CN110362964B - High-capacity reversible information hiding method based on multi-histogram modification - Google Patents

Abstract

The invention provides a high-capacity reversible information hiding method based on multi-histogram modification, which can be used for losslessly recovering an image carrier while extracting secret information at a receiving end, greatly improving the embedding capacity by selecting a plurality of pairs of histograms for information embedding, quickly obtaining an approximately optimal solution of an optimization problem through a greedy search algorithm, and further improving the embedding performance by adaptively selecting a plurality of parameters according to load requirements and image contents.

Description

High-capacity reversible information hiding method based on multi-histogram modification

Technical Field

The invention relates to the technical field of information hiding, in particular to a reversible information hiding method for a high-capacity image based on multi-histogram modification.

Background

Information Hiding (Information Hiding) technology is intended to protect the contents of digital multimedia from being stolen or tampered by unauthorized parties, and is widely used for content authentication, copyright protection, and the like. However, in some sensitive application scenarios, such as military and medical image processing, not only the embedded secret information needs to be extracted, but also the carrier data needs to be recovered without any distortion. To meet this demand, Reversible Data Hiding (Reversible Data Hiding) technology has been developed and is attracting more and more attention of researchers.

Embedding capacity and Peak Signal-to-Noise Ratio (Peak Signal-to-Noise Ratio) are generally considered as criteria for measuring the performance of information hiding techniques. As the embedding capacity increases, the carrier image is modified more and the degree of distortion of the image is higher. Therefore, it is a goal of researchers how to introduce as much lower distortion as possible when embedding capacity is higher. In addition, when the method is applied to the mobile internet, the mobile terminal and other scenes, how to reduce the computational complexity of the information hiding algorithm to meet the requirement of real-time application is another problem to be solved.

Li et al propose a reversible information hiding algorithm based on multiple histogram modifications. In the method of Li et al, for each pixel x in the carrier image_iCalculating to obtain a prediction error e by using a diamond predictor_iAnd calculating the corresponding complexity n according to the neighborhood pixels_iWherein i is more than or equal to 1 and less than or equal to N, and N represents the total pixel number of the image. Then according to the complexity n of the pixel_iUniformly dividing pixels of an image into M subsets, and correspondingly generating a prediction error histogram h by calculating the frequency of prediction errors of each set of pixels_n：

h_n(e)＝#{1≤i≤N:e_i＝e,n_i＝n}，

Wherein n is more than or equal to 1 and less than or equal to M. Finally, M prediction error histograms are obtained.

For each prediction error histogram h_nSelecting two parameters a_nAnd b_n(a_n<b_n) So that the prediction error value is a_nAnd b_nIs expanded to embed information with a prediction error value less than a_nAnd is greater than b_nThe columns of the graph are shifted to the left and right, respectively, and the prediction error value is at a_nAnd b_nThe figure pillars of (a) remain unchanged. Therefore, the prediction error after embedding the information is:

where m ∈ {0,1} is the embedded binary information bit. FIG. 1 illustrates an embedding rule based on multiple histogram modification, where the points identified by rectangles represent the parameter a selected on each histogram_nAnd b_n。

Parameter a_nAnd b_nTo be able to adaptively select parameters for different image contents and embedding load requirements, the method of Li et al employs an exhaustive search to determine the most suitableAnd (4) a good parameter. For a on each histogram_nAnd b_nLet a be_n+b_n-1 and for histograms of low to high complexity, parameter b_nIs non-decreasing and the maximum value does not exceed 7. These two assumptions were set up from an observation of the distribution of the prediction error histogram, which resembles a laplacian distribution, taking a peak at 0 and strongly decaying at the tails on both sides. Under the set limiting conditions, exhaustive search is carried out on the parameters, wherein in the case that the embedding capacity meets the load requirement, the solution which enables the ratio of the embedding distortion to the embedding capacity to be minimum is the optimal solution. It can be seen that the complexity of the method is exponential, assuming that the size of the parameter candidate set is S, the algorithm complexity is O (S)^M)。

