CN114612317B - 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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CN114612317B
CN114612317B CN202210116389.0A CN202210116389A CN114612317B CN 114612317 B CN114612317 B CN 114612317B CN 202210116389 A CN202210116389 A CN 202210116389A CN 114612317 B CN114612317 B CN 114612317B
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CN114612317A (en
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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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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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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, adjusting the original carrier images to obtain a recombined carrier image with the same size as the secret image, wherein 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: and (1) a special file storage structure of the digital image. 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 method comprises the following steps that (1) correlation exists between adjacent pixel values, and coherence and correlation exist between adjacent pixel points of an image, so that the leakage of image secret information can be caused, and therefore, the secret image sharing scheme needs to consider the single sharing safety and the vision safety 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 sc 1 ,sc 2 ,…,sc n The specific scheme is as follows:
(1) In an initialization phase, the value of a threshold (k, n) is determined, where k ≦ n. A large prime number p is selected, p > n and p > s are satisfied, GF (p) is a finite field, all elements are the elements of GF (p), and all operations are performed in the finite field GF (p).
(2) In the sharing phase, s is encrypted to a shadow value sc i Randomly generating a k-1 degree polynomial in the finite field GF (p):
f(x)＝a 0 +a 1 x+…+a k-1 x k-1
in which a secret s is embedded in the first coefficient of a polynomial, i.e. a 0 = s, the remaining coefficients a 1 ,…,a k-1 Randomly chosen in the finite field GF (p). Then calculate
sc 1 ＝f(1),…,sc k ＝f(k),…,sc n ＝f(n)
Taking (i, sc) i ) As a shadow pair, where i is taken as an information tag or sequence number tag, sc i As 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 GDA0004083510610000021
Wherein the content of the first and second substances,
Figure GDA0004083510610000022
the following system of linear equations can be constructed:
Figure GDA0004083510610000031
because i is l (1 ≦ l ≦ k) are all different, so the following polynomial can be constructed from the Lagrangian interpolation formula:
Figure GDA0004083510610000032
so that the secret s = f (0) is available. 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 i l Different, each shadow share corresponds to a unique polynomial and satisfies a formula linear equation system, so that known k-1 shadows cannot be solvedThis solution is complete because there is a linear system of k unknowns, and thus no information about the secret is available.
In recent years, with the emergence of various security issues for social networks, social networks have become a complex place of network attack and defense that must 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 filters, samples and compresses 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 concealment, which focuses on JPEG compression resistance (whether concealment is done in spatial or temporal domain, or in combination with different distortion function syntax trellis frames). 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 countervailing also include the common types of image processing that are filtering, sampling, rotation, and so on. 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, the researches on robust secret image sharing of the antagonistic image processing class are less, and the antagonistic image processing types mainly comprise 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. This is a robust SIS threshold scheme without pixel expansion proposed based on the 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:
s1, acquiring a secret image and n original carrier images serving as carriers for 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;
s2, respectively fusing the image information of the secret image to the n recombined carrier images 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;
s3, calculating the mean value of 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;
and S4, sending the n expanded shadow images which are subjected to the neighborhood pixel adjustment to a receiving party by the sending party, and recovering the secret image by the receiving party based on the received n expanded shadow images which are subjected to the neighborhood pixel adjustment.
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 × 3 image blocks, wherein the total number of the image blocks is r × r, extracting intermediate pixels of each image block, and forming the recombined carrier image with the size of r × 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 to obtain the n shadow images respectively 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 images 1 ，i 2 ，...，i n By combining the ith pixel with a set of pixels { i } 1 ，i 2 ，...，i n The fusion is performed to obtain { i } 1’ ，i 2’ ，...，i n’ 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, 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 having the same size as the original carrier image, which 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 blocks 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 × 3r.
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 determined 1 And selecting m at will from each neighborhood pixel of the non-expanded pixel after subtracting the integer part of the difference value 1 A neighborhood of pixels, the m 1 The pixel value of each of the neighborhood pixels is reduced by 1, so that m after 1 reduction 1 The pixel values of the neighborhood pixels range from 0,255]If said m after subtracting 1 1 The 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, m 1 Is 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 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 determined 2 Selecting m from each neighborhood pixel of the non-expanded pixel to which the absolute value of the integer part of the difference is added 2 A number of neighborhood pixels, m 2 Adding 1 to the pixel value of each of the neighborhood pixels so that m after adding 1 is obtained 2 The pixel values of the neighborhood pixels range from 0,255]If said 1 added m 2 Ranges of pixel values for individual neighborhood pixelsIs not enclosed in [0,255]]And assigning the pixel value of the non-expanded pixel to the neighborhood pixel m 2 Is a positive integer.
