society and life, and various digital media works have brought new challenges while enriching people's lives. The low cost of copying and distributing digital multimedia works makes digital piracy very common. Therefore, security issues such as digital copyright protection and content integrity verification have become urgent problems to be solved. Digital watermark hides some information in digital image, text, video or audio signal, and has become an effective means to protect the security of digital media content. In most existing digital watermarking methods, the host media will be permanently changed due to the embedding of the watermark signal and cannot be restored to the state before the watermark is embedded. Although the distortion introduced by the watermark is usually not easy to be detected by the human perception system, in some special fields that require extremely high data fidelity, such as military images, medical images, satellite remote sensing images, or legal evidence images, any tiny Distortion is not allowed. Therefore, the application of digital watermarking technology in these fields has been greatly restricted. In order to solve this problem, the concept of reversible digital watermarking is proposed. This watermarking scheme can ensure that the host media can be accurately restored to its original state when the watermark is not embedded at the extraction end while embedding watermark information to protect digital copyright. Since Barton first proposed the concept of reversible watermarking in 1997, some scholars have proposed some reversible watermarking algorithms in recent years. The existing reversible watermarking algorithms basically include two methods, that is, embedding in the space domain and embedding in the frequency domain.

Embedding reversible watermarking in airspace has become a recent research hotspot because of its relatively simple implementation and relatively large embedding capacity. Invisible reversible watermarking in the air domain is mainly divided into three categories: image compression-based, difference expansion-based and histogram modification-based.

Algorithms based on image compression generally use lossless compression algorithms to compress the image in the insensitive part of the human eye to make room for embedding watermarks. The embedding capacity depends on the compression rate, and the embedding capacity is generally not large, and efficient image compression operations are complex. Therefore, the computational complexity of this type of watermark is relatively high; the reversible image algorithm based on histogram modification uses the statistical characteristics of image pixels to move the histogram to obtain the embedding space; the algorithm based on difference expansion uses the correlation of image content, adjacent Pixels usually have relatively similar values, so the difference between two adjacent pixels is small. By expanding the difference between adjacent pixels, two-bit data can be embedded in it without causing obvious distortion.

Reversible image watermarking based on Difference Expansion (DE) was first proposed by Tian in 2003 (see J. Tian. Reversible data embedding using a difference expansion [J]. IEEE Trans. Circuits Systems and Video Technology. 2003, 13(8): 890-896). Difference expansion can also be regarded as an integer wavelet transform, which expands the high-frequency part of wavelet transform and embeds watermark information in it. DE is also sometimes called displacement expansion, because the process of embedding watermark can be regarded as a process of displacement. Assuming that the binary representation of the difference d is (d _n-1 d _n-2 ...d ₁ d ₀ ) ₂ , then the binary representation of the difference d′ after embedding the watermark is (d _n-1 d _n-2 . ..d ₁ d ₀ b) ₂ . This is equivalent to shifting d to the left by one bit, and then embedding the watermark b into the vacated lowest bit. Alattar (AMAlattar.Reversible watermark using difference expansion of triplets[C].Proc.IEEE ICIP.2003:501-504; AMAlattar.Reversible watermark using difference expansion of quads[C].Proc.ICASSP.2004:377-380) Tian’s Ideas apply to vectors of three and four pixels. The advantage of this is to increase the number of scalable differences, and to reduce the space occupied by the Location Map.

In short, in the existing method, the embedding capacity is small, and the quality of the image cannot be guaranteed when embedding a large-capacity watermark. Therefore, the present invention utilizes the complexity of different parts of the image to perform adaptive embedding on different regions to achieve Larger embedding capacity and better image quality.

Contents of the invention

The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a reversible image watermark based on adaptive difference expansion. This method can provide greater embedding capacity and Better image quality.

