CN114612317A - Secret image sharing method and system for resisting mean filtering - Google Patents

Abstract

The present invention proposes a secret image sharing method and system for anti-average filtering. Including: acquiring the secret image and n original carrier images as carriers for sharing the image information of the secret image, the original carrier image is adjusted to obtain a recombined carrier image with the same size as the secret image, n is a positive integer; Respectively fuse to n reconstructed carrier images to obtain n shadow images, perform neighborhood expansion on each pixel of the shadow image, and use the original carrier image to fill the expanded neighborhood to obtain an extended shadow image; The average value of the neighbor pixels of each non-extended pixel is adjusted based on the difference between the mean value and the corresponding non-extended pixel. The sender sends to the receiver to recover the secret image.

Description

A secret image sharing method and system for adversarial mean filtering

technical field

The invention belongs to the field of image processing, and in particular relates to a secret image sharing method and system for countering mean value filtering.

Background technique

Secret sharing technology encrypts secret information into multiple shadow images and distributes them to multiple participants. Only a subset of authorized participants can decrypt them together, while non-authorized subsets cannot. A secret sharing algorithm generally includes two stages of secret sharing and recovery, sometimes called encryption and decryption or encoding and decoding. In the (k,n) threshold secret sharing scheme, where k≤n, the secret information is encrypted into n shadow images. The original secret can only be decrypted when equal to or greater than k shadow images are obtained; and no secret can be obtained when there are less than k shadow images.

Digital images are one of the most important media types, and secret image sharing techniques that apply secret sharing techniques to digital image objects are flourishing. Compared with data, the particularity of digital images in the field of secret image sharing lies in: (1) The special file storage structure of digital images. Taking the digital image in grayscale BMP format as an example, its pixel value value space is [0, 255], so in the secret image sharing scheme, the value range of secret value, shared value and related parameters should be fully considered to avoid sharing or restoration. In the process, information is lost, which makes it impossible to recover the secret image; (2) The digital image is composed of a large number of pixels, and the secret sharing is only performed for one or a few pixel values at a time. The efficiency of the recovery algorithm; (3) There is correlation between adjacent pixel values, and there is coherence and correlation between adjacent image pixels, which may lead to the leakage of image secret information, so the secret image sharing scheme should be considered at the same time. Single sharing security and visual security; (4) The image transmission is ultimately recognized by the human visual system. Due to the low-pass filtering characteristics of the human eye, it does not require lossless restoration of the image; (5) The image is special data, secret image sharing The scheme can be applied to general data secret sharing situations with simple changes. The performance evaluation indicators of the secret image sharing scheme include: the restoration quality of the secret image, the presence or absence of pixel dilation, the (k,n) threshold, the complexity of the secret image restoration, the comprehensibility of the shadow image, the progressiveness, and the type of the secret image.

The mainstream principles of secret sharing include: polynomial-based (k,n) threshold secret sharing scheme, Chinese remainder theorem-based secret sharing scheme, and visual encryption scheme. The polynomial secret sharing scheme embeds the secret into a random k-1 polynomial, which can be reconstructed by Lagrangian interpolation during decryption to obtain the secret information embedded in the polynomial. Knowing the secret information s, share it as n shadow shares sc1,sc2,...,sc _n , the specific scheme is as follows:

(1) In the initialization phase, determine the value of the threshold (k, n), where k≤n. Choose a large prime p, satisfying p>n and p>s, let GF(p) be a finite field, all elements are elements of GF(p), and all operations are performed in the finite field GF(p) .

(2) In the sharing stage, in order to encrypt s into a shadow value sc _i , a polynomial of degree k-1 is randomly generated in the finite field GF(p):

f(x)=a ₀ +a ₁ x+…+a _k-1 x ^k-1

Among them, the secret s is embedded in the first coefficient of the polynomial, that is, a ₀ =s, and the remaining coefficients a ₁ , . . . , a _k-1 are randomly selected in the finite field GF(p). then calculate

sc ₁ =f(1),...,sc _k =f(k),...,sc _n =f(n)

Take (i, sc _i ) as a shadow pair, where i is an information label or a serial number label, and sc _i is a shadow pixel value. The secret sharing is completed by distributing n shadow shares to n participants respectively.

其中，

可以构建如下的线性方程组：(3) In the recovery phase, obtain any k secret pairs held by n participants

in,

The following system of linear equations can be constructed:

Because i _l (1≤l≤k) are all different, the following polynomial can be constructed from the Lagrangian interpolation formula:

Thus the secret s=f(0) can be obtained. If k-1 participants want to obtain a secret, k-1 equations can be constructed and formed into a linear system of equations, where the k coefficients of the sharing polynomial are unknowns. Because the labels i _l are different, each shadow share corresponds to a unique polynomial that satisfies the linear equation system of the formula, so it is known that k-1 shadows cannot solve the linear equation system containing k unknowns, so that no information about the secret can be obtained. , so this scheme is perfect.

In recent years, with the emergence of various security problems of social networks, social networks have become a complex position that must be considered in network attacks and defenses. The social network communication channel will cause various noises, and the network server performs various image processing (recompression, downsampling, filtering, sampling) on the secret carrier, but since the recovery of the secret image is based on mathematical operations (such as Lagrange interpolation, XOR etc.), when transmitting and storing images, the communication channel usually filters, samples, compresses the images, etc., and also generates noise, which leads to the change and loss of shared data, which further leads to the change and loss of data in the recovered secret image, It makes the existing traditional secret image sharing scheme inapplicable. The secret image recovery of the shadow image in the case of lossy and image processing is an important problem (robustness) that must be solved in practice. Robust and robust sharing of secret images is required if confidential information is to be transmitted reliably and smoothly.

Currently, there is a growing body of research on robust information hiding, which focuses on anti-JPEG compression (whether hiding in spatial or temporal domain, or in combination with syndrome trellis codin frameworks with different distortion functions). However, few studies focus on robust secret image sharing, and existing schemes generally suffer from pixel expansion and high recovery complexity. In the current research, the objects of robust secret sharing against image processing mainly include JPEG compression, salt and pepper noise, and least significant bit noise. The current research in this area has the following shortcomings: (1) There are very few researches on robust secret sharing against image processing; (2) The single image processing type is not comprehensive, such as only the least significant bit noise, JPEG compression and Salt and pepper noise has a certain robustness, and is invalid for filtering, sampling and other operations; (3) Robustness is achieved by means of steganography. This method has high computational complexity and will cause shadow image pixel expansion, which cannot be achieved. Lossless recovery. The research on robust secret sharing against image processing is the only way and foundation for applying secret image sharing to social networks. The single image processing types that must be considered against are also common image processing types such as filtering, sampling, and rotation. In addition, better secret image sharing properties such as lossless recovery should be pursued.