According to the method of the first aspect of the present invention, the receiving side performs mean filtering and image extraction 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, adjust respective neighborhood pixels of the non-extended pixels based on a difference value between the mean value and the corresponding non-extended pixel;
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 × 3 image blocks, wherein the total number of the image blocks is r × r, extracting intermediate pixels of each image block, and forming the recombined carrier image with the size of r × 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 recombination carrier images 1 ，i 2 ，...，i n By combining the ith pixel with a set of pixels { i } 1 ，i 2 ，...，i n Get { i } by fusion 1’ ，i 2’ ，...，i n’ 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 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 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 × 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 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 setting a range of pixel values of each neighborhood pixel after subtracting the integer part of the difference value to be [0,255], if the range of pixel values of each neighborhood pixel after subtracting the integer part of the difference value is not within [0,255], assigning the pixel value of the non-extension pixel to the neighborhood pixel thereof;
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 determined 1 Randomly selecting m from each neighborhood pixel of the non-expanded pixel after subtracting the integer part of the difference value 1 A number of neighborhood pixels, m 1 The pixel value of each neighborhood pixel in the neighborhood pixels is reduced by 1, so that m after 1 is reduced 1 The pixel values of the neighborhood pixels range from 0,255]If said m after subtracting 1 1 The 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, 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 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;
adding the absolute value of the integer part of the difference value to each neighborhood pixel of the non-expanded pixelThen, a value m obtained by multiplying the decimal part of the difference by 8 is determined 2 Selecting m from each neighborhood pixel of the unexpanded pixel added with the absolute value of the integer part of the difference value 2 A number of neighborhood pixels, m 2 Adding 1 to the pixel value of each of the neighborhood pixels so that m is added by 1 2 The pixel values of the neighborhood pixels range from 0,255]If said 1 added m 2 The 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, m 2 Is a positive integer.
According to the system of the second aspect of the present invention, the receiving side performs mean filtering and image extraction 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 includes a memory storing a computer program and a processor, and when the processor executes the computer program, the electronic device implements the steps of a secret image sharing method for resisting mean filtering according to any one of the first aspect of the disclosure.
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 resisting mean filtering according to any one of the first aspect of the present disclosure.
The technical scheme provided by the invention is that a hidden secret image S and n original carrier image covers are given i In the case of (1), n shadow images SC are generated i ', such that k or more SCs i ' may still be recovered after being subjected to the mean filtering process. The scheme is directed to mean filtering and further decimation
′
The formed shadow image is just equal toIn direct input of carrier image cover i And 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.
Drawings
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 flow chart of a secret image sharing method for countering mean filtering according to an embodiment of the invention;
FIG. 2 is a block diagram of a secret image sharing scheme against mean filtering according to an embodiment of the present 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 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, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. 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 flowchart of a secret image sharing method for countering mean filtering according to an embodiment of the present invention; as shown in fig. 1, the method includes:
s1, acquiring a secret image and n original carrier images serving as carriers for 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;
s2, respectively fusing the image information of the secret image to the n recombined carrier images 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;
s3, calculating the mean value of 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;
and S4, sending the n expanded shadow images which are subjected to the neighborhood pixel adjustment to a receiving party by the sending party, and recovering the secret image by the receiving party based on the received n expanded shadow images which are subjected to the neighborhood pixel adjustment.
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 recombined 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, the size of the n original carrier images is 3r, r ≧ 2 and is a positive integer; in step S1, adjusting the original carrier image to obtain the recombined carrier image having the same size as the secret image includes: and dividing the original carrier image into 3 × 3 image blocks, wherein the total number of the image blocks is r × r, extracting intermediate pixels of each image block, and forming the recombined carrier image with the size of r × r by using the intermediate pixels.
Specifically (as shown in fig. 2), after an original carrier image (with a size of 3r × 3 r) is obtained, 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 respectively fused to the n recombined carrier images 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, 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 images 1 ，i 2 ，...，i n By combining the ith pixel with a set of pixels { i } 1 ，i 2 ，...，i n The fusion is performed to obtain { i } 1’ ，i 2’ ，...，i n’ 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 polynomial is utilized to respectively store the image information of the secret imageAnd storing the images into n recombined carrier images 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 image 1 It is decomposed into n sub-information r 1-1 ，r 1-2 ，r 1-3 ，...，r 1-(n-1) ，r 1-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 r 2 ，r 3 ，...，r r*r-1 ，r r*r The 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 blocks 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.3r.
