Discrete manifold harmonic three-dimensional geographic information data compliance export traceability and integrity verification method

Abstract

The application discloses a discrete manifold harmonic three-dimensional geographic information data compliance outbound traceability and integrity verification method. The application provides a technical scheme capable of hiding compliance approval information in the frequency domain characteristics of a three-dimensional model without destroying the precision of model engineering, resisting conventional geometric attacks and format conversion, and mainly applied to the ownership right confirmation, flow direction control and compliance audit of high-precision geometric models such as engineering building information models (BIM) and desensitized real scene three-dimensional data in cross-border circulation scenarios.

Description

Technical Field

[0001] This invention relates to a method for compliant export traceability and integrity verification of discrete manifold harmonic 3D geographic information data for cross-border trusted data spaces, belonging to the interdisciplinary fields of information security and computer graphics. Background Technology

[0002] With the globalization of the digital economy, the cross-border demand for 3D spatial data (such as BIM building information models and industrial digital twins) is increasing in scenarios such as transnational engineering construction and high-end manufacturing supply chain collaboration. According to the *Data Security Law of the People's Republic of China* and the *Measures for Security Assessment of Data Export*, such data must undergo rigorous security assessments and de-identification processes before export to remove classified and sensitive information. However, the data transfer process after compliant export still faces significant technical challenges: First, traditional 3D watermarking techniques are mostly based on the spatial domain, that is, embedding information by fine-tuning the geometric coordinates of grid vertices. Although this method is simple to implement, it inevitably introduces geometric errors, destroying the high-precision properties of surveying-grade data (such as millimeter-level tolerances), making the data unusable for high-precision engineering simulations or construction guidance at the receiving end.

[0003] Secondly, cross-border data exchange is often accompanied by data format conversion, resampling, or geometric attacks (such as rotation, scaling, and translation) between heterogeneous systems. Existing fragile watermarking schemes are prone to losing watermark information after undergoing such non-rigid transformations or data cleaning, making it impossible to prove the legitimate origin of the data or provide effective electronic evidence in subsequent accountability.

[0004] Finally, existing data export management methods mainly focus on administrative approvals before export, lacking technical-level endogenous control after export. Once compliant data is illegally redistributed or tampered with overseas, regulators and data owners lack an indelible digital compliance certificate strongly bound to the data itself to monitor its flow throughout its entire lifecycle. Summary of the Invention

[0005] The technical problem this invention aims to solve is that three-dimensional spatial data watermarks have poor robustness, are easily compromised in geometric accuracy, and lack an endogenous traceability mechanism for cross-border compliance scenarios.

[0006] To address the aforementioned technical problems, the present invention discloses a method for compliant export tracing and integrity verification of discrete manifold harmonic three-dimensional geographic information data, characterized by comprising the following steps: Compliance preprocessing and discrete manifold construction: Coordinate desensitization and topology cleaning are performed on the 3D mesh data to be exported, a discrete Laplacian operator matrix based on the cotangent weight scheme is constructed, and the manifold geometric expression of the 3D data model is established. Manifold harmonic spectral decomposition and frequency domain mapping: Solve the generalized eigenvalue problem of the discrete Laplace operator matrix to obtain the manifold harmonic basis characterizing the intrinsic geometric features of the model, and map the three-dimensional spatial coordinate signal into frequency domain spectral coefficients; Spread spectrum modulation and adaptive embedding of compliance credentials: Generate a digital digest containing the data export security assessment number and authorization scope, convert it into a pseudo-random noise sequence using spread spectrum technology, and adaptively modulate it into the mid-frequency spectral coefficients according to the spectral energy distribution; Model inverse transformation reconstruction and accuracy tolerance control: Perform inverse manifold harmonic transformation to reconstruct the 3D model, and introduce a root mean square error feedback mechanism to ensure that the reconstructed model meets the geometric accuracy standards of surveying or engineering. Cross-border integrity verification based on blind detection: At the data receiving end or audit node, the frequency domain watermark is extracted without the need for the original model reference by utilizing the isometric transformation invariance of manifold harmonics to verify the source compliance and content integrity of the data.

