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

Secret image sharing method and system for resisting mean filtering Download PDF

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CN114612317A
CN114612317A CN202210116389.0A CN202210116389A CN114612317A CN 114612317 A CN114612317 A CN 114612317A CN 202210116389 A CN202210116389 A CN 202210116389A CN 114612317 A CN114612317 A CN 114612317A
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姜越
杨国正
刘林涛
程静文
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National University of Defense Technology
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Abstract

The invention provides a secret image sharing method and system for resisting mean filtering. The method comprises the following steps: acquiring a secret image and n original carrier images serving as carriers for sharing image information of the secret image, wherein the original carrier images are adjusted to obtain a recombined carrier image with the same size as the secret image, and n is a positive integer; respectively fusing image information of the secret image to n recombinant vector images to obtain n shadow images, performing neighborhood expansion on each pixel of the shadow images, and filling the expanded neighborhood by using the original vector image to obtain an expanded shadow image; calculating the mean value of neighborhood pixels of each non-extension pixel in the extension shadow image, and adjusting each neighborhood pixel of the non-extension pixels based on the difference value between the mean value and the corresponding non-extension pixel; and sending the n expanded shadow images which are adjusted by the neighborhood pixels to a receiving party by a sending party to restore the secret image.

Description

Secret image sharing method and system for resisting mean filtering
Technical Field
The invention belongs to the field of image processing, and particularly relates to a secret image sharing method and system for resisting mean filtering.
Background
The secret sharing technology encrypts secret information into a plurality of shadow images and distributes the shadow images to a plurality of participants, only a subset of authorized participants can be decrypted together, and an unauthorized subset cannot be decrypted. A secret sharing algorithm generally includes two phases, sometimes referred to as encryption and decryption or encoding and decoding, of secret sharing and recovery. In a (k, n) threshold secret sharing scheme, where k is less than or equal to n, secret information is encrypted into n shadow images. Only when k shadow images or more are obtained, the original secret can be decrypted; and less than k shadow images cannot obtain any secret.
Digital images are one of the most important media types, and a secret image sharing technology that applies a secret sharing technology to digital image objects is developed vigorously. With respect to data, the particularity of digital images in the field of secret image sharing lies in: (1) a special file storage structure for digital images. Taking a gray-scale BMP format digital image as an example, the pixel value space is [0,255], so that the value ranges of a secret value, a sharing value and related parameters are fully considered in a secret image sharing scheme, and the condition that the secret image cannot be recovered due to information loss in the sharing or recovery process is avoided; (2) the digital image is composed of a large number of pixel points, and secret sharing is only performed aiming at one or a plurality of pixel values each time, so that the high efficiency of a sharing and recovery algorithm is emphasized in the scheme design process; (3) the adjacent pixel values have relevance, and the consistency and relevance exist between the adjacent pixel points of the image, which may cause the leakage of image secret information, so that the secret image sharing scheme needs to consider the single-time sharing security and the visual security at the same time; (4) the image transmission is finally identified by a human eye vision system, and lossless recovery of the image is not required due to the low-pass filtering characteristic of human eyes; (5) the image is special data, and the secret image sharing scheme can be applied to the secret sharing occasion of general data through simple change. The performance evaluation indexes of the secret image sharing scheme comprise: the recovery quality of the secret image, whether pixel expansion exists or not, (k, n) threshold, the recovery complexity of the secret image, comprehensibility, progressiveness and type of the shadow image.
The mainstream principles of secret sharing include: a polynomial-based (k, n) threshold secret sharing scheme, a Chinese remainder theorem-based secret sharing scheme, a visual encryption scheme, etc. The polynomial secret sharing scheme embeds the secret into a random k-1 degree polynomial, and the polynomial can be reconstructed by a Lagrange interpolation method during decryption, so that the secret information embedded into the polynomial is obtained. Knowing the secret information s, sharing it into n shadow shares sc1, sc2, …, scnThe specific scheme is as follows:
(1) in an initialization phase, the value of a threshold (k, n) is determined, where k ≦ n. Choosing a large prime number p, satisfying p > n and p > s, letting gf (p) be a finite field, all elements being those of gf (p), and all operations being performed in the finite field gf (p).
(2) In the sharing phase, s is encrypted to a shadow value sciRandomly generating a k-1 degree polynomial in a finite field GF (p):
f(x)＝a0+a1x+…+ak-1xk-1
in which a secret s is embedded in the first coefficient of a polynomial, i.e. a0S, the remaining coefficients a1,…,ak-1Randomly selected in the finite field gf (p). Then calculate
sc1＝f(1),…,sck＝f(k),…,scn＝f(n)
Taking (i, sc)i) As a shadow pair, where i is taken as an information tag or sequence number tag, sciAs a shadow pixel value. And distributing the n shadow shares to the n participants respectively to complete secret sharing.
(3) In the recovery phase, any k secret pairs held in the acquiring n participants
Figure BDA0003496553850000021
Wherein the content of the first and second substances,
Figure BDA0003496553850000022
the following system of linear equations can be constructed:
Figure BDA0003496553850000031
because i isl(1 ≦ l ≦ k) are all different, so the following polynomial can be constructed from the Lagrangian interpolation formula:
Figure BDA0003496553850000032
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 grouped into a linear system of equations where the k coefficients sharing the polynomial are unknowns. Due to the label ilIn contrast, each shadow share corresponds to a unique polynomial to satisfy a formula linear equation system, so that the known k-1 shadows cannot solve the linear equation system containing k unknowns, so that no information about secrets can be obtained, and therefore the scheme is complete.
In recent years, with the emergence of various security issues for social networks, social networks have become a complex position for network attacks and defense to be considered. The social network communication channel can cause various noises, the network server performs various image processing (recompression, downsampling, filtering and sampling) on a secret carrier, however, since the recovery of the secret image is based on mathematical operations (such as Lagrange interpolation, XOR and the like), when the image is transmitted and stored, the communication channel usually performs filtering, sampling and compression on the image, and in addition, noise is generated, so that shared data changes and is lost, further data in the recovered secret image changes and is lost, and the conventional secret image sharing scheme is not applicable. The recovery of the secret image of the shadow image in case of damage and image processing is an important problem (robustness) that must be solved in practice. Robust and robust secret image sharing is needed if confidential information is to be transmitted reliably and smoothly.
