Three-dimensional mesh model reversible information hiding method based on binary sorting

Abstract

The invention discloses a three-dimensional grid model reversible information hiding method based on binary sorting, which comprises the following steps: a sender preprocesses an original grid model to obtain a preprocessed grid model; in combination with secret information to be hidden, a secret-carrying grid model is generated through a secret information embedding algorithm based on binary sorting; after receiving the secret-carrying grid model, a receiver performs preprocessing of the same steps on the secret-carrying grid model; and an original grid model and complete secret information are synchronously recovered through a binary sorting-based secret information extraction algorithm. The method has good reversibility and concealment, and is suitable for the fields of copyright protection, content integrity authentication and the like of the three-dimensional model.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of information security, and in particular to a three-dimensional grid model reversible information hiding method based on binary sorting. BACKGROUND

[0002] Three-dimensional grid reversible information hiding is a cutting-edge information security technology, which aims to embed secret information into a three-dimensional model and achieve complete extraction at the receiving end and lossless recovery of the carrier. The core value of this technology lies in its reversibility, that is, while performing the information hiding function, it can completely eliminate the modifications caused by the embedding operation on the original model, thus showing important application potential in the fields of copyright protection and data security of three-dimensional models. In the fields of cultural heritage protection and high-value industrial design, this technology can be used to embed reversible copyright marks, which can provide irrefutable digital evidence for infringement identification and maintain the visual integrity and commercial value of the model in daily use, achieving the unity of copyright protection and model fidelity. In scenarios such as military command, judicial evidence, and remote medical care, where data authenticity is highly required, any irreversible tampering can lead to serious consequences. Taking remote medical care as an example, doctors can embed diagnostic annotation information in three-dimensional organ models to assist in research and judgment, and then completely remove these annotations after diagnosis to restore the original clinical data state, thus ensuring information exchange efficiency while maintaining the integrity of medical data and the reliability of diagnosis. Existing three-dimensional model reversible information hiding schemes can be mainly divided into three categories: three-dimensional grid reversible information hiding methods based on difference expansion (DE), three-dimensional grid reversible information hiding methods based on histogram shifting (HS), and three-dimensional grid reversible information hiding methods based on prediction error expansion (PEE). Although these basic schemes successfully introduced the concept of reversible embedding into three-dimensional space, they all have obvious limitations in practical applications: DE methods have considerable capacity but significant geometric distortion; HS methods can control distortion but are limited by inherent capacity; and PEE frameworks achieve a better trade-off, but their performance largely depends on prediction accuracy. SUMMARY

[0003] The present application provides a three-dimensional grid model reversible information hiding method based on binary sorting to overcome the problems of considerable capacity but significant geometric distortion, control of distortion but limitation by inherent capacity, and better trade-off but performance largely dependent on prediction accuracy in the prior art.

[0004] To achieve the above-mentioned purpose, the technical scheme of the present application is as follows: A three-dimensional grid model reversible information hiding method based on binary sorting, comprising: S1, the sender pre-processes the original grid model to obtain a pre-processed grid model; S2, obtaining the steganographic grid model according to the pretreated grid model and the secret information through the secret information embedding algorithm based on binary sorting; S3, the receiver receives the steganographic grid model and pretreats the steganographic grid model to obtain the pretreated steganographic grid model; S4, obtaining the original grid model and the secret information through the secret information extraction algorithm based on binary sorting according to the pretreated steganographic grid model.

[0005] Further, the embedding information flow of the secret information embedding algorithm based on binary sorting is as follows: S21, performing three-layer vertex division on the pretreated grid model to obtain a candidate set and a reference set; S22, obtaining a spatial n-gon according to the reference set, obtaining a plurality of embedding units according to the spatial n-gon and the candidate set, obtaining a predicted position of the center vertex of each embedding unit through the arithmetic mean of the vertex coordinates of the spatial n-gon, and then obtaining a prediction error vector and combining the prediction error vectors into a prediction error sequence; S23, adding the internal angles corresponding to each vertex in the spatial n-gon to obtain the internal angle sum of the spatial n-gon, obtaining the edge length of each edge of the spatial n-gon through the coordinates of each vertex in the spatial n-gon, and then obtaining the edge length variance of the spatial n-gon, obtaining the binary sorting parameter value corresponding to each embedding unit according to the internal angle sum of the spatial n-gon and the edge length variance of the spatial n-gon, arranging the embedding units in ascending order according to the binary sorting parameter value to obtain the sorted embedding units, and sorting the prediction error vectors corresponding to the embedding units according to the sorted embedding units to obtain the sorted prediction error sequence; S24, embedding the preset auxiliary information bit stream and the payload bit stream containing the secret information into the sorted prediction error sequence to obtain a modified prediction error sequence; S25, adding the modified prediction error sequence and the predicted position of the center vertex of each embedding unit to obtain the position of the updated vertex, and converting the position coordinates of the updated vertex into floating-point numbers to obtain the steganographic grid model embedding initial information; S26, according to the steganographic grid model embedding initial information, performing S21 to S25 again to finally obtain the steganographic grid model.