In the method of Li et al, a plurality of histograms are generated by dividing a set of pixels of different complexity, making full use of the spatial redundancy of image information, and achieving good performance by adaptively fine-tuning parameters. This method still has very significant drawbacks. On the one hand, the method selects only one pair of bins for information embedding per histogram, so that the maximum allowable embedding capacity is very limited. For example, for the image Lena, the maximum allowable embedding capacity is only 62,000 bits. On the other hand, the method searches for the optimal solution in an exhaustive manner, which is time-consuming, and thus leads to a situation that the solution cannot be expanded to high-capacity embedding.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a high-capacity reversible information hiding method based on multi-histogram modification, which can be used for nondestructively recovering an image carrier while extracting secret information at a receiving end, and can be used for carrying out information embedding by selecting a plurality of pairs of histograms on each histogram, thereby greatly improving the embedding capacity, quickly obtaining an approximately optimal solution of an optimization problem through a greedy search algorithm, and adaptively selecting a plurality of parameters according to load requirements and image contents, thereby further improving the embedding performance.

In order to achieve the purpose, the technical scheme adopted by the invention is as follows:

a high-capacity reversible information hiding method based on multi-histogram modification comprises the following steps:

firstly, preprocessing a carrier image, and performing partial pixel x with the value in a specific range in the image_iModifying, and establishing a position table to record the position of the modified pixel;

specifically, the partial pixel x_iModified according to the following formula:

computing pixel x from neighborhood_iPrediction error e of_iAnd complexity n_iGenerating M prediction error histograms;

at each histogram h_nSelecting K pairs of columns, corresponding to K parameters, and determining optimal parameters according to a greedy search algorithm;

generating auxiliary information capable of ensuring lossless recovery of the carrier image, wherein the auxiliary information comprises a position table, M-1 thresholds for dividing the histogram and parameters corresponding to the histogram;

dividing all pixels of the carrier image into two layers, and embedding the secret information and the auxiliary information to be embedded into the K pairs of image columns in a layering manner according to the determined optimal parameters, wherein the auxiliary information is embedded into the head of the image;

obtaining modified prediction error after embedding

According to the embedded pixels

An embedded carrier image is obtained.

Further, information is embedded in the sequence from left to right and from top to bottom, and information is embedded in the first layer and then in the second layer.

Further, the prediction error

The prediction value of the pixel is calculated according to the diamond predictor.

Further, complexity n_iThe calculation method comprises the following steps: in the neighborhood of 12 pixels, the average value of the difference values of every two consecutive pixels in the horizontal and vertical directions is calculated, namely the complexity n_i。

Further, the corresponding parameter of K to the figure column is { (a)_n,k,b_n,k) L 1 is less than or equal to K, wherein a_n,K<…<a_n,1<0≤b_n,1<…<b_n,KThen, the embedding rule of the multiple pairs of the drawing columns is as follows:

wherein

And m ∈ {0,1} represents the prediction error of the embedded image, and is an embedded binary information bit.

Further, the optimal parameter determination according to the greedy search algorithm comprises the following steps:

calculating to obtain a single histogram h_nCapacity of embedding EC when using multiple parameters_nAnd embedding distortion ED_n，

Wherein h () represents a prediction error histogram, and h (a) represents the frequency count of the prediction error of a;

solving an optimization problem by using a greedy search algorithm, and determining optimal parameters, wherein the optimization problem is as follows:

where P denotes a given load requirement and consists of secret information and side information to be embedded.

Further, the value ranges of the parameters are as follows:

where T represents an integer threshold.

Further, the greedy search algorithm is that in a solution space, an origin of the solution space is used as an initial state, from the initial state, a current optimal direction is selected to advance to search for a next state, and the search is performed iteratively until an end point in the solution space is reached.

Further, solving the optimization problem by using a greedy search algorithm specifically comprises:

constructing an M-dimensional solution space, points (X) in the solution space₁,…X_M) Represents a complete parameter required for embedding, wherein X_nIs represented in histogram h_nThe parameters are selected, and all candidates are arranged in ascending order according to the size of the embedding capacity in each dimension of the space;

with the origin of the solution space as the initial state W₀Selecting a candidate which enables the ratio of embedding distortion to embedding capacity to be minimum as a next state, and iteratively searching the next state until an end point in a solution space is reached to obtain a search path in the solution space;

on this path, finding the point where the ratio of embedding distortion to embedding capacity is minimal while satisfying the load requirement is the optimal solution.

Further, the auxiliary information is embedded in the header of the picture by least significant bit replacement.