Currently, there is an increasing research on robust information hiding, which focuses on anti-JPEG compression (either in spatial or temporal domain, or in combination with a different distortion function syndrome trellis code framework). But few researches focus on robust secret image sharing, and the existing scheme generally has the problems of pixel expansion and high recovery complexity. In the current research, objects for robust secret sharing countermeasure against image processing class mainly include JPEG compression, salt and pepper noise and least significant bit noise. The current research in this area has the following disadvantages: (1) there has been very little research directed at robust secret sharing against image processing classes; (2) the specific single image processing type is not comprehensive, for example, the specific single image processing type only has certain robustness on least significant bit noise, JPEG (joint photographic experts group) compression and salt and pepper noise, and is ineffective in operations such as filtering and sampling; (3) robustness is achieved by means of steganography, and the method has high computational complexity, can cause shadow image pixel expansion, and cannot achieve lossless recovery. Research against robust secret sharing of image processing classes is a must-go and foundation for applying secret image sharing to social networks. The single image processing types that must be considered in the confrontation also include the common image processing types of filtering, sampling, rotation, etc. In addition, better secret image sharing properties, such as lossless restoration, should be pursued.
At present, few researches are focused on robust secret image sharing, and researches on robust secret image sharing of a countermeasure image processing class are less, and the countermeasure image processing types mainly include JPEG compression, salt and pepper noise and least significant bit noise. There is currently no relevant research on robust secret image sharing schemes that combat filtering, an image processing type. The robust (k, n) threshold SIS algorithm in the prior art skillfully embeds error-correcting codes into shadow images through a screening mechanism in a shadow generation stage without causing shadow expansion. Finally, the principle of secret image sharing based on the Chinese remainder theorem is utilized to realize the advantages of 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 screening the random numbers, the scheme is designed to achieve error correction capability without increasing the size of the shadow during the shadow generation phase. The method is a robust SIS threshold scheme without pixel expansion based on Chinese remainder theorem and error correcting codes. However, the scheme has certain robustness only to least significant bit noise, JPEG compression and salt and pepper noise, and is ineffective in operations such as filtering and sampling. While filtering, sampling, etc. image processing operations are operations that are common in practice in communication channels. It is known from shannon theory that to achieve perfect security, the key must be as long as the plaintext and the same key cannot be used twice. The polynomial based secret image sharing is simple to implement, easy to understand and ideal and perfect. The secret image sharing shadow image based on the Chinese remainder theorem is larger than the secret image, and secret information leakage is caused if the secret image sharing shadow image is forcibly limited to be larger than the secret image and the like.
Disclosure of Invention
In order to solve the technical problems and solve the current researches on secret image sharing schemes which are robust to least significant bit noise, JPEG compression and salt-and-pepper noise, and do not relate to the research on secret image sharing schemes for resisting mean filtering, the application provides a secret image sharing scheme for resisting mean filtering so as to realize more excellent characteristics of the traditional secret sharing scheme, such as lossless recovery, comprehension of shadow images and (k, n) threshold.
The invention discloses a secret image sharing method for resisting mean filtering in a first aspect.
The method comprises the following steps:
step S1, acquiring a secret image and n original carrier images serving as carriers sharing image information of the secret image, wherein the secret image is a gray image, the original carrier images are adjusted to obtain a recombined carrier image with the same size as the secret image, and n is a positive integer;
step S2, fusing the image information of the secret image to the n recombined carrier images respectively to obtain n shadow images, performing neighborhood expansion on each pixel of the shadow images, and filling the expanded neighborhood with the original carrier image to obtain an expanded shadow image with the same size as the original carrier image;
step S3, calculating the mean value of the neighborhood pixels of each non-expansion pixel in the expansion shadow image, and adjusting each neighborhood pixel of the non-expansion pixels based on the difference value between the mean value and the corresponding non-expansion pixel;
step S4, the n expanded shadow images of which the adjustment of the neighborhood pixels is completed are sent to a receiving party by a sending party, and the receiving party recovers the secret image based on the received n expanded shadow images of which the adjustment of the neighborhood pixels is completed.
According to the method of the first aspect of the present invention, the size of the secret image is r, the size of the n original carrier images is 3r, r is greater than or equal to 2 and is a positive integer; in step S1, adjusting the original carrier image to obtain the recombined carrier image with the same size as the secret image includes: and dividing the original carrier image into 3 x 3 image blocks, wherein the image blocks have r x r in total, extracting intermediate pixels of each image block, and forming the recombined carrier image with the size of r x r by using the intermediate pixels.
According to the method of the first aspect of the present invention, in step S2, fusing the image information of the secret image to the n recombination carrier images respectively to obtain the n shadow images specifically includes: for the ith pixel in the secret image, i is more than or equal to 1 and less than or equal to r, and acquiring a pixel { i ] of the ith pixel at the corresponding pixel position in the n recombined carrier images1，i2，...，inBy combining the ith pixel with a set of pixels { i }1，i2，...，inGet { i } by fusion1’，i2’，...，in’And taking the n shadow images as the pixels of the n shadow images at the corresponding pixel positions, wherein the size of the n shadow images is r x r.
According to the method of the first aspect of the present invention, in step S2, performing neighborhood expansion on each pixel of the shadow image, and filling the expanded neighborhood with the original carrier image to obtain an expanded shadow image with the same size as the original carrier image, specifically including: performing neighborhood expansion on each pixel in the shadow image to expand 8 surrounding neighborhood pixels; filling 8 neighborhood pixels of middle pixels of the image block to 8 neighborhood pixels expanded from pixels corresponding to the middle pixels in the expanded shadow image by using r × r image blocks obtained by 3 × 3 division of the original carrier image; the size of the extended shadow image is 3r x 3 r.
According to the method of the first aspect of the present invention, in step S3, adjusting each neighborhood pixel of the non-extended pixels based on the difference between the mean value and the corresponding non-extended pixel specifically includes:
for the case that the difference value is a positive number, subtracting an integer part of the difference value from each neighborhood pixel of each non-extension pixel in the extension shadow image, and the range of the pixel value of each neighborhood pixel after subtracting the integer part of the difference value 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 [0,255], assigning the pixel value of the non-extension pixel to the neighborhood pixel;
after the integer part of the difference value is subtracted from each neighborhood pixel of the non-expanded pixel, the value m obtained by multiplying the decimal part of the difference value by 8 is determined1Randomly selecting m from each neighborhood pixel of the non-expanded pixel after subtracting the integer part of the difference value1A number of neighborhood pixels, m1The pixel value of each of the neighborhood pixels is reduced by 1, so that m after 1 reduction1The pixel values of the neighborhood pixels range from 0,255]If said m after subtracting 11The pixel values of the neighborhood pixels are not in the range of [0,255%]And assigning the pixel value of the non-expanded pixel to its neighborhood pixel, m1Is a positive integer.