The technical solution adopted by the present invention to solve its technical problems: a reversible image watermark based on adaptive difference expansion, including watermark embedding process, watermark extraction process and image recovery process; before watermark embedding, the original image needs to be pre-prepared Processing, including alternate division, difference calculation, calculating image complexity and setting parameters; in the embedding process, use adaptive expansion to perform corresponding watermark embedding; then additional information will be embedded, and watermark data will be mixed with additional information in certain cases Embedding; in the extraction process, first perform additional information extraction and difference calculation; then perform the inverse operation of adaptive difference expansion, extract watermark data and restore the original difference; finally restore the image through the restored difference ;

The preprocessing process is:

(1) Alternate division. Alternately divide the original image to obtain two disjoint pixel sets S ₁ and S ₂ , and construct a context for each pixel in the image, so as to facilitate the calculation of image complexity and the realization of pixel estimation.

(2) Difference calculation. Using the context constructed in step (1) of the preprocessing process, calculate the estimated value of each pixel in the image, and then calculate the difference by comparing with the original pixel. This step can be divided into two parts: first, in the first part, use S ₁ to estimate the pixels in S ₂ , at this time S ₁ is the original pixel value; then in the second part, use the pixels in S ₂ to estimate the pixels in S ₁ , at this time S ₂ is the embedded watermark Pixel values.

(3) Parameter setting. This step mainly includes two aspects of parameter setting. First, for the original image, the feature description α of the image complexity is calculated by using the statistical properties of the generalized Gaussian distribution; then, according to the amount of embedded watermark data, the adaptive difference expansion is determined. There are two parameters c and T. Finally, when the user's needs cannot be met, it is also possible to judge whether to report embedding failure.

In the process of watermark embedding, watermark data embedding is the process of embedding user data into the carrier image through adaptive expansion after the parameters are determined. In certain cases, watermark data and additional information will be mixed and embedded, and then it is necessary to ensure that the watermark data and additional information are distinguishable and synchronized. Additional information embedded. After the user data (or part of the information) is embedded, there are generally some additional information, including parameters c, T and the location table for recording pixel overflow information, so some strategy is needed to embed them into the carrier image . These additional information are often necessary to start watermark extraction, so it is necessary to ensure that it can be calculated first when the watermark is extracted. A simple strategy is shown in Figure 2, which embeds additional information into image edge pixels in the form of LSB (least significant bit) replacement.

The extraction and image restoration process of reversible image watermarking based on adaptive difference expansion is as follows:

1) Additional information extraction. This process needs to first obtain the additional information necessary to start watermark extraction, including the two parameters c and T of adaptive difference expansion, and the image complexity parameter α. In addition, if the watermark extraction has already been started, it must be obtained for the next step The additional information for guiding watermark extraction is location table information. For example, it is necessary to know whether the next delta is extended, or what condition marks the end of all extraction processes.

2) Difference calculation. This process is the same as the difference calculation in the process of watermark embedding, and it must be completely matched with the difference calculation during embedding. Here, the division of pixels is mainly consistent. It is worth noting that S 2 is first followed by S ₁ when watermark is _{embedded, and S 1 is first followed by S 2 when extracted} .

3) Watermark data extraction. This step is mainly to perform the inverse operation of adaptive difference expansion to extract data and restore the original difference. When performing the extraction operation, the information in the location table needs to be referred to, because some pixels are not watermarked due to the overflow problem.

4) Image restoration. This step needs to restore the current pixel to its original state through the restored difference and the reference environment.

Compared with the prior art, the present invention has the following advantages:

(1) The present invention obtains the different complexity of each part of the image through the generalized Gaussian distribution, and performs adaptive difference expansion watermark embedding and extraction, that is, a small amount of embedding is performed in complex areas of the image, and a large amount of data is performed in gentle areas of the image Compared with the traditional method, the embedding capacity of the watermark is significantly increased and the visual quality of the image is improved.

(2) Since the present invention completely constructs the context, it improves the capacity-to-distortion ratio compared with the general method at the same PSNR.

(3) In the present invention, by embedding more watermarks in the stable region of the image, a better effect can be obtained when there are more embedded watermark data.