A method for extracting information aiming at the embedded carrier image obtained by the method comprises the following steps:

extracting auxiliary information from the header of the embedded carrier image;

and extracting the embedded secret information from the image and recovering the carrier according to the position table in the auxiliary information, the threshold values of the M-1 partition histograms and the parameters corresponding to the histograms.

Compared with the prior art, the invention has the beneficial effects that:

the invention can realize the embedding and extraction of the secret information in the image, can provide higher embedding capacity, and can quickly realize the approximately optimal embedding, thereby ensuring that the distortion degree of the carrier image with the secret information is lower than that of the prior reversible information hiding algorithm. Therefore, the method is a reversible information hiding algorithm with good performance and can be used in the fields of content authentication, secret communication and the like.

Drawings

FIG. 1 is a schematic diagram of embedding rules based on multiple histogram modifications;

FIG. 2 is a schematic diagram of the histogram mapping rule using multiple pairs of bins for the present method;

FIG. 3 is a schematic diagram of the ordered solution space (M ═ 2) and the greedy search mechanism constructed by the method, (a) is 2 pairs of pillars (-2,1) and (-4,3), (b) is 3 pairs of pillars (-1,0), (-2,1) and (-3, 2);

FIG. 4 is a comparison of the performance of the present method and the prior art method;

FIG. 5 is a schematic diagram of the dual layer embedding scheme of the present method;

FIG. 6 is a diagram of a diamond predictor;

fig. 7 is a schematic diagram of pixel complexity calculation.

Detailed Description

In order to make the aforementioned and other features and advantages of the invention more comprehensible, embodiments accompanied with figures are described in detail below.

The embodiment provides a high-capacity reversible information hiding method based on multi-histogram modification, which realizes the function of reversibly embedding and extracting secret information in an image and obtains a carrier image with small distortion degree, and the method comprises the following steps:

1. the method uses a double-layer embedding mode to divide all pixels of the whole image into two parts, and then layered embedding is carried out. As shown in fig. 5, the empty area pixels represent the first layer and the shaded area pixels represent the second layer. When embedding information, the information is embedded from left to right and from top to bottom, and the information is embedded in the first layer and then embedded in the second layer.

2. Preprocessing a carrier image: to prevent overflow of the modified pixel values, some pixels x_iModifications need to be made in advance, where K is the logarithm of the graph columns selected in the algorithm (number of calls):

and a position table is established to record the position of the modified pixel, which becomes part of the auxiliary information after compression.

3. Computing the prediction error e of a pixel from the neighborhood_iAnd complexity n_iAnd generating M prediction error histograms. Computing prediction values for pixels using diamond predictors

Fig. 6 shows the calculation of the diamond predictor:

after obtaining the predicted value, calculating to obtain the prediction error

Complexity n of a pixel_iThe calculation of (a) is as follows, i.e. the average value of the difference values of every two consecutive pixels in the horizontal and vertical directions is calculated in the neighborhood of 12 pixels:

n_i＝|u₂-u₅|+|u₅-u₉|+|u₆-u₁₀|+|u₃-u₇|+|u₇-u₁₁|+|u₁-u₄|+|u₄-u₈|+|u₈-u₁₂|+|u₃-u₄|+|u₅-u₆|+|u₆-u₇|+|u₇-u₈|+|u₉-u₁₀|+|u₁₀-u₁₁|+|u₁₁-u₁₂|

in order to improve the embedding capacity, for the generated M histograms, K is selected on each histogram for information embedding, namely the corresponding parameter is { (a)_n,k,b_n,k) L 1 is less than or equal to K, wherein a_n,K<…<a_n,1<0≤b_n,1<…<b_n,K. The embedding rule using pairs of pillars is then:

wherein

And m ∈ {0,1} represents the prediction error of the embedded image, and is an embedded binary information bit.

Fig. 2 shows a histogram mapping method for embedding information into a histogram using 2 pairs of bins and 3 pairs of bins, respectively. Wherein the points identified by the rectangles represent a plurality of parameters a selected on each histogram_n,kAnd b_n,k。

4. Determining approximately optimal parameters according to a greedy search algorithm, for each histogram b_nIn other words, there are K parameters { b }_n,k|1≤k≤K}。

Specifically, a single histogram h is calculated_nCapacity of embedding EC when using multiple parameters_nAnd embedding distortion ED_n，

In order to find the optimal parameters, the following optimization problem needs to be solved:

where P denotes a given load requirement and consists of secret information and side information to be embedded.