According to the method of the first aspect of the present invention, in step S3, adjusting each neighborhood pixel of the non-extended pixels based on the difference between the mean value and the corresponding non-extended pixel specifically includes:
for the negative difference, adding the absolute value of the integer part of the difference to each neighborhood pixel of each non-expanded pixel in the expanded shadow image, and the range of the pixel value of each neighborhood pixel after adding the absolute value of the integer part of the difference 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 is not in [0,255], assigning the pixel value of the non-expanded pixel to the neighborhood pixel;
after the absolute value of the integer part of the difference value is added to each neighborhood pixel of the non-expanded pixel, the numerical value m obtained by multiplying the decimal part of the difference value by 8 is determined2Selecting m from each neighborhood pixel of the unexpanded pixel added with the absolute value of the integer part of the difference value2A number of neighborhood pixels, m2Adding 1 to the pixel value of each of the neighborhood pixels so that m after adding 1 is obtained2The pixel values of the neighborhood pixels range from 0,255]If said 1 added m2The pixel values of the neighborhood pixels are not in the range of [0,255%]And assigning the pixel value of the non-expanded pixel to its neighborhood pixel, m2Is a positive integer.
According to the method of the first aspect of the present invention, the receiving side performs mean filtering on the received n extended shadow images whose neighborhood pixels have been adjusted, and the pixel value of each pixel in the obtained result image is consistent with the pixel value of each pixel in the shadow image, thereby realizing sharing of the secret image capable of resisting mean filtering.
The invention discloses a secret image sharing system for resisting mean filtering in a second aspect.
The system comprises:
the image processing device comprises a first processing unit, a second processing unit and a third processing unit, wherein the first processing unit is configured to acquire a secret image and n original carrier images serving as carriers sharing image information of the secret image, the secret image is a gray image, the original carrier images are adjusted to obtain a recombined carrier image with the same size as the secret image, and n is a positive integer;
a second processing unit, configured to fuse image information of the secret image to the n recombined carrier images respectively to obtain n shadow images, perform neighborhood expansion on each pixel of the shadow images, and fill the expanded neighborhood with the original carrier image to obtain an expanded shadow image having the same size as the original carrier image;
a third processing unit configured to calculate a mean value of neighborhood pixels of each non-extended pixel in the extended shadow image, and adjust respective neighborhood pixels of the non-extended pixels based on a difference value between the mean value and the corresponding non-extended pixels;
a fourth processing unit, configured to send the n extended shadow images that have been adjusted by the neighborhood pixels from the sender to the receiver, where the receiver recovers the secret image based on the received n extended shadow images that have been adjusted by the neighborhood pixels.
According to the system of the second aspect of the present invention, the size of the secret image is r, the size of the n original carrier images is 3r, r is greater than or equal to 2 and is a positive integer; the first processing unit is specifically configured to adjust the original carrier image to obtain the recombined carrier image with the same size as the secret image, and specifically includes: and dividing the original carrier image into 3 x 3 image blocks, wherein the image blocks have r x r in total, extracting intermediate pixels of each image block, and forming the recombined carrier image with the size of r x r by using the intermediate pixels.
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 to the n recombination carrier images to obtain the n shadow images, respectively, and specifically includes: for the ith pixel in the secret image, i is more than or equal to 1 and less than or equal to r, and acquiring a pixel { i ] of the ith pixel at the corresponding pixel position in the n recombined carrier images1，i2，...，inH, by combining the ith pixel with a set of pixels { i }1，i2，...，inGet { i } by fusion1’，i2’，...，in’As the corresponding pixels of the n shadow imagesAnd the size of the n shadow images is r x 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, fill the expanded neighborhood with the original carrier image, and obtain an expanded shadow image with the same size as the original carrier image, and specifically includes: performing neighborhood expansion on each pixel in the shadow image to expand 8 surrounding neighborhood pixels; filling 8 neighborhood pixels of middle pixels of the image block to 8 neighborhood pixels expanded from pixels corresponding to the middle pixels in the expanded shadow image by using r × r image blocks obtained by 3 × 3 division of the original carrier image; the size of the extended shadow image is 3r x 3 r.
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 pixels based on the difference between the mean value and the corresponding non-extended pixel, and specifically comprises:
for the case that the difference value is a positive number, subtracting an integer part of the difference value from each neighborhood pixel of each non-extension pixel in the extension shadow image, and the range of the pixel value of each neighborhood pixel after subtracting the integer part of the difference value 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 [0,255], assigning the pixel value of the non-extension pixel to the neighborhood pixel;
after subtracting the integer part of the difference value from each neighborhood pixel of the non-expansion pixel, determining a value m obtained by multiplying the decimal part of the difference value by 81Randomly selecting m from each neighborhood pixel of the non-expanded pixel after subtracting the integer part of the difference value1A number of neighborhood pixels, m1The pixel value of each of the neighborhood pixels is reduced by 1, so that m after 1 reduction1The pixel values of the neighborhood pixels range from 0,255]If said m after subtracting 11The pixel values of the neighborhood pixels are not in the range of [0,255%]If not, then the above-mentionedThe pixel value of an extended pixel is assigned to its neighboring pixels, m1Is 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 pixels based on the difference between the mean value and the corresponding non-extended pixel, and specifically comprises:
for the negative difference, adding the absolute value of the integer part of the difference to each neighborhood pixel of each non-expanded pixel in the expanded shadow image, and the range of the pixel value of each neighborhood pixel after adding the absolute value of the integer part of the difference 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 is not in [0,255], assigning the pixel value of the non-expanded pixel to the neighborhood pixel;
after the absolute value of the integer part of the difference value is added to each neighborhood pixel of the non-expanded pixel, the numerical value m obtained by multiplying the decimal part of the difference value by 8 is determined2Selecting m from each neighborhood pixel of the unexpanded pixel added with the absolute value of the integer part of the difference value2A number of neighborhood pixels, m2Adding 1 to the pixel value of each of the neighborhood pixels so that m after adding 1 is obtained2The pixel values of the neighborhood pixels range from 0,255]If said m after addition of 12The pixel values of the neighborhood pixels are not in the range of [0,255]]And assigning the pixel value of the non-expanded pixel to its neighborhood pixel, m2Is a positive integer.
According to the system of the second aspect of the present invention, the receiving side performs mean filtering on the received n extended shadow images whose neighborhood pixels have been adjusted, and the pixel value of each pixel in the obtained result image is consistent with the pixel value of each pixel in the shadow image, thereby realizing sharing of the secret image capable of resisting mean filtering.
A third aspect of the invention discloses an electronic device. The electronic device comprises a memory storing a computer program and a processor implementing the steps of a secret image sharing method for countering mean filtering according to any one of the first aspect of the disclosure when the processor executes the computer program.
A fourth aspect of the invention discloses a computer-readable storage medium. The computer-readable storage medium has stored thereon a computer program which, when executed by a processor, implements the steps in a secret image sharing method for countering mean filtering according to any one of the first aspects of the disclosure.
