Reversible data hiding method and system based on adaptive modification of multiple histograms

Abstract

The present invention belongs to the field of information security technology, provides a reversible data hiding method and system based on multiple histogram adaptive modification, designs a more general MHM framework to define multiple spatial extensions, instead of selecting only one pair of expansion spaces in each PEH, multiple pairs of expansion spaces are used in each PEH for expansion. In addition, the embedding performance is optimized by the proposed expansion space selection strategy. Therefore, according to the sharpness of the distribution, multiple PEHs are allowed to be embedded with different capacities, that is, low-refractive-index PEHs composed of smoother pixels are embedded with a larger capacity than high-refractive-index pixels.

Description

Technical Field

[0001] The present invention belongs to the field of information security technology, and in particular relates to a reversible data hiding method and system based on adaptive modification of multiple histograms. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Existing reversible data hiding methods include those based on histogram shift and differential expansion. Histogram shift uses the peak points of the image histogram to embed data, while differential expansion embeds data by expanding the difference between two pixels. Currently, histograms use multiple histogram modifications (MHM). Through MHM, multiple histograms can be modified differently to obtain good embedding performance. However, since the maximum modification to each pixel value is 1, only one pair of spaces in the expanded prediction error histogram (PEH) is allowed for data embedding. This shortcoming leads to low capacity and limits its expansion to high-capacity scenarios. Summary of the invention

[0004] In order to solve at least one technical problem existing in the above-mentioned background technology, the present invention provides a reversible data hiding method and system based on multiple histogram adaptive modification, which utilizes multi-directional prediction of predicted pixels to improve accuracy and designs a more general MHM framework to define multiple spatial extensions.

[0005] In order to achieve the above object, the present invention adopts the following technical solution:

[0006] A first aspect of the present invention provides a reversible data hiding method based on adaptive modification of multiple histograms, comprising the following steps:

[0007] Obtaining an original image, preprocessing the original image, dividing the original image pixels into a shadow layer and a blank layer according to a chessboard pattern, and embedding data on the shadow layer and the blank layer pixels respectively;

[0008] The directional expansion prediction method is used to predict the horizontal and vertical directions of the pixels respectively. The prediction error with the smaller prediction error in the two directions is selected as the prediction error of the predicted pixel to obtain the prediction error of all pixels of the image. When the embedding condition is met, the prediction errors of all pixels are plotted into multiple prediction error histograms according to different smoothness levels.

[0009] Multiple prediction error histograms select each adaptive expansion space pair, and use a multiple histogram modification method to perform adaptive modification. Multiple pairs of expansion spaces are used for expansion in each prediction error histogram. According to the sharpness of the distribution, multiple prediction error histograms embed data with each adaptive capacity.

[0010] A second aspect of the present invention provides a reversible data hiding system based on adaptive modification of multiple histograms.

[0011] include:

[0012] The original image preprocessing module is configured to: obtain the original image, preprocess the original image, divide the original image pixels into a shadow layer and a blank layer according to a chessboard pattern, and embed data on the two layers of pixels in the shadow layer and the blank layer respectively;

[0013] The prediction error histogram generation module is configured to: use a directional expansion prediction method to predict the horizontal and vertical directions of the pixel respectively, select the prediction error with the smaller prediction error in the two directions as the prediction error of the predicted pixel, obtain the prediction error of all pixels of the image, and plot the prediction errors of all pixels into multiple prediction error histograms according to different smoothness levels when the embedding condition is met;

[0014] The data embedding module is configured as follows: multiple prediction error histograms select each adaptive expansion space pair, use a multiple histogram modification method to perform adaptive modification, use multiple pairs of expansion spaces to expand each prediction error histogram, and according to the sharpness of the distribution, multiple prediction error histograms embed data with each adaptive capacity.

[0015] A third aspect of the present invention provides a computer-readable storage medium.

[0016] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps in the reversible data hiding method based on adaptive modification of multiple histograms as described above.

[0017] A fourth aspect of the present invention provides a computer device.

[0018] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps in the reversible data hiding method based on adaptive modification of multiple histograms as described above are implemented.