[0006] Further, the extraction information flow of the secret information extraction algorithm based on binary sorting is as follows: S41, performing three-layer vertex division on the pretreated steganographic grid model to obtain a candidate set of steganographic model vertices and a reference set of steganographic model vertices; S42, obtaining a spatial n-gon according to the reference set of the steganographic model vertexes, obtaining a plurality of embedding units of the steganographic model according to the spatial n-gon and the candidate set of the steganographic model vertexes, obtaining the predicted position of the center vertex of each embedding unit of the steganographic model through the arithmetic mean of the spatial n-gon vertex coordinates, further obtaining the prediction error vector of the steganographic model, and combining the prediction error vectors of the steganographic model into the prediction error sequence of the steganographic model; S43, adding the internal angles corresponding to each vertex in the spatial n-gon to obtain the internal angle sum of the spatial n-gon, obtaining the edge length of each edge of the spatial n-gon through the coordinates of each vertex in the spatial n-gon, further obtaining the edge length variance of the spatial n-gon, obtaining the binary sorting parameter value corresponding to each embedding unit of the steganographic model according to the internal angle sum of the spatial n-gon and the edge length variance of the spatial n-gon, arranging the embedding units of the steganographic model in ascending order according to the binary sorting parameter value to obtain the embedding units of the steganographic model after sorting, and sorting the prediction error vectors of the steganographic model corresponding to the embedding units of the steganographic model according to the embedding units of the steganographic model after sorting to obtain the sorted prediction error sequence of the steganographic model; S44, extracting the auxiliary information bit stream and the payload bit stream from the sorted prediction error sequence of the steganographic model in sequence to obtain the auxiliary information, the payload, and the recovered prediction error sequence, and obtaining the secret information through the payload; S45, adding the predicted position of the center vertex of each embedding unit of the steganographic model to the recovered prediction error sequence to obtain the position of the updated steganographic model vertex, and obtaining the initial recovered mesh model by transforming the position coordinates of the updated original steganographic model vertex into floating-point numbers; S46, executing S41 to S45 again according to the initial recovered mesh model to finally obtain the original mesh model.

[0007] Further, the three-layer vertex division is to divide the mesh model vertexes into three independent point sets through modulo three operation, and the expression for dividing the vertexes is: (1) In the formula, is a subset of the vertex set; is the vertex with index number u is the vertex index number; u is the vertex index number; is the modulo three operation; is the hierarchical variable.

[0008] Further, the specific steps for calculating the predicted position of the center vertex of the embedding unit and further obtaining the prediction error vector are as follows: S221, obtaining the position coordinates of the predicted center vertex through the arithmetic mean of the spatial n-gon vertex coordinates, and the expression is: (2) wherein, is the position coordinate of the predicted center vertex; is the horizontal axis coordinate value of the predicted center vertex; is the vertical axis coordinate value of the predicted center vertex; is the depth axis coordinate value of the predicted center vertex: is the number of vertices of the spatial n-gon; is the center vertex of the embedding unit; is a vertex of the spatial n-gon; is the integer coordinate value of a vertex of the spatial n-gon in the horizontal axis; is the integer coordinate value of a vertex of the spatial n-gon in the vertical axis; is the integer coordinate value of a vertex of the spatial n-gon in the depth axis; S222, obtaining a prediction error vector according to the position coordinate of the predicted center vertex and the position coordinate of the real center vertex, and the expression is: (3) wherein, is the prediction error vector of the center vertex of the embedding unit; is the prediction error of the center vertex of the embedding unit in the horizontal axis; is the prediction error of the center vertex of the embedding unit in the vertical axis; is the prediction error of the center vertex of the embedding unit in the depth axis; is the position coordinate of the real center vertex.

[0009] Further, the specific steps of obtaining the binary ordering parameter value of the embedding unit according to the internal angle sum of the spatial n-gon and the side length variance of the spatial n-gon include: S231, obtaining the main ordering parameter value of the embedding unit according to the internal angle sum of the spatial n-gon, and the expression of the main ordering parameter value of the embedding unit is: (4) wherein, is the main ordering parameter value of the embedding unit: is the internal angle corresponding to a vertex of the spatial n-gon; is the internal angle sum of the spatial n-gon; S232, ordering the embedding unit sequence according to the main ordering parameter value of the embedding unit, and evenly dividing the embedding unit sequence to obtain L continuous subsequences; S233, obtaining the auxiliary ordering parameter value of the embedding unit according to the side length variance of the spatial n-gon, and the expression of the auxiliary ordering parameter value of the embedding unit is: (5) wherein, obtaining the auxiliary sorting parameter value of the embedding unit; obtaining the average length of the n-gon in the space; n obtaining the average length of the n-gon in the space; j obtaining the average length of the n-gon in the space; obtaining the average length of the n-gon in the space; n obtaining the average length of the n-gon in the space; j+ obtaining the average length of the n-gon in the space; obtaining the average length of the n-gon in the space; obtaining the average length of the n-gon in the space; obtaining the average length of the n-gon in the space; (6); S234, obtaining the binary sorting parameter according to the auxiliary sorting parameter value of the embedding unit and the L continuous sub-sequences; the expression of the binary sorting parameter is: (7) wherein, obtaining the auxiliary sorting parameter value of the embedding unit; obtaining the sequence number of the continuous sub-sequence; obtaining the total number of the continuous sub-sequences.