At present, few researches focus on robust secret image sharing, and there are even fewer researches on robust secret image sharing in adversarial image processing. The types of adversarial image processing mainly include JPEG compression, salt and pepper noise, and least significant bit noise. There is no related research on a robust secret image sharing scheme for this type of image processing, adversarial filtering. The robust (k, n) threshold SIS algorithm in the prior art cleverly embeds the error-correcting code into the shadow image through the screening mechanism in the shadow generation stage without causing shadow expansion. Finally, the principle of secret image sharing based on the Chinese remainder theorem is used to achieve no pixel expansion, low recovery complexity, and certain robustness to certain types of noise (such as least significant bit noise, JPEG compression, and salt and pepper noise). By sifting random numbers, the scheme is designed to achieve error correction capability without increasing the shadow size during the shadow generation stage. This is a robust SIS threshold scheme without pixel dilation based on the Chinese remainder theorem and error correction codes. However, this scheme is only robust to least significant bit noise, JPEG compression and salt and pepper noise, and is ineffective for operations such as filtering and sampling. Image processing operations such as filtering and sampling are commonly used operations in communication channels in practice. According to Shannon's theory, to achieve perfect security, the key must be as long as the plaintext and the same key cannot be used twice. The implementation of polynomial-based secret image sharing is simple, understandable, ideal and perfect. Based on the Chinese remainder theorem, the secret image sharing shadow image is larger than the secret image. If the secret image sharing is forced to restrict the sharing of the shadow image than the secret image, it will lead to the leakage of secret information.

SUMMARY OF THE INVENTION

In order to solve the above-mentioned technical problems, and in view of the fact that most of the current researches are robust to the least significant bit noise, JPEG compression and salt-and-pepper noise, and there is no research on the secret image sharing scheme against mean filtering, this application proposes a A secret image sharing scheme for adversarial mean filtering to achieve more good characteristics of traditional secret sharing schemes, such as lossless recovery, shadow image intelligibility, (k,n) threshold.

A first aspect of the present invention discloses a secret image sharing method for anti-average filtering.

The method includes:

Step S1, obtaining a secret image and n original carrier images as carriers for sharing the image information of the secret image, the secret image is a grayscale image, and the original carrier image is adjusted to obtain the same size as the secret image. , where n is a positive integer;

Step S2, fuse the image information of the secret image into n of the reorganized carrier images respectively to obtain n shadow images, carry out neighborhood expansion to each pixel of the shadow images, and use the original carrier image to fill an expanded neighborhood to obtain an expanded shadow image of the same size as the original carrier image;

Step S3, calculate the mean value of the neighborhood pixels of each non-expanded pixel in the expanded shadow image, and adjust each neighborhood pixel of the non-expanded pixel based on the difference between the mean value and the corresponding non-expanded pixel ;

Step S4, sending the n extended shadow images that have completed neighborhood pixel adjustment from the sender to the receiver, and the receiver recovers the secret image based on the received n extended shadow images that have completed neighborhood pixel adjustment. .

According to the method of the first aspect of the present invention, the size of the secret image is r*r, and the size of the n original carrier images is 3r*3r, where r≥2 and is a positive integer; in the step S1, for Adjusting the original carrier image to obtain the reconstructed carrier image with the same size as the secret image, specifically including: dividing the original carrier image into 3*3 image blocks, and there are r*r image blocks in total , extract the intermediate pixels of each of the image blocks, and use each of the intermediate pixels to form the reconstructed carrier image with a size of r*r.

According to the method of the first aspect of the present invention, in the step S2, fusing the image information of the secret image into the n recombined carrier images respectively to obtain the n shadow images specifically includes: for the secret image The i-th pixel in , 1≤i≤r*r, obtains the pixel {i ₁ , i ₂ ,..., i of the i-th pixel at the corresponding pixel position in the n reconstructed carrier images _n }, by fusing the i-th pixel with the pixel set {i ₁ , i ₂ , ..., i _n } to obtain {i _1' , i _2' , ..., i _n' }, as For the pixels of the n shadow images at the corresponding pixel positions, the size of the n shadow images is r*r.

According to the method of the first aspect of the present invention, in the step S2, neighborhood expansion is performed on each pixel of the shadow image, and the expanded neighborhood is filled with the original carrier image, so as to obtain a The extended shadow image with the same size as the carrier image, specifically includes: performing neighborhood expansion on each pixel in the shadow image to expand the surrounding 8 neighborhood pixels; using the original carrier image after 3*3 segmentation For the obtained r*r image blocks, the 8 neighborhood pixels of the intermediate pixels of the image blocks are filled into the 8 neighborhood pixels extended from the pixels corresponding to the intermediate pixels in the extended shadow image; The size of the extended shadow image is 3r*3r.

According to the method of the first aspect of the present invention, in the step S3, adjusting each neighborhood pixel of the non-extended pixel based on the difference between the mean value and the corresponding non-extended pixel specifically includes:

In the case where the difference value is a positive number, each neighboring pixel of each non-extended pixel in the extended shadow image subtracts the integer part of the difference value respectively, and subtracts the integer part of the difference value. The range of the pixel value of each neighborhood pixel is [0, 255], if the range of the pixel value of each neighborhood pixel after subtracting the integer part of the difference value is not within [0, 255], the non- The pixel value of the extended pixel is assigned to its neighbor pixels;

After the integer part of the difference value is respectively subtracted from each neighboring pixel of the non-extended pixel, a numerical value m ₁ obtained by multiplying the decimal part of the difference value by 8 is determined, and the integer part of the difference value is subtracted from M _{1 neighborhood pixels are arbitrarily selected from each neighborhood pixel of the subsequent non-extended pixel, and the pixel value of each neighborhood pixel in the m 1 neighborhood} pixels is reduced by 1, so that the m after the reduction of 1 is reduced by 1. The range of the pixel value of ₁ neighborhood pixel is [0, 255], if the range of the pixel value of the m ₁ neighborhood pixel after subtracting 1 is not within [0, 255], then assign the pixel value of the non-extended pixel to Given its neighborhood pixels, m ₁ is a positive integer.

According to the method of the first aspect of the present invention, in the step S3, adjusting each neighborhood pixel of the non-extended pixel based on the difference between the mean value and the corresponding non-extended pixel specifically includes:

In the case where the difference value is negative, add the absolute value of the integer part of the difference value to each neighboring pixel of each non-extended pixel in the extended shadow image, and add the integer value of the difference value The range of the pixel value of each neighborhood pixel after the absolute value of the part is [0, 255], if the range of the pixel value of each neighborhood pixel after adding the absolute value of the integer part of the difference value is not in [ 0,255], then assign the pixel value of the non-expanded pixel to its neighborhood pixel;

After the absolute value of the integer part of the difference value is added to each neighboring pixel of the non-extended pixel, the numerical value m ₂ obtained by multiplying the decimal part of the difference value by 8 is determined, and the difference value is added from the M ₂ neighborhood pixels are arbitrarily selected from each neighborhood pixel of the non _- extended pixel after the absolute value of the integer part of The range of the pixel values of the m ₂ neighborhood pixels after adding 1 is [0, 255], if the range of the pixel values of the m ₂ neighborhood pixels after adding 1 is not within [0, 255], the non- The pixel value of the extended pixel is assigned to its neighbor pixels, and m ₂ is a positive integer.

According to the method of the first aspect of the present invention, the receiver performs mean filtering on the received n extended shadow images with pixel adjustment in the neighborhood, and the pixel value of each pixel in the obtained result image is the same as that of the shadow image. The pixel values of each pixel are consistent, thereby realizing the sharing of the secret image that can resist mean filtering.