[0019] Compared with the prior art, the present invention has the following beneficial effects:

[0020] The present invention improves the prediction method for higher capacity, uses multi-directional prediction of prediction pixels to improve accuracy, and designs a more general MHM framework to define multiple spatial extensions, that is, instead of selecting only one pair of expansion spaces in each PEH, multiple pairs of expansion spaces are used for expansion in each PEH. In addition, the embedding performance is optimized by the proposed expansion space selection strategy. Therefore, depending on the sharpness of the distribution, multiple PEHs are allowed to be embedded with different capacities, that is, low-refractive-index PEHs composed of smoother pixels are embedded with a larger capacity than high-refractive-index pixels, which is not achievable with the traditional MHM method. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0022] Figure 1 It is a schematic flow chart of a reversible data hiding method based on adaptive modification of multiple histograms according to a first embodiment of the present invention;

[0023] Figure 2 This is a schematic diagram of pixel chessboard layering in an embodiment of the present invention;

[0024] Figure 3 This is a schematic diagram of an example of modifying a single histogram. DETAILED DESCRIPTION

[0025] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0026] It should be noted that the following detailed descriptions are all illustrative and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0027] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0028] Explanation of terms

[0029] RDH: (reversible data hiding), reversible data hiding;

[0030] PEH: (Prediction Error Histogram), prediction error histogram;

[0031] Reversible data hiding (RDH) is the study of how to reversibly embed data into digital work without introducing permanent distortion. Unlike traditional data hiding, RDH provides a key to handling information processing in sensitive fields due to its perfect ability to recover secret data and original media. Due to these characteristics, RDH plays an important role in many multimedia applications, such as medical image processing, multimedia archive management, image transcoding, 3D mesh model protection, etc.

[0032] For RDH, embedding performance is measured by the trade-off between embedding capacity and image fidelity. Capacity corresponds to the amount of hidden data, and fidelity is the peak signal-to-noise ratio (PSNR) of the labeled image relative to the original image. The required capacity of an RDH method depends on the specific scenario in which it is applied. For example, in a hospital information system, a lot of information such as patient information, doctor's diagnosis and other treatment information should be hidden in a medical image. In this case, a high capacity is indeed required to accommodate such a large payload. In addition, high-capacity embedding creates a strategic advantage, helping the encoder to embed more data per media, thus using less obvious media for secure data transmission. Therefore, the risk of being discovered may be reduced. However, the increase in capacity often comes at the cost of distortion. Therefore, it is necessary to achieve high capacity while keeping the distortion rate low.

[0033] Embodiment 1

[0034] The present invention proposes an effective high-capacity embedding solution. For higher capacity, the prediction method is improved, the prediction accuracy is improved by using multi-directional prediction of predicted pixels, and a more general MHM framework is designed to define multiple spatial extensions, that is, instead of selecting only one pair of expansion spaces in each PEH, multiple pairs of expansion spaces are used in each PEH for expansion. In addition, the embedding performance is optimized by the proposed expansion space selection strategy. Therefore, depending on the sharpness of the distribution, multiple PEHs are allowed to be embedded with different capacities, that is, low-refractive-index PEHs composed of smoother pixels are embedded with a larger capacity than high-refractive-index pixels. This is not achievable with the traditional MHM method.

[0035] like Figure 1 As shown, this embodiment 1 provides a reversible data hiding method based on adaptive modification of multiple histograms, including the following steps:

[0036] Step 1: Get the original image, pre-process the original image, divide the original image pixels into shadow layer and blank layer according to the chessboard pattern, embed half of the payload in each layer, and embed data on the shadow layer and blank layer pixels respectively;

[0037] Step 2: Use the directional expansion prediction method to predict the horizontal and vertical directions of the pixel respectively, select the prediction error with the smaller prediction error in the two directions as the prediction error of the predicted pixel, and obtain the prediction error of all pixels in the image. Under the condition of meeting the embedding condition, the prediction errors of all pixels are plotted into multiple prediction error histograms according to different smoothness levels;

[0038] Step 3: Multiple prediction error histograms select each adaptive expansion space pair, and use a multiple histogram modification method to perform adaptive modification. Multiple pairs of expansion spaces are used in each prediction error histogram for expansion. According to the sharpness of the distribution, multiple prediction error histograms embed data with each adaptive capacity.

[0039] In step 2, the embedding process does not satisfy the embedding conditions for all directions of prediction, which are:

[0040] The prediction errors are limited to the prediction errors in both directions having the same sign, i.e., both are greater than or equal to zero or both are less than zero;

[0041] Or, the predicted pixel value is the average of the predicted values ​​in both directions plus the pixels between one and the maximum predicted value or the average of the predicted values ​​in both directions minus the pixels between one and the minimum predicted value.

[0042] In step 2, the step of drawing a plurality of prediction error histograms according to different smoothness levels includes: collecting pixels with a given smoothness together to generate a prediction error histogram, and by changing the smoothness to cover the entire image, a series of histogram sequences can be derived.