[0010] Further, the specific steps of obtaining the modified prediction error sequence include: S241, extracting the least significant bit of the first 64 prediction errors of the sorted prediction error sequence; the expression is: (8) wherein, obtaining the least significant bit of the prediction error of the center vertex of the embedding unit on the k-axis; obtaining the prediction error of the center vertex of the embedding unit; obtaining the variable of the coordinate axis; respectively, the horizontal axis, the vertical axis and the depth axis; S242, embedding the preset auxiliary information bit stream into the least significant bit of the first 64 prediction errors of the sorted prediction error sequence; the expression is: (9) wherein, obtaining the prediction error of the center vertex of the embedding unit on the k-axis after embedding the auxiliary information bit; obtaining one bit of the auxiliary information; S243, embedding the payload bit stream into the remaining prediction errors of the sorted prediction error sequence by the extended translation method, to obtain the modified prediction error sequence; the prediction error of the modified prediction error sequence embedded with the payload bit is: (10) wherein, The center vertex of the embedding unit is embedded with a load bit k Prediction error modified on the axis; And The preset integer for controlling the embedding capacity; One bit of the load.

[0011] Further, the specific steps for obtaining the recovered prediction error sequence include: S441, read the least significant bits of the first 64 prediction errors of the sorted steganographic model prediction error sequence to obtain an auxiliary information bit stream; the auxiliary information bits of the auxiliary information bit stream are represented by the following formula: (11); S442, perform a recovery operation on the least significant bits of the first 64 prediction errors to obtain the first 64 recovered prediction errors; the first 64 recovered prediction errors are: (12); S443, extract the expression of the load from the remaining prediction errors of the sorted steganographic model prediction error sequence by reverse spreading: (13); S444, perform a recovery operation on the prediction errors after load extraction to obtain a recovered prediction error sequence; the expression of the recovery operation on the prediction errors after load extraction is: (14).

[0012] Beneficial effects: The three-dimensional grid model reversible information hiding method based on binary sorting can obtain the topological correlation of multiple neighborhood vertices of the center vertex of the embedding unit through the prediction scheme of the spatial n-polygon, accurately predict the position of the center vertex of the embedding unit, effectively generate smaller prediction errors, and further obtain superior embedding performance. Through the binary sorting scheme, the internal angle and the length variance of the spatial n-polygon are fused to comprehensively evaluate the smoothness of the embedding unit; all embedding units are arranged in ascending order according to the calculated binary sorting parameter value; embedding is performed by preferentially selecting embedding units with higher smoothness, effectively reducing the geometric distortion of the model caused by information hiding, and significantly improving the visual quality of the steganographic model. BRIEF DESCRIPTION OF DRAWINGS

[0013] In order to make the technical solutions of the embodiments of the present application or the prior art clearer, the accompanying drawings needed in the embodiments or prior art description will be briefly introduced. Obviously, the accompanying drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort on the basis of these drawings.

[0014] Figure 1 Flow chart of the reversible information hiding method of the present application; Figure 2 Flow chart of the secret information embedding algorithm and the secret information extraction algorithm in the embodiment of the present application; Figure 3 Schematic diagram of the center vertex of the embedding unit in the embodiment of the present application; Figure 4 SNR curve of different grid models under different embedding rates in the embodiment of the present application; Figure 5 Visual effect diagram of the stego grid model under a given embedding rate in the embodiment of the present application; Figure 6 Performance comparison diagram of the existing algorithm in the embodiment of the present application. DETAILED DESCRIPTION

[0015] In order to make the technical solutions of the embodiments of the present application or the prior art clearer, the accompanying drawings needed in the embodiments or prior art description will be briefly introduced. Obviously, the accompanying drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort on the basis of these drawings.

[0016] The embodiment provides a three-dimensional grid model reversible information hiding method based on binary ordering, as shown in the following formula (1), which comprises the following steps: Figure 1 S1, a sender pre-processes an original grid model to obtain a pre-processed grid model; S2, according to the pre-processed grid model and secret information, a secret information embedding algorithm based on binary ordering is used to obtain a stego grid model; S3, a receiver receives the stego grid model and pre-processes the stego grid model to obtain a pre-processed stego grid model; S4, according to the pre-processed stego grid model, a secret information extraction algorithm based on binary ordering is used to obtain the original grid model and the secret information.

[0017] ​In specific embodiments, the preprocessing quantifies the floating-point coordinates of the vertices uniformly into integer data by introducing a truncation function, and defines an integerization function as: (1) wherein, is the integer coordinate value of the vertex; is the floating-point coordinate value of the vertex; is the variable of the coordinate axis; is the horizontal axis, the vertical axis and the depth axis, respectively; is the precision parameter.