Specifically (as shown in fig. 2), in the process of generating an understandable shadow image capable of resisting mean filtering, neighborhood expansion is performed on the interpolated carrier image first, 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 each neighborhood pixel of the non-extended pixels is adjusted based on a difference value between the mean value and the corresponding non-extended pixel.
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 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 determined 1 And selecting m at will from each neighborhood pixel of the non-expanded pixel after subtracting the integer part of the difference value 1 A neighborhood of pixels, the m 1 The pixel value of each of the neighborhood pixels is reduced by 1, so that m after 1 reduction 1 The pixel values of the neighborhood pixels range from 0,255]If said m after subtracting 1 1 The 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, m 1 Is a positive integer.
Specifically (as shown in FIG. 2), when the difference value difference > 0, after determining the integer part int (difference) of the difference value subtracted from the neighborhood pixel, the pixel value thereof falls to [0,255]]If the number of the neighborhood points is 8, executing a neighborhood pixel to subtract an integer part int (buffer) of 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 pixel value is further subtracted by the fractional part (differential-int (differential)) x 8 of the 8 (times) difference values]If yes, a subtraction operation is performed (note that subtraction can be performed on any number of (1-8) neighborhood pixels, as long as the sum of the subtraction is (differential-int (d))iffer)) 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, m 1 And equally distribute it to m 1 Adjusting 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 middle 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]Insofar as the 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, 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 (buffer-int (buffer)). Times.8 pixels in the neighboring pixels are greater than or equal to 1, if yes, a subtraction operation is performed on the randomly selected (buffer-int (buffer)). Times.8 pixels in the neighboring pixels, and the subtracted value is the buffer-int (buffer).
In some embodiments, 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 is respectively added to each neighborhood pixel of the non-expansion pixel, the numerical value m obtained by multiplying the decimal part of the difference by 8 is determined 2 Selecting m from each neighborhood pixel of the non-expanded pixel to which the absolute value of the integer part of the difference is added 2 A neighborhood of pixels, the m 2 Each neighborhood in each neighborhood pixelThe pixel values of the pixels are all added with 1, so that m after 1 is added 2 The pixel values of the neighborhood pixels range from 0,255]If said 1 added m 2 The 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, m 2 Is a positive integer.
Specifically (as shown in FIG. 2), when the difference value difference < 0, after determining the absolute value int (abs) of the integer part of the neighborhood pixels plus the difference value, the pixel value falls to [0,255]]If the number of the neighborhood points is 8, the absolute value int (abs (differential)) of the integer part of the difference value added to the neighborhood pixels is executed, otherwise, the pixel value of the intermediate 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 yes, performing addition operation (note that addition can be performed on any plurality of (1-8) neighborhood pixels, as long as the sum of the addition is [ abs (differential) -int (abs (differential))]*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, m 2 And equally distribute it to m 2 Adjusting 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 middle pixel surrounded by the 8 neighborhood pixels to the 8 neighborhood pixels. Note that the above conditional decision process is intended to ensure that the adjusted individual pixel values still fall within 0,255]Insofar as the 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, the adjustment method/condition determination method is not limited to the above one. For example, FIG. 2 also shows a way to determine if there are more than [ abs ] -int (abs) ] in the neighborhood pixels]* The pixel value of 8 pixel points is less than or equal to 255, if yes, the random selection [ abs (differential) -int (abs (differential))]*8 field pixel points execute addition operation, and the added value is abs (differential) -int (abs (differential)).
In step S4, the sender sends the n extended shadow images that have been adjusted by the neighborhood pixels to the receiver, and the receiver recovers the secret image based on the received n extended shadow images that have been adjusted by the neighborhood pixels.
Specifically (as shown in fig. 2), the receiving side recovers the secret image based on the n shadow images, i.e., 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 and image extraction 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 3r 1 ,cover 2 ,…,cover n . 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' i Inputting the result into a secret sharing algorithm which is understandable by the shadow image and based on a polynomial, and outputting a result SC 1 ,SC 2 ,…,SC n 。
(3) For SC i Each 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 =0,2, \8230;, r-1,q =0,2, \8230;, 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 SC i [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 for each pixel in the 8 neighborhood, otherwise step 8 is skipped. Whether the value of more than or equal to [ abs (buffer) -int (abs (buffer)) ]multipliedby 8 pixels is more than or equal to 1 is judged in the 8 adjacent pixels. If yes, randomly selecting [ abs (divider) -int (abs (divider)) ]x8 pixels which are more than or equal to 1 and minus 1. Otherwise jump to step 8.
