CN114140304A - Reversible embedding method based on adaptive modification of multiple difference value histograms - Google Patents
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Abstract
The invention is suitable for the field of reversible information hiding, and provides a reversible embedding method based on a plurality of difference histogram adaptive modifications, which is used for carrying out image difference calculation on an original image to obtain a difference sequence; classifying the difference values according to the pseudo-random sequences, uniformly dividing the difference value sequences into N parts, counting the number of the difference values, and generating N difference value histograms; selecting a pair of expansion points for each difference histogram, embedding secret information, and obtaining a parameter N by adopting exhaustive optimization to minimize the offset of the difference histogram; obtaining modification parameters, fixing according to the pseudorandom sequence, and modifying the pixels of the difference value histogram image as a fixed rule of each embedding; the carrier image and the secret information are restored. The method solves the technical problems that after secret information is embedded into a carrier, a difference value histogram can generate irregular change, a peak value is no longer a zero point position, and an attacker can easily find the secret information from histogram statistical characteristics of the difference value histogram.
Description
Technical Field
The invention belongs to the field of reversible information hiding, and particularly relates to a reversible embedding method based on adaptive modification of a plurality of difference value histograms.
Background
With the coming of the comprehensive information era, the digital economy is rapidly developed, and various information safety problems such as information leakage, information resource copyright dispute, difficulty in distinguishing the true and false of information contents and the like are brought while the information resources bring convenience to people. These problems hinder the development of digital economy, undermine personal rights and even threaten national security. How to deal with the relationship between the information mass increase and the digital economic development, strengthen the safety protection of the data resource in the whole life cycle and ensure the information safety becomes one of the key problems which need to be solved urgently in social development.
Information hiding is a key technology for protecting information security, effective hiding of secret information can be achieved on the premise that carrier use is not affected, and the information hiding is widely concerned by overseas and overseas researchers in recent years. The reversible information hiding aims to realize lossless recovery of the embedded secret information and the original carrier on the premise of a certain auxiliary message, and has important application value in the sensitive image processing field with higher requirements on the recovery of the original carrier. In general, a concealment algorithm can evaluate its performance in terms of imperceptibility, visual quality of the embedded image, and embedding capacity. Aiming at improving the embedding capacity and the visual quality of the embedded image, a large number of reversible hiding schemes, such as a reversible hiding method based on difference expansion, a reversible hiding method based on prediction error histogram shift, etc., have been proposed by many scholars at present. The methods generate a corresponding histogram through some characteristics of a statistical image, expand and shift partial point values for generating the histogram, and reversibly embed in a non-overlapping point mode. However, there are currently few relevant studies directed to imperceptibility. In fact, for most of the existing reversible hiding methods, after the secret information is embedded into the carrier, the difference value histogram generates irregular changes, the peak value is no longer a zero point position, and an attacker can easily find the existence of the secret information from the histogram statistical characteristics. Under the condition, if the algorithm cannot guarantee certain anti-statistical characteristic detectability, the advantages of the reversible hidden algorithm cannot be reflected, and effective protection of secret information is not facilitated. On the premise of ensuring reversibility, the embedding mode needs to be changed, and the imperceptibility of the reversible embedding algorithm is further improved.
Disclosure of Invention
The invention aims to provide a reversible embedding method based on a plurality of difference value histograms for self-adaptive modification, and aims to solve the technical problems that after secret information is embedded into a carrier, the difference value histograms generate irregular change, peak values are no longer zero positions, and an attacker can easily find the secret information from histogram statistical characteristics of the secret information in most of the conventional reversible hiding methods.
The invention is realized in such a way that a reversible embedding method based on a plurality of difference value histograms self-adaptive modification comprises the following steps:
step S1: carrying out image difference calculation on the original image to obtain a difference sequence;
step S2: classifying the difference values according to the pseudo-random sequences, uniformly dividing the difference value sequences into N parts, counting the number of the difference values, and generating N difference value histograms;
step S3: selecting a pair of expansion points for each difference histogram, embedding secret information, and obtaining a parameter N by adopting exhaustive optimization to minimize the offset of the difference histogram;
step S4: obtaining modification parameters, fixing according to the pseudorandom sequence, and modifying the pixels of the difference value histogram image as a fixed rule of each embedding;
step S5: and recovering the carrier image and the secret information, namely completing reversible embedded recovery.