A second aspect of the present invention discloses a secret image sharing system for anti-average filtering.

The system includes:

The first processing unit is configured to acquire a secret image and n original carrier images serving as carriers for sharing image information of the secret image, the secret images are grayscale images, and the original carrier image is adjusted to obtain the same value as the original carrier image. The reconstructed carrier images with the same size of the secret image, and n is a positive integer;

The second processing unit is configured to fuse the image information of the secret image into the n reconstituted carrier images respectively to obtain n shadow images, perform neighborhood expansion on each pixel of the shadow images, and use the using the original carrier image to fill the extended neighborhood to obtain an extended shadow image of the same size as the original carrier image;

a third processing unit configured to calculate a mean value of neighboring pixels of each non-expanded pixel in the expanded shadow image, and adjust the non-expanded pixel based on the difference between the mean value and the corresponding non-expanded pixel each neighborhood pixel of the pixel;

The fourth processing unit is configured to send the n extended shadow images that have completed the neighborhood pixel adjustment from the sender to the receiver, and the receiver is based on the received n extended shadow images that have completed the neighborhood pixel adjustment. The secret image is recovered.

According to the system of the second aspect of the present invention, the size of the secret image is r*r, the size of the n original carrier images is 3r*3r, r≥2 and is a positive integer; the first processing unit is specifically configured by The configuration is to adjust the original carrier image to obtain the reconstituted carrier image with the same size as the secret image, which specifically includes: dividing the original carrier image into 3*3 image blocks, with a total of r*r pieces For the image block, the intermediate pixels of each of the image blocks are extracted, and each of the intermediate pixels is used to form the reconstructed carrier image with a size of r*r.

According to the system of the second aspect of the present invention, the second processing unit is specifically configured to fuse the image information of the secret image into the n reconstituted carrier images respectively to obtain the n shadow images, which specifically includes: for For the ith pixel in the secret image, 1≤i≤r*r, obtain the pixel {i ₁ , i ₂ , . .., i _n }, by fusing the i-th pixel with the pixel set {i ₁ , i ₂ , ..., i _n } to obtain {i _1' , i _2' , ..., i _{n '} }, as the pixels of the n shadow images at the corresponding pixel positions, the size of the n shadow images is r*r.

According to the system of the second aspect of the present invention, the second processing unit is specifically configured to perform neighborhood expansion on each pixel of the shadow image, and fill the expanded neighborhood with the original carrier image to obtain The expanded shadow image with the same size as the original carrier image specifically includes: performing neighborhood expansion on each pixel in the shadow image to expand the surrounding 8 neighborhood pixels; using the original carrier image after 3 *3 For the r*r image blocks obtained after division, the 8 neighboring pixels of the middle pixel of the image block are filled to the 8 pixels extended from the pixels corresponding to the middle pixel in the extended shadow image Neighborhood pixels; the size of the extended shadow image is 3r*3r.

According to the system of the second aspect of the present invention, the third processing unit is specifically configured to adjust each neighborhood pixel of the non-extended pixel based on the difference between the mean value and the corresponding non-extended pixel specifically includes:

In the case where the difference value is a positive number, each neighboring pixel of each non-extended pixel in the extended shadow image subtracts the integer part of the difference value respectively, and subtracts the integer part of the difference value. The range of the pixel value of each neighborhood pixel is [0, 255], if the range of the pixel value of each neighborhood pixel after subtracting the integer part of the difference value is not within [0, 255], the non- The pixel value of the extended pixel is assigned to its neighbor pixels;

After the integer part of the difference value is respectively subtracted from each neighboring pixel of the non-extended pixel, a numerical value m ₁ obtained by multiplying the decimal part of the difference value by 8 is determined, and the integer part of the difference value is subtracted from M _{1 neighborhood pixels are arbitrarily selected from each neighborhood pixel of the subsequent non-extended pixel, and the pixel value of each neighborhood pixel in the m 1 neighborhood} pixels is reduced by 1, so that the m after the reduction of 1 is reduced by 1. The range of the pixel value of ₁ neighborhood pixel is [0, 255], if the range of the pixel value of the m ₁ neighborhood pixel after subtracting 1 is not within [0, 255], then assign the pixel value of the non-extended pixel to Given its neighborhood pixels, m ₁ is a positive integer.

According to the system of the second aspect of the present invention, the third processing unit is specifically configured to adjust each neighborhood pixel of the non-extended pixel based on the difference between the mean value and the corresponding non-extended pixel specifically includes:

In the case where the difference value is negative, add the absolute value of the integer part of the difference value to each neighboring pixel of each non-extended pixel in the extended shadow image, and add the integer value of the difference value The range of the pixel value of each neighborhood pixel after the absolute value of the part is [0, 255], if the range of the pixel value of each neighborhood pixel after adding the absolute value of the integer part of the difference value is not in [ 0,255], then assign the pixel value of the non-expanded pixel to its neighborhood pixel;

After the absolute value of the integer part of the difference value is added to each neighboring pixel of the non-extended pixel, the numerical value m ₂ obtained by multiplying the decimal part of the difference value by 8 is determined, and the difference value is added from the M ₂ neighborhood pixels are arbitrarily selected from each neighborhood pixel of the non _- extended pixel after the absolute value of the integer part of The range of the pixel values of the m ₂ neighborhood pixels after adding 1 is [0, 255], if the range of the pixel values of the m ₂ neighborhood pixels after adding 1 is not within [0, 255], the non- The pixel value of the extended pixel is assigned to its neighbor pixels, and m ₂ is a positive integer.

According to the system according to the second aspect of the present invention, the receiver performs mean filtering on the received n extended shadow images that have completed neighborhood pixel adjustment, and the pixel value of each pixel in the obtained result image is the same as that of the shadow image. The pixel values of each pixel are consistent, thereby realizing the sharing of the secret image that can resist mean filtering.

A third aspect of the present invention discloses an electronic device. The electronic device includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, the method for anti-mean filtering described in any one of the first aspects of the present disclosure is implemented. Steps in the Secret Image Sharing Method.

A fourth aspect of the present invention discloses a computer-readable storage medium. The computer-readable storage medium stores a computer program, and when the computer program is executed by the processor, implements the method for sharing a secret image for anti-mean filtering according to any one of the first aspects of the present disclosure. step.

The technical solution provided by the present invention generates n shadow images SC' _i given a hidden secret image S and n original carrier images cover _i , so that k or more SC' _i are filtered by the mean value It will still be restored after processing. The scheme aims to generate shadow images SC' _i after mean filtering and further decimation exactly equal to the results obtained after directly inputting the carrier images cover' _i and S to the secret sharing scheme. The scheme achieves good secret sharing scheme characteristics, such as lossless recovery, shadow image comprehension, (k,n) threshold, and can be applied in the fields of steganalysis and covert communication for social networks.

Description of drawings

In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the accompanying drawings that need to be used in the description of the specific embodiments or the prior art. Obviously, the accompanying drawings in the following description These are some embodiments of the present invention, and for those of ordinary skill in the art, other drawings can also be obtained from these drawings without any creative effort.