Description of drawings

Fig. 1 is a schematic diagram of the reversible image watermarking method of adaptive difference expansion in the present invention;

Fig. 2 is a schematic diagram of embedding additional information in the present invention;

FIG. 3 is a schematic diagram of a watermark context model in the present invention;

Fig. 4 is a schematic diagram of alternate division of watermark images in the present invention;

Fig. 5 is a schematic diagram of horizontal and vertical contexts in the present invention.

Detailed ways

The present invention first obtains the image complexity based on Gaussian statistical characteristics, then proposes a new pixel division, that is, alternately divides to obtain the context estimation model, and then obtains the estimated difference value, and finally uses the existing image complexity and estimated difference value to perform self-adaptation Difference expansion to realize watermark embedding and extraction.

As shown in FIG. 1 , the overall process of the present invention includes two parts: a watermark embedding part and a watermark extraction part. The watermark embedding part includes the preprocessing process and the watermark embedding process; the watermark extraction part includes the extraction preprocessing process and the watermark extraction process. Before the watermark is embedded, the original image needs to be preprocessed. The preprocessing process includes alternate division, difference calculation, image complexity calculation and parameter setting, as shown in the dotted line box on the upper left side of Figure 1; during the watermark embedding process , use adaptive expansion to embed the corresponding watermark, and then embed additional information, as shown in the dotted box on the lower left side in Figure 1. In the process of extracting and preprocessing, the additional information is first extracted, the difference is calculated, and then the inverse operation of adaptive difference expansion is performed to extract the watermark data and restore the original difference, as shown in the dotted line box on the upper right side of Figure 1 ; Finally, in the watermark extraction process, the watermark is extracted and the image is restored through the restored difference value, as shown in the dotted line box on the right side of Fig. 1 . The above four processes are described in detail below, namely the preprocessing process and the watermark embedding process, the extraction preprocessing process and the watermark extraction process.

1. as shown in Figure 1, the specific implementation steps of the pretreatment process of the present invention are as follows:

Step 1: Divide alternately. For adaptive interpolation, all pixels around the current pixel are used to build a context model. Considering that among the eight pixels around the current pixel, the four pixels closest to the current pixel are the horizontal and vertical four pixels, so these four pixels are used to construct the context, as shown in FIG. 3 . Let the original image be

l={x(i, j)|1≤i≤H, 1≤j≤W}, i, j are pixel coordinate positions (1)

where H and W represent the height and width of the image, respectively. In order to construct a context for each pixel, all pixels in the original image are first divided into two disjoint pixel sets S ₁ and S ₂ , that is, alternately divided, as shown in Figure 4, the pixel sets are composed of

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; mod</span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CirclePlus;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; mod</span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \}</span>\\ {\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; mod</span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CirclePlus;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; mod</span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \}</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

represent respectively, where 1≤i≤H1≤j≤W, mod is to take the remainder, is XOR, since the pixels at the edge of the image (shown in gray in FIG. 4 ) do not have complete context, the present invention does not perform differential extension on them.

Step 2: Difference calculation. For the context that has been constructed, the estimated value of each pixel in the image is calculated, and then the difference is calculated by comparing with the original pixel. This step can be divided into two parts. First, the first part uses the pixels in _S1 to estimate the pixels in _S2 . At this time, _S1 is the original pixel value; then the second part uses the pixels in _S2 to estimate The pixel in S ₁ , at this time S ₂ is the pixel value after embedding the watermark.

The specific algorithm divides the four neighbor pixels into orthogonal horizontal and vertical directions, as shown in Figure 5, the neighbor pixels are x _u , x _d , x _l , x _r , and the two pixels in each direction are calculated separately mean, and give these two mean values different weights to estimate the center pixel x. The average value of the two directions is calculated according to formula (3).