The further technical scheme of the invention is as follows: the specific step of step S1 is to first, assuming an a × B image I, form two non-overlapping adjacent pixels in the image into a pixel pair (x) in the order from left to right and from top to bottom2i-1,x2i) Wherein, i is more than or equal to 1 and less than or equal to [ A multiplied by B/2]]Then its pixel pair difference can be calculated as:
di＝x2i-x2i-1
wherein d is-255-diIs less than or equal to 255. The corresponding obtained difference sequence is D ═ D1,...,dA×B/2}。
The further technical scheme of the invention is as follows: the specific step of step S2 is to pass through a fixed N-ary pseudo-random number sequence S1,...,sA×B/2}, sorting the difference values siI.e. the difference diThereby evenly dividing the difference sequence into N parts of { D0,...,DN-1}; for each N is more than or equal to 0 and less than or equal to N-1, counting DnThe number of the intermediate difference values is used for generating N histograms { h0,...,hN-1In which h isnIs defined as
hn(k)＝#{1≤i≤A×B/2:di＝k,si＝n}
Where # indicates the cardinality of the set.
The further technical scheme of the invention is as follows: the detailed step of step S3 is to select a pair of extension points (a) for each difference histogramn,bn) The embedding mode is expressed as that N is more than or equal to 0 and less than or equal to N-1, i is more than or equal to 1 and less than or equal to [ A multiplied by B/2]]Then, then
Where m is a secret information {0,1}, di' for the modified pixel difference, in practice, the embedding method is a generalized extension of the conventional difference extension, which corresponds to this method (a)n,bn) (ii) (-1,0), 0. ltoreq. n.ltoreq.N-1; wherein, the difference histogram is unchanged at the point-1 or moves to the left by one unit, is unchanged at the point 0 or moves to the right by one unit, and other values correspondingly move by one unit to create a space for reversible embedding, and the total difference histogram of the image is defined as:
H(k)＝#{1≤i≤[A×B/2]:di＝k}
taking Lena as an example, for the conventional reversible scheme of the difference histogram, the difference histogram generated before embedding the image is compared with the difference histogram regenerated after embedding 10,000 bits, so that it can be obtained that after modifying the histogram, the distribution trend of the histogram is obviously changed because the frequency of the selected expansion points is reduced to half of the original frequency, and half of the expansion points are moved to the adjacent points on the right or left, and the rest points are moved by a unit distance to the left or right, thereby generating a distribution different from the original difference histogram;
further choose different (a)n,bn) Under the condition, the change generated by the image difference histogram is further analyzed, full embedding is considered to be carried out on the image, and the modified difference histogram hn', N is not less than 0 and not more than N-1, having
While
In practice, by selecting (a) for different difference histogramsn,bn) When n.ltoreq.n (-N, N-1) 0.ltoreq.n-1 greatly reduces the difference in distribution of H(s) and H'(s), a specific embedding manner thereof can be expressed as, for n.ltoreq.n-1 0.ltoreq.i.ltoreq.AxB/2]Then there is
Under the embedding rule, 10,000 bits are also embedded in the Lena image, the difference histogram of the image before embedding and the difference histogram after embedding can be obtained, and when the number N of the histograms is 64, it can be seen that after the difference histogram is modified under the embedding rule, the distribution difference between the difference histogram and the original difference histogram is obviously reduced, and for the selection of the parameter N, further, the offset before and after embedding the difference histogram is defined as:
due to the nth histogram hnEmbedded capacity EC ofnCan be calculated as
ECn＝hn(-n)+hn(n-1)
For a given embedding capacity P, an optimization equation can be established:
according to the optimization equation, an optimal N can be determined by an exhaustive method, namely, the corresponding SD is minimum under the condition of meeting the embedding capacity.