1 is a flowchart of a secret image sharing method for anti-average filtering according to an embodiment of the present invention;

2 is a framework diagram of a secret image sharing scheme against mean filtering according to an embodiment of the present invention;

FIG. 3 (groups (a)-(q)) is the experimental result of the shadow image resisting mean value filtering in the generation stage according to an embodiment of the present invention;

FIG. 4 (groups (a)-(j)) is an experimental result of a shadow image against mean filtering in the restoration stage according to an embodiment of the present invention;

5 is a structural diagram of a secret image sharing system for anti-average filtering according to an embodiment of the present invention;

FIG. 6 is a structural diagram of an electronic device according to an embodiment of the present invention.

Detailed ways

In order to make the purposes, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments It is only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

A first aspect of the present invention discloses a secret image sharing method for anti-average filtering. FIG. 1 is a flowchart of a secret image sharing method for anti-average filtering according to an embodiment of the present invention; as shown in FIG. 1 , the method includes:

Step S1, obtaining a secret image and n original carrier images as carriers for sharing the image information of the secret image, the secret image is a grayscale image, and the original carrier image is adjusted to obtain the same size as the secret image. , where n is a positive integer;

Step S2, fuse the image information of the secret image into n of the reorganized carrier images respectively to obtain n shadow images, carry out neighborhood expansion to each pixel of the shadow images, and use the original carrier image to fill an expanded neighborhood to obtain an expanded shadow image of the same size as the original carrier image;

Step S3, calculate the mean value of the neighborhood pixels of each non-expanded pixel in the expanded shadow image, and adjust each neighborhood pixel of the non-expanded pixel based on the difference between the mean value and the corresponding non-expanded pixel ;

Step S4, sending the n extended shadow images that have completed neighborhood pixel adjustment from the sender to the receiver, and the receiver recovers the secret image based on the received n extended shadow images that have completed neighborhood pixel adjustment. .

FIG. 2 is a frame diagram of a secret image sharing scheme against mean filtering according to an embodiment of the present invention; the method of the first aspect of the present invention will be described in detail below with reference to FIG. 2 .

In step S1, a secret image and n original carrier images serving as carriers for sharing image information of the secret image are obtained, the secret images are grayscale images, and the original carrier image is adjusted to obtain the same size as the secret image The same reconstituted vector image, n is a positive integer.

In some embodiments, the size of the secret image is r*r, the size of the n original carrier images is 3r*3r, r≥2 and is a positive integer; in the step S1, the original The carrier image is adjusted to obtain the reconstructed carrier image with the same size as the secret image, which specifically includes: dividing the original carrier image into 3*3 image blocks, there are r*r image blocks in total, and extracting each Each of the intermediate pixels of the image block is used to form the reconstructed carrier image with a size of r*r.

Specifically (as shown in Figure 2), after obtaining the original carrier image (with a size of 3r*3r), adjust the size of the original carrier image, divide it into 3*3 image blocks by matrix division, and extract the image size of each block. Intermediate elements and recombined (recombined vector image, size r*r). Obtain an image to be shared, and obtain a secret image (size r*r) by performing grayscale processing on the image to be shared.

In step S2, the image information of the secret image is respectively fused into n of the reconstructed carrier images to obtain n shadow images, and each pixel of the shadow images is expanded by neighborhood, and the original carrier image is used to obtain n shadow images. The expanded neighborhood is filled to obtain an expanded shadow image of the same size as the original carrier image.

In some embodiments, in the step S2, respectively fusing the image information of the secret image into the n reconstructed carrier images to obtain the n shadow images specifically includes: for the first image in the secret image i pixels, 1≤i≤r*r, obtain the pixel {i ₁ , _{i 2} , . By fusing the i-th pixel with the pixel set _{{ i 1} , _{i 2} , _. The pixels of the shadow images at the corresponding pixel positions, and the size of the n shadow images is r*r.

Specifically (as shown in FIG. 2 ), a polynomial-based secret image sharing algorithm is used to store the image information of the secret image into the n recombined carrier images respectively, so as to obtain n interpolated carrier images. The interpolation method may be Lagrangian interpolation or other interpolation methods commonly used in the art. For example, for the first pixel r ₁ of r*r pixels in the secret image, decompose it into n sub-information r _1-1 , r _1-2 , r _1-3 , ..., r _{1- (n-1)} , r _1-n ; insert n pieces of sub-information into the n pieces of the recombined carrier images respectively; for example, adopt a polynomial-based secret sharing method. Ditto for other pixels r ₂ , r ₃ , . . . , r _r*r-1 , r _r*r .

In some embodiments, in the step S2, neighborhood expansion is performed on each pixel of the shadow image, and the expanded neighborhood is filled with the original carrier image, so as to obtain the same size as the original carrier image. The same extended shadow image specifically includes: performing neighborhood expansion on each pixel in the shadow image to expand the surrounding 8 neighborhood pixels; using the r obtained by dividing the original carrier image by 3*3 *r of the image blocks, filling the 8 neighboring pixels of the intermediate pixel of the image block to the 8 neighboring pixels extended from the pixels corresponding to the intermediate pixels in the extended shadow image; the extended shadow image The size of the shadow image is 3r*3r.

Specifically (as shown in Figure 2), in the process of generating an intelligible shadow image that can resist mean filtering, the interpolated carrier image is first subjected to neighborhood expansion, and each pixel is subjected to 8 neighborhood expansion, and the expanded pixel bits Fill it with the 8-neighborhood of the original carrier image.

In step S3, calculate the mean value of the neighborhood pixels of each non-expanded pixel in the expanded shadow image, and adjust each neighborhood of the non-expanded pixel based on the difference between the mean value and the corresponding non-expanded pixel pixel.

Specifically (as shown in FIG. 2 ), calculate each pixel value (each pixel in the interpolated carrier image, that is, the corresponding pixel in the extended carrier image) in the corresponding neighborhood pixel of the extended carrier image. Mean, which further computes the difference between the mean and the middle pixel surrounded by 8 neighbor pixels.

In some embodiments, in the step S3, adjusting each neighborhood pixel of the non-extended pixel based on the difference between the mean value and the corresponding non-extended pixel specifically includes:

In the case where the difference value is a positive number, each neighboring pixel of each non-extended pixel in the extended shadow image subtracts the integer part of the difference value respectively, and subtracts the integer part of the difference value. The range of the pixel value of each neighborhood pixel is [0, 255], if the range of the pixel value of each neighborhood pixel after subtracting the integer part of the difference value is not within [0, 255], the non- The pixel value of the extended pixel is assigned to its neighbor pixels;

After the integer part of the difference value is respectively subtracted from each neighboring pixel of the non-extended pixel, a numerical value m ₁ obtained by multiplying the decimal part of the difference value by 8 is determined, and the integer part of the difference value is subtracted from M _{1 neighborhood pixels are arbitrarily selected from each neighborhood pixel of the subsequent non-extended pixel, and the pixel value of each neighborhood pixel in the m 1 neighborhood} pixels is reduced by 1, so that the m after the reduction of 1 is reduced by 1. The range of the pixel value of ₁ neighborhood pixel is [0, 255], if the range of the pixel value of the m ₁ neighborhood pixel after subtracting 1 is not within [0, 255], then assign the pixel value of the non-extended pixel to Given its neighborhood pixels, m ₁ is a positive integer.