[0007] Preferably, the constructed discrete Laplace operator matrix is ​​denoted as L, then:

[0008] In the formula: A is a diagonal mass matrix, where the diagonal elements are... Defined as the area of ​​the mixed Voronoi region at vertex i in a 3D surface mesh; W is a sparse symmetric stiffness matrix, where the elements are... For any edge e connecting vertices i and j in a 3D curved surface mesh ij The weighting coefficients are calculated using the cotangent formula derived from the finite element method.

[0009] Preferably, the area of ​​the mixed Voronoi region is a weighted combination of the Voronoi region surrounding vertex i and the area of ​​the triangle.

[0010] Preferably, the Calculate using the following formula:

[0011] in, and They are respectively edge e ij The interior angle values ​​corresponding to the two adjacent triangular facets they share; If the vertices are not adjacent, the corresponding weight is zero.

[0012] Preferably, the spectral coefficient matrix obtained based on the manifold harmonic spectral decomposition and frequency domain mapping is represented as follows: Then we have:

[0013] In the formula: H is the eigenvector basis obtained based on the manifold harmonic basis; V is the Cartesian coordinate matrix of all normalized vertices of the three-dimensional data model.

[0014] Preferably, in the spread spectrum modulation and adaptive embedding of the compliance certificate, for the first Selected spectral coefficient vectors The modified value is obtained using the following formula. :

[0015] In the formula, For multiplicative embedding strength factor, For additive embedding intensity factor, For the spreading watermark component corresponding to the current spectral coefficient vector, For local curvature factor; Traversing the spectrum coefficient matrix After selecting all the spectral coefficient vectors, obtain the modified spectral coefficients. .

[0016] Preferably, in the model inverse transformation reconstruction and accuracy tolerance control: Using the modified spectral coefficients Calculate the low-frequency and mid-frequency reconstruction parts using the eigenvector basis H. , ; Calculate the high-frequency residuals in the original three-dimensional data model V that did not participate in spectral decomposition. , ; High-frequency residual part Directly superimposed back onto the reconstructed model, i.e., the final reconstructed coordinates. , .

[0017] Preferably, in the model inverse transformation reconstruction and accuracy tolerance control: the reconstructed model is calculated in real time. The Hausdorff distance and root mean square error between the model and the original 3D data V are compared with the root mean square error and a preset engineering tolerance threshold. After comparison, if it exceeds the engineering tolerance threshold Then feedback adjustment is performed according to the preset attenuation coefficient. Reduce the multiplicative embedding strength factor γ and the additive embedding strength factor Then, the adaptive embedding and the inverse model transformation reconstruction are repeated until the root mean square error converges within the compliance threshold.

[0018] Preferably, the feedback adjustment employs PID controller logic: when the root mean square error exceeds the engineering tolerance threshold... In this case, the multiplicative embedding strength factor γ is prioritized, and the additive embedding strength factor is only decayed when the multiplicative embedding strength factor γ decays to below a preset proportion of its initial value and the error still does not meet the target. .

[0019] This invention provides a technical solution that can covertly embed compliance approval information into the frequency domain features of a 3D model without compromising the accuracy of the model engineering and resisting conventional geometric attacks and format conversions. It is mainly applied to the ownership confirmation, flow control and compliance audit of high-precision geometric models such as Building Information Modeling (BIM) and desensitized real-scene 3D data in cross-border transfer scenarios.

[0020] Compared with existing technical solutions, the present invention has the following beneficial effects: 1. Achieved closed-loop compliance management of cross-border data throughout its entire lifecycle. This invention creatively embeds compliance metadata such as data export approval and filing numbers and recipient identification into the frequency domain features of a 3D model through spread spectrum modulation. This "strong binding of data and credentials" mechanism fills the gap in the current reliance on administrative approvals alone, which lacks the technical means to control the flow of data "after export," giving data transferred overseas an endogenous traceability identifier and effectively supporting compliance auditing.

[0021] 2. This invention overcomes the contradiction between geometric accuracy and robustness in 3D watermarking technology. By introducing an inverse manifold harmonic transform based on residual compensation and a closed-loop accuracy feedback control mechanism, this invention ensures that the root mean square error of the model after watermark embedding strictly converges to the tolerance range of surveying or precision engineering (e.g., micrometer level). Simultaneously, by utilizing the isometric transformation invariance of the discrete Laplace-Beltrami operator, the watermark can resist conventional geometric attacks and format conversions such as rotation, translation, and scaling, solving the problem that traditional spatial domain watermarks destroy model accuracy and are easily lost.