[0018] Preferably, as shown in Figure 2 , the embedding information flow of the secret information embedding algorithm based on the binary sorting is as follows: S21, performing three-layer vertex division on the preprocessed mesh model to obtain a candidate set and a reference set; S22, obtaining a spatial n-gon according to the reference set, obtaining a plurality of embedding units according to the spatial n-gon and the candidate set, obtaining a predicted position of a center vertex of each embedding unit through an arithmetic mean of vertex coordinates of the spatial n-gon, and then obtaining a prediction error vector, and combining the prediction error vectors into a prediction error sequence; S23, adding the internal angles corresponding to each vertex in the spatial n-gon to obtain a spatial n-gon internal angle sum, obtaining the lengths of the edges of the spatial n-gon through the coordinates of each vertex in the spatial n-gon, and then obtaining a spatial n-gon edge length variance, obtaining a binary sorting parameter value corresponding to each embedding unit according to the spatial n-gon internal angle sum and the spatial n-gon edge length variance, arranging the embedding units in ascending order according to the binary sorting parameter value to obtain sorted embedding units, and sorting the prediction error vectors corresponding to the embedding units according to the sorted embedding units to obtain a sorted prediction error sequence; S24, embedding a preset auxiliary information bit stream and a payload bit stream containing secret information into the sorted prediction error sequence to obtain a modified prediction error sequence; S25, adding the modified prediction error sequence and the predicted position of the center vertex of each embedding unit to obtain the updated position of the vertex, and obtaining a steganographic mesh model embedded with initial information by converting the coordinates of the updated vertex position into floating-point numbers; S26, according to the steganographic mesh model embedded with initial information, performing S21 to S25 again to finally obtain a steganographic mesh model.

[0019] Preferably, as shown in Figure 2 , the extraction information flow of the secret information extraction algorithm based on the binary sorting is as follows: S41. Perform three-layer vertex partitioning on the preprocessed dense mesh model to obtain the candidate set of vertices of the dense model and the reference set of vertices of the dense model. S42. Based on the reference set of the vertices of the dense model, obtain the spatial n-gon; based on the spatial n-gon and the candidate set of the vertices of the dense model, obtain multiple embedded units of the dense model; through the arithmetic mean of the vertex coordinates of the spatial n-gon, obtain the predicted position of the center vertex of each embedded unit of the dense model, and then obtain the prediction error vector of the dense model, and combine the prediction error vector of the dense model into the prediction error sequence of the dense model. S43. Add the interior angles corresponding to each vertex of the spatial n-sided polygon to obtain the sum of the interior angles of the spatial n-sided polygon; obtain the side lengths of each side of the spatial n-sided polygon using the coordinates of each vertex, and then obtain the variance of the side lengths of the spatial n-sided polygon; obtain the binary sorting parameter value corresponding to each embedded unit of the dense model based on the sum of the interior angles of the spatial n-sided polygon and the variance of the side lengths of the spatial n-sided polygon; arrange the embedded units of the dense model in ascending order according to the binary sorting parameter values ​​to obtain the sorted embedded units of the dense model; sort the prediction error vectors of the dense model corresponding to the embedded units of the dense model according to the sorted embedded units of the dense model to obtain the sorted prediction error sequence of the dense model. S44. Extract the auxiliary information bitstream and payload bitstream sequentially from the sorted prediction error sequence of the secret model to obtain the auxiliary information, payload, and recovered prediction error sequence; obtain the secret information through the payload. S45. Add the predicted positions of the center vertices of each embedded unit in the dense model to the recovered prediction error sequence to obtain the updated positions of the vertices of the dense model; by transforming the position coordinates of the updated original dense model vertices into floating-point numbers, the initial recovered mesh model is obtained. S46. Based on the initially recovered mesh model, execute S41 to S45 again to finally obtain the original mesh model.

[0020] Preferably, the three-layer vertex partitioning is performed by using a modulo-3 operation to divide the vertices of the mesh model into three independent point sets. The expression for partitioning the vertices is as follows: (2) In the formula, It is a subset of the vertex set; For index number u The vertex; u Assign vertex index numbers; Modulo 3 operation; These are stratified variables.

[0021] Specifically, the reversible information hiding method in this embodiment designs a two-round iterative embedding strategy. In the first round of embedding, the candidate set is set as... Reference set For; in the second round of embedding, the candidate set is set as The reference set is ,in, The vertex whose coordinates were modified in the first round gather; The embedding process for each round is as follows: According to equation (2) Figure 3 The red vertex {3,9,12,15} in the equation belongs to... D 1. The green vertices {4,7,10,16} belong to D 2. The blue vertices {2,5,8,11} belong to D 3; Select vertex 9 as the embedded vertex. In the ring of adjacent vertices of vertex 9, the vertex set {2,4,5,8,7} is used to predict the position of vertex 9; Based on the predicted position of vertex 9, after embedding the information, modify the coordinates of vertex 9. Changing the position coordinates of the embedded vertex will not affect the position coordinates of the reference vertex; the three-layer vertex partitioning mechanism ensures that the prediction results of the reference set for the vertex coordinates of the candidate set remain consistent during the data embedding and extraction process, thus guaranteeing the reversibility of the algorithm.

[0022] In this embodiment, a spatial n-sided polygon prediction scheme is proposed, which achieves a better balance between embedding capacity and visual quality by utilizing the topological connectivity between adjacent vertices. The spatial n-gon prediction scheme is given the following two definitions: Define a spatial n-gon: for a finite number of points in space By connecting straight line segments in a certain order to form a closed spatial polygonal line, a spatial dimension can be obtained. n polygon; Define the interior angles of an n-sided polygon in space: In plane geometry, the interior angles of a polygon are formed by two adjacent sides; for non-planar spaces... n An interior angle at a vertex of a polygon is an angle formed by its two adjacent sides on a uniquely defined plane, with a value in the range [0, π). Given a vertex to be embedded as the center vertex, its ring of adjacent vertices belongs to the reference set. R of n The vertices constitute a space. n polygon; central vertex and space n The polygons form an embedded unit; Based on the principles of computer graphics and mesh analysis, spatial n The sum of the interior angles of a polygon and the theoretical value of its corresponding planar polygon ( n The degree of closeness to -2)×π can serve as an important indicator for evaluating local geometric features; space nThe inner angle of a polygon is closer to π / 2 (180°) as the polygon is closer to a circle. n -2) x π, indicating that the embedding unit is smoother.