Specifically (as shown in Figure 2), when the difference value is greater than 0, it is determined that after subtracting the integer part int(differ) of the difference value from the neighbor pixels, the number of neighbor points whose pixel value falls within [0,255] , if it is 8, subtract the integer part int(differ) of the difference from the neighbor pixels, otherwise, assign the pixel value of the middle pixel surrounded by the 8 neighbor pixels to the 8 neighbor pixels. Then, it is determined whether the pixel value of the neighbor pixel is still in [0, 255] after further subtracting the fractional part of the difference of 8 (times) difference-int(differ)*8, and if so, perform the subtraction operation (note that, Subtraction can be performed on any number of (1-8) neighborhood pixels, as long as the sum of the subtraction is differ-int(differ)*8, and the above range conditions are met, but a better solution is to determine the decimal Part of the value after *8, this value is an integer value, such as m ₁ , and it is evenly distributed to m ₁ neighborhood pixels for adjustment. This adjustment method is smooth and uniform, and can better protect image information), if not, assign the pixel value of the middle pixel surrounded by the 8 neighboring pixels to the 8 neighboring pixels. Note that the above conditional judgment process aims to ensure that the adjusted pixel values still fall within the range of [0, 255]. The above adjustment scheme aims to make the difference between the average value of the intermediate pixel and the neighboring pixel zero, and the adjustment method / The method of conditional judgment is not limited to the above one. For example, Figure 2 also provides a way to judge whether there are more than differ-int(differ)*8 pixels in the neighborhood pixels whose pixel value is greater than or equal to 1, if so, for the randomly selected differ- int(differ)*8 domain pixels perform a subtraction operation, and the subtracted value is differ-int(differ).

In some embodiments, in the step S3, adjusting each neighborhood pixel of the non-extended pixel based on the difference between the mean value and the corresponding non-extended pixel specifically includes:

In the case where the difference value is negative, add the absolute value of the integer part of the difference value to each neighboring pixel of each non-extended pixel in the extended shadow image, and add the integer value of the difference value The range of the pixel value of each neighborhood pixel after the absolute value of the part is [0, 255], if the range of the pixel value of each neighborhood pixel after adding the absolute value of the integer part of the difference value is not in [ 0,255], then assign the pixel value of the non-expanded pixel to its neighborhood pixel;

After the absolute value of the integer part of the difference value is added to each neighboring pixel of the non-extended pixel, the numerical value m ₂ obtained by multiplying the decimal part of the difference value by 8 is determined, and the difference value is added from the M ₂ neighborhood pixels are arbitrarily selected from each neighborhood pixel of the non _- extended pixel after the absolute value of the integer part of The range of the pixel values of the m ₂ neighborhood pixels after adding 1 is [0, 255], if the range of the pixel values of the m ₂ neighborhood pixels after adding 1 is not within [0, 255], the non- The pixel value of the extended pixel is assigned to its neighbor pixels, and m ₂ is a positive integer.

Specifically (as shown in Figure 2), when the difference value is less than 0, after determining the absolute value int(abs(differ)) of the integer part of the difference value added to the adjacent pixels, its pixel value falls within the range of [0,255] The number of neighborhood points, if it is 8, execute the neighborhood pixel plus the absolute value of the integer part of the difference int(abs(differ)), otherwise, will be surrounded by the 8 neighborhood pixels. Pixel values are assigned to the 8 neighbor pixels. Then, judge whether the pixel value of the neighbor pixel is still in [0,255 after adding the absolute value of the fractional part of the difference of 8 (times) [abs(differ)-int(abs(differ))]*8. ], if so, perform the addition operation (note that the addition can be performed on any number of (1-8) neighborhood pixels, as long as the sum of the additions is [abs(differ)-int(abs(differ))]* 8, and the above range conditions are satisfied, but a better solution is to determine the value after the fractional part * 8, which is an integer value, such as m ₂ , and distribute it evenly to m ₂ neighborhood pixels The adjustment method is smooth and uniform, which can better protect the image information), if not, assign the pixel value of the middle pixel surrounded by the 8 neighbor pixels to the 8 neighbor pixels. domain pixels. Note that the above conditional judgment process aims to ensure that the adjusted pixel values still fall within the range of [0, 255]. The above adjustment scheme aims to make the difference between the average value of the intermediate pixel and the neighboring pixel zero, and the adjustment method / The method of conditional judgment is not limited to the above one. For example, Figure 2 also provides a way to determine whether there are more than [abs(differ)-int(abs(differ))]*8 pixels in the neighborhood pixels whose pixel value is less than or equal to 255, if , then perform the addition operation on the randomly selected [abs(differ)-int(abs(differ))]*8 domain pixels, and the added value is abs(differ)-int(abs(differ)).

In step S4, the n extended shadow images whose neighborhood pixels have been adjusted are sent from the sender to the receiver, and the receiver recovers the secret based on the received n extended shadow images whose neighborhood pixels have been adjusted. image.

Specifically (as shown in FIG. 2 ), the receiver restores the secret image based on the n shadow images, that is, performs subsequent mean filtering, image extraction, and other operations on the shadow image to restore the secret image.

In some embodiments, the receiver performs mean filtering on the received n extended shadow images that have completed neighborhood pixel adjustment, and obtains the pixel value of each pixel in the resulting image and the pixel value of each pixel in the shadow image. The pixel values are consistent, thereby realizing the sharing of the secret image that can resist mean filtering.

In another embodiment, the above method can be implemented through the following algorithm flow:

Algorithm: A robust secret image sharing scheme against mean filtering based on shadow image comprehensibility of (k, n) threshold polynomials. Inputs: threshold k; number of shadows n; ID serial number list id; a grayscale secret image of size r*r; n original grayscale carrier images of size 3r×3r cover ₁ ,cover ₂ ,…,cover _n . Output: n grayscale shadow images SC' ₁ , SC' ₂ , ..., SC' _n that can be anti-average filtered.

(1) For each original carrier image, it is divided into 3*3 blocks. The intermediate elements of each block are extracted and reassembled into an image cover' _i of size r×r.

(2) Input the grayscale secret image S and cover' _i into a polynomial-based secret sharing algorithm that can be understood by the shadow image, and output the results SC ₁ , SC ₂ ,...,SC _n .

(3) For each pixel of SC _i , extend the pixels of 8 neighborhoods. The final image matrix is denoted as m. Divide m into r 3x3 blocks, each represented as square[p][q], where p=0,2,...,r-1,q=0,2,...,r-1.

(4) For each square[p][q], fill the 8-neighborhood of the extension with the center pixel corresponding to the original carrier image.

(5) For each block square[p][q], calculate the mean of 8 neighborhoods. Calculate the difference between the mean and SC _i [p][q]. If difference>0, go to step 6, otherwise go to step 7.

(6) For the 8-neighborhood of the current block, calculate each pixel minus the integer part of the difference. Calculate the number of the value falling between 0 and 255. If it is 8, subtract int(different) for each pixel in the neighborhood of 8, otherwise skip to step 8. It is judged whether there is a value greater than or equal to (differ-int(differ))×8 pixels in the 8-neighborhood pixels greater than or equal to 1. If so, randomly select (differ-int(differ))×8 pixels greater than or equal to 1 minus 1. Otherwise skip to step 8.