[0043] like Figure 2 As shown, for the smoothness L of the partition histogram standard i , as shown in formula (1), is obtained by summing the smoothness in the horizontal direction and the smoothness in the vertical direction, as shown in formula (2) and formula (3), the horizontal smoothness L h and the vertical smoothness L v are the sum of the absolute differences between adjacent pixels in the horizontal and vertical directions, respectively.

[0044] L i =L v +L h (1)

[0045] L v =|ω 2 -ω 5 |+|ω 5 -ω 9 |+|ω 3 -ω 7 |+|ω4 -ω 6 |

[0046] +|ω 6 -ω 11 |+|ω 10 -ω 8 |+|ω 8 -ω 12 |+|ω 12 -ω 13 |+|ω 2 -ω 4 | (2)

[0047] L h =|ω 5 -ω 3 |+|ω 3 -ω 6 |+|ω 6 -ω 12 |+|ω 9 -ω 7 |+|ω 7 -ω 11 |+|ω 11 -ω 13 | (3)

[0048] Dividing the smoothness into multiple subsets will generate the same number of PEHs. For example, suppose the full range of smoothness is subdivided into 16 intervals, including [k 0 , k 1 ],[k 1 +1, k 2 ],…,[k 15 +1, k 16 ], so that each interval contains an approximately equal number of forecast errors. Here, we will 0 and k 16 Set to zero and maximum values ​​of smoothness respectively. In this way, no matter what the image is, the number of multiple PEHs is fixed to 16. The image is modified in a pixel-wise manner, i.e. from left to right and from top to bottom, and data embedding will stop until the payload is fully embedded.

[0049] The existing technology uses diamond prediction or median edge detection to calculate the prediction error. The present invention uses a directional expansion prediction method, which is more accurate. The more compact and steep the PEH is, the better the embedding performance is.

[0050] The data embedding and extraction process has the same mechanism for modifying a single PEH, except that the number of expansion space pairs adaptively selected for each PEH is different. The present invention selects each adaptive expansion space pair according to different PEHs to achieve the purpose of obtaining the highest embedding capacity under low distortion.

[0051] In step 3, multiple pairs of expansion spaces are used in each prediction error histogram for expansion, including:

[0052] (1) Set each prediction error histogram h n The expansion space in is:

[0053]

[0054] Where A represents the space of the left part of the histogram where the prediction error is 0 in PEH, B represents the space of the right part of the histogram where the prediction error is 0 in PEH, and q n Indicates that the prediction error size of the right part of the nth histogram where the prediction error is 0 is q n space; p n The prediction error on the left side is p n space.

[0055] (2) The prediction error is modified using formula (5). The extraction process is the inverse process of embedding.

[0056]

[0057] where i∈{1,...,p n},j∈{1,...,q n}, are -∞ and +∞ respectively, m is the secret data to be embedded, m∈(0,1), e represents the prediction error, and e′ represents the prediction error after the original prediction error is modified by the embedding process.

[0058] For high-capacity embedding, the idea of ​​designing an efficient MHM in this embodiment is: on the one hand, in order to obtain high capacity, the common method is to improve the prediction accuracy and maximize the capacity of the PEH, that is, the highest space can be higher and use the highest space for expansion. On the other hand, in order to achieve adaptive embedding, some expansion spaces need to be adaptively modified. For these reasons, the present invention uses the prediction error close to zero as much as possible and maintains a certain degree of freedom in the selection of the expansion space.

[0059] Therefore, among multiple spaces in PEH, we make adaptive selection for a pair of spaces and select the other extended space as the highest one in PEH. For multiple PEH, the encoder can set the maximum amplitude of each PEH differently.

[0060] Assume that the maximum modification of a pixel by the PEH error histogram is δ n , then in formula (5) we have q n =p n =δ n .

[0061] δ n It means the modifiable expansion space. The subscript is added because there are n histograms, and the space modified for each histogram is different. It has the same meaning as the following text, but it only explains the choice of δ. There is no subscript because the process of selecting δ is the same.

[0062] The parameters of the expansion space are {(A n，δn , ..., A n，1 , B n，1 , ..., B n，δn )}. According to formula (5), a single PEH h in this method is selected n The multiple expansion spaces of are:

[0063]

[0064] Here, the first condition in formula (6) means to symmetrically choose δ n The second condition is set to select the highest δ n -1 expands the space, and the last condition gives the freedom to determine a pair of spaces within a finite range.