The further technical scheme of the invention is as follows: the specific step of step S4 is to obtain the modification parameters, fix the parameters according to the pseudo-random sequence, use the parameters as the fixed rule of each embedding, without using additional auxiliary information, modify the pixels according to the embedding rule to realize the embedding, N is more than or equal to 0 and less than or equal to N-1, i is more than or equal to 1 and less than or equal to [ A × B/2], if N is more than or equal to 0 and less than or equal to N-1, then
Wherein x2i' is the pixel after embedding, and x2i-1The parameter N selected needs to be embedded as auxiliary information in the carrier in order to ensure that the user can retrieve the embedded information and the carrier image completely at the extraction side, which remains unchanged.
The further technical scheme of the invention is as follows: the specific step of step S5 is to, for the recovery process of the carrier image and the secret information, first, extract the previous pixel acquisition parameter N, pair the images sequentially, then divide the pixel pairs of the images into N parts uniformly according to the pseudo-random sequence, and calculate the difference d 'of all the pixel pairs'i＝x'2i-x'2i-1Wherein, the pixel is due to x2i-1Can be directly restored to x without modification during embedding2i-1＝x2i-1', corresponds to x2iCan be restored to
And the embedded secret information m can be recovered as
The invention has the beneficial effects that: compared with the traditional reversible hiding method, the method disclosed by the invention designs the self-adaptive reversible embedding rule corresponding to the difference value histogram by analyzing the statistical characteristics of the generated difference value histograms under different embedding rules, so that the statistical characteristics of the embedded histograms are maintained to the maximum extent. Under the same embedding capacity, the invention can realize higher statistical property maintaining performance.
Drawings
FIG. 1 is an overall block diagram of an embedding process provided by an embodiment of the present invention;
FIG. 2 is a plurality of difference histograms generated by an image Lena according to an embodiment of the present invention;
FIG. 3 is a comparison of a prior-to-embedding difference histogram and a 10,000-bit-after-embedding difference histogram according to a conventional method provided by an embodiment of the present invention;
FIG. 4 is a comparison of the difference histogram before embedding and the difference histogram after embedding 10,000 bits according to the present invention;
FIG. 5 is a graph showing the variation trend of SD with N for different images embedded with 10,000 bits according to an embodiment of the present invention;
fig. 6 shows comparison of histogram change of difference values before and after embedding in airplan image with 40,000 bits according to the two methods provided by the embodiment of the present invention;
FIG. 7 shows the comparison between the histogram changes of the difference before and after the Baboon image is embedded with 40,000 bits according to the two methods provided by the embodiment of the present invention;
FIG. 8 is a comparison of the difference histogram change before and after the embedding of the Barbara image into 40,000 bits according to the two methods provided by the embodiment of the present invention;
FIG. 9 shows the comparison between the change of the difference histogram before and after embedding in the Lena image with 40,000 bits according to the two methods provided by the embodiment of the present invention;
fig. 10 is a comparison of histogram offsets SD before and after embedding according to two methods provided by embodiments of the present invention.
Detailed Description
Fig. 1-10 illustrate reversible information hiding of digital images, which is achieved by adaptively modifying a plurality of difference histograms to maintain the statistical properties of the images, according to the invention, reversible hiding based on the modification of the difference histograms mainly generates the difference histograms by counting the difference values obtained by subtracting two adjacent pixels in the images, and performs extended shifting on the histograms to realize reversible embedding. Unlike the conventional method for modifying a single difference histogram, the method uniformly divides the image pixel pairs into N parts according to a pseudo-random sequence, calculates the difference statistics of the N parts, and generates N difference histograms. Based on the generated multiple difference value histograms, the reversible embedding rule for keeping the statistical characteristics is further analyzed and designed, the optimal parameter N meeting the embedding capacity is obtained through self-adaptive optimization, and the image pixels are modified to realize the final embedding of the secret message image, so that the reversible hiding of the statistical characteristics is completed.