(7) If differ=0, go to step 8. For the 8-neighborhood of the current block, compute each pixel plus the integer part of the absolute value of the difference. Calculate the number of the value falling between 0 and 255. If it is 8, add int(abs(differ)) to each pixel in the neighborhood of 8, otherwise skip to step 8. Determine whether there are values greater than or equal to (abs(differ)-int(differ))×8 pixels in the 8-neighborhood pixels and less than or equal to 254. If so, randomly select (differ-int(differ))×8 pixels less than or equal to 245 plus 1. Otherwise skip to step 8.

(8) Set square[p][q][s][t]=SC _i [p][q], where p=0,2,...,r-1, q=0,2,...,r- 1, s=0,1,2, t=0,1,2.

(9) Output n anti-average filtered shadow images SC' ₁ , SC' ₂ , . . . , SC' _n .

In yet another embodiment, the mean-resistant secret image sharing method can be divided into two stages: a mean-resistant intelligible shadow image generation stage and a secret image restoration stage.

In the understandable shadow image generation stage of anti-canonical image processing, the original carrier image is first resized to be consistent with the secret image. Generally speaking, each original carrier image will be divided into blocks of equal size (here, divided into 3×3 blocks), and the pixels at specific positions (here, the central pixels are extracted) are extracted and recombined into a new carrier image cover' _i . The principle of adjustment is to ensure that the adjusted image looks similar to the original image and retains the full image meaning, but only changes the size of the original carrier image. It is worth noting that the size of the original carrier image depends on the type of image processing and the secret image. For example, if filtering against the mean, then the size of the original carrier image should be 9 times the size of the secret image. The binary carrier image in the proposed scheme is treated as the highest bit of the gray-scale carrier image.

The specific algorithm is as follows:

Algorithm 2: A (k, n) threshold secret image sharing scheme based on polynomial shadow image comprehension. Inputs: threshold k; number n of shadows; ID list id; a grayscale secret image S; n binary carrier images C ₁ , C ₂ ,...,C _n . Output: n grayscale shadow images SC ₁ , SC ₂ , . . . , SC _n .

Convert the gray value sequence [SC ₁ (i,j),…,SC _n (i,j)] into a binary sequence [BSC ₁ ,…,BSC _n ] with a threshold of 125

To ensure lossless recovery, set p=257. The cover' _i and S secret images are input into the secret image sharing scheme comprehensible based on polynomial shadow images, and finally SC _i is obtained. Expand each pixel of SC _i (here, 8-neighborhood is expanded for each pixel). Use the pixels at the corresponding positions of the original carrier image to assign values to the pixels at the corresponding positions of the expanded shadow image. For each pixel in each block, its value is slightly adjusted so that the fine-tuned image is exactly the same as the original shadow image after image processing and further image decimation. It is guaranteed that the secret image can be successfully recovered in the end.

In the recovery stage, two steps are included: image extraction and Lagrangian interpolation. Different from the traditional polynomial-based SIS, image extraction is first required here. According to the specific strategy against image processing designed above, pixels at important positions will be extracted and reorganized into SC _i ".

Optionally and additionally, Fig. 3 (panel) shows the experimental results of the shadow image generation phase of the robust SIS against mean filtering with (k, n) threshold shadow image comprehensibility, where k = 3, n = 4 , p=257. Figure 3(a) shows the input grayscale secret image with size 128×128. Figures 3(b)-(e) are the original understandable grayscale carrier images of the input size cover ₁ , cover ₂ , cover ₃ , cover ₄ . The resized carrier images cover ₁ ', cover ₂ ', cover ₃ ', cover ₄ are shown in Fig. 3(f)-(i), whose size is equal to that of the secret image S. Figure ₃ (g)-(m) show the intelligible shadow images SC1, _SC2 , SC3 and _SC4 obtained by inputting the resized shadow image and secret image to the polynomial _- based SIS algorithm. Here, the polynomial-based SIS algorithm ensures that the first two bits of each pixel of the resized carrier image are equal to the first two bits of each pixel of the corresponding shadow image. Finally, after three steps of pixel expansion, pixel assignment, and pixel fine-tuning, a shadow image SC' ₁ , SC' ₂ , SC' ₃ , SC' ₄ that can resist these three image processing is generated. In Figure 3(n)-(q ) are displayed.

是将SC”₁，SC”₂，SC”₃，SC”₄分成3×3的块并抽取每一块的中心像素重新组成的新图像。图4(i)展示了通过拉格朗日插值从

两个个恢复的秘密图像。图4(j)展示了通过拉格朗日插值从

中三个或四个恢复的秘密图像。Figure 4 shows the experimental results of the shadow image restoration stage against mean filtering for a robust SIS understandable by (k,n) thresholded shadow images, where k=3, n=4, p=257. Figure 4(a)-(d) SC" ₁ , SC" ₂ , SC" ₃ , SC" ₄ are represented as SC' ₁ , SC' ₂ , SC' ₃ , SC' ₄ through mean filtering with a kernel of 3×3 smoother results. Figure 4(e)-(h)

It is a new image formed by dividing SC" ₁ , SC" ₂ , SC" ₃ , SC" ₄ into 3×3 blocks and extracting the center pixel of each block. Figure 4(i) shows that by Lagrangian interpolation from

Two recovered secret images. Figure 4(j) shows that by Lagrangian interpolation from

Three or four recovered secret images.

A second aspect of the present invention discloses a secret image sharing system for anti-average filtering. FIG. 5 is a structural diagram of a secret image sharing system for anti-average filtering according to an embodiment of the present invention; as shown in FIG. 5 , the system 500 includes:

The first processing unit 501 is configured to acquire a secret image and n original carrier images serving as carriers for sharing image information of the secret image, the secret images are grayscale images, and the original carrier images are obtained after adjustment. The reconstructed carrier image with the same size as the secret image, and n is a positive integer;

The second processing unit 502 is configured to fuse the image information of the secret image into the n reconstituted carrier images respectively to obtain n shadow images, perform neighborhood expansion on each pixel of the shadow images, and use the original carrier image to fill the expanded neighborhood to obtain an extended shadow image of the same size as the original carrier image;

The third processing unit 503 is configured to calculate the average value of the neighborhood pixels of each non-extended pixel in the extended shadow image, and adjust the non-extended pixel based on the difference between the average value and the corresponding non-extended pixel Expand each neighborhood pixel of the pixel;

The fourth processing unit 504 is configured to send the n extended shadow images that have completed neighborhood pixel adjustment from the sender to the receiver, where the receiver is based on the received n extended shadow images that have completed neighborhood pixel adjustment. The image recovers the secret image.

According to the system of the second aspect of the present invention, the size of the secret image is r*r, the size of the n original carrier images is 3r*3r, r≥2 and is a positive integer; the first processing unit 501 specifically is configured to adjust the original carrier image to obtain the reconstituted carrier image with the same size as the secret image, specifically including: dividing the original carrier image into 3*3 image blocks, with a total of r*r Each of the image blocks is extracted, and the intermediate pixels of each of the image blocks are extracted, and each of the intermediate pixels is used to form the reconstructed carrier image with a size of r*r.