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

的计算方式为Let the weights of the vertical average x _v and the horizontal average x _h be w _v , w _h , then

is calculated as

$\left\{\begin{array}{c}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}\\ {\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Let σ(h) and σ(v) be the mean square error in the horizontal and vertical directions respectively, according to the formula

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; avg</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; avg</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Calculate, where x _avg is the average value of adjacent pixels

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; avg</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

And let S _v and _Sh be pixel sets:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; \}</span>\\ {\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; \}</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

The weights w _v and w _h are calculated as

${\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

后，可根据When obtaining the estimated value of the pixel

later, according to

$\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

Computes the estimation error of x. The sets E ₁ and E ₂ composed of the estimation errors of S ₁ and S ₂ are

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \}</span>\\ {\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

Where e(i, j) is the estimation error of pixel x(i, j) calculated by formula (9). These two sets of estimation errors will be used to embed the watermark data.

Step 3: Parameter setting. This step mainly includes parameter settings in two aspects. First, calculate the image complexity; then, according to the amount of embedded watermark data, determine the two parameters c and T of adaptive difference expansion; finally, when the user's needs cannot be met , which also determines whether to report embedding failures.

Estimation of image complexity: Using the shape parameter of the density function of the generalized Gaussian distribution (GGD) in the wavelet domain as a measure of image complexity, the estimation of image complexity is converted into an estimate of the shape parameter of the density function, through the curve The fitting method is estimated, and the final estimated value is the image complexity α.

For the generalized Gaussian distribution, the case where the mean value of the Gaussian distribution is u=0 is generally considered. Let x=(x ₁ , x ₂ ,...,x _n ) be a sample from the GGD population X with mean u=0, because GGD is symmetrically distributed, its first-order origin moment is zero, so the absolute moment can be used to Calculation.

When u=0, the first-order absolute moment is

${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \}</span>$

$<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}^{<span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&infin;</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; |</span>\frac{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&beta;\&Gamma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; |</span>\frac{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}\mathrm{<span\; class="notranslate">\; dx</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;\&Gamma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&infin;</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; |</span>\frac{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}\mathrm{<span\; class="notranslate">\; dx</span>}$

make Get x=βy ^1/α , Substitute into the above formula to get

$\frac{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;\&Gamma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}}\mathrm{<span\; class="notranslate">\; dy</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}\frac{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

代入得then

substitute

${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}\frac{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>}{\sqrt{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

Similarly, the second moment can be obtained as

m ₂ =E{|x ² |}=σ ² (14)

记and

remember

$\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \}</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>}{\sqrt{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

可由下式得到R(α) is called the generalized Gaussian parameter ratio function; and the estimation of m ₁ and m ₂

can be obtained by the following formula

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span>$ ${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

The shape parameter α is thus estimated as

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\frac{{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

in

$\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}{\sqrt{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; )</span>$

The analytical formula of the inverse function R ^-1 (x) of R(x) is difficult to obtain, so the method of numerical fitting is adopted.

The hyperbolic function fits the original function R(x) to establish a fitting model y=a+b/x, and adopts the least squares method to fit, and the approximation function of the original function is

$\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0.77127</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 0.26961</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}$

The original function of the approximation function is thus

${\mathrm{<span\; class="notranslate">\; R</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.26961</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.77127</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 19</span>}<span\; class="notranslate">\; )</span>$

利用最小二乘法求得反函数的拟合函数为So the fitted model is

Using the least squares method to obtain the fitting function of the inverse function is

${\mathrm{<span\; class="notranslate">\; R</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 0.2718</span>}}{\mathrm{<span\; class="notranslate">\; 0.7697</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.1247</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 20</span>}<span\; class="notranslate">\; )</span>$

To sum up, the parameter α is estimated by formulas (17) and (20), and then the image complexity is obtained.

