CN100492401C - A Method of Embedding and Extracting Watermark on Binary Image - Google Patents

Abstract

It is a method that embedded the watermark on binary image. It comprises the following steps: a. taking the edge of binary image; b. analyzing the edge point, and calculating the priority of variable pixel; c. mixing the binary image; d. convolutional encoding the watermark signal; e. embedding the watermark in the mixed binary image. The watermark-extracting method comprises: a'.mixing and blocking the binary image that embedded the watermark; b'. extracting a bit of watermark information from each sub-block; c'. Viterbi decoding the watermark matrix, and getting the wanted watermark. The method can change the priority by calculating edge point of binary image. When embedding the watermark, the point with high priority is considered first, which can realize the least distortion of binary image that embedded the watermark. This invention embeds a meaningful watermark signal in binary image, and the extraction of watermark need no information of original image information.

Description

A Method of Embedding and Extracting Watermark on Binary Image

technical field

The invention relates to a method for inserting and extracting a watermark, in particular to a method for inserting and extracting a watermark on a binary image.

Background technique

With the rapid development of computer networks and multimedia systems, digital media (digital audio, digital image, digital video) are widely used, and the copyright protection and integrity protection of digital media has become an urgent problem to be solved. Digital watermarking technology is one of the effective methods to solve this problem. Digital watermarking is to directly embed some marking information related or irrelevant to digital media content into digital media content, but it does not affect the value of the original content, and cannot be perceived or noticed by the human perception system. Through the information hidden in the digital media content, the purpose of confirming content creators, buyers, or whether the content is authentic and complete can be achieved.

Most of the currently proposed digital watermarking algorithms are aimed at digital media such as audio, video, color images and grayscale images. However, digital watermarking algorithms for binary images (such as maps, engineering drawings, barcodes, signatures and fax documents, etc.) that can meet the above requirements are rarely seen. Due to the particularity of binary image structure, the existing watermarking algorithms for color or grayscale images are difficult to apply directly to binary images. Because, modifications to binary image pixels are easily detected. The current existing algorithms (see references) are not robust, and the visual effect of the image after embedding the watermark is not good. There are four comparable technical literatures:

1. M.Y.Wu and J.H.Lee. “A Novel Data Embedding Method for Two-Color Facsimile Image” in “Proceedings of International Symposium on Multimedia Information Processing,” Tai-wan, R.O.C, December 1998.

2. H.C.Wang, C.Y.Lin, C.C.Huang, "Data Hiding in a binary image by the modified digital halftoning techniques, proceedings", "1999 Conference on Computer Vision, Graphics and Image Processing", pp.183-190, Tanpei, Taiwan, August, 1999.

3. Yu-Yuan Chen, Hsiang-Kuang Pan, and Yu-Chee Tseng, "A Secure Data Hiding Scheme for Two-Color Image", in "IEEE Symp. on Computers and Communications", 2000.

4. Yu-Chee Tseng, Hsiang-Kuang Pan, "Data Hiding in 2-Color Images", "IEEE TRANSACTIONS ON COMPUTERS", VOL.51, NO.7, JUL Y 2002.

Contents of the invention

The purpose of the present invention is to provide a method for inserting and extracting watermarks on binary images. This method improves the visual effect of the image after embedding the watermark, and the robustness of the algorithm is also enhanced.

In order to achieve the above object, the present invention adopts following technical scheme:

A method for embedding a watermark on a binary image, comprising the following steps:

a. Extract the edge of the binary image, use a 3×3 window to scan the entire image from left to right, from top to bottom, use “1” to represent black pixels, and “0” to represent white pixels, for a 3×3 window If the nature of the pixels is different (that is, there are black pixels and white pixels), and the center pixel value of the window is 1, then it is determined that the center point of the window is the edge point of the image, and the other cases are not edge points; record these edges point, the embedding of the watermark is carried out at the edge point;

b. Analyze the edge points, calculate the priority of modifiable pixels, center on the edge point, divide the edge point into 4 priorities according to the distribution of black and white pixels in the 3×3 window;

c. Scramble the binary image, regard the digital binary image as a matrix, the black point is 1, the white point is 0, apply the Arnold transformation to scramble the image, the Arnold transformation of the position-based image scrambling can be written as:

$\left(\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&prime;</span>\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&prime;</span>\end{array}\right)<span\; class="notranslate">\; =</span>\left(\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 2</span>}\end{array}\right)\left(\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}\end{array}\right)<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; mod</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; )</span>$

Wherein x, y ∈ (0, 1, 2, ..., N-1), represent the coordinates of a certain pixel point, x', y' are transformed coordinates, and N is the order of the image matrix;

d. Watermark preprocessing. Before inserting the watermark, the watermark is preprocessed. Since the watermark is also a digital binary image, it can also be regarded as a matrix, and the watermark is encoded with a convolutional code, that is, the convolutional code is used. generate a digital image matrix multiplied by the watermark;

e. To embed the watermark image in the scrambled binary image, first divide the scrambled binary image into disjoint M×M sub-blocks, the value of M is related to the data size of the watermark, set two The size of the value image is N×N, and the size of the watermark image after convolution coding is I×I, then

Since the scrambled binary image is divided into ¹² sub-blocks of M×M, which correspond to the I×I matrix formed after watermark encoding, each of the sub-blocks of M×M corresponds to I× The point on the corresponding position of the I watermark matrix;

If the watermark point is 0, then embed 0 in the M×M sub-block,

If the number of points of black pixels in the M×M sub-block is an even number, no modification is made;

If the number of points of black pixels in the M×M sub-block is an odd number, then according to the priority set in step b, select one of the points with the highest priority and modify the polarity;

If the watermark point is 1, then embed 1 in the M×M sub-block,

If the number of black pixel points in the M×M sub-block is an odd number, no modification is made;

If the number of points of black pixels in the M×M sub-block is an even number, then according to the priority set in step b, select one of the points with the highest priority and modify the polarity;

After all the watermark information is embedded, the Arnold inverse transform is performed on the image to obtain the image after embedding the watermark.

A method for extracting a watermark, extracting a watermark embedded according to the above method, comprising the following steps:

a'. Arnold transform the binary image embedded with watermark, the formula used is the same as the formula used in step c when embedding the watermark, divide the scrambled binary image into several disjoint M×M sub-blocks, M The value of M is the same as the value of M when the watermark is embedded, and each M×M sub-block can extract one bit of watermark information, and a total ^{of I2} can be extracted as watermark information, and I is the same as the size I of the watermark when the watermark is embedded;

b'. For each M×M sub-block,

If the number of points of black pixels in the sub-block is an odd number, the extracted watermark information is 1;

If the number of points of black pixels in the sub-block is even, the extracted watermark information is 0;

The extracted watermark information forms an I×I matrix, which is a matrix of embedded watermark information encoded by a convolutional code;

的矩阵，c'. Use the Viterbi algorithm to decode the I×I watermark matrix to obtain a

matrix,

It is the watermark matrix to be extracted.

Due to the adoption of the above technical solution, the method for inserting and extracting watermarks on binary images of the present invention first performs convolutional coding on the watermark signal, then embeds it into the protected binary image, extracts the watermark, and decodes it via Viterbi. The watermark signal is obtained, because the Viterbi algorithm has a strong error correction ability, so that the watermark image of this method can still extract a reliable watermark signal after some general geometric deformation operations.

Description of drawings

Fig. 1 is the flowchart of the method for inserting watermark on binary image of the present invention;

Fig. 2 is the flow chart of the method for extracting watermark on binary image of the present invention;

Fig. 3 is a schematic diagram of priority edge features of a 3×3 window;

Fig. 4 is the trellis diagram of the Vierbi decoding algorithm for (2,1,2) convolutional code when L=5;

The original situation figure of Fig. 5-binary image;

Fig. 6 is the edge image extracted to the binary image of Fig. 5;

Fig. 7 is a watermark image;

Fig. 8 is the image obtained after the watermark image in Fig. 7 is convolved;

Fig. 9 is the image after the binary image of Fig. 5 is inserted into the watermark of Fig. 7;

Fig. 10 is the absolute error image of Fig. 9 and Fig. 5;