In order to achieve the above object, the statistical characteristic preserving reversible concealment method based on multiple difference histogram modifications mainly includes the following two parts: (1) evenly dividing the image pixel pairs into N parts, and counting to generate N image difference value histograms; (2) adaptive embedding rules are designed to modify the histogram and embed the secret information. The histogram modification and information embedding part comprises the following steps: analyzing and designing embedding rules of different difference value histograms; establishing an optimization equation for optimization to obtain the optimal N; modifying image pixels enables reversible embedding.
The generation process of the difference value histograms of the plurality of images comprises the following steps: combining all non-overlapping adjacent two pixels of the image to obtain a plurality of pixel pairs, and uniformly dividing the pixel pairs into N parts according to a fixed pseudo-random sequence, wherein N is greater than 1. Then, calculating the difference value of each group of pixel pairs, and counting the difference values of the pixel pairs of different classes to generate N difference value histograms. The choice of N is related to the embedding capacity and the embedding rules.
The adaptive modification process based on the multiple image difference value histograms is as follows: first, considering the modification with a pair of extension points for each difference histogram, each difference histogram may have a different mapping rule. By analyzing different embedding rules, namely the selection of different expansion points, a reversible embedding rule capable of keeping the image difference histogram basically unchanged is designed aiming at the change of the statistical characteristics of the generated multiple difference histograms. Then, an optimization equation is established, and N which enables the embedded histogram statistical characteristic offset to be minimum is obtained through an exhaustion method, so that the whole embedding process is established. And finally, the reversible embedding is completed by correspondingly modifying the image pixels and embedding the parameter N recorded in advance into the carrier as auxiliary information.
A reversible embedding method based on multiple difference histogram adaptive modifications as shown in fig. 1, the reversible embedding method comprising the steps of:
step S1: carrying out image difference calculation on the original image to obtain a difference sequence; the specific steps are that firstly, assuming an A multiplied by B image I, two non-overlapping adjacent pixels in the image form a pixel pair (x) according to the sequence from left to right and from top to bottom2i-1,x2i) Wherein, i is more than or equal to 1 and less than or equal to [ A multiplied by B/2]]Then its pixel pair difference can be calculated as:
di＝x2i-x2i-1
wherein d is-255-diIs less than or equal to 255. The corresponding obtained difference sequence is D ═ D1,...,dA×B/2}。
Step S2: classifying the difference values according to the pseudo-random sequences, uniformly dividing the difference value sequences into N parts, counting the number of the difference values, and generating N difference value histograms; the specific steps are that a fixed N-system pseudo-random number sequence { s }is passed1,...,sA×B/2}, sorting the difference values siI.e. the difference diThereby evenly dividing the difference sequence into N parts of { D0,...,DN-1}; for each N is more than or equal to 0 and less than or equal to N-1, counting DnThe number of the intermediate difference values is used for generating N histograms { h0,...,hN-1In which h isnIs defined as
hn(k)＝#{1≤i≤A×B/2:di＝k,si＝n}
Where # indicates the cardinality of the set. Taking a gray scale image Lena of 512 × 512 as an example, 8 difference histograms { h) generated corresponding to N ═ 8 are taken0,...,h7Since each histogram is generated statistically from randomly chosen pixels, the different histogram distributions are substantially the same, as shown in fig. 2. Reversible concealment is achieved by modifying these generated difference histograms by selecting a corresponding extension point for each histogram and performing an extension shift on the histogram.