The technical scheme provided by the invention is that a hidden secret image S and n original carrier image covers are giveniIn the case of (1), n shadow images SC 'are generated'iSo that k or more SC'iAnd still be recovered after being subjected to the mean filtering process. This scheme is intended to the shadow image SC 'generated after mean filtering and further decimation'iExactly equal to direct input carrier image cover'iAnd S is the result obtained after the secret sharing scheme. The scheme realizes good secret sharing scheme characteristics such as lossless recovery, comprehensibility of shadow images and (k, n) threshold, and can be applied to the fields of steganalysis and hidden communication facing to a social network.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the description in the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a flowchart of a secret image sharing method for countering mean filtering according to an embodiment of the present invention;
FIG. 2 is a block diagram of a secret image sharing scheme against mean filtering according to an embodiment of the invention;
FIG. 3 (sets of graphs (a) - (q)) is an experimental result of a shadow image against mean filtering at a generation stage according to an embodiment of the present invention;
FIG. 4 (panels (a) - (j)) is an experimental result of a shadow image against mean filtering in a recovery phase according to an embodiment of the invention;
FIG. 5 is a block diagram of a secret image sharing system for countering mean filtering according to an embodiment of the present invention;
fig. 6 is a block diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
In order to make the objects, 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 drawings in the embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention discloses a secret image sharing method for resisting mean filtering in a first aspect. FIG. 1 is a flow chart of a secret image sharing method for countering mean filtering according to an embodiment of the invention; as shown in fig. 1, the method includes:
step S1, acquiring a secret image and n original carrier images serving as carriers sharing image information of the secret image, wherein the secret image is a gray image, the original carrier images are adjusted to obtain a recombined carrier image with the same size as the secret image, and n is a positive integer;
step S2, fusing the image information of the secret image to the n recombined carrier images respectively to obtain n shadow images, performing neighborhood expansion on each pixel of the shadow images, and filling the expanded neighborhood with the original carrier image to obtain an expanded shadow image with the same size as the original carrier image;
step S3, calculating the mean value of the neighborhood pixels of each non-expansion pixel in the expansion shadow image, and adjusting each neighborhood pixel of the non-expansion pixels based on the difference value between the mean value and the corresponding non-expansion pixel;
step S4, the n expanded shadow images of which the adjustment of the neighborhood pixels is completed are sent to a receiving party by a sending party, and the receiving party recovers the secret image based on the received n expanded shadow images of which the adjustment of the neighborhood pixels is completed.
FIG. 2 is a block 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 sharing image information of the secret image are obtained, the secret image is a grayscale image, the original carrier images are adjusted to obtain a reconstructed carrier image having the same size as the secret image, and n is a positive integer.
In some embodiments, the size of the secret image is r x r, the size of the n original carrier images is 3r x 3r, r ≧ 2 and a positive integer; in step S1, adjusting the original carrier image to obtain the recombined carrier image with the same size as the secret image includes: and dividing the original carrier image into 3 x 3 image blocks, wherein the image blocks have r x r in total, extracting intermediate pixels of each image block, and forming the recombined carrier image with the size of r x r by using the intermediate pixels.
Specifically (as shown in fig. 2), after an original carrier image (with a size of 3r × 3r) is acquired, the size of the original carrier image is adjusted, the original carrier image is divided into 3 × 3 image blocks by means of matrix division, and the intermediate elements of each block are extracted and recombined (recombined carrier image, with a size of r × r). And acquiring an image to be shared, and performing gray processing on the image to be shared to obtain a secret image (with the size of r).
In step S2, the image information of the secret image is fused to the n reconstructed carrier images respectively to obtain n shadow images, each pixel of the shadow images is neighborhood-expanded, and the expanded neighborhood is filled with the original carrier image to obtain an expanded shadow image having the same size as the original carrier image.
In some embodiments, in step S2, fusing the image information of the secret image to the n recombination carrier images to obtain the n shadow images respectively includes: for the ith pixel in the secret image, i is more than or equal to 1 and less than or equal to r, and acquiring a pixel { i ] of the ith pixel at the corresponding pixel position in the n recombined carrier images1，i2，...，inH, by combining the ith pixel with a set of pixels { i }1，i2，...，inGet { i } by fusion1’，i2’，...，in’And taking the n shadow images as the pixels of the n shadow images at the corresponding pixel positions, wherein the size of the n shadow images is r x r.
Specifically (as shown in fig. 2), the secret image sharing algorithm based on the polynomial is utilized to realize that the image information of the secret image is respectively stored into n recombined carrier images so as to obtain n interpolated carrier images. The interpolation may be lagrange interpolation or other interpolation commonly used in the art. For example, for the first pixel r of r x r pixels in the secret image1It is decomposed into n sub-information r1-1，r1-2，r1-3，...，r1-(n-1)，r1-n(ii) a Inserting n pieces of sub information into the n recombinant vector images, respectively; for example, a polynomial-based secret sharing method is employed. For other pixels r2，r3，...，rr*r-1，rr*rThe same operations as above are performed.
In some embodiments, in step S2, performing neighborhood expansion on each pixel of the shadow image, and filling the expanded neighborhood with the original carrier image to obtain an expanded shadow image with the same size as the original carrier image, specifically including: performing neighborhood expansion on each pixel in the shadow image to expand 8 surrounding neighborhood pixels; filling 8 neighborhood pixels of middle pixels of the image block to 8 neighborhood pixels expanded from pixels corresponding to the middle pixels in the expanded shadow image by using r × r image blocks obtained by 3 × 3 division of the original carrier image; the size of the extended shadow image is 3r x 3 r.
Specifically (as shown in fig. 2), in the process of generating a understandable shadow image capable of resisting mean filtering, neighborhood expansion is performed on the interpolated carrier image, 8 neighborhood expansion is performed on each pixel, and the expanded pixel bits are correspondingly filled in 8 neighborhoods of the original carrier image.
In step S3, a mean value of neighborhood pixels of each non-extended pixel in the extended shadow image is calculated, and the respective neighborhood pixels of the non-extended pixels are adjusted based on a difference value between the mean value and the corresponding non-extended pixels.
Specifically (as shown in fig. 2), a mean value of 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 in the extended carrier image is calculated, and a difference value between the mean value and an intermediate pixel surrounded by 8 neighborhood pixels is further calculated.
In some embodiments, in the step S3, adjusting each neighborhood pixel of the non-expanded pixels based on the difference between the mean value and the corresponding non-expanded pixel specifically includes:
for the case that the difference value is a positive number, subtracting an integer part of the difference value from each neighborhood pixel of each non-extension pixel in the extension shadow image, and the range of the pixel value of each neighborhood pixel after subtracting the integer part of the difference value 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 [0,255], assigning the pixel value of the non-extension pixel to the neighborhood pixel;
after the integer part of the difference value is subtracted from each neighborhood pixel of the non-expanded pixel, the value m obtained by multiplying the decimal part of the difference value by 8 is determined1Randomly selecting m from each neighborhood pixel of the non-expanded pixel after subtracting the integer part of the difference value1A neighborhood of pixels, the m1The pixel value of each of the neighborhood pixels is reduced by 1, so that m after 1 reduction1Is adjacent toThe range of pixel values of the domain pixels is 0,255]If said m after subtracting 11The pixel values of the neighborhood pixels are not in the range of [0,255%]And assigning the pixel value of the non-expanded pixel to its neighborhood pixel, m1Is a positive integer.