Fig. 11 is the watermark image directly extracted without processing;

Fig. 12 is the watermark image extracted after linear interpolation enlargement of the image after watermarking in Fig. 5;

Fig. 13 is the watermark image extracted after the image watermarked in Fig. 5 is reduced by linear interpolation;

Fig. 14 is the image that the image after Fig. 5 adds watermark is cropped once;

Figure 15 is the watermark image extracted from Figure 14;

Fig. 16 is the image of the image after adding watermark in Fig. 5 through secondary cropping;

Figure 17 is the watermark image extracted from Figure 16;

Figure 18 The image after adding salt and pepper noise to the watermarked image in Figure 5;

Figure 19 is the watermark image extracted from Figure 18.

Detailed ways

The technical solutions of the present invention will be further described below in conjunction with the drawings and embodiments.

Fig. 1 is the flowchart of the method for inserting watermark on binary image of the present invention, as shown in Fig. 1, the method for inserting watermark on binary image of the present invention comprises the following steps:

a. Extract the edge of the binary image, use a 3×3 window to scan the entire image from left to right, from top to bottom, use “1” to represent black pixels, and “0” to represent white pixels, for a 3×3 window If the nature of the pixels is different (that is, there are black pixels and white pixels), and the center pixel value of the window is 1, then it is determined that the center point of the window is the edge point of the image, and the other cases are not edge points; record these edges point, the embedding of the watermark is performed at the edge point. In the above embodiments, a 3×3 window is used to scan the entire image, and a 5×5 or 7×7 window can also be used for scanning, but it is most convenient to use a 3×3 window. FIG. 5 is an original image of a binary image, and FIG. 6 is an image obtained after using a 3×3 window to extract edge points according to the above embodiment.

b. Analyze the edge points and calculate the priority of the modifiable pixels. Taking the 3×3 window in the above embodiment as an example, take the edge point as the center, and divide the edge points according to the distribution of black and white pixels in the 3×3 window Divided into 4 priorities. Figure 3 is a schematic diagram of the priority edge features of a 3×3 window, if the two horizontal or vertical points of the central edge point are black pixels, as shown in (a) and (b) of Figure 3, then set the central edge The modifiable priority of the point is level 1; if the central edge point forms a 45-degree or 135-degree oblique edge with other two black pixels, as shown in (c) and (d) of Figure 3, the central edge The modifiable priority of the point is level 2; if the edge distribution is as shown in the figure (e), (f), (g), (h), the modifiable priority of the center edge point is level 3; such as the edge distribution As shown in Figures (i), (j), (k), and (1), the center edge point can be modified to a priority of 4, where the gray point indicates that it can be changed from white to black.

c. Scrambling the binary image, the scrambling algorithm can be used as a key in the watermark embedding and extraction algorithm. There are two purposes of scrambling: (1) evenly distribute the modifiable pixels in each part of the image; (2) increase the confidentiality of the algorithm. The scrambled image is further divided into many sub-blocks of the same size, and one bit of watermark information is embedded in each sub-block. The digital binary image is regarded as a matrix, the black point is 1, and the white point is 0, and the Arnold transformation is applied for image scrambling. The Arnold transformation of position-based image scrambling can be written as:

$\left(\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&prime;</span>\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&prime;</span>\end{array}\right)<span\; class="notranslate">\; =</span>\left(\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 2</span>}\end{array}\right)\left(\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}\end{array}\right)<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; mod</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; )</span>$

Wherein x, y ∈ (0, 1, 2, ..., N-1), represent the coordinates of a certain pixel point, x', y' are transformed coordinates, and N is the order of the image matrix;

d. Watermark preprocessing. Before inserting the watermark, the watermark is preprocessed. Since the watermark is also a digital binary image, it can also be regarded as a matrix, and the watermark is encoded with a convolutional code, that is, the convolutional code is used. A digital image matrix that generates a matrix multiplied by a watermark. In convolutional coding, the parity element of this group is not only related to the information element of this group, but also related to the information group input to the encoder at each previous moment. In the decoding process of convolutional codes, not only the decoding information is extracted from the code group received at this moment, but also relevant information is extracted from the code group received at previous or subsequent times. Taking (2, 1, 2) convolutional code as an example, its generator matrix is G(D)=(1+D+D ² , 1+D ² ), 1 represents the current input, and D represents the previous time period The input of ^D2 represents the input of the previous two time periods. If the input sequence M=(0010100001), then the code sequence C=(00,00,11,10,00,10,11,00,00,11) output by the (2,1,2) encoder.