(7) If differential =0, jump 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) is added to each pixel in the 8 neighborhood, otherwise step 8 is skipped. Whether the value of more than or equal to [ abs (buffer) -int (abs (buffer)) ]multipliedby 8 pixels in 8 neighborhood pixels is less than or equal to 254 is judged. If so, a pixel having [ abs (differential) -int (abs (differential)) ] × 8 less than or equal to 254 plus 1 is randomly selected. Otherwise jump to step 8.
(8) Setting square [ p ]][q][s][t]＝SC i [p][q]Wherein p =0,2, \8230;, r-1, q =0,2, \8230;, r-1, s =0,1,2, t =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. Each original carrier image is generally divided into equally large blocks (here into 3 x 3 blocks) andextracting the pixel at the specific position (here, extracting the central pixel) to recombine 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 C 1 ,C 2 ,…,C n . And (3) outputting: n gray-scale shadow images SC 1 ,SC 2 ,…,SC n 。
Figure GDA0004083510610000191
Figure GDA0004083510610000201
′
To guarantee lossless recovery, p =257 is set. Will cover i And 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 obtained i . To SC i Is extended (here an 8-neighborhood is extended 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 processing i ″。
Alternatively and additionally, fig. 3 (set of diagrams) shows experimental results of the robust SIS's shadow image generation phase against mean filtering with an (k, n) threshold shadow image intelligible, where k =3, n =4, p =257. Fig. 3 (a) shows an input grayscale secret image, 128 × 128 in size. FIGS. 3 (b) - (e) are original understandable grayscale carrier image cover 1 ，cover 2 ，cover 3 ，cover 4 . Size tune
”′
Finished carrier image cover 1 ，cover 2 ，cover 3 ，cover 4 In fig. 3 (f) - (i) it is shown that its size is equal to the size of the secret image S. FIGS. 3 (g) - (m) show understandable shadow images SC obtained by inputting resized support images and secret images into a polynomial-based SIS algorithm 1 ，SC 2 ,SC 3 And SC 4 . Here it is ensured in the polynomial based SIS algorithm 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 adjustment, a shadow image SC capable of resisting the three image processing is generated 1 ′,SC′ 2 ,SC 3 ′,SC′ 4 Shown in fig. 3 (n) - (q).
Fig. 4 shows experimental results of the shadow image restoration phase against mean filtering of robust SIS that is understandable by (k, n) threshold shadow images, where k =3,n =4,p =257. FIGS. 4 (a) - (d) SC ″ 1 ，SC″ 2 ，SC″ 3 ，SC″ 4 Is represented by SC' 1 ，SC′ 2 ，SC′ 3 ，SC′ 4 The result smoothed by a 3 × 3 kernel averaging filter. FIG. 4 (e) - (h)
Figure GDA0004083510610000211
Is to mix SC 1 ，SC″ 2 ，SC″ 3 ，SC″ 4 Divide into 3 x 3 blocks and extract a new image reconstructed from the central pixels of each block. FIG. 4 (i) illustrates slave @byLagrangian interpolation>
Figure GDA0004083510610000212
Two recovered secret images. FIG. 4 (j) illustrates slave @byLagrangian interpolation>
Figure GDA0004083510610000213
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 obtain 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 that have been adjusted by the neighboring pixel from the sending party to the receiving party, where the receiving party recovers the secret image based on the received n extended shadow images that have been adjusted by the neighboring pixel.
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 × 3 image blocks, wherein the total number of the image blocks is r × r, extracting intermediate pixels of each image block, and forming the recombined carrier image with the size of r × 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 images 1 ，i 2 ，...，i n By combining the ith pixel with a set of pixels { i } 1 ，i 2 ，...，i n Get { i } by fusion 1’ ，i 2’ ，...，i n’ 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 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 middle pixels of the image blocks 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 × 3r.
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 setting a range of pixel values of each neighborhood pixel after subtracting the integer part of the difference value to be [0,255], if the range of pixel values of each neighborhood pixel after subtracting the integer part of the difference value is not within [0,255], assigning the pixel value of the non-extension pixel to the neighborhood pixel thereof;
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 determined 1 And selecting m at will from each neighborhood pixel of the non-expanded pixel after subtracting the integer part of the difference value 1 A number of neighborhood pixels, m 1 The pixel value of each of the neighborhood pixels is reduced by 1, so that m after 1 reduction 1 The pixel values of the neighborhood pixels range from 0,255]If said m after subtracting 1 1 The 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, 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 value between the mean value and the corresponding non-extended pixel specifically includes:
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 determined 2 Selecting m from each neighborhood pixel of the unexpanded pixel added with the absolute value of the integer part of the difference value 2 A number of neighborhood pixels, m 2 Adding 1 to the pixel value of each of the neighborhood pixels so that m after adding 1 is obtained 2 The pixel values of the neighborhood pixels range from 0,255]If said 1 added m 2 The 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, m 2 Is a positive integer.