[0022] 3. Provides offshore blind detection capabilities without the need for original data. The blind extraction algorithm designed in this invention allows regulators or recipients to complete integrity verification based solely on the data to be tested, without transmitting high-precision original models or relying on original coordinate references. This feature greatly reduces cross-border network transmission overhead, avoids the security risks of secondary cross-border repatriation of original sensitive data, and fully complies with the regulatory principle of minimizing data outflow. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the overall technical process of the method of the present invention, which shows the complete closed-loop logic from data compliance preprocessing, frequency domain watermark embedding to cross-border blind detection; Figure 2The diagram shows the frequency domain signal processing and hybrid modulation logic of the method of the present invention, illustrating the signal processing logic of the core algorithm of the present invention, which adopts a horizontal dual-channel convergence structure. Detailed Implementation

[0024] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0025] The purpose of this invention, which discloses a method for compliant traceability and integrity verification of discrete manifold harmonic 3D geographic information data exported across borders, is to address the technical problems that traditional spatial domain watermarking technology struggles to maintain both high geometric accuracy and robust traceability during the cross-border transfer of existing 3D spatial data, and lacks an endogenous verification mechanism for data export compliance. The disclosed method treats the desensitized 3D mesh model as a Riemannian manifold and utilizes the spectral analysis characteristics of the Laplace-Beltrammé operator (LBO) to embed compliance credentials bound to the export approval results in the frequency domain, thereby achieving zero geometric loss traceability and tamper-proof verification throughout the entire lifecycle of data transfer.

[0026] This invention uses de-identified LOD 400 level 3D mesh data of precision components from a multinational high-end manufacturing project as the processing object. Relying on a trusted computing unit deployed at the gateway of a dedicated cross-border data channel, it performs full-process compliance traceability and integrity verification for outbound exports. This embodiment aims to reveal how to embed tamper-resistant, compliant digital credentials through frequency domain signal processing technology without compromising the micron-level geometric tolerances of the model. Specifically, it includes the following steps: Step 1: Manifold topology normalization and compliance-compliant desensitization and cleaning of 3D meshes.

[0027] Before performing frequency domain transformation, it is essential to ensure that the 3D data meets the topological prerequisites for constructing the Laplacian operator. The system reads the original 3D model data, initiates a manifold geometry check program, and uses a half-edge data structure to traverse the mesh topology, automatically repairing non-manifold edges and isolated vertices to ensure that the mesh surface satisfies the differential geometry definition of a 2D Riemannian manifold, i.e., the local neighborhood of any vertex is homeomorphic to a Euclidean disk. Simultaneously, the system performs coordinate compliance processing, translating the coordinates of all vertexes of the model to their geometric centroid origin and normalizing and scaling them according to the bounding box size. This operation aims to eliminate absolute geodetic coordinate information to comply with the requirements for exporting surveying data, while also improving the numerical stability of subsequent floating-point matrix operations.

[0028] Step 2: Construction of the discrete Laplace operator based on the cotangent weight scheme.

[0029] To accurately capture the intrinsic geometric features of 3D surfaces, this embodiment constructs a Discrete Laplace-Beltrammé operator (LBO). The system first establishes a sparse, symmetric stiffness matrix W. For any edge e connecting vertices i and j in the mesh... ij The weighting coefficients are calculated using the cotangent formula derived from the finite element method. The calculation formula is as follows:

[0030] in, and They are respectively edge e ij The interior angle values ​​corresponding to the two adjacent triangular faces they share; if the vertices are not adjacent, the weight is zero.

[0031] Subsequently, a diagonal mass matrix A is constructed, where the diagonal elements Defined as the area of ​​the mixed Voronoi region at vertex i, it is specifically calculated as a weighted combination of the Voronoi region around the vertex and the area of ​​the triangle, used to compensate for the discretization error caused by uneven grid sampling density.