Step S3: selecting a pair of expansion points for each difference histogram, embedding secret information, and obtaining a parameter N by adopting exhaustive optimization to minimize the offset of the difference histogram; the specific steps are to select a pair of extension points (a) for each difference histogramn,bn) The embedding mode is expressed as that N is more than or equal to 0 and less than or equal to N-1, i is more than or equal to 1 and less than or equal to [ A multiplied by B/2]]Then, then
Where m is a secret information {0,1}, di' for the modified pixel difference, in practice, the embedding method is a generalized extension of the conventional difference extension, which corresponds to this method (a)n,bn) (ii) (-1,0), 0. ltoreq. n.ltoreq.N-1; wherein, the difference histogram is unchanged at the point-1 or moves to the left by one unit, is unchanged at the point 0 or moves to the right by one unit, and other values correspondingly move by one unit to create a space for reversible embedding, and the total difference histogram of the image is defined as:
H(k)＝#{1≤i≤[A×B/2]:di＝k}
taking Lena as an example, for the conventional reversible scheme of the difference histogram, the difference histogram generated before embedding the image is compared with the difference histogram regenerated after embedding 10,000 bits, as shown in fig. 3, it can be obtained that after modifying the histogram, the distribution trend of the histogram is obviously changed because the frequency of the selected expansion points is reduced to half of the original frequency, and half of the number is moved to the adjacent points on the right or left, and the rest of the points are moved by a unit distance to the left or right, thereby generating a distribution different from the original difference histogram;
further choose different (a)n,bn) Under the condition, the change generated by the image difference histogram is further analyzed, full embedding is considered to be carried out on the image, and the modified difference histogram hn'，0N is not less than N and not more than N-1, having
While
In practice, by selecting (a) for different difference histogramsn,bn) When n.ltoreq.n (-N, N-1) 0.ltoreq.n-1 greatly reduces the difference in distribution of H(s) and H'(s), a specific embedding manner thereof can be expressed as, for n.ltoreq.n-1 0.ltoreq.i.ltoreq.AxB/2]Then there is
Under the embedding rule, 10,000 bits are embedded in the Lena image, and the difference histogram of the image before embedding and the difference histogram after embedding are compared, as shown in fig. 4, in this example, when the number N of the histograms is 64, it can be seen that after the difference histogram is modified under the embedding rule, the distribution difference between the difference histogram and the original difference histogram is significantly reduced, and for the selection of the parameter N, further, the offset before and after embedding the difference histogram is defined as:
due to the nth histogram hnEmbedded capacity EC ofnCan be calculated as
ECn＝hn(-n)+hn(n-1)
For a given embedding capacity P, an optimization equation can be established:
according to the optimization equation, an optimal N can be determined by an exhaustive method, namely, the corresponding SD is minimum under the condition of meeting the embedding capacity.
Step S4: obtaining modification parameters, fixing according to the pseudorandom sequence, and modifying the pixels of the difference value histogram image as a fixed rule of each embedding; the specific steps are that after obtaining modification parameters, the modification parameters are fixed according to a pseudo-random sequence and are used as a fixed rule for each embedding, the modification is carried out on pixels according to an embedding rule without additionally used as auxiliary information to realize the embedding, N is more than or equal to 0 and less than or equal to N-1, i is more than or equal to 1 and less than or equal to [ A multiplied by B/2], and then
Wherein x2i' is the pixel after embedding, and x2i-1The parameter N selected needs to be embedded as auxiliary information in the carrier in order to ensure that the user can retrieve the embedded information and the carrier image completely at the extraction side, which remains unchanged.
Step S5: restoring the carrier image and the secret information, namely finishing reversible embedding restoration; the method specifically comprises the steps of for the recovery process of a carrier image and secret information, firstly, extracting a previous pixel to obtain a parameter N, sequentially pairing the images, then uniformly dividing pixel pairs of the images into N according to a pseudorandom sequence, and calculating the difference d 'of all the pixel pairs'i＝x'2i-x'2i-1Wherein, the pixel is due to x2i-1Can be directly restored to x without modification during embedding2i-1＝x2i-1', corresponds to x2iCan be restored to
And the embedded secret information m can be recovered as
In order to effectively illustrate the performance of the present invention, the experimental results are shown and analyzed by using the figures and table data, thereby proving that the present invention has excellent performance.
Fig. 5 shows the trend of the histogram offset SD before and after embedding with 10,000 bits as a function of N for 4 different images, namely airplan, Baboon, Barbara, Lena. The four images are reversible and hide images commonly used for testing, and are relatively representative. In the experiment, the value range of N is set as [1,128 ]. It can be seen that the determined optimal parameter N varies according to the variation of the image content, but the trend is approximately the same, and the deviation amount first decreases and then becomes stable along with the increase of N, and the optimal value is obtained between 100 and 128.