Determine the two-parameter constant c and embedding capacity T of the adaptive difference expansion, as shown in Figure 5, the smoothness of the region is obtained by the variance σ ² ,

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 4</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; avg</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; \}</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; one</span>}<span\; class="notranslate">\; )</span>$

in

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; avg</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; two</span>}<span\; class="notranslate">\; )</span>$

Thus, the base of difference expansion can be obtained by

Among them, c is a constant, α is the complexity of the carrier image, T is the threshold, c and T are used to control the embedding capacity of the watermark of the image. In order to prevent the seriousness of pixel overflow, it is necessary to ensure that 2≤T≤10. For the constant c, generally speaking, the larger the value, the more embedded watermarks but the more serious image distortion, and vice versa.

2. Watermark embedding process

In the watermark embedding process, the adaptive extension base b _ij is determined by the image complexity α, the adaptive extension parameters c and T. Assuming that w represents the watermark data to be embedded with a length of l, for the convenience of expression, let w=w ₁ , w ₂ ,..., w _n , where n=l/8 and w ₁ , i=1, 2, .. .n contains 8-bit binary data. The detailed implementation steps are given below:

(2.1) Determine the adaptive extension base b _ij , through the image complexity α, and the adaptive extension parameters c and T, calculated by the formula

Determine the adaptive expansion base b _ij , where σ ² is the variance, which is used to measure the stability of the region;

(2.2) Assuming that w represents the binary watermark data to be embedded with a length of l, divide w into n 8-bit blocks, let w=w ₁ , w ₂ ,..., w _n , where n=l/8 And head w _t , t=1, 2,... n contains 8-bit binary data;

(2.3) Read the watermark data w _t and convert it to decimal w _dt , in order to judge whether w _dt is embedded or not, give the variable u for identification, and initialize u to 1;

(2.4) Scan the carrier image, for a specific pixel x _ij , known estimated value x _ij ′, adaptive extension base b _ij , and estimated difference e _ij , get here by r _{i, j} = w _{d, r} mod b _ij The final embedded content r _{i, j} , and then use the formula

${\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; four</span>}<span\; class="notranslate">\; )</span>$

Perform adaptive embedding to obtain the embedded pixel value x _ij ";

In the adaptive embedding process in (2.4), if x">255 or x"<0, then skip the watermark embedding of the pixel, and use the position table to record the position and pixel overflow information of the pixel;

u＝u×b_ij，若u＞255，读入下一个水印数据w_t+1并置u＝1，转入步骤(2.3)嵌入下一位水印；否则转入步骤(2.4)继续w_d，t的嵌入；(2.5) After step (2.4) is embedded, update

u=u×b _ij , if u>255, read in the next watermark data w _t+1 and set u=1, go to step (2.3) to embed the next watermark; otherwise go to step (2.4) and continue w _{d , the embedding of t} ;

(2.6) Carry out additional information embedding, described additional information comprises parameter c, T, and parameter α is image complexity and the location table of recording pixel overflow information in embedding process (2.5); So far the watermark embedding process ends, obtains the image after embedding;

After the watermark embedding is completed, the additional information embedding process is carried out. Additional information includes parameters c, T and a location table that records pixel overflow information. These additional information are necessary to start the watermark extraction, so it needs to be guaranteed that it can be calculated first when the watermark is extracted. A simple strategy, shown in Figure 2, embeds additional information into image edge pixels in the form of LSB replacement. At this point, the watermark embedding is completed, and the embedded image is obtained.

3. The watermark extraction part includes extraction preprocessing.

In the extraction preprocessing process, the additional information is extracted first, and this process is the reverse process of embedding additional information.

(3.1) Firstly, the additional information extraction process is carried out. This process is the inverse process of additional information embedding, and the two parameters c and T of adaptive difference expansion, the image complexity parameter α and the position table are obtained. For example, if LSB (least effective bit) to reversibly embed the additional information into the edge pixels of the image, then the LSB watermark extraction algorithm can be used to extract the additional information from the edge pixels of the image;