[0023] Preferably, the specific steps for calculating the predicted position of the center vertex of the embedding unit, and then obtaining the prediction error vector, are as follows: S221, the position coordinates of the predicted center vertex are obtained by the arithmetic mean of the spatial n-polygon vertex coordinates, expressed as: (3) In the formula, is the position coordinates of the predicted center vertex; is the horizontal axis coordinate value of the predicted center vertex; is the vertical axis coordinate value of the predicted center vertex; is the depth axis coordinate value of the predicted center vertex: is the number of vertices of the spatial n-polygon; is the center vertex of the embedding unit; is the vertex of the spatial n-polygon; is the integer coordinate value of the vertex of the spatial n-polygon in the horizontal axis; is the integer coordinate value of the vertex of the spatial n-polygon in the vertical axis; is the integer coordinate value of the vertex of the spatial n-polygon in the depth axis; S222, the prediction error vector is obtained according to the position coordinates of the predicted center vertex and the position coordinates of the real center vertex, expressed as: (4) In the formula, is the prediction error vector of the center vertex of the embedding unit; is the prediction error of the center vertex of the embedding unit in the horizontal axis; is the prediction error of the center vertex of the embedding unit in the vertical axis; is the prediction error of the center vertex of the embedding unit in the depth axis; is the position coordinates of the real center vertex.

[0024] In this embodiment, a binary sorting method based on local mesh smoothness analysis is proposed. When embedding secret information into the surface of a mesh model, geometrically "smoother" embedding units are preferentially selected. The smoothness of the embedding units is precisely quantified by defining binary sorting parameters. All embeddable regions are sorted according to the binary sorting parameters to ensure that the smoothest regions are used first. The binary sorting parameters are obtained based on two key geometric features. The first geometric feature is the sum of the interior angles of a spatial n-gon, which characterizes the degree of deviation of the local surface from the ideal plane. The closer its value is to the theoretical value, the flatter the region is. The second is the variance of the side length of the spatial n-gon, which characterizes the regularity of the local region in the side length dimension. The smaller the variance, the more regular the shape.

[0025] Preferably, the specific steps for obtaining the binary sorting parameter values ​​of the embedded unit based on the sum of the interior angles of the n-sided polygon and the variance of the side lengths of the n-sided polygon include: S231. Based on the sum of the interior angles of the n-sided polygon in space, the value of the main sorting parameter of the embedded element is obtained. The expression for the value of the main sorting parameter of the embedded element is: (5) In the formula, For the main sorting parameter value of the embedded unit: The interior angles corresponding to the vertices of the n-sided polygon in space; It is the sum of the interior angles of an n-sided polygon in space; S232. Sort the embedding unit sequence according to the main sorting parameter value of the embedding unit, and divide the embedding unit sequence into L consecutive subsequences on an average basis. S233. Based on the variance of the side length of the spatial n-gon, the value of the auxiliary sorting parameter of the embedded unit is obtained. The expression for the value of the auxiliary sorting parameter of the embedded unit is: (6) In the formula, For the auxiliary sorting parameter values ​​of the embedded unit; For space n The first polygon j Vertex coordinates; For space n The first polygon j+ One vertex coordinate; Let be the side length; The mean side length of a spatial n-gon; Let V be the variance of the side lengths of a spatial n-gon; where the expression for the mean of the side lengths of a spatial n-gon is: (7); S234. Based on the embedded unit auxiliary sorting parameter value and L consecutive subsequences, obtain the binary sorting parameter; the expression of the binary sorting parameter is: (8) In the formula, The value of the binary sorting parameter for the embedded unit; The index of the continuous subsequence; The total number of consecutive subsequences.

[0026] Preferably, the specific steps for obtaining the modified prediction error sequence include: S241. The expression for extracting the least significant bits of the first 64 prediction errors from the sorted prediction error sequence is: (9) In the formula, The least significant bit of the prediction error of the center vertex of the embedded cell on the k-axis; The prediction error is the center vertex of the embedded unit; The variables are the coordinate axes; These are the horizontal axis, vertical axis, and depth axis, respectively. S242. Embed the preset auxiliary information bitstream into the least significant bits of the first 64 prediction errors in the sorted prediction error sequence, as expressed in the following expression: (10) In the formula, The prediction error on the k-axis after embedding auxiliary information bits into the center vertex of the embedding unit; One bit for auxiliary information; S243. By using an extended translation method, the payload bit stream is embedded into the remaining prediction error of the sorted prediction error sequence to obtain the modified prediction error sequence; the prediction error of the embedded payload bits in the modified prediction error sequence is: (11) In the formula, After embedding the payload bits at the center vertex of the embedding unit, k On-axis modified prediction error; and A preset integer for controlling the embedding capacity; One bit of the payload; From equation (11), we know that the capacity of the embedded load is determined by... The number of prediction errors determines the value; if the interval is too large, it affects distortion, and if it is too small, it limits the embedding capacity; in this embodiment, an appropriate threshold is determined by iterative search. Specifically, the initial settings during the first iteration and ;if If the number of prediction errors is greater than or equal to the embedding capacity, the search process ends and the threshold is obtained; otherwise, the search continues alternately. minus 1 and The search process continues until the interval The sufficient number of prediction errors is provided.