矩阵，这样，在经(2，1，2)卷积码编码后，可将水印变成一个I×I的数字矩阵。In this embodiment, the above-mentioned (2, 1, 2) convolutional code and its generation matrix are used, and of course other forms of convolutional codes may also be used. Due to the use of (2, 1, 2) convolutional codes, in this embodiment, the watermark to be inserted should meet the aspect ratio of 2:1, that is, the watermark is a

In this way, after being encoded by (2, 1, 2) convolutional code, the watermark can be changed into a digital matrix of I×I.

Fig. 7 is an original image of a watermark, and Fig. 8 is an image of the watermark encoded by the (2, 1, 2) convolutional code described in the above embodiment.

e. To embed the watermark image in the scrambled binary image, first divide the scrambled binary image into disjoint M×M sub-blocks, the value of M is related to the data size of the watermark, set two The size of the value image is N×N, and the size of the watermark image after convolution coding is I×I, then ; Since M adopts the above-mentioned value-taking method, it can be known by calculation that an N×N watermark image can be divided into I ² blocks, which is just equal to the number of points in the encoded watermark matrix, so each sub-block can correspond to a Points in the watermark matrix.

Since the scrambled binary image is divided into ¹² sub-blocks of M×M, which correspond to the I×I matrix formed after watermark encoding, each of the sub-blocks of M×M corresponds to I× The point on the corresponding position of the I watermark matrix;

If the watermark point is 0, then embed 0 in the M×M sub-block,

If the number of points of black pixels in the M×M sub-block is an even number, no modification is made;

If the number of points of black pixels in the M×M sub-block is an odd number, then according to the priority set in step b, select one of the points with the highest priority and modify the polarity;

If the watermark point is 1, then embed 1 in the M×M sub-block,

If the number of black pixel points in the M×M sub-block is an odd number, no modification is made;

If the number of points of black pixels in the M×M sub-block is an even number, then according to the priority set in step b, select one of the points with the highest priority and modify the polarity;

After all the watermark information is embedded, the Arnold inverse transform is performed on the image to obtain the image after embedding the watermark.

In order to achieve a better effect, the side length of the binary image is at least 6 times the side length of the watermark image, that is, N≥6I.

Fig. 9 is the image after the binary image of Fig. 5 is inserted into the watermark of Fig. 7;

FIG. 10 is an absolute error graph of FIG. 9 and FIG. 5 .

Fig. 2 is the flowchart of the method for extracting watermark on binary image of the present invention, comprises the following steps:

a'. Arnold transform the binary image embedded with watermark, the formula used is the same as the formula used in step c when embedding the watermark, divide the scrambled binary image into several disjoint M×M sub-blocks, M The value of M is the same as the value of M when the watermark is embedded, and each M×M sub-block can extract one bit of watermark information, and a total ^{of I2} can be extracted as watermark information, and I is the same as the size I of the watermark when the watermark is embedded;

b'. For each M×M sub-block,

If the number of points of black pixels in the sub-block is an odd number, the extracted watermark information is 1;

If the number of points of black pixels in the sub-block is even, the extracted watermark information is 0;

The extracted watermark information forms an I×I matrix, which is a matrix of embedded watermark information encoded by a convolutional code;