[0065] For each candidate δ, the encoder processes the optimization and obtains a parameter set, selecting the best amplitude δ in the pool. opt As the δ that produces the highest PSNR at a given capacity opt Therefore, once embedded, it is necessary to change from 1≤δ≤δ max Select the optimal amplitude δ opt , where δ max represents the maximum value of candidate δ in the cycle.

[0066] The purpose of using multiple histogram modification methods for adaptive modification is to select different expansion spaces according to different histograms to modify them, which can maximize the embedding capacity;

[0067] The best expansion space pair in each histogram is selected according to δ to achieve high capacity embedding.

[0068] Instead of enumerating all amplitudes, the present invention adopts a quasi-greedy search to find the minimum amplitude to satisfy the capacity, and then performs local optimization with a larger value. If better performance is obtained, the optimal amplitude will be updated. In most cases, the quasi-greedy search provides almost the same performance as the exhaustive search, but can reduce the computational burden.

[0069] This example mainly evaluates the embedding performance between the capacity (bits per pixel, bpp) of the method and the PSNR value (db) of the labeled image.

[0070] The proposed method is compared with three high-capacity RDH methods proposed by Sachnev et al. [2], four state-of-the-art methods including Dragoi and Coltuc et al. [1], Wang et al. [3], and an MHM-based method [4].

[0071] According to the PSNR comparison of images at the same embedding rate given in Table 1 (the symbol "-" indicates that the method cannot meet the capacity), it is found that the performance of the method of the present invention is the best. Compared with an MHM-based method, the method of the present invention can obtain a slight gain, and the gain is mainly due to the fact that the method of the present invention has more expansion space options, so as to obtain some more reasonable modification methods to improve the embedding capacity.

[0072] Table 1 PSNR comparison of images at the same embedding rate

[0073]

[0074]

[0075] like Figure 3 As shown in the figure, this embodiment is an example of the proposed single PEH modification mechanism. The expansion space is δ = 3 and (B n，1 , B n,2 , B n,3 )=(0,1,4), that is, there are three pairs of expansion spaces in a single PEH. Among them, two pairs of spaces (-2,1) and (-1,0) are selected as the highest pair in the space in PEH, and then according to the first and third conditions in condition (4), from B n,3 ∈{2,...,8,∞} and A n,3 =-1-B n，3 The remaining spaces are used to shift to create empty spaces.

[0076] Embodiment 2

[0077] This embodiment provides a reversible data hiding system based on adaptive modification of multiple histograms, including:

[0078] The original image preprocessing module is configured to: obtain the original image, preprocess the original image, divide the original image pixels into a shadow layer and a blank layer according to a chessboard pattern, and embed data on the two layers of pixels in the shadow layer and the blank layer respectively;

[0079] The prediction error histogram generation module is configured to: use a directional expansion prediction method to predict the horizontal and vertical directions of the pixel respectively, select the prediction error with the smaller prediction error in the two directions as the prediction error of the predicted pixel, obtain the prediction error of all pixels of the image, and plot the prediction errors of all pixels into multiple prediction error histograms according to different smoothness levels when the embedding condition is met;

[0080] The data embedding module is configured as follows: multiple prediction error histograms select each adaptive expansion space pair, use a multiple histogram modification method to perform adaptive modification, use multiple pairs of expansion spaces to expand each prediction error histogram, and according to the sharpness of the distribution, multiple prediction error histograms embed data with each adaptive capacity.

[0081] Embodiment 3

[0082] This embodiment provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the steps in the reversible data hiding method based on adaptive modification of multiple histograms as described above are implemented.

[0083] Embodiment 4

[0084] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps in the reversible data hiding method based on adaptive modification of multiple histograms as described above are implemented.

[0085] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of hardware embodiments, software embodiments, or embodiments combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage and optical storage, etc.) containing computer-usable program code.

[0086] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0087] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0088] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0089] A person skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium, and when the program is executed, it can include the processes of the embodiments of the above-mentioned methods. The storage medium can be a disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM), etc.