Specifically (as shown in fig. 2), when the difference value difference > 0, after determining that the integer part int (difference) of the difference value is subtracted from the neighborhood pixel, the pixel value thereof falls to [0,255 []If the number of the neighborhood points is 8, executing an integer part int (buffer) of the neighborhood pixels minus the difference, otherwise, assigning the pixel value of the intermediate pixel surrounded by the 8 neighborhood pixels to the 8 neighborhood pixels. Subsequently, it is determined whether or not the pixel value of the neighborhood pixel still falls within [0,255] after the fractional portion of 8 (times) the difference value is further subtracted from the neighborhood pixel, i.e., the fractional portion of [ 0-int (differential) } 8]If so, a subtraction operation is performed (note that, the subtraction may be performed on any number of (1-8) neighborhood pixels, as long as the total subtracted is buffer-int (buffer) 8 and the above range condition is satisfied, but it is more preferable to determine a value after the fractional part 8, where the value is an integer value, for example, m1And equally distribute it to m1Adjusting in each neighborhood pixel, wherein the adjusting mode is smooth and uniform, and can better protect image information), and if not, assigning the pixel value of the intermediate pixel surrounded by the 8 neighborhood pixels to the 8 neighborhood pixels. Note that the above-described conditional decision process is intended to ensure that the adjusted individual pixel values still fall within 0,255]Within the scope, the above adjustment scheme is intended to make the difference between the mean value of the intermediate pixel and the mean value of the neighboring pixels zero, and the adjustment method/condition determination method is not limited to the above one. For example, fig. 2 also shows a manner, that is, it is determined whether the pixel values of more than differ-int (differ) × 8 pixels in the neighboring pixels are greater than or equal to 1, if yes, subtraction is performed on randomly selected differ-int (differ) × 8 pixels in the domain, and the subtracted value is differ-int (differ).
In some embodiments, in the step S3, adjusting each neighborhood pixel of the non-expanded pixels based on the difference between the mean value and the corresponding non-expanded pixel specifically includes:
for the negative difference, adding the absolute value of the integer part of the difference to each neighborhood pixel of each non-expanded pixel in the expanded shadow image, and the range of the pixel value of each neighborhood pixel after adding the absolute value of the integer part of the difference 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 is not in [0,255], assigning the pixel value of the non-expanded pixel to the neighborhood pixel;
after the absolute value of the integer part of the difference value is added to each neighborhood pixel of the non-expanded pixel, the numerical value m obtained by multiplying the decimal part of the difference value by 8 is determined2Selecting m from each neighborhood pixel of the unexpanded pixel added with the absolute value of the integer part of the difference value2A number of neighborhood pixels, m2Adding 1 to the pixel value of each of the neighborhood pixels so that m after adding 1 is obtained2The pixel values of the neighborhood pixels range from 0,255]If said 1 added m2The pixel values of the neighborhood pixels are not in the range of [0,255%]And assigning the pixel value of the non-expanded pixel to its neighborhood pixel, m2Is a positive integer.
Specifically (as shown in fig. 2), when the difference value difference < 0, after determining the absolute value int (abs (difference)) of the integer part of the neighborhood pixels plus the difference value, the pixel value thereof falls within [0,255 []If the number of the neighborhood points is 8, an absolute value int (abs (differential)) of an integer part of a neighborhood pixel plus a difference is performed, otherwise, a pixel value of a middle pixel surrounded by the 8 neighborhood pixels is assigned to the 8 neighborhood pixels. Subsequently, it is judged that the neighborhood pixel is further added with the absolute value [ abs (differential) -int (abs (differential)) of the fractional part of the 8 (times) difference values]After 8, whether its pixel value still falls within [0,255]]If so, performing addition operation (note that addition can be performed on any number of (1-8) neighborhood pixels, as long as the sum of the addition is [ abs (buffer) -int (abs (buffer))]8, and the above range condition is satisfied, but it is more preferable to determine a value after the decimal part 8, which is an integer value, for example, m2And equally distribute it to m2Adjusting in each neighborhood pixel, wherein the adjusting mode is smooth and uniform, and can better protect image information), and if not, assigning the pixel value of the intermediate pixel surrounded by the 8 neighborhood pixels to the 8 neighborhood pixels. Note that the above-described conditional decision process is intended to ensure that the adjusted individual pixel values still fall within 0,255]Within the scope, the above adjustment scheme is intended to make the difference between the mean value of the intermediate pixel and the mean value of the neighboring pixels zero, and the adjustment method/condition determination method is not limited to the above one. For example, FIG. 2 also shows a way to determine whether there are more than [ abs (differential) -int (abs (differential) ]neighboring pixels]Pixel values of 8 pixel points are less than or equal to 255, if yes, then [ abs (buffer) -int (abs (buffer))]And 8 field pixel points execute addition operation, and the added value is abs (differential) -int (abs (differential)).
In step S4, the n extended shadow images whose adjustment of the neighborhood pixels is completed are sent by the sender to the receiver, and the receiver restores the secret image based on the received n extended shadow images whose adjustment of the neighborhood pixels is completed.
Specifically (as shown in fig. 2), the receiving side recovers the secret image based on the n shadow images, that is, performs subsequent operations of mean filtering, image extraction, and the like on the shadow images to recover the secret image.
In some embodiments, the receiving side performs mean filtering on the received n extended shadow images with neighborhood pixel adjustment completed, and a pixel value of each pixel in an obtained result image is consistent with a pixel value of each pixel of the shadow image, thereby realizing sharing of the secret image capable of resisting mean filtering.
In another embodiment, the above method may be implemented by the following algorithm flow:
the algorithm is as follows: a shadow image based on a (k, n) threshold polynomial may understand a robust secret image sharing scheme against mean filtering. Inputting: a threshold k; the number n of shadows; ID serial number list ID; a grayscale secret image of size r; n original gray carrier image covers with size of 3r multiplied by 3r1,cover2,…,covern. And (3) outputting: n grayscale shadow images SC 'capable of resisting mean value filtering'1,SC'2,…,SC'n。
(1) For each original carrier image, 3 x 3 blocks are divided. The intermediate elements of each block are decimated and recombined into an image cover of size r × r'i。
(2) The gray secret images S and cover'iInputting the result into a secret sharing algorithm which is understandable by the shadow image and based on a polynomial, and outputting a result SC1,SC2,…,SCn。
(3) For SCiEach pixel of (2) expands to 8 neighborhood pixels. The final image matrix is denoted m. M is divided into r 3 x 3 blocks, each of which is denoted square p][q]Wherein p is 0,2, …, r-1, q is 0,2, …, r-1.