(3.2) Then the difference calculation is performed through the same division as in the preprocessing process of watermark embedding. This process is the same as the difference calculation in the preprocessing process (2.1), and it must be done with the difference calculation during embedding. to a complete match, that is, the division of pixels remains consistent, because when the watermark is embedded, the difference calculation is to calculate the difference of the set S ₂ first, and then use the result of S ₂ to calculate the difference of S ₁ , so the extraction is to calculate S ₁ first difference, and then calculate the difference of _S2 ;

4. Watermark extraction process

The watermark extraction process is the process of watermark extraction and image restoration: the image complexity α is obtained through the extraction of additional information, the adaptive expansion parameters c, T and the position table are obtained, and the estimated difference of the embedded image is obtained by using the construction of the context, and then The detailed implementation steps are given below:

The watermark extraction process is the inverse process of the embedding process, and the specific steps are as follows:

(4.1) Initialize the identification variable u to be 1, because the watermark is not embedded in the image edge area, so, for the area of i=1 or j=1, the image pixels remain unchanged and are directly restored;

(4.2) Scanning the embedded image, for a specific pixel x″, knowing the estimated value x′, adaptively expanding the base b _ij , and estimating the difference e′ _ij , through the formula

r _ij ＝e _ij ′% b _ij , b _ij ≠1

Get the embedded watermark r _{i, j} here, and then use the formula

Restore the original difference e _ij , and then get the original pixel of the image;

During the extraction process in (4.2), if the location is recorded in the location table, the watermark extraction of this location is skipped, while keeping the pixel unchanged.

(4.3) After step (4.2) is extracted, put r _{i, j} , b _ij into sets R _t , B _t respectively, _{i, j in r i, j} , b _ij are the coordinates, which are in R _t , The position in B _t is the order of putting in, and update u=u ×b _ij ;

If u>255, record the size of the set R at this time as m, through the formula

${\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; m</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}\end{array}\right.$

Then the complete watermark w _t =w _t (1), reset u=1, proceed to step (4.2) to extract the next watermark w _t+1 , if u≤255, proceed to step (4.2).

The contents not described in detail in the description of the present invention belong to the prior art known to those skilled in the art.

Claims (3)

1. reversible image watermark method based on self-adaptation difference expansion, it is characterized in that: comprise watermark embedded part and watermark extracting part two large divisions, the watermark embedded part comprises preprocessing process and watermark embed process; Watermark extracting partly comprises extracts preprocessing process and watermark extraction process;

Described preprocessing process is:

(1.1) alternately divide, construct the context relation of pixel, original image is divided into disjoint set of pixels S ₁And S ₂, be used for the calculating of image complexity and the realization that pixel is estimated;

(1.2) difference is calculated, and uses the context that constructs in the preprocessing process step (1), the estimated value of each pixel in the computed image, then by with original pixels relatively ask difference, this step can be divided into two parts successively: first at first, utilize S ₁In pixel estimate S ₂In pixel, this moment S ₁Be original pixel value; Second portion utilizes S then ₂In pixel estimate S ₁In pixel, this moment S ₂Be the pixel value behind the embed watermark;

(1.3) parameter setting, comprise the parameter setting of two aspects, at first at original image, the form parameter α of density function that utilizes the generalized Gaussian distribution (GGD) in the wavelet field is as the measurement parameter of image complexity, and by curve-fitting method parameter alpha is estimated, parameter alpha is defined as image complexity; Then, according to what of embed watermark data, determine two parameter c and the T of self-adaptation difference expansion, c and T are similar to the parameter used in the generality expansion, are used for the embedding capacity of watermark of control chart picture;

Described watermark embed process:

(2.1) determine self-adaptation expansion radix b _Ij, by the parameter alpha that preprocessing process step (1.3) obtains, promptly image complexity reaches self-adaptation spreading parameter c and T, calculates by formula

Determine self-adaptation expansion radix b _Ij, i, j are coordinate, σ ²Be variance, be used to weigh the steady degree in zone;

(2.2) suppose that w represents that length is the scale-of-two watermark data for the treatment of embedding of l, the piece with w is divided into n 8 makes w=w ₁, w ₂..., w _n, wherein n=l/8 and w _t, t=1,2 ... n comprises 8 bit binary data;