[0032] Finally, the generated generalized Laplace matrix L is defined as:

[0033] The generalized Laplace matrix L can accurately describe the diffusion behavior of a scalar field on a surface, and this operator is completely determined by the local geometry of the mesh, possessing natural rotation and translation invariance.

[0034] Step 3: Implicit restart of Arnoldi iterative solution for the feature subspace.

[0035] Given that sophisticated engineering models typically contain a massive number of vertices (on the order of magnitude) The computational overhead of full matrix eigenvalue decomposition is too high. This embodiment configures an implicitly restarted Arnoldi iterative solver with shift inverses, specifically designed for efficiently solving eigenpairs of large sparse matrices. The system sets a truncation threshold. Solve the following generalized characteristic equation:

[0036] In the formula, f is the eigenvector describing the basic deformation mode of the three-dimensional model, i.e., the mode shape vector. The first k smallest non-zero generalized eigenvalues ​​of the generalized Laplace matrix L are calculated (excluding the fundamental frequency, which is always zero). Arrange the calculated eigenvalues ​​in ascending order, satisfying... The relationship between them and their corresponding orthogonal eigenvector basis This set of eigenvector basis H constitutes the manifold frequency domain coordinate system for the geometric deformation of the model, where, For corresponding frequency The mode shape vector.

[0037] Step 4: Forward manifold harmonic transformation and full-band spectrum mapping.

[0038] Using the eigenvector basis H obtained in step 3, the system maps the 3D model from the Euclidean space domain to the manifold frequency domain. The Cartesian coordinate matrix V (of size N×3) of all normalized vertices of the model is projected onto this basis, and a manifold harmonic transformation is performed. The calculation formula is as follows:

[0039] in, The calculated spectral coefficient matrix has a size of . ; is the transpose matrix of the eigenvector basis; A This is the mass matrix. The resulting mass matrix is... The geometric information of the model is effectively orthogonally decomposed into three parts: low frequency (representing the overall topological skeleton), mid frequency (representing geometric texture features), and high frequency (representing minute noise and sharp edges), providing a mathematical basis for subsequent watermarking operations in non-interfering frequency bands.

[0040] Step 5: Hash encoding of compliance metadata and generation of spread spectrum sequence.

[0041] The system obtains the outbound approval and filing number and the digital identity of the receiving company for this transmission mission through the data outbound security assessment interface. After concatenating the aforementioned compliant metadata, a fixed-length hash digest is generated using the SHA-256 algorithm, and then binarized into a payload sequence. Where M=64. To achieve imperceptibility and resistance to geometric attacks in the watermarking, direct sequence spread spectrum technology is used. Using the private key distributed by the regulatory agency as a seed, a Gaussian pseudo-random sequence of length L=12800 is generated. Each bit of payload information b... j The extended modulation is a high-bandwidth watermark signal sequence S. The watermark signal sequence S exhibits white noise-like characteristics in statistical properties, making it extremely difficult for unauthorized parties to detect or remove.

[0042] Step 6: Adaptive frequency band locking based on spectral energy sensing.

[0043] To ensure robustness while minimizing the impact on model appearance, the system introduces a spectral energy sensing mechanism. The algorithm traverses the spectral coefficient matrix. Calculate the frequency components of each order. L2 norm energy value The system automatically avoids the top N units with the highest energy percentage. low=50 low-frequency coefficients are selected to prevent visually noticeable low-frequency distortions in the model caused by modifications; at the same time, high-frequency coefficients with extremely rapid energy decay are avoided to prevent the watermark from being filtered out by subsequent compression algorithms. The algorithm dynamically locks the mid-frequency range with the most stable energy distribution (e.g., the index range [51, 350]) as the optimal embedding domain for the watermark.

[0044] Step 7: Frequency domain embedding of additive and multiplicative hybrid modulation.

[0045] Within a defined mid-frequency band, the system performs the watermark signal embedding operation. Considering the order-of-magnitude differences in coefficient values ​​across different frequency bands, this embodiment employs a hybrid additive and multiplicative modulation strategy. For the first... Selected spectral coefficient vectors Its modified value The calculation formula is:

[0046] in: This is a multiplicative embedding strength factor used to control relative error and ensure watermark strength at high energy coefficients; This is an additive embedding intensity factor used to control the absolute noise floor and prevent numerical instability when the coefficients are close to zero. For the corresponding spread spectrum watermark components; Local curvature factor The larger the value, the sharper the geometry at that vertex. This strategy significantly improves the adaptability of the watermark in flat and complex textured regions of the model.