(4) For each square p q, fill the 8 neighbors of the expansion with the corresponding center pixel of the original carrier image.
(5) For each square [ p ]][q]And calculating the mean value of the 8 neighborhoods. Calculating mean and SCi[p][q]The difference of (1). If differ is greater than 0, jumping to step 6, otherwise jumping to step 7.
(6) For an 8-neighborhood of the current block, the integer part of each pixel minus the difference is computed. The number of values falling between 0 and 255 is calculated, and if 8, int (buffer) is subtracted from each pixel in the 8 neighborhood, otherwise step 8 is skipped. Whether the value of (buffer-int (buffer)) x 8 pixels in the 8 adjacent pixels is more than or equal to 1 is judged. If yes, (buffer-int (buffer)) x 8 pixels greater than or equal to 1 are randomly selected minus 1. Otherwise jump to step 8.
(7) If the difference is 0, go to step 8. For the 8 neighbourhood of the current block, the integer part of each pixel plus the absolute value of the difference is calculated. The number of values falling between 0 and 255 is calculated, and if 8, int (abs (buffer)) is added to each pixel in the 8 neighborhood, otherwise step 8 is skipped. It is determined whether or not the values of (abs) - (flag) -int (flag) -x 8 pixels in the 8-neighborhood pixels are equal to or less than 254. If so, a pixel less than or equal to (buffer-int (buffer)) 8 plus 1 is randomly selected. Otherwise jump to step 8.
(8) Setting square [ p ]][q][s][t]＝SCi[p][q]Where p is 0,2, …, r-1, q is 0,2, …, r-1, s is 0,1,2, t is 0,1, 2.
(9) Outputting n mean value filtering resistant shadow images SC'1,SC'2,…,SC'n。
In yet another embodiment, the secret image sharing method against the mean filtering can be divided into two stages: an understandable shadow image generation phase and a secret image recovery phase of the anti-mean filtering.
In the understandable shadow image generation phase, which is resistant to typical image processing, the original carrier image is first resized to coincide with the secret image. Generally, each original carrier image is divided into equal-sized blocks (here, divided into 3 × 3 blocks), and pixels at specific positions (here, pixels at the center of the extraction) 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 meaning of the complete image, only the size of the original carrier image is changed. It is noted that the size of the original carrier image depends on the type of image processing and the secret image. For example, if one is fighting against mean filtering, the size of the original carrier image should be 9 times the size of the secret image. The binary carrier image in the proposed solution is treated as the most significant bit of the grayscale carrier image.
The specific algorithm is as follows:
algorithm 2 (k, n) threshold secret image sharing scheme understandable based on polynomial shadow images. Inputting: a threshold k; the number n of shadows; ID list ID; a gray-scale secret image S; n binary carrier images C1,C2,…,Cn. And (3) outputting: n gray-scale shadow images SC1,SC2,…,SCn。
Figure BDA0003496553850000191
Sequence of gray values [ SC ] with 125 as threshold1(i,j),…,SCn(i,j)]Conversion to binary sequence [ BSC1,…,BSCn]
Figure BDA0003496553850000192
To ensure lossless recovery, p is set to 257. Fruit of cover'iAnd S secret image is input into a secret image sharing scheme which can be understood by a shadow image based on a polynomial, and finally SC is obtainedi. For SCiIs expanded (here an 8-neighborhood is expanded for each pixel). And assigning values to the pixels at the corresponding positions of the expanded shadow images by using the pixels at the corresponding positions of the original carrier images. The value of each pixel in each block is slightly adjusted so that the trimmed image is exactly the same as the original shadow image after image processing and further image extraction. Ensuring that the secret image can be successfully recovered finally.
In the recovery phase, two steps are involved: image extraction and lagrange interpolation. Unlike conventional polynomial-based SIS, where image decimation is first required, pixels are decimated and recombined into SCs at important locations according to the above-designed strategy of specifically countering image processingi″。
Alternatively and additionally, fig. 3 (set of diagrams) shows experimental results of the shadow image generation stage of robust SIS robust mean filtering, where k is 3, n is 4, and p is 257, as understood by a (k, n) threshold shadow image. Fig. 3(a) shows an input grayscale secret image, 128 × 128 in size. FIGS. 3(b) - (e) are diagrams of an original understandable grayscale carrier image cover of input size1，cover2，cover3，cover4. Carrier image cover after size adjustment1'，cover2'，cover3'，cover4In fig. 3(f) - (i) it is shown that the size is equal to the size of the secret image S. FIGS. 3(g) - (m) show understandable shadow images SC obtained by inputting resized shadow images and secret images to a polynomial-based SIS algorithm1，SC2,SC3And SC4. Herein based onThe first two bits of each pixel of the resized carrier image are guaranteed to be equal to the first two bits of each pixel of the corresponding shadow image in the SIS algorithm of the polynomial. Finally generating a shadow image SC 'which can resist the three image processing after three steps of pixel expansion, pixel assignment and pixel fine adjustment'1,SC'2,SC'3,SC'4Shown in FIGS. 3(n) - (q).
Fig. 4 shows the experimental results of the shadow image restoration phase against mean filtering for robust SIS that is understandable for (k, n) threshold shadow images, where k is 3, n is 4, and p is 257. FIGS. 4(a) - (d) SC "1，SC”2，SC”3，SC”4Is represented by SC'1，SC'2，SC'3，SC'4The result smoothed by a 3 × 3 kernel averaging filter. FIG. 4(e) - (h)
Figure BDA0003496553850000211
Is prepared from SC "1，SC”2，SC”3，SC”4Split into 3 x 3 blocks and decimate the new image reconstructed from the central pixels of each block. FIG. 4(i) shows interpolation from Lagrangian
Figure BDA0003496553850000212
Two recovered secret images. FIG. 4(j) shows interpolation from Lagrangian
Figure BDA0003496553850000213
Three or four recovered secret images.
The invention discloses a secret image sharing system for resisting mean filtering in a second aspect. FIG. 5 is a block diagram of a secret image sharing system for countering mean filtering according to an embodiment of the present invention; as shown in fig. 5, the system 500 includes:
a first processing unit 501, configured to acquire a secret image and n original carrier images serving as carriers sharing image information of the secret image, where the secret image is a grayscale image, the original carrier images are adjusted to obtain a recombined carrier image having the same size as the secret image, and n is a positive integer;
a second processing unit 502, configured to fuse image information of the secret image to n reconstructed carrier images respectively to obtain n shadow images, perform neighborhood expansion on each pixel of the shadow images, and fill expanded neighborhoods with the original carrier image to obtain an expanded shadow image with the same size as the original carrier image;
a third processing unit 503 configured to calculate a mean value of neighborhood pixels of each non-extended pixel in the extended shadow image, and adjust each neighborhood pixel of the non-extended pixels based on a difference value between the mean value and the corresponding non-extended pixel;
a fourth processing unit 504, configured to send the n extended shadow images with the neighborhood pixels adjusted completed to a receiving party by the sending party, where the receiving party recovers the secret image based on the received n extended shadow images with the neighborhood pixels adjusted completed.