Here, the value range of the parameter is limited based on the distribution property of the prediction error histogram, as follows:

where T represents a threshold value of an integer, which can be adjusted to define the range of the parameter, b_n,kInfinity means that k-1 is used at most for information embedding in the graph column. For a given logarithm of the bin K,

representing the number of all possible parameter selection cases. If an exhaustive search is used, the computational complexity is O (S)^M). For example, when K is 4, M is 16, and T is 8, the computational complexity approaches O (2)¹¹⁸). In the face of such a large solution space, it is impractical to use an exhaustive approach.

In order to quickly solve the optimization problem, the method provides a greedy search algorithm. Definition of X_n＝(b_n,1,...,b_n,K) For the nth histogram h_nCandidate of (1), EC_n(X_n) And ED_n(X_n) Respectively its corresponding embedding capacity and embedding distortion. First, an M-dimensional solution space is constructed, points (X) in the solution space₁,…X_M) Represents an embedding schemeRequired complete parameter, wherein X_nIs represented in histogram h_nThe above selected parameters. In particular, in each dimension of space, all candidates are arranged in ascending order according to the size of the embedding capacity. Thus, the optimization problem described above can be viewed as searching for an optimal solution in the constructed ordered solution space. Fig. 3 shows the constructed solution space, where M is 2 and the horizontal axis represents the space at h₁The vertical axis represents the value in h₂The above parameters are selected.

Next, a greedy search strategy is implemented in the constructed solution space. With the origin of the solution space as the initial state W₀The embedding capacity at this time is 0. Then iteratively find the next state W_mUntil reaching an end point W in the solution space_endThe end point represents the parameter scheme with the maximum embedding capacity. At each iteration, only one histogram is selected to increase capacity, i.e. only W is modified at a time_mOne of the items corresponds to that the current point selects one of the M dimensions at a time in the solution space, and moves one step forward along the dimension. Therefore, the next state, which has a total of M possibilities, is selected as the next state W as the candidate that minimizes the ratio of embedding distortion to embedding capacity_m+1. This is the greedy idea of selecting the current optimal direction to proceed each time one step is taken in the direction of increasing capacity. For example, in FIG. 3, W_mRepresenting the current state, the next reachable states are A and B, and A with smaller ratio is selected as the next state W by comparing ED (A)/EC (A) with ED (B)/EC (B)_m+1. Repeating the above process until reaching W_endAnd finally obtaining a search path in the solution space. The point on this path that minimizes the ratio of embedding distortion to embedding capacity while meeting the load requirements is the optimal solution. W in FIG. 3_optIs an example of the resulting optimal solution.

Obviously, the complexity of determining parameters is greatly reduced by using the proposed greedy search algorithm, and the algorithm complexity is O (MS). Efficient algorithms make it possible to extend the multi-histogram based modification approach to high-volume solutions and can be adapted to real-time application scenarios.

It can be seen that the computational complexity of the greedy search depends on the number M of histograms and the size S of the candidate set, where S is determined by the logarithm K of the parameter. Table 1 shows the average run time of the proposed greedy search algorithm over the test picture set for different parameter pairs K when M ═ 16. The result display algorithm is very efficient and can meet the requirements of real-time application.

TABLE 1 running time of the greedy search algorithm of the present method

K	1	2	3	4
					Average run time (seconds)	0.013	0.023	0.038	0.059

5. Auxiliary information is generated which ensures a lossless restoration of the carrier image. The auxiliary information comprises a compression position table obtained in the process, M-1 thresholds for dividing the histogram and a parameter b obtained by algorithm solution_n,k. The auxiliary information is embedded in the header of the image by using a least significant bit replacement method.

6. Embedding information according to the optimal parameters determined in the process to obtain the modified prediction error

The embedded carrier pixel is

An embedded carrier image is obtained.

7. The extraction process and the embedding process are in reverse order, auxiliary information is extracted from the image header, and information can be extracted from the image and the carrier can be recovered according to parameters in the auxiliary information.

At the receiving end, the original prediction error is recovered by the following formula,

further, the secret information is extracted according to the following formula,

fig. 4 shows the performance comparison of the method and four other classical reversible information hiding algorithms, namely the comparison of PSNR of the embedded image when the embedding capacity is from 10,000 bits to 160,000 bits for a gray scale image Lena of 512x512 size. Where the solid dots identify the original multi-histogram modification based approach of Li et al, it can be seen that the embedding capacity of this approach is much smaller than that of the present approach. Compared with other methods, the method has better embedding performance, namely, the same information is embedded, and the image distortion is smaller.