[0047] Step 8: High-frequency residual compensation reconstruction and inverse manifold harmonic transformation.

[0048] To prevent [the problem caused by only using it before] To address the loss of detail caused by reconstructing individual eigenvectors (i.e., the Gibbs effect), this embodiment employs a residual compensation reconstruction method. This involves superimposing high-frequency residuals... Previously, normal vector uniformity smoothing was performed to eliminate normal vector flipping noise caused by inverse transform truncation error. The system first utilizes the modified spectral coefficients. Calculate the low-frequency and mid-frequency reconstruction parts using the eigenvector basis H. :

[0049] Subsequently, the high-frequency residuals in the original model that did not participate in spectral decomposition were calculated. :

[0050] Finally, these coordinates are directly superimposed back onto the reconstructed model, resulting in the final reconstructed coordinates. :

[0051] This step ensures that high-frequency geometric features in the model that are not involved in watermark embedding, such as sharp edges and tiny chamfers, are perfectly preserved, achieving compatibility between watermark embedding and high precision.

[0052] Step 9: Closed-loop accuracy control based on geometric tolerance feedback. This is a crucial step to ensure that the technical solution meets "surveying grade" requirements.

[0053] System Real-time Computation Reconstruction Model The Hausdorff distance (i.e., bidirectional maximum-minimum distance) and root mean square error (RMSE) between the original desensitization model V and the original model. The system presets engineering tolerance thresholds. (e.g., precision grade) (meters). If the calculated error The system will trigger the feedback adjustment loop, adjusting according to the preset attenuation coefficient. (like The modulation intensity factors γ and β in step 7 are reduced, and modulation and reconstruction are reverted. This iterative process continues until the error index converges within the compliance threshold, thereby ensuring the engineering usability of the delivered data at the physical level. The feedback control loop uses PID (proportional-integral-derivative) controller logic: when the RMSE error exceeds the threshold... When adjusting the multiplicative factor γ, the additive factor β is only adjusted when γ decays to less than 30% of its initial value and the error still does not meet the target.

[0054] Step 10: Blind detection and compliance audit based on the invariance of isometric transformation.

[0055] When data is transferred overseas or ownership disputes arise, the watermark extraction process is initiated. The detection end does not need to possess the original model; it only needs to reconstruct the LBO from the received model under test and extract the corresponding mid-frequency spectral coefficients. Utilizing the isometric transformation invariance of the LBO operator, even if the model undergoes rigid body rotation, translation, or uniform scaling at any angle overseas, the relative distribution characteristics of its spectral coefficients remain stable. The detector uses a locally pre-stored PN code sequence to perform sliding normalized cross-correlation calculations with the extracted coefficients. When the correlation peak exceeds the statistical significance threshold, despreading is performed to restore the "exit approval filing number," thereby completing the endogeneity technical verification of the data source legality and content integrity.

Claims

1. A method for compliant export tracing and integrity verification of discrete manifold harmonic 3D geographic information data, characterized in that, Includes the following steps: Compliance preprocessing and discrete manifold construction: Coordinate desensitization and topology cleaning are performed on the 3D mesh data to be exported, a discrete Laplacian operator matrix based on the cotangent weight scheme is constructed, and the manifold geometric expression of the 3D data model is established. Manifold harmonic spectral decomposition and frequency domain mapping: Solve the generalized eigenvalue problem of the discrete Laplace operator matrix to obtain the manifold harmonic basis characterizing the intrinsic geometric features of the model, and map the three-dimensional spatial coordinate signal into frequency domain spectral coefficients; Spread spectrum modulation and adaptive embedding of compliance credentials: Generate a digital digest containing the data export security assessment number and authorization scope, convert it into a pseudo-random noise sequence using spread spectrum technology, and adaptively modulate it into the mid-frequency spectral coefficients according to the spectral energy distribution; Model inverse transformation reconstruction and accuracy tolerance control: Perform inverse manifold harmonic transformation to reconstruct the 3D model and introduce a root mean square error feedback mechanism to ensure that the reconstructed model meets the geometric accuracy standards of surveying or engineering. Cross-border integrity verification based on blind detection: At the data receiving end or audit node, the frequency domain watermark is extracted without the need for the original model reference, utilizing the isometric transformation invariance of manifold harmonics to verify the compliance of the data source and the integrity of the content.