[0027] Preferably, the specific steps of obtaining the recovered prediction error sequence include: S441, reading the least significant bits of the first 64 prediction errors of the sorted prediction error sequence of the stego model to obtain an auxiliary information bit stream; the auxiliary information bits of the auxiliary information bit stream are represented by the following formula: (12); S442, performing a recovery operation on the least significant bits of the first 64 prediction errors to obtain the first 64 recovered prediction errors; the first 64 recovered prediction errors are: (13); S443, extracting the expression of the payload from the remaining prediction errors of the sorted prediction error sequence of the stego model by reverse spreading: (14); S444, performing a recovery operation on the prediction errors after payload extraction to obtain a recovered prediction error sequence; the expression of the recovery operation on the prediction errors after payload extraction is: (15).

[0028] In a specific embodiment, the reversible information hiding method of the present embodiment is implemented by programming using C++ programming language under Windows 10 operating system. The secret information embedded in the mesh model is a randomly generated 0 / 1 string; the precision parameter used in the embedding and extraction process p is set to 4; the number of sub-sequences L is set to 4; The mesh model data comes from the public dataset of the Computer Graphics Lab of Stanford University and the Image Information and Information System Lab (LIRIS) of the French National Scientific Research Center; the present embodiment uses 6 mesh models, including: rabbit, horse, casting, crank, Venus and dragon; the specific information of the mesh models is shown in Table 1: Table 1 Mesh Model Information

[0029] In order to better analyze and discuss the performance of the reversible information hiding method of the present embodiment, the average embedding amount of information on each vertex is used to measure the embedding rate (ER), i.e. the length of embedded information is divided by the number of vertices in the mesh model; the larger the embedding rate, the larger the embedding capacity; The signal-to-noise ratio (SNR) is used to evaluate the visual quality of the mesh model. For a mesh model with N vertices, the SNR after embedding information can be defined as: N (16) In the formula, P0represents the original position coordinates of the vertex P; P represents the average value of the position coordinates of all vertices in the mesh model; and P represents the position coordinates of the vertex P after modification. u u The greater the SNR value is, the more similar the model structure is, and the smaller the model distortion is. The SNR curves of the 6 mesh models under different embedding rates are shown in FIG. 6. The embedding performance curves of each mesh model are not the same. With the increase of the embedding rate, the SNR values of all the models gradually decrease. When the embedding rate is 0.8 bpv (bit per vertex), the SNR values of all the mesh models remain above 50 dB. When the embedding rate is 1.4 bpv, the SNR values of all the mesh models still remain above 40 dB. Figure 4 According to the results, the reversible information hiding method of the embodiment can meet the large-capacity mesh reversible information hiding under the premise of ensuring the visual quality of the model. The visual comparison effects of the mesh models under different embedding rates are shown in FIG. 7. Under a lower embedding rate, the visual distortion degree of the model carrying information is low. With the gradual increase of the embedding rate, the distortion phenomenon increases, but even when the embedding rate reaches 1.4 bpv, the distortion is still controlled within a relatively inconspicuous range. According to the results, the reversible information hiding method of the embodiment can effectively maintain the visual distortion within an acceptable level within a relatively wide embedding rate range. Figure 5 In specific embodiments, in order to verify the comprehensive performance advantages of the reversible information hiding method of the embodiment, comparative experiments are performed on the current mainstream three-dimensional mesh reversible information hiding methods. The selected comparative methods include the representative methods of Wu et al., Jiang et al., and Zhang et al. The performance curves of the algorithms under different embedding rates on the 6 mesh models are shown in FIG. 8. The reversible information hiding method of the embodiment is higher than the other three methods on the 6 models under different embedding rates, and the model distortion is the smallest. The signal-to-noise ratio (SNR) of the model carrying information of the Wu method is relatively low, indicating that the model distortion is relatively significant.

[0030] Figure 6

[0031] ​​​​​​​​​According to the results, compared with the three existing algorithms, the reversible information hiding method of the embodiment can more effectively control the distortion while maintaining a higher embedding capacity, and has obvious advantages in overall performance.

[0032] In specific embodiments, to verify the effectiveness of the reversible information hiding method of the embodiment for the system, we carried out comparative experiments on the rabbit, horse, casting and crank four standard mesh models under different embedding rates for the prediction error binary sorting strategy and the unsorted strategy respectively, and the experimental results are shown in Table 2. Table 2 SNR comparison of sorting and unsorting

[0033] From Table 2, under the same embedding rate, the binary sorting method embeds a larger SNR value than the unsorted embedding; in addition, for the crank model with special vertex distribution, the present application has more obvious advantages. According to the results, the binary sorting algorithm has more advantages in overall performance and better performance stability.