The above embodiments are only intended to illustrate the technical solution of the present invention and not to limit the same, and a person skilled in the art can modify the technical solution of the present invention or substitute the same without departing from the spirit and scope of the present invention, and the scope of the present invention should be determined by the claims.

Claims (10)

1. A high-capacity reversible information hiding method based on multi-histogram modification comprises the following steps:

preprocessing a carrier image, and performing partial pixel x with the value in the image within a specific range_iThe modification is performed according to the following formula, a position table is established to record the position of the modified pixel,

computing pixel x from neighborhood_iPrediction error e of_iAnd complexity n_iGenerating M prediction error histograms;

at each histogram h_nSelecting K pairs of columns, corresponding to K parameters, and determining optimal parameters according to a greedy search algorithm;

generating auxiliary information capable of ensuring lossless recovery of the carrier image, wherein the auxiliary information comprises a position table, M-1 thresholds for dividing the histogram and parameters corresponding to the histogram;

dividing all pixels of the carrier image into two layers, and embedding the secret information and the auxiliary information to be embedded into the K pairs of image columns in a layering manner according to the determined optimal parameters, wherein the auxiliary information is embedded into the head of the image;

obtaining modified prediction error after embedding

According to the embedded pixels

An embedded carrier image is obtained.

2. The method of claim 1, wherein the prediction error is

The prediction value of the pixel is calculated according to the diamond predictor.

3. The method of claim 1, in which complexity n_iThe calculation method comprises the following steps: in the neighborhood of 12 pixels, the average value of the difference values of every two consecutive pixels in the horizontal and vertical directions is calculated, namely the complexity n_i。

4. The method of claim 1, wherein the parameters for K pairs of columns are { (a)_n,k,b_n,k) L 1 is less than or equal to K, wherein a_n,K<…<a_n,1<0≤b_n,1<…<b_n,KThen, the embedding rule of the multiple pairs of the drawing columns is as follows:

wherein

And m ∈ {0,1} represents the prediction error of the embedded image, and is an embedded binary information bit.

5. The method of claim 4, wherein determining optimal parameters according to a greedy search algorithm comprises the steps of:

calculating to obtain a single histogram h_nCapacity of embedding EC when using multiple parameters_nAnd embedding distortion ED_n，

Where h () represents the frequency count of the prediction error for a certain value;

solving an optimization problem by using a greedy search algorithm, and determining optimal parameters, wherein the optimization problem is as follows:

where P denotes a given load requirement and consists of secret information and side information to be embedded.

6. The method of claim 5, wherein the parameters have the following ranges:

where T represents an integer threshold.

7. The method as claimed in claim 1 or 5, wherein the greedy search algorithm is that in the solution space, the origin of the solution space is used as an initial state, from the initial state, the current optimal direction is selected to advance to search for the next state, and the search is performed iteratively until the end point in the solution space is reached.

8. The method of claim 7, wherein solving the optimization problem using a greedy search algorithm is specifically:

constructing an M-dimensional solution space, points (X) in the solution space₁,…X_M) Represents a complete parameter required for embedding, wherein X_nIs represented in histogram h_nThe parameters are selected, and all candidates are arranged in ascending order according to the size of the embedding capacity in each dimension of the space;

with the origin of the solution space as the initial state W₀Selecting the candidate which minimizes the ratio of embedding distortion to embedding capacity as the next state, and iteratively searching the next state until the next state is reachedReaching the end point in the solution space to obtain a search path in the solution space;

on this path, finding the point where the ratio of embedding distortion to embedding capacity is minimal while satisfying the load requirement is the optimal solution.

9. The method of claim 1, wherein the information is embedded in a left-to-right, top-to-bottom order, with the information being embedded first at a first layer and then at a second layer.

10. A method for extracting information from an embedded carrier image obtained by the method of any one of claims 1 to 9, comprising the steps of:

extracting auxiliary information from the header of the embedded carrier image;

and extracting the embedded secret information from the image and recovering the carrier according to the position table in the auxiliary information, the threshold values of the M-1 partition histograms and the parameters corresponding to the histograms.

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