的矩阵，既是要提取的水印矩阵。Viterbi算法是一种最大似然译码算法，编码器从全为0的S₀状态时所输出的码序列，称为结尾卷积码序列。因此，当送完L段信息序列后，还必须在送入m段全0序列。图4是Vierbi译码算法对于(2，1，2)卷积码在L＝5时的网格图。如图4所示，图中实线表示输入为0，虚线表示输入为1。S₀S₁S₂S₃表示的时编码器的4种状态。该实施例采用的是Viterbi的硬判决，对于(2，1，2)卷积码，每个状态的入度为2，如当前时刻的状态S₀它接受由前一时刻S₀S₂状态转入的分支值(00)(11)。设前一时刻S₀S₂所经过的路径分别为pathl、path3，最小海明距离分别为d1、d3。将输入的值与(00)(11)比较，所得的距离为D1、D3，选择d1+D1、d3+D3中小的一个值给d1，当前选择的路径就是海明距离小的那条路径，更新pathl的值。其他三条路径的选择同样。当全部输入完毕后，从四条路径中选取一条海明距离最小的即为所要的路径，该路径上的值就是译码值。c'. Use the Viterbi algorithm to decode the I×I watermark matrix to obtain a

The matrix of is the watermark matrix to be extracted. The Viterbi algorithm is a maximum likelihood decoding algorithm. The code sequence output by the encoder from the S ₀ state of all 0s is called the end convolutional code sequence. Therefore, after the L-segment information sequence is sent, the m-segment all-0 sequence must be sent. FIG. 4 is a trellis diagram of the Vierbi decoding algorithm for (2, 1, 2) convolutional codes when L=5. As shown in Figure 4, the solid line in the figure indicates that the input is 0, and the dotted line indicates that the input is 1. S ₀ S ₁ S ₂ S ₃ represents the 4 states of the encoder. This embodiment adopts Viterbi's hard decision. For (2, 1, 2) convolutional codes, the in-degree of each state is 2, such as the state S ₀ at the current moment, which accepts the state S ₀ S ₂ from the previous moment The value of the branch transferred in (00)(11). Assume that the paths S ₀ S ₂ passed at the previous moment are path1 and path3 respectively, and the minimum Hamming distances are d1 and d3 respectively. Comparing the input value with (00)(11), the obtained distances are D1 and D3, select the smaller value among d1+D1 and d3+D3 for d1, the currently selected path is the path with the smaller Hamming distance, Update the value of pathl. The selection of the other three paths is the same. After all the input is completed, select a path with the smallest Hamming distance from the four paths as the desired path, and the value on this path is the decoding value.

Because the Viterbi algorithm has strong error correction ability, the watermarked image of this method can still extract a reliable watermark signal after some general geometric deformation operations.

Figure 11 is the watermark image directly extracted without processing; Figure 12 is the watermark image extracted after the watermarked image in Figure 5 is enlarged by linear interpolation; Figure 13 is the watermarked image in Figure 5 extracted after linear interpolation reduction Watermark image. Comparing these three pictures, it can be seen that due to the use of the Viterbi algorithm, the watermark extracted after the geometric deformation operation is still recognizable.

Several examples are given below to further illustrate that the method of the present invention for embedding a watermark on a binary image and extracting a watermark has strong error correction capability and robustness.

Figure 14 is the cropped image of the watermarked image in Figure 5; Figure 15 is the watermarked image extracted from Figure 14.

Fig. 16 is the image of the watermarked image in Fig. 5 after secondary cropping; Fig. 17 is the watermarked image extracted from Fig. 16 .

Figure 18 is the watermarked image in Figure 5 and the image after adding salt and pepper noise; Figure 19 is the watermarked image extracted from Figure 18.

It can be seen from the above three examples that the method for embedding and extracting watermarks on binary images of the present invention has strong anti-interference ability, and can still extract a clearer and more reliable image when noise is added. watermark.

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

Analyze and classify the edge points of the binary image, calculate the modifiable priority level of the edge points, and give priority to the points with a higher level when embedding the watermark; this ensures the minimum distortion of the binary image after the watermark is embedded;

The watermark extraction process does not require any original image information;

Using the Vierbi decoding algorithm makes the watermark extraction have a strong error correction ability, and this technology has significantly improved the confidentiality and robustness of the watermark.