Figures 6, 7, 8, and 9 are sequentially airplan, Baboon, Barbara, Lena, and the difference histogram change contrast before and after embedding 40,000 bits for each of the two methods. As can be seen. The original method changes the histogram significantly after embedding, especially for intermediate values. This is because the conventional difference expansion method selects the same expansion point (-1,0) for different histograms such that its frequency is reduced, and moves a number of half the capacity size to a point adjacent to the right (left), and the remaining points move a distance of one unit to the left (right), thereby generating a distribution significantly different from the original difference histogram. The method can well keep the distribution characteristic of the embedded difference value histogram, and the histogram characteristic can basically keep unchanged after different expansion points are selected for embedding different difference value histograms.
Referring to fig. 10, table 1 shows a comparison of the values of the histogram shift SD before and after embedding obtained from different images at different embedding capacities. It can be seen that the proposed method can achieve either significantly smaller offsets for any image and embedding capacity, and the advantage is significant that the method can well preserve the distribution characteristics of the embedded difference histogram.
Therefore, the reversible hiding method for keeping the statistical characteristics based on the modification of the plurality of difference value histograms can realize good histogram statistical characteristic protection in different embedding capacities and different carrier images, and still ensure the invariance of the image statistical characteristics after the reversible information is embedded, so that the imperceptibility of an algorithm is improved, the safety of the embedded information is fully protected, and the embedding work of the reversible information hiding for keeping the statistical characteristics is ideally realized.
Compared with the traditional reversible hiding method, the method disclosed by the invention designs the self-adaptive reversible embedding rule corresponding to the difference value histogram by analyzing the statistical characteristics of the generated difference value histograms under different embedding rules, so that the statistical characteristics of the embedded histograms are maintained to the maximum extent. Under the same embedding capacity, the invention can realize higher statistical property maintaining performance.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (6)
1. A reversible embedding method based on multiple difference histogram adaptive modifications, characterized in that the reversible embedding method comprises the steps of:
step S1: carrying out image difference calculation on the original image to obtain a difference sequence;
step S2: classifying the difference values according to the pseudo-random sequences, uniformly dividing the difference value sequences into N parts, counting the number of the difference values, and generating N difference value histograms;
step S3: selecting a pair of expansion points for each difference histogram, embedding secret information, and obtaining a parameter N by adopting exhaustive optimization to minimize the offset of the difference histogram;
step S4: obtaining modification parameters, fixing according to the pseudorandom sequence, and modifying the pixels of the difference value histogram image as a fixed rule of each embedding;
step S5: and recovering the carrier image and the secret information, namely completing reversible embedded recovery.
2. The reversible embedding method according to claim 1, wherein the specific step of step S1 is to assume an a x B image I, and to arrange two non-overlapping adjacent pixels in the image in the order from left to right and from top to bottomForm a pixel pair (x)2i-1,x2i) Wherein, i is more than or equal to 1 and less than or equal to [ A multiplied by B/2]]Then its pixel pair difference can be calculated as:
di＝x2i-x2i-1
wherein d is-255-diIs less than or equal to 255, and the corresponding obtained difference sequence is D ═ D1,...,dA×B/2}。
3. The reversible embedding method according to claim 2, characterized in that said step S2 is embodied by a fixed N-ary pseudo-random number sequence { S }1,...,sA×B/2}, sorting the difference values siI.e. the difference diThereby evenly dividing the difference sequence into N parts of { D0,...,DN-1}; for each N is more than or equal to 0 and less than or equal to N-1, counting DnThe number of the intermediate difference values is used for generating N histograms { h0,...,hN-1In which h isnIs defined as
hn(k)＝#{1≤i≤A×B/2:di＝k,si＝n}
Where # indicates the cardinality of the set.