According to the system of the second aspect of the present invention, the receiving side performs mean filtering and image extraction 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.
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 communicating with an external terminal in a wired or wireless mode, and the wireless mode 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 resisting mean filtering according to any one of the first aspect of the present disclosure.
The technical scheme provided by the invention is that a hidden secret image S and n original carrier image covers are given i In the case of (1), n shadow images SC are generated i ', such that k or more SCs i ' may still be recovered after being subjected to the mean filtering process. The solution is directed to a shadow image SC generated after mean filtering and further decimation i ' exactly equal to directly inputting carrier image cover i ' and S to the result obtained after the secret sharing scheme. The scheme realizes good secret sharing scheme characteristics such as lossless recovery, understandable shadow image and (k, n) threshold, and can be applied to the fields of steganalysis and covert communication facing to social networks.
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 (9)

1. A secret image sharing method for countering mean filtering, the method comprising:
s1, acquiring a secret image and n original carrier images serving as carriers for 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;
s2, respectively fusing the image information of the secret image to the n recombined carrier images 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;
s3, calculating the mean value of 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;
s4, sending the n expanded shadow images which are subjected to the neighborhood pixel adjustment to a receiving party by the sending party, and recovering the secret image by the receiving party based on the received n expanded shadow images which are subjected to the neighborhood pixel adjustment;
the receiving party performs mean filtering and image extraction on the received n extended shadow images with the neighborhood pixel adjustment completed, 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, so that the secret image sharing capable of resisting the mean filtering is realized.
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, r is more than or equal to 2 and is a positive integer;
in step S1, adjusting the original carrier image to obtain the recombined carrier image having the same size as the secret image includes: and dividing the original carrier image into 3 × 3 image blocks, wherein the total number of the image blocks is r × r, extracting intermediate pixels of each image block, and forming the recombined carrier image with the size of r × r by using the intermediate pixels.
3. The secret image sharing method for countering mean value filtering according to claim 2, wherein in the step S2, respectively fusing 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 images 1 ，i 2 ，...，i n By combining the ith pixel with a set of pixels { i } 1 ，i 2 ，...，i n Get { i } by fusion 1’ ，i 2’ ，...，i n’ And as pixels of the n shadow images at the corresponding pixel positions, the size of the n shadow images is r x r.
4. The secret image sharing method for resisting 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 middle pixels of the image blocks 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 × 3r.
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 setting a range of pixel values of each neighborhood pixel after subtracting the integer part of the difference value to be [0,255], if the range of pixel values of each neighborhood pixel after subtracting the integer part of the difference value is not within [0,255], assigning the pixel value of the non-extension pixel to the neighborhood pixel thereof;
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 8 1 Randomly selecting m from each neighborhood pixel of the non-expanded pixel after subtracting the integer part of the difference value 1 A number of neighborhood pixels, m 1 The pixel value of each of the neighborhood pixels is reduced by 1, so that m after 1 reduction 1 The pixel values of the neighborhood pixels range from 0,255]If said m after subtracting 1 1 The 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 the neighborhood pixel m 1 Is 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 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 is respectively added to each neighborhood pixel of the non-expansion pixel, the numerical value m obtained by multiplying the decimal part of the difference by 8 is determined 2 Selecting m from each neighborhood pixel of the non-expanded pixel to which the absolute value of the integer part of the difference is added 2 A number of neighborhood pixels, m 2 Adding 1 to the pixel value of each of the neighborhood pixels so that m after adding 1 is obtained 2 The pixel values of the neighborhood pixels range from 0,255]If said 1 added m 2 The 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, m 2 Is a positive integer.
7. 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;
the receiving party performs mean filtering and image extraction on the received n extended shadow images with the neighborhood pixel adjustment completed, 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, so that the secret image sharing capable of resisting the mean filtering is realized.
8. An electronic device, characterized in that the electronic device comprises a memory and a processor, the memory stores a computer program, and the processor implements the steps of any one of claims 1 to 6 in a secret image sharing method for countering mean filtering.
9. A computer-readable storage medium, having stored thereon a computer program which, when executed by a processor, implements the steps of any one of claims 1 to 6 in a secret image sharing method for countering mean filtering.
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