(2.3) read watermark data w _t, and be converted into decimal system w _{D, t}, in order to judge w _{D, t}Whether embedding finishes, and provides variable u and identifies, and initialization u is 1;

(2.4) scanning carrier image is at concrete pixel x _Ij, known estimated value x _Ij', self-adaptation expansion radix b _Ij, estimate difference e _Ij, pass through r _{I, j}=w _{D, t}Mod b _IjObtain final embedding content r herein _{I, j}Utilize formula then

$e^{\&prime;}=\left\{\begin{array}{cc}e\&times;b+r,& b=1\\ e,& b=1\end{array}\right.$

Carry out self-adaptation and embed, thereby obtain embedding back pixel value x _Ij";

In the self-adaptation telescopiny in (2.4), "＞255 or x "＜0 if x, the watermark of then skipping this pixel embeds, and utilizes location tables to write down this locations of pixels and pixel flooding information;

(2.5) after step (2.4) embeds and finishes, upgrade

U=u * b _Ij, if next watermark data w is read in u＞255 _T+1And put u=1, change step (2.3) over to and embed the next bit watermark; Otherwise change step (2.4) over to and continue w _{D, t}Embedding;

(2.6) carry out additional information and embed, described additional information comprises parameter c, T, and parameter alpha is the location tables of recording pixel flooding information in image complexity and the telescopiny (2.5); So far watermark embed process finishes, and obtains embedding the back image;

Described extraction preprocessing process:

(3.1) at first carry out the additional information leaching process, this process is the inverse process that additional information embeds, and obtains two parameter c and the T of self-adaptation difference expansion, image complexity parameter alpha and location tables;

(3.2) carrying out difference by division identical in the preprocessing process (1.1) then calculates, this process is calculated identical with the difference in the preprocessing process (2.1), and the difference when accomplishing and embedding is calculated and is accomplished to mate fully, the division that is pixel is consistent, and calculating is first S because watermark embeds time difference value ₂Back S ₁So, be first S when extracting ₁Back S ₂

Described watermark extraction process is the inverse process of telescopiny, and concrete steps are as follows:

(4.1) initialization marking variable u is 1, because the embedding of watermark is not carried out in the zone, image border, so to the zone of i=1 or j=1, image pixel remains unchanged, and directly reduction;

(4.2) scanning embedded images is at concrete pixel x ", known estimated value x ', self-adaptation expansion radix b _Ij, the estimation difference e ' _Ij, pass through formula

r _ij＝e _ij′％b _ij，b _ij≠1

Obtain embed watermark r herein _Ij, utilize formula then

Recover original difference e _Ij, and then obtain the image original pixels;

In the leaching process in (4.2),, then skip the watermark extracting of this position, keep pixel constant simultaneously if write down this position in the location tables.

(4.3) after step (4.2) is extracted and is finished, with r _{I, j}, b _IjPut into set R respectively _t, B _tIn, r _{I, j}b _IjIn i, j is a coordinate, it is at R _t, B _tIn the position be the order of putting into, and upgrade u=u * b _Ij

If u＞255, the size that note is gathered R this moment is m, passes through formula

$w_t\left(i\right)=\left\{\begin{array}{cc}{w}_t(i+1)\&times;B\left(i\right)+R\left(i\right),& 2\&le;i<m\\ 1,& i=m\end{array}\right.$

Then complete watermark w _t=w _t(1), puts u=1 again, carry out step (4.2) and extract next bit watermark w _T+1, if step (4.2) item is proceeded in u≤255.

2. the reversible image watermark method based on the expansion of self-adaptation difference according to claim 1, it is characterized in that: the value of described T is 2≤T≤10.

3. the reversible image watermark method based on the expansion of self-adaptation difference according to claim 1 is characterized in that: described additional information is to be embedded in the image edge pixels in the mode that LSB (Least Significant Bit least significant bit (LSB)) replaces.

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