4. Reversible embedding method according to claim 3, characterized in that said specific step of step S3 consists in selecting for each difference histogram a pair of extension points (a)n,bn) The embedding mode is expressed as that N is more than or equal to 0 and less than or equal to N-1, i is more than or equal to 1 and less than or equal to [ A multiplied by B/2]]Then, then
Where m is a secret information {0,1}, di' for the modified pixel difference, in practice, the embedding method is a generalized extension of the conventional difference extension, which corresponds to this method (a)n,bn) (ii) (-1,0), 0. ltoreq. n.ltoreq.N-1; wherein, the difference histogram is unchanged or moves to the left by one unit at the point-1, is unchanged or moves to the right by one unit at the point 0, and other values correspondingly moveOne unit creates space for reversible embedding, defining the total difference histogram of the image as:
H(k)＝#{1≤i≤[A×B/2]:di＝k}
taking Lena as an example, for the conventional reversible scheme of the difference histogram, the difference histogram generated before embedding the image is compared with the difference histogram regenerated after embedding 10,000 bits, so that it can be obtained that after modifying the histogram, the distribution trend of the histogram is obviously changed because the frequency of the selected expansion points is reduced to half of the original frequency, and half of the expansion points are moved to the adjacent points on the right or left, and the rest points are moved by a unit distance to the left or right, thereby generating a distribution different from the original difference histogram;
further choose different (a)n,bn) Under the condition, the change generated by the image difference histogram is further analyzed, full embedding is considered to be carried out on the image, and the modified difference histogram hn', N is not less than 0 and not more than N-1, having
While
In practice, by selecting (a) for different difference histogramsn,bn) When n.ltoreq.n (-N, N-1) 0.ltoreq.n-1 greatly reduces the difference in distribution of H(s) and H'(s), a specific embedding manner thereof can be expressed as, for n.ltoreq.n-1 0.ltoreq.i.ltoreq.AxB/2]Then there is
Under the embedding rule, 10,000 bits are also embedded in the Lena image, the difference histogram of the image before embedding and the difference histogram after embedding can be obtained, and when the number N of the histograms is 64, it can be seen that after the difference histogram is modified under the embedding rule, the distribution difference between the difference histogram and the original difference histogram is obviously reduced, and for the selection of the parameter N, further, the offset before and after embedding the difference histogram is defined as:
due to the nth histogram hnEmbedded capacity EC ofnCan be calculated as
ECn＝hn(-n)+hn(n-1)
For a given embedding capacity P, an optimization equation can be established:
according to the optimization equation, an optimal N can be determined by an exhaustive method, namely, the corresponding SD is minimum under the condition of meeting the embedding capacity.
5. The reversible embedding method as claimed in claim 4, wherein the specific step of step S4 is to modify the pixels according to the embedding rule to realize embedding after obtaining the modification parameters, and fixing according to the pseudo-random sequence as the fixing rule of each embedding without additionally using as auxiliary information, and N is greater than or equal to 0 and less than or equal to N-1,1 is greater than or equal to i and less than or equal to [ A x B/2], and then
Wherein x2i' is the pixel after embedding, and x2i-1The parameter N selected needs to be embedded as auxiliary information in the carrier in order to ensure that the user can retrieve the embedded information and the carrier image completely at the extraction side, which remains unchanged.
6. The reversible embedding method according to claim 5, characterized in that the specific step of step S5 is toIn the recovery process of the carrier image and the secret information, firstly, extracting the former pixel to obtain a parameter N, sequentially pairing the images, then uniformly dividing the pixel pairs of the images into N according to a pseudorandom sequence, and calculating the difference d 'of all the pixel pairs'i＝x'2i-x'2i-1Wherein, the pixel is due to x2i-1Can be directly restored to x without modification during embedding2i-1＝x2i-1', corresponds to x2iCan be restored to
And the embedded secret information m can be recovered as
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| CN115604401A (en) * | 2022-12-13 | 2023-01-13 | 无锡弘鼎软件科技有限公司（Cn） | Traceable electronic seal encryption method |
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