According to the system of the second aspect of the present invention, the size of the secret image is r, the size of the n original carrier images is 3r, r is greater than or equal to 2 and is a positive integer; the first processing unit 501 is specifically configured to adjust the original carrier image to obtain the recombined carrier image with the same size as the secret image, and specifically includes: and dividing the original carrier image into 3 x 3 image blocks, wherein the image blocks have r x r in total, extracting intermediate pixels of each image block, and forming the recombined carrier image with the size of r x r by using the intermediate pixels.
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 to the n recombination carrier images respectively to obtain the n shadow images specifically includes: for the ith pixel in the secret image, i is more than or equal to 1 and less than or equal to r, and acquiring a pixel { i ] of the ith pixel at the corresponding pixel position in the n recombined carrier images1，i2，...，inBy combining the ith pixel with a set of pixels { i }1，i2，...，inGet { i } by fusion1’，i2’，...，in’And as pixels of the n shadow images at the corresponding pixel positions, the size of the n shadow images is r x 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 fill the expanded neighborhood with the original carrier image to obtain an expanded shadow image with the same size as the original carrier image, and specifically includes: performing neighborhood expansion on each pixel in the shadow image to expand 8 surrounding neighborhood pixels; filling 8 neighborhood pixels of a middle pixel of the image block to 8 neighborhood pixels expanded from a pixel corresponding to the middle pixel in the expanded shadow image by using r image blocks obtained by 3-by-3 division of the original carrier image; the size of the extended shadow image is 3r x 3 r.
According to the system of the second aspect of the present invention, the third processing unit 503 is specifically configured to, based on the difference between the mean value and the corresponding non-expanded pixel, adjust each neighborhood pixel of the non-expanded pixel specifically includes:
for the case that the difference value is a positive number, subtracting an integer part of the difference value from each neighborhood pixel of each non-extension pixel in the extension shadow image, and the range of the pixel value of each neighborhood pixel after subtracting the integer part of the difference value 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 [0,255], assigning the pixel value of the non-extension pixel to the neighborhood pixel;
after the integer part of the difference value is subtracted from each neighborhood pixel of the non-expanded pixel, the value m obtained by multiplying the decimal part of the difference value by 8 is determined1And selecting m at will from each neighborhood pixel of the non-expanded pixel after subtracting the integer part of the difference value1A neighborhood of pixels, the m1The pixel value of each neighborhood pixel in the neighborhood pixels is reduced by 1 to ensure thatTo get m after subtracting 11The pixel values of the neighborhood pixels range from 0,255]If said m after subtracting 11The pixel values of the neighborhood pixels are not in the range of [0,255%]And assigning the pixel value of the non-expanded pixel to its neighborhood pixel, m1Is a positive integer.
According to the system of the second aspect of the present invention, the third processing unit 503 is specifically configured to, based on the difference between the mean value and the corresponding non-expanded pixel, adjust each neighborhood pixel of the non-expanded pixel specifically includes:
for the negative difference, adding the absolute value of the integer part of the difference to each neighborhood pixel of each non-expanded pixel in the expanded shadow image, and the range of the pixel value of each neighborhood pixel after adding the absolute value of the integer part of the difference 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 is not in [0,255], assigning the pixel value of the non-expanded pixel to the neighborhood pixel;
after the absolute value of the integer part of the difference value is added to each neighborhood pixel of the non-expanded pixel, the numerical value m obtained by multiplying the decimal part of the difference value by 8 is determined2Selecting m from each neighborhood pixel of the unexpanded pixel added with the absolute value of the integer part of the difference value2A number of neighborhood pixels, m2Adding 1 to the pixel value of each of the neighborhood pixels so that m after adding 1 is obtained2The pixel values of the neighborhood pixels range from 0,255]If said 1 added m2The pixel values of the neighborhood pixels are not in the range of [0,255%]And assigning the pixel value of the non-expanded pixel to its neighborhood pixel, m2Is a positive integer.
According to the system of the second aspect of the present invention, the receiving party performs mean filtering on the received n extended shadow images whose neighboring pixels have been adjusted, and the pixel value of each pixel in the resulting image is identical to the pixel value of each pixel in the shadow image, thereby realizing sharing of the secret image that is capable of resisting the mean filtering.
A third aspect of the invention discloses an electronic device. The electronic device comprises a memory storing a computer program and a processor implementing the steps of a secret image sharing method for countering mean filtering according to any one of the first aspect of the disclosure when the processor executes the computer program.
Fig. 6 is a block diagram of an electronic device according to an embodiment of the present invention, and as shown in fig. 6, the electronic device includes a processor, a memory, a communication interface, a display screen, and an input device, which are connected by a system bus. Wherein the processor of the electronic device is configured to provide computing and control capabilities. The memory of the electronic equipment comprises a nonvolatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of an operating system and computer programs in the non-volatile storage medium. The communication interface of the electronic device is used for carrying out wired or wireless communication with an external terminal, and the wireless communication can be realized through WIFI, an operator network, Near Field Communication (NFC) or other technologies. The display screen of the electronic equipment can be a liquid crystal display screen or an electronic ink display screen, and the input device of the electronic equipment can be a touch layer covered on the display screen, a key, a track ball or a touch pad arranged on the shell of the electronic equipment, an external keyboard, a touch pad or a mouse and the like.
It will be understood by those skilled in the art that the structure shown in fig. 6 is only a partial block diagram related to the technical solution of the present disclosure, and does not constitute a limitation of the electronic device to which the solution of the present application is applied, and a specific electronic device may include more or less components than those shown in the drawings, or combine some components, or have a different arrangement of components.
A fourth aspect of the invention discloses a computer-readable storage medium. The computer-readable storage medium has stored thereon a computer program which, when executed by a processor, implements the steps in a secret image sharing method for countering mean filtering according to any one of the first aspects of the disclosure.
The technical scheme provided by the invention is that a hidden secret image S and n original carrier image covers are giveniIn the case of (1), n shadow images SC 'are generated'iSo that k or more SC'iAnd still be recovered after being subjected to the mean filtering process. This scheme is intended to be a shadow image SC 'generated after mean filtering and further decimation'iExactly equal to direct input carrier image cover'iAnd S is the result obtained after the secret sharing scheme. The scheme realizes good secret sharing scheme characteristics such as lossless recovery, comprehensibility of shadow images and (k, n) threshold, and can be applied to the fields of steganalysis and hidden communication facing to a social network.