[0034] The present application has the following advantages: The reversible information hiding method of a three-dimensional mesh model based on binary sorting of the present application obtains the topological correlation of the multiple neighborhood vertices of the center vertex of the embedding unit through the prediction scheme of the spatial n-gon, realizes accurate prediction of the position of the center vertex of the embedding unit, can effectively generate smaller prediction errors, and further obtain superior embedding performance. Through the binary sorting scheme, the internal angle and the edge length variance of the spatial n-gon are fused to comprehensively evaluate the smoothness of the embedding unit; all embedding units are arranged in ascending order according to the calculated binary sorting parameter value; embedding is performed by preferentially selecting embedding units with higher smoothness, effectively reducing the geometric distortion of the model caused by information hiding, and thereby significantly improving the visual quality of the stego model.

[0035] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or make equivalent substitutions for part or all of the technical features; and these modifications or substitutions do not make the essence of the corresponding technical solution deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A reversible information hiding method for a 3D mesh model based on binary sorting, characterized in that, include: S1. The sender preprocesses the original mesh model to obtain a preprocessed mesh model; S2. Based on the preprocessed grid model and secret information, a secret-carrying grid model is obtained through a binary sorting secret information embedding algorithm; S3. The receiver receives the dense mesh model and preprocesses it to obtain a preprocessed dense mesh model. S4. Based on the preprocessed secret grid model, the original grid model and secret information are obtained through a binary sorting secret information extraction algorithm.

2. The reversible information hiding method for a three-dimensional mesh model based on binary sorting according to claim 1, characterized in that, The embedding process based on the binary sorting secret information embedding algorithm is as follows: S21. Divide the preprocessed mesh model into three-layer vertices to obtain the candidate set and the reference set; S22. Based on the reference set, obtain the spatial n-gon; Based on the spatial n-gon and the candidate set, multiple embedding units are obtained; The predicted position of the center vertex of each embedded unit is obtained by the arithmetic mean of the vertex coordinates of the n-sided polygon in space, and then the prediction error vector is obtained. The prediction error vector is then combined into a prediction error sequence. S23. Add the interior angles corresponding to each vertex of the spatial n-sided polygon to obtain the sum of the interior angles of the spatial n-sided polygon; obtain the side length of each side of the spatial n-sided polygon using the coordinates of each vertex, and then obtain the variance of the side length of the spatial n-sided polygon; obtain the binary sorting parameter value corresponding to each embedding unit based on the sum of the interior angles of the spatial n-sided polygon and the variance of the side length of the spatial n-sided polygon; arrange the embedding units in ascending order according to the binary sorting parameter value to obtain the sorted embedding units; sort the prediction error vectors corresponding to the embedding units according to the sorted embedding units to obtain the sorted prediction error sequence. S24. Embed the preset auxiliary information bit stream and the payload bit stream containing secret information into the sorted prediction error sequence to obtain the modified prediction error sequence. S25. Add the modified prediction error sequence and the predicted position of the center vertex of each embedded unit to obtain the updated vertex position; by transforming the updated vertex position coordinates into floating-point numbers, the dense grid model with embedded initial information is obtained. S26. Based on the dense mesh model with embedded initial information, execute S21 to S25 again to finally obtain the dense mesh model.

3. The reversible information hiding method for a three-dimensional mesh model based on binary sorting according to claim 2, characterized in that, The information extraction process based on the binary sorting secret information extraction algorithm is as follows: S41. Perform three-layer vertex partitioning on the preprocessed dense mesh model to obtain the candidate set of vertices of the dense model and the reference set of vertices of the dense model. S42. Based on the reference set of the vertices of the dense model, obtain the spatial n-gon; Based on the candidate set of the spatial n-gon and the vertices of the dense model, multiple embedding units of the dense model are obtained; The predicted position of the center vertex of each embedded unit of the dense model is obtained by the arithmetic mean of the vertex coordinates of the n-sided polygon in space. Then, the prediction error vector of the dense model is obtained, and the prediction error vector of the dense model is combined into the prediction error sequence of the dense model. S43. Add the interior angles corresponding to each vertex of the spatial n-sided polygon to obtain the sum of the interior angles of the spatial n-sided polygon; obtain the side lengths of each side of the spatial n-sided polygon using the coordinates of each vertex, and then obtain the variance of the side lengths of the spatial n-sided polygon; obtain the binary sorting parameter value corresponding to each embedded unit of the dense model based on the sum of the interior angles of the spatial n-sided polygon and the variance of the side lengths of the spatial n-sided polygon; arrange the embedded units of the dense model in ascending order according to the binary sorting parameter values ​​to obtain the sorted embedded units of the dense model; sort the prediction error vectors of the dense model corresponding to the embedded units of the dense model according to the sorted embedded units of the dense model to obtain the sorted prediction error sequence of the dense model. S44. Extract the auxiliary information bitstream and payload bitstream sequentially from the sorted prediction error sequence of the secret model to obtain the auxiliary information, payload, and recovered prediction error sequence; obtain the secret information through the payload. S45. Add the predicted positions of the center vertices of each embedded unit in the dense model to the recovered prediction error sequence to obtain the updated positions of the vertices of the dense model; by transforming the position coordinates of the updated original dense model vertices into floating-point numbers, the initial recovered mesh model is obtained. S46. Based on the initially recovered mesh model, execute S41 to S45 again to finally obtain the original mesh model.

4. The reversible information hiding method for a three-dimensional mesh model based on binary sorting according to claim 2, characterized in that, The three-layer vertex partitioning is achieved by using modulo-3 operations to divide the vertices of the mesh model into three independent point sets. The expression for this vertex partitioning is as follows: （1） In the formula, It is a subset of the vertex set; For index number u The vertex; u Assign vertex index numbers; Modulo 3 operation; These are stratified variables.