According to the system of the second aspect of the present invention, the second processing unit 502 is specifically configured to fuse the image information of the secret image into the n reconstituted carrier images respectively to obtain the n shadow images, which specifically includes: For the ith pixel in the secret image, 1≤i≤r*r, obtain the pixel {i 1 , i 2 , the pixel position {i ₁ , i ₂ , of the ith pixel at the corresponding pixel position in the n reconstituted carrier images, ..., i _n }, by fusing the i-th pixel with the pixel set {i ₁ , i ₂ , ..., i _n } to obtain {i _1' , i _2' , ..., i _n' }, as the pixels of the n shadow images at the corresponding pixel positions, the size of the n shadow images is r*r.

According to the system of the second aspect of the present invention, the second processing unit 502 is specifically configured to perform neighborhood expansion on each pixel of the shadow image, and use the original carrier image to fill the expanded neighborhood to Obtaining an expanded shadow image with the same size as the original carrier image, specifically comprising: performing neighborhood expansion on each pixel in the shadow image to expand 8 surrounding pixels; The r*r image blocks obtained after 3*3 division are filled with 8 neighboring pixels of the middle pixel of the image block to the 8 pixels extended from the pixels corresponding to the middle pixel in the extended shadow image. neighborhood pixels; the size of the extended shadow image is 3r*3r.

According to the system of the second aspect of the present invention, the third processing unit 503 is specifically configured to adjust each neighborhood pixel of the non-extended pixel based on the difference between the mean value and the corresponding non-extended pixel, specifically including: :

In the case where the difference value is a positive number, each neighboring pixel of each non-extended pixel in the extended shadow image subtracts the integer part of the difference value respectively, and subtracts the integer part of the difference value. The range of the pixel value of each neighborhood pixel is [0, 255], if the range of the pixel value of each neighborhood pixel after subtracting the integer part of the difference value is not within [0, 255], the non- The pixel value of the extended pixel is assigned to its neighbor pixels;

After the integer part of the difference value is respectively subtracted from each neighboring pixel of the non-extended pixel, a numerical value m ₁ obtained by multiplying the decimal part of the difference value by 8 is determined, and the integer part of the difference value is subtracted from M _{1 neighborhood pixels are arbitrarily selected from each neighborhood pixel of the subsequent non-extended pixel, and the pixel value of each neighborhood pixel in the m 1 neighborhood} pixels is reduced by 1, so that the m after the reduction of 1 is reduced by 1. The range of the pixel value of ₁ neighborhood pixel is [0, 255], if the range of the pixel value of the m ₁ neighborhood pixel after subtracting 1 is not within [0, 255], then assign the pixel value of the non-extended pixel to Given its neighborhood pixels, m ₁ is a positive integer.

According to the system of the second aspect of the present invention, the third processing unit 503 is specifically configured to adjust each neighborhood pixel of the non-extended pixel based on the difference between the mean value and the corresponding non-extended pixel, specifically including: :

In the case where the difference value is negative, add the absolute value of the integer part of the difference value to each neighboring pixel of each non-extended pixel in the extended shadow image, and add the integer value of the difference value The range of the pixel value of each neighborhood pixel after the absolute value of the part is [0, 255], if the range of the pixel value of each neighborhood pixel after adding the absolute value of the integer part of the difference value is not in [ 0,255], then assign the pixel value of the non-expanded pixel to its neighborhood pixel;

After the absolute value of the integer part of the difference value is added to each neighboring pixel of the non-extended pixel, the numerical value m ₂ obtained by multiplying the decimal part of the difference value by 8 is determined, and the difference value is added from the M ₂ neighborhood pixels are arbitrarily selected from each neighborhood pixel of the non _- extended pixel after the absolute value of the integer part of The range of the pixel values of the m ₂ neighborhood pixels after adding 1 is [0, 255], if the range of the pixel values of the m ₂ neighborhood pixels after adding 1 is not within [0, 255], the non- The pixel value of the extended pixel is assigned to its neighbor pixels, and m ₂ is a positive integer.

According to the system according to the second aspect of the present invention, the receiver performs mean filtering on the received n extended shadow images that have completed neighborhood pixel adjustment, and the pixel value of each pixel in the obtained result image is the same as that of the shadow image. The pixel values of each pixel are consistent, thereby realizing the sharing of the secret image that can resist mean filtering.

A third aspect of the present invention discloses an electronic device. The electronic device includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, the method for anti-mean filtering described in any one of the first aspects of the present disclosure is implemented. Steps in the Secret Image Sharing Method.

FIG. 6 is a structural diagram of an electronic device according to an embodiment of the present invention. As shown in FIG. 6 , the electronic device includes a processor, a memory, a communication interface, a display screen, and an input device connected through a system bus. Among them, the processor of the electronic device is used to provide computing and control capabilities. The memory of the electronic device includes a non-volatile storage medium and an internal memory. The nonvolatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the execution of the operating system and computer programs in the non-volatile storage medium. The communication interface of the electronic device is used for wired or wireless communication with an external terminal, and the wireless communication can be realized by WIFI, operator network, near field communication (NFC) or other technologies. The display screen of the electronic device may be a liquid crystal display screen or an electronic ink display screen, and the input device of the electronic device may be a touch layer covered on the display screen, or a button, a trackball or a touchpad set on the shell of the electronic device , or an external keyboard, trackpad, or mouse.

Those skilled in the art can understand that the structure shown in FIG. 6 is only a structural diagram of a part related to the technical solution of the present disclosure, and does not constitute a limitation on the electronic equipment to which the solution of the present application is applied. A device may include more or fewer components than shown in the figures, or combine certain components, or have a different arrangement of components.

A fourth aspect of the present invention discloses a computer-readable storage medium. The computer-readable storage medium stores a computer program, and when the computer program is executed by the processor, implements the method for sharing a secret image for anti-mean filtering according to any one of the first aspects of the present disclosure. step.

The technical solution provided by the present invention generates n shadow images SC' _i given a hidden secret image S and n original carrier images cover _i , so that k or more SC' _i are filtered by the mean value It will still be restored after processing. The scheme aims to generate shadow images SC' _i after mean filtering and further decimation exactly equal to the results obtained after directly inputting the carrier images cover' _i and S to the secret sharing scheme. The scheme achieves good secret sharing scheme characteristics, such as lossless recovery, shadow image comprehension, (k,n) threshold, and can be applied in the fields of steganalysis and covert communication for social networks.

Please note that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, all possible combinations of the technical features in the above embodiments are not described. However, as long as there is no contradiction in the combination of these technical features , should be considered to be within the scope of this specification. The above-mentioned embodiments only represent several embodiments of the present application, and the descriptions thereof are relatively specific and detailed, but should not be construed as a limitation on the scope of the invention patent. It should be pointed out that for those skilled in the art, without departing from the concept of the present application, several modifications and improvements can be made, which all belong to the protection scope of the present application. Therefore, the scope of protection of the patent of the present application shall be subject to the appended claims.