[0090] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A reversible data hiding method based on adaptive modification of multiple histograms, characterized in that: The steps include: Obtaining an original image, preprocessing the original image, dividing the original image pixels into a shadow layer and a blank layer according to a chessboard pattern, and embedding data on the shadow layer and the blank layer pixels respectively; The directional expansion prediction method is used to predict the horizontal and vertical directions of the pixels respectively. The prediction error with the smaller prediction error in the two directions is selected as the prediction error of the predicted pixel to obtain the prediction error of all pixels of the image. When the embedding condition is met, the prediction errors of all pixels are plotted into multiple prediction error histograms according to different smoothness levels. Multiple prediction error histograms select each adaptive expansion space pair, use a multiple histogram modification method to perform adaptive modification, use multiple pairs of expansion spaces to expand each prediction error histogram, select the best expansion space pair in each histogram according to the modifiable expansion space, and embed data in multiple prediction error histograms with each adaptive capacity; Multiple expansion spaces for a single prediction error histogram include: Symmetrically select a pixel with the maximum modification and then expand the space; Select the maximum modification of the highest pixel minus 1 to expand the space; Determine a pair of spatial degrees of freedom within a finite range.

2. The reversible data hiding method based on adaptive modification of multiple histograms as claimed in claim 1, characterized in that: The embedding conditions are: The prediction errors are limited to the prediction errors in both directions having the same sign, i.e., both are greater than or equal to zero or both are less than zero; Or, the predicted pixel value is the average of the predicted values ​​in both directions plus the pixels between one and the maximum predicted value or the average of the predicted values ​​in both directions minus the pixels between one and the minimum predicted value.

3. The reversible data hiding method based on adaptive modification of multiple histograms as claimed in claim 1, characterized in that: The smoothness of the partition prediction error histogram standard is obtained by the sum of the smoothness in the horizontal direction and the smoothness in the vertical direction, wherein the smoothness in the horizontal direction and the smoothness in the vertical direction are the sum of the absolute differences of adjacent pixels in the horizontal direction and the vertical direction, respectively.

4. The reversible data hiding method based on adaptive modification of multiple histograms as claimed in claim 1, characterized in that: The expansion space in each prediction error histogram is: Where A represents the space of the left part of the histogram in PEH where the prediction error is 0, B represents the space of the right part of the histogram in PEH where the prediction error is 0; n represents the number of histograms, which is n; q n Indicates that the prediction error size of the right part of the nth histogram where the prediction error is 0 is q n space; p n The prediction error on the left side is p n space.

5. The reversible data hiding method based on adaptive modification of multiple histograms as claimed in claim 1, characterized in that: The process of adaptive modification using the multiple histogram modification method is: where i∈{1,...,p n },j∈{1,...,q n }, are -∞ and +∞ respectively, m is the secret data to be embedded, m∈(0,1), e represents the prediction error, e′ represents the prediction error modified by the embedding process, and n represents the number of histograms. n Indicates that the prediction error size of the right part of the nth histogram where the prediction error is 0 is q n space; p n The prediction error on the left side is p n space.

6. The reversible data hiding method based on adaptive modification of multiple histograms as claimed in claim 1, characterized in that: The process of obtaining the maximum modification of a pixel is as follows: For each candidate δ, the encoder processes the optimization and obtains a parameter set, selecting the best amplitude δ in the pool. opt As the δ that produces the highest PSNR at a given capacity opt , from 1≤δ≤δ max Select the optimal amplitude δ opt , where δ max represents the maximum value of candidate δ in the cycle.

7. A reversible data hiding system based on adaptive modification of multiple histograms, characterized in that: include: The original image preprocessing module is configured to: obtain the original image, preprocess the original image, divide the original image pixels into a shadow layer and a blank layer according to a chessboard pattern, and embed data on the two layers of pixels in the shadow layer and the blank layer respectively; The prediction error histogram generation module is configured to: use a directional expansion prediction method to predict the horizontal and vertical directions of the pixel respectively, select the prediction error with the smaller prediction error in the two directions as the prediction error of the predicted pixel, obtain the prediction error of all pixels of the image, and plot the prediction errors of all pixels into multiple prediction error histograms according to different smoothness levels when the embedding condition is met; The data embedding module is configured to: select each adaptive expansion space pair from a plurality of prediction error histograms, perform adaptive modification using a multiple histogram modification method, use multiple pairs of expansion spaces for expansion in each prediction error histogram, select the best expansion space pair in each histogram according to the modifiable expansion space, and embed data in the plurality of prediction error histograms with each adaptive capacity; Multiple expansion spaces for a single prediction error histogram include: Symmetrically select a pixel with the maximum modification and then expand the space; Select the maximum modification of the highest pixel minus 1 to expand the space; Determine a pair of spatial degrees of freedom within a finite range.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the reversible data hiding method based on adaptive modification of multiple histograms as described in any one of claims 1 to 6 are implemented.

9. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps in the reversible data hiding method based on adaptive modification of multiple histograms as described in any one of claims 1 to 6 are implemented.

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