2. The method for compliant export tracing and integrity verification of discrete manifold harmonic 3D geographic information data as described in claim 1, characterized in that, The constructed discrete Laplace operator matrix is ​​denoted as L, then: In the formula: A is a diagonal mass matrix, where the diagonal elements are... Defined as the area of ​​the mixed Voronoi region at vertex i in a 3D surface mesh; W is a sparse symmetric stiffness matrix, where the elements are... For any edge e connecting vertices i and j in a 3D curved surface mesh ij The weighting coefficients are calculated using the cotangent formula derived from the finite element method.

3. The method for compliant export tracing and integrity verification of discrete manifold harmonic 3D geographic information data as described in claim 2, characterized in that, The area of ​​the mixed Voronoi region is a weighted combination of the Voronoi region surrounding vertex i and the area of ​​the triangle.

4. The method for compliant export tracing and integrity verification of discrete manifold harmonic 3D geographic information data as described in claim 2, characterized in that, The Calculate using the following formula: ,in, and They are respectively edge e ij The interior angle values ​​corresponding to the two adjacent triangular faces they share; if the vertices are not adjacent, the corresponding weight is zero.

5. The method for compliant export tracing and integrity verification of discrete manifold harmonic 3D geographic information data as described in claim 4, characterized in that, The spectral coefficient matrix obtained based on the aforementioned manifold harmonic spectral decomposition and frequency domain mapping is expressed as follows: Then we have: In the formula: H is the eigenvector basis obtained based on the manifold harmonic basis; V is the Cartesian coordinate matrix of all normalized vertices of the three-dimensional data model.

6. The method for compliant export tracing and integrity verification of discrete manifold harmonic 3D geographic information data as described in claim 5, characterized in that, In the spread spectrum modulation and adaptive embedding of the compliance credential, for the first Selected spectral coefficient vectors The modified value is obtained using the following formula. : In the formula, For multiplicative embedding strength factor, For additive embedding intensity factor, For the spreading watermark component corresponding to the current spectral coefficient vector, For local curvature factors; ergodic spectrum coefficient matrix After selecting all the spectral coefficient vectors, obtain the modified spectral coefficients. .

7. The method for compliant export tracing and integrity verification of discrete manifold harmonic 3D geographic information data as described in claim 6, characterized in that, In the inverse transformation reconstruction and accuracy tolerance control of the model: the modified spectral coefficients are used. Calculate the low-frequency and mid-frequency reconstruction parts using the eigenvector basis H. , ; Calculate the high-frequency residuals in the original three-dimensional data model V that did not participate in spectral decomposition. , ; the high-frequency residual part Directly superimposed back onto the reconstructed model, i.e., the final reconstructed coordinates. , .

8. The method for compliant export tracing and integrity verification of discrete manifold harmonic three-dimensional geographic information data as described in claim 6, characterized in that, In the inverse transformation reconstruction and accuracy tolerance control of the model: real-time calculation of the reconstructed model The Hausdorff distance and root mean square error between the model and the original 3D data V are compared with the root mean square error and a preset engineering tolerance threshold. After comparison, if it exceeds the engineering tolerance threshold Then feedback adjustment is performed according to the preset attenuation coefficient. Reduce the multiplicative embedding strength factor γ and the additive embedding strength factor Then, the adaptive embedding and the inverse model transformation reconstruction are repeated until the root mean square error converges within the compliance threshold.

9. The method for compliant export tracing and integrity verification of discrete manifold harmonic three-dimensional geographic information data as described in claim 8, characterized in that, The feedback adjustment employs PID controller logic: when the root mean square error exceeds the engineering tolerance threshold... In this case, the multiplicative embedding strength factor γ is prioritized, and the additive embedding strength factor is only decayed when the multiplicative embedding strength factor γ decays to below a preset proportion of its initial value and the error still does not meet the target. .

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