It should be noted that the technical features of the above embodiments can be arbitrarily combined, and 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 between the combinations of the technical features, the scope of the present description should be considered. The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (10)

1. A secret image sharing method for countering mean filtering, the method comprising:
step S1, acquiring a secret image and n original carrier images serving as carriers sharing image information of the secret image, wherein the secret image is a gray image, the original carrier images are adjusted to obtain a recombined carrier image with the same size as the secret image, and n is a positive integer;
step S2, fusing the image information of the secret image to the n recombined carrier images respectively to obtain n shadow images, performing neighborhood expansion on each pixel of the shadow images, and filling the expanded neighborhood with the original carrier image to obtain an expanded shadow image with the same size as the original carrier image;
step S3, calculating the mean value of the neighborhood pixels of each non-expansion pixel in the expansion shadow image, and adjusting each neighborhood pixel of the non-expansion pixels based on the difference value between the mean value and the corresponding non-expansion pixel;
step S4, the n expanded shadow images of which the adjustment of the neighborhood pixels is completed are sent to a receiving party by a sending party, and the receiving party recovers the secret image based on the received n expanded shadow images of which the adjustment of the neighborhood pixels is completed.
2. The secret image sharing method against the average filtering according to claim 1, wherein:
the size of the secret image is r, the size of the n original carrier images is 3r, and r is not less than 2 and is a positive integer;
in step S1, adjusting the original carrier image to obtain the recombined carrier image with the same size as the secret image includes: and dividing the original carrier image into 3 x 3 image blocks, wherein the image blocks have r x r in total, extracting intermediate pixels of each image block, and forming the recombined carrier image with the size of r x r by using each intermediate pixel.
3. The secret image sharing method for countering mean value filtering according to claim 2, wherein in the step S2, respectively fusing the image information of the secret image to the n recombination carrier images to obtain the n shadow images specifically includes: for the ith pixel in the secret image, i is more than or equal to 1 and less than or equal to r, and acquiring a pixel { i ] of the ith pixel at the corresponding pixel position in the n recombined carrier images1，i2，...，inH, by combining the ith pixel with a set of pixels { i }1，i2，...，inGet { i } by fusion1’，i2’，...，in’And taking the n shadow images as the pixels of the n shadow images at the corresponding pixel positions, wherein the size of the n shadow images is r x r.
4. The secret image sharing method against mean filtering according to claim 3, wherein 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 to obtain 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 neighborhood pixels; filling 8 neighborhood pixels of a middle pixel of the image block to 8 neighborhood pixels expanded from a pixel corresponding to the middle pixel in the expanded shadow image by using r image blocks obtained by 3-by-3 division of the original carrier image; the size of the extended shadow image is 3r x 3 r.
5. The secret image sharing method for resisting mean filtering according to claim 4, wherein in the step S3, adjusting each neighborhood pixel of the non-extended pixels based on the difference between the mean and the corresponding non-extended pixels specifically comprises:
for the case that the difference value is a positive number, subtracting an integer part of the difference value from each neighborhood pixel of each non-extension pixel in the extension shadow image, and the range of the pixel value of each neighborhood pixel after subtracting the integer part of the difference value 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 [0,255], assigning the pixel value of the non-extension pixel to the neighborhood pixel;
after the integer part of the difference value is subtracted from each neighborhood pixel of the non-expanded pixel, the value m obtained by multiplying the decimal part of the difference value by 8 is determined1From subtracting the integer part of the differenceRandomly selecting m from each neighborhood pixel of the non-expanded pixel1A number of neighborhood pixels, m1The pixel value of each of the neighborhood pixels is reduced by 1, so that m after 1 reduction1The pixel values of the neighborhood pixels range from 0,255]If said m after subtracting 11The pixel values of the neighborhood pixels are not in the range of [0,255%]And assigning the pixel value of the non-expanded pixel to its neighborhood pixel, m1Is a positive integer.
6. The secret image sharing method for resisting mean filtering according to claim 4, wherein in the step S3, adjusting each neighborhood pixel of the non-extended pixels based on the difference between the mean and the corresponding non-extended pixels specifically comprises:
for the case that the difference is negative, adding the absolute value of the integer part of the difference to each neighborhood pixel of each non-extension pixel in the extension shadow image, and the range of the pixel value of each neighborhood pixel after adding the absolute value of the integer part of the difference 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 is not in [0,255], assigning the pixel value of the non-extension pixel to its neighborhood pixel;
after the absolute value of the integer part of the difference value is added to each neighborhood pixel of the non-expanded pixel, the numerical value m obtained by multiplying the decimal part of the difference value by 8 is determined2Selecting m from each neighborhood pixel of the unexpanded pixel added with the absolute value of the integer part of the difference value2A number of neighborhood pixels, m2Adding 1 to the pixel value of each of the neighborhood pixels so that m after adding 1 is obtained2The pixel values of the neighborhood pixels range from 0,255]If said 1 added m2The pixel values of the neighborhood pixels are not in the range of [0,255%]And assigning the pixel value of the non-expanded pixel to its neighborhood pixel, m2Is a positive integer.
7. The secret image sharing method for countering mean value filtering according to any one of claims 5 or 6, characterized in that the receiving party performs mean value filtering on the received n extended shadow images with neighborhood pixel adjustment completed, and a pixel value of each pixel in a result image is consistent with a pixel value of each pixel of the shadow images, so as to realize sharing of the secret image capable of countering mean value filtering.
8. A secret image sharing system for countering mean filtering, the system comprising:
the image processing device comprises a first processing unit, a second processing unit and a third processing unit, wherein the first processing unit is configured to acquire a secret image and n original carrier images serving as carriers sharing image information of the secret image, the secret image is a gray image, the original carrier images are adjusted to obtain a recombined carrier image with the same size as the secret image, and n is a positive integer;
a second processing unit, configured to fuse image information of the secret image to the n recombined carrier images respectively to obtain n shadow images, perform neighborhood expansion on each pixel of the shadow images, and fill the expanded neighborhood with the original carrier image to obtain an expanded shadow image having the same size as the original carrier image;
a third processing unit configured to calculate a mean value of neighborhood pixels of each non-extended pixel in the extended shadow image, and adjust respective neighborhood pixels of the non-extended pixels based on a difference value between the mean value and the corresponding non-extended pixels;
a fourth processing unit, configured to send the n extended shadow images that have been adjusted by the neighborhood pixels from the sender to the receiver, where the receiver recovers the secret image based on the received n extended shadow images that have been adjusted by the neighborhood pixels.
9. An electronic device, characterized in that the electronic device comprises a memory and a processor, the memory stores a computer program, and the processor, when executing the computer program, implements the steps in a secret image sharing method for countering mean filtering according to any one of claims 1 to 7.
10. A computer-readable storage medium, having stored thereon a computer program which, when being executed by a processor, carries out the steps of a secret image sharing method for countering mean filtering according to any one of claims 1 to 7.
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