Claims (10)

1. A secret image sharing method for antagonizing mean filtering, wherein the method comprises: Step S1, obtaining a secret image and n original carrier images as carriers for sharing the image information of the secret image, the secret image is a grayscale image, and the original carrier image is adjusted to obtain the same size as the secret image. , where n is a positive integer; Step S2, fuse the image information of the secret image into n of the reorganized carrier images respectively to obtain n shadow images, carry out neighborhood expansion to each pixel of the shadow images, and use the original carrier image to fill an expanded neighborhood to obtain an expanded shadow image of the same size as the original carrier image; Step S3, calculate the mean value of the neighborhood pixels of each non-expanded pixel in the expanded shadow image, and adjust each neighborhood pixel of the non-expanded pixel based on the difference between the mean value and the corresponding non-expanded pixel ; Step S4, sending the n extended shadow images that have completed neighborhood pixel adjustment from the sender to the receiver, and the receiver recovers the secret image based on the received n extended shadow images that have completed neighborhood pixel adjustment. . 2. A kind of secret image sharing method for anti-mean filtering according to claim 1, is characterized in that, wherein: The size of the secret image is r*r, the size of the n original carrier images is 3r*3r, r≥2 and a positive integer; In the step S1, the original carrier image is adjusted to obtain the reconstructed carrier image with the same size as the secret image, which specifically includes: dividing the original carrier image into 3*3 image blocks, with a total of The r*r image blocks are extracted, and the intermediate pixels of each of the image blocks are extracted, and each of the intermediate pixels is used to form the reconstructed carrier image with a size of r*r. 3. A secret image sharing method for anti-average filtering according to claim 2, characterized in that, in the step S2, the image information of the secret image is fused into n of the recombination carriers respectively The image to obtain the n shadow images specifically includes: for the ith pixel in the secret image, 1≤i≤r*r, obtaining the corresponding pixel of the ith pixel in the n recombined carrier images. _{Pixels { i 1} , _{i 2} , . _1' , i _2' ,...,in _' }, as the pixels of the n shadow images at the corresponding pixel positions, the size of the n shadow images is r*r. 4. A secret image sharing method for anti-average filtering according to claim 3, characterized in that, in the step S2, each pixel of the shadow image is subjected to neighborhood expansion, using the The original carrier image is used to fill the extended neighborhood to obtain an extended shadow image with the same size as the original carrier image, which specifically includes: performing neighborhood extension on each pixel in the shadow image to extend the surrounding 8 using the r*r image blocks obtained by dividing the original carrier image by 3*3, and filling the 8 neighborhood pixels of the middle pixel of the image block into the extended shadow image 8 neighboring pixels extended from the pixel corresponding to the intermediate pixel; the size of the extended shadow image is 3r*3r. 5. A secret image sharing method for anti-average filtering according to claim 4, characterized in that, in the step S3, adjustment is made based on the difference between the average and the corresponding non-extended pixels Each neighborhood pixel of the non-extended pixel specifically includes: In the case where the difference value is a positive number, each neighboring pixel of each non-extended pixel in the extended shadow image subtracts the integer part of the difference value respectively, and subtracts the integer part of the difference value. The range of the pixel value of each neighborhood pixel is [0, 255], if the range of the pixel value of each neighborhood pixel after subtracting the integer part of the difference value is not within [0, 255], the non- The pixel value of the extended pixel is assigned to its neighbor pixels; After the integer part of the difference value is respectively subtracted from each neighboring pixel of the non-extended pixel, a numerical value m ₁ obtained by multiplying the decimal part of the difference value by 8 is determined, and the integer part of the difference value is subtracted from M _{1 neighborhood pixels are arbitrarily selected from each neighborhood pixel of the subsequent non-extended pixel, and the pixel value of each neighborhood pixel in the m 1 neighborhood} pixels is reduced by 1, so that the m after the reduction of 1 is reduced by 1. The range of the pixel value of ₁ neighborhood pixel is [0, 255], if the range of the pixel value of the m ₁ neighborhood pixel after subtracting 1 is not within [0, 255], then assign the pixel value of the non-extended pixel to Given its neighborhood pixels, m ₁ is a positive integer. 6 . The secret image sharing method for anti-average filtering according to claim 4 , wherein, in the step S3 , adjustment is made based on the difference between the average and the corresponding non-extended pixels. 7 . Each neighborhood pixel of the non-extended pixel specifically includes: In the case where the difference value is negative, add the absolute value of the integer part of the difference value to each neighboring pixel of each non-extended pixel in the extended shadow image, and add the integer value of the difference value The range of the pixel value of each neighborhood pixel after the absolute value of the part is [0, 255], if the range of the pixel value of each neighborhood pixel after adding the absolute value of the integer part of the difference value is not in [ 0,255], then assign the pixel value of the non-expanded pixel to its neighborhood pixel; After the absolute value of the integer part of the difference value is added to each neighboring pixel of the non-extended pixel, the numerical value m ₂ obtained by multiplying the decimal part of the difference value by 8 is determined, and the difference value is added from the M ₂ neighborhood pixels are arbitrarily selected from each neighborhood pixel of the non _- extended pixel after the absolute value of the integer part of The range of the pixel values of the m ₂ neighborhood pixels after adding 1 is [0, 255], if the range of the pixel values of the m ₂ neighborhood pixels after adding 1 is not within [0, 255], the non- The pixel value of the extended pixel is assigned to its neighbor pixels, and m ₂ is a positive integer. 7. A secret image sharing method for anti-average filtering according to any one of claims 5 or 6, wherein the receiver performs the received n extensions of pixel adjustment in the neighborhood The shadow image is subjected to mean filtering, and the pixel value of each pixel in the obtained result image is consistent with the pixel value of each pixel of the shadow image, thereby realizing the sharing of the secret image that can resist mean filtering. 8. A secret image sharing system for anti-mean filtering, wherein the system comprises: The first processing unit is configured to acquire a secret image and n original carrier images serving as carriers for sharing image information of the secret image, the secret images are grayscale images, and the original carrier image is adjusted to obtain the same value as the original carrier image. The reconstructed carrier images with the same size of the secret image, and n is a positive integer; The second processing unit is configured to fuse the image information of the secret image into the n reconstituted carrier images respectively to obtain n shadow images, perform neighborhood expansion on each pixel of the shadow images, and use the using the original carrier image to fill the extended neighborhood to obtain an extended shadow image of the same size as the original carrier image; a third processing unit configured to calculate a mean value of neighboring pixels of each non-expanded pixel in the expanded shadow image, and adjust the non-expanded pixel based on the difference between the mean value and the corresponding non-expanded pixel each neighborhood pixel of the pixel; The fourth processing unit is configured to send the n extended shadow images that have completed the neighborhood pixel adjustment from the sender to the receiver, and the receiver is based on the received n extended shadow images that have completed the neighborhood pixel adjustment. The secret image is recovered. 9. An electronic device, characterized in that the electronic device comprises a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, any one of claims 1 to 7 is implemented Steps in the described method for sharing secret images against mean filtering. 10. A computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the computer program of any one of claims 1 to 7 is implemented. Steps in a secret image sharing method for adversarial mean filtering.

Images