Claims (5)

1. A method for embedding a watermark on a binary image, comprising the following steps: a. Extract the edge of the binary image, use a 3×3 window to scan the entire image from left to right, from top to bottom, use “1” to represent black pixels, and “0” to represent white pixels, for a 3×3 window If the nature of the pixels is different, that is, there are black pixels and white pixels, and the center pixel value of the window is 1, then it is determined that the center point of the window is the edge point of the image, and the other cases are not edge points; record these edge points , the embedding of the watermark is carried out at the edge point; b. Analyze the edge points, calculate the priority of modifiable pixels, center on the edge point, divide the edge point into 4 priorities according to the distribution of black and white pixels in the 3×3 window; c. Scramble the binary image, regard the digital binary image as a matrix, the black point is 1, the white point is 0, apply the Arnold transformation to scramble the image, the Arnold transformation of the position-based image scrambling can be written as: $\left(\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&prime;</span>\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&prime;</span>\end{array}\right)<span\; class="notranslate">\; =</span>\left(\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 2</span>}\end{array}\right)\left(\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}\end{array}\right)<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; mod</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; )</span>$ Wherein x, y ∈ (0, 1, 2, ..., N-1), represent the coordinates of a certain pixel point, x', y' are transformed coordinates, and N is the order of the image matrix; d. Watermark preprocessing, before inserting the watermark, the watermark is preprocessed, and the watermark is encoded with a convolutional code, that is, the digital image matrix of the watermark is multiplied by the generation matrix of the convolutional code; e. To embed the watermark image in the scrambled binary image, first divide the scrambled binary image into disjoint M×M sub-blocks, the value of M is related to the data size of the watermark, set two The size of the value image is N×N, and the size of the watermark image after convolutional encoding is I×I, then M=rounding

The binary image after scrambling is divided into ^{1 or 2} sub-blocks of M×M, corresponding to the I×I matrix formed after watermark encoding, and each of the sub-blocks of M×M corresponds to I×I watermark Points at the corresponding positions of the matrix; If the watermark point is 0, then embed 0 in the M×M sub-block, If the number of points of black pixels in the M×M sub-block is an even number, no modification is made; If the number of points of black pixels in the M×M sub-block is an odd number, then according to the priority set in step b, select one of the points with the highest priority and modify the polarity; If the watermark point is 1, then embed 1 in the M×M sub-block, If the number of black pixel points in the M×M sub-block is an odd number, no modification is made; If the number of points of black pixels in the M×M sub-block is an even number, then according to the priority set in step b, select one of the points with the highest priority and modify the polarity; After all the watermark information is embedded, the Arnold inverse transform is performed on the image to obtain the image after embedding the watermark. 2. the method for embedding watermark on binary image as claimed in claim 1, is characterized in that, described watermark is a rectangle, and length is 2 times of its width, is a

matrix. 3. the method for embedding watermark on binary image as claimed in claim 2, it is characterized in that, described step d watermark preprocessing adopts (2,1,2) convolutional code to encode watermark, its generation The matrix is G(D)=(1+D+D ² , 1+D ² ), 1 represents the current input, D represents the input of the previous time period, D ² represents the input of the previous two time periods, and the A matrix of I×I is formed after multiplication of the watermark digital matrix. 4. The method for embedding a watermark on a binary image as claimed in claim 1 or 2, wherein the side length of the binary image is at least 6 times the side length of the watermark image, that is, N≥6I . 5. A method for extracting a watermark, extracting the watermark embedded in the method according to claim 1, comprising the following steps: a'. Arnold transform the binary image embedded with watermark, the formula used is the same as the formula used in step c when embedding the watermark, divide the scrambled binary image into several disjoint M×M sub-blocks, M The value of M is the same as the value of M when the watermark is embedded, and each M×M sub-block can extract one bit of watermark information, and a total ^{of I2} can be extracted as watermark information, and I is the same as the size I of the watermark when the watermark is embedded; b'. For each M×M sub-block, If the number of points of black pixels in the sub-block is an odd number, the extracted watermark information is 1; If the number of points of black pixels in the sub-block is even, the extracted watermark information is 0; The extracted watermark information forms an I×I matrix, which is a matrix of embedded watermark information encoded by a convolutional code; c'. Use the Viterbi algorithm to decode the I×I watermark matrix to obtain a

The matrix of is the watermark matrix to be extracted.

Images