5. The reversible information hiding method for a three-dimensional mesh model based on binary sorting according to claim 2, characterized in that, The specific steps for calculating the predicted position of the center vertex of the embedded unit and thus obtaining the prediction error vector are as follows: S221. The position coordinates of the predicted center vertex are obtained by using the arithmetic mean of the vertex coordinates of the spatial n-sided polygon. The expression is: （2） In the formula, To predict the position coordinates of the center vertex; To predict the x-axis coordinates of the center vertex; To predict the ordinate value of the center vertex; To predict the depth axis coordinates of the center vertex: The number of vertices of the n-sided polygon in space; The central vertex of the embedded unit; Let be the vertices of the n-gon in space; Let be the integer coordinates of the vertices of the n-sided polygon in space on the horizontal axis; Let be the integer coordinates of the vertices of the n-sided polygon in space along the vertical axis; For each vertex of the n-sided polygon in space, the coordinates are integers along the depth axis. S222. Based on the predicted center vertex's position coordinates and the actual center vertex's position coordinates, the prediction error vector is obtained, expressed as: （3） In the formula, The prediction error vector is the one embedded at the center vertex of the cell. The prediction error of the center vertex of the embedded unit on the horizontal axis; The prediction error of the center vertex of the embedded unit on the vertical axis; The prediction error of the center vertex of the embedded cell on the depth axis; These are the coordinates of the actual center vertex.

6. The reversible information hiding method for a three-dimensional mesh model based on binary sorting according to claim 2, characterized in that, The specific steps for obtaining the binary sorting parameter values ​​of the embedded unit based on the sum of the interior angles of the n-sided polygon and the variance of the side length of the n-sided polygon include: S231. Based on the sum of the interior angles of the n-sided polygon in space, the value of the main sorting parameter of the embedded element is obtained. The expression for the value of the main sorting parameter of the embedded element is: （4） In the formula, The value of the main sorting parameter for the embedded unit; The interior angles corresponding to the vertices of the n-sided polygon in space; It is the sum of the interior angles of an n-sided polygon in space; S232. Sort the embedding unit sequence according to the main sorting parameter value of the embedding unit, and divide the embedding unit sequence into L consecutive subsequences on an average basis. S233. Based on the variance of the side length of the spatial n-gon, the value of the auxiliary sorting parameter of the embedded unit is obtained. The expression for the value of the auxiliary sorting parameter of the embedded unit is: （5） In the formula, For the auxiliary sorting parameter values ​​of the embedded unit; For space n The first polygon j Vertex coordinates; For space n The first polygon j+ One vertex coordinate; Let be the side length; The mean side length of a spatial n-gon; Let V be the variance of the side lengths of a spatial n-gon; where the expression for the mean of the side lengths of a spatial n-gon is: （6）； S234. Based on the embedded unit auxiliary sorting parameter value and L consecutive subsequences, obtain the binary sorting parameter; the expression of the binary sorting parameter is: （7） In the formula, The value of the binary sorting parameter for the embedded unit; The index of the continuous subsequence; The total number of consecutive subsequences.

7. The reversible information hiding method for a three-dimensional mesh model based on binary sorting according to claim 2, characterized in that, The specific steps to obtain the modified prediction error sequence include: S241. The expression for extracting the least significant bits of the first 64 prediction errors from the sorted prediction error sequence is: （8） In the formula, The least significant bit of the prediction error of the center vertex of the embedded cell on the k-axis; The prediction error is the center vertex of the embedded unit; The variables are the coordinate axes; These are the horizontal axis, vertical axis, and depth axis, respectively. S242. Embed the preset auxiliary information bitstream into the least significant bits of the first 64 prediction errors in the sorted prediction error sequence, as expressed in the following expression: （9） In the formula, The prediction error on the k-axis after embedding auxiliary information bits at the center vertex of the embedding unit; One bit for auxiliary information; S243. By using an extended translation method, the payload bit stream is embedded into the remaining prediction error of the sorted prediction error sequence to obtain the modified prediction error sequence; the prediction error of the embedded payload bits in the modified prediction error sequence is: （10） In the formula, The prediction error modified on the k-axis after embedding the payload bit at the center vertex of the embedding unit; and A preset integer for controlling the embedding capacity; This is one bit of the payload.

8. The reversible information hiding method for a three-dimensional mesh model based on binary sorting according to claim 3, characterized in that, The specific steps to obtain the recovered prediction error sequence include: S441. Read the least significant bits of the first 64 prediction errors in the sorted prediction error sequence of the encrypted model to obtain the auxiliary information bit stream; the auxiliary information bits of the auxiliary information bit stream are represented by the following formula: （11）； S442. Perform a recovery operation on the least significant bits of the first 64 prediction errors to obtain the first 64 recovered prediction errors; the first 64 recovered prediction errors are: （12）； S443. The expression for extracting the load from the remaining prediction errors in the sorted prediction error sequence of the load-density model through reverse expansion is as follows: （13）； S444. By performing a reverse translation, the prediction error after load extraction is restored to obtain the restored prediction error sequence; the expression for the restoration operation of the prediction error after load extraction is: （14）。

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