An ancient artifact ornament extraction and digital restoration method based on a point cloud model

Abstract

This invention relates to the field of digital preservation and restoration of cultural relics, specifically a method for extracting and digitally restoring ancient artifact patterns based on point cloud models. It includes modules for manifold frequency domain mapping, spectral domain signal separation, topological skeleton repair, and Poisson fusion generation. The system constructs a Laplace-Beltramm operator to map the point cloud to the frequency domain, uses a bandpass filter to remove weathering noise and enhance the pattern layer, extracts the pattern skeleton to identify breakpoints, and combines a knowledge graph for non-rigid registration to generate a deformation guidance field. Its core is to use Poisson fusion to fill in missing information and output a restoration confidence heatmap, effectively solving the problem of aliasing between weathering noise and weak feature signals, achieving micron-level high-fidelity restoration.

Description

Technical Field

[0001] This invention relates to the field of digital preservation and restoration of cultural relics, specifically a method for extracting and digitally restoring ancient artifact patterns based on point cloud models. Background Technology

[0002] In current applications of digital preservation and restoration of ancient artifacts, high-precision 3D scanning equipment is typically used to acquire the original point cloud data of the artifacts. This data carries the shallow relief patterns and topological geometric information of the artifact surface, and the data often exhibits discrete characteristics such as severe surface weathering, incomplete patterns, and fractures.

[0003] To extract and restore patterns from these complex data, existing solutions generally employ traditional geometric filtering denoising algorithms and hole repair techniques based on geometric interpolation. While these solutions possess some repair capabilities when processing conventional models, the spatial frequency domain exhibits signal aliasing due to weathering and erosion noise and faint bas-relief features on ancient artifacts. Furthermore, traditional geometric filling lacks logical support based on archaeological semantics, making it difficult for existing technologies to completely preserve micron-level pattern details while removing weathering noise at the same scale. The resulting repaired areas are often meaningless geometric fills, and there is a lack of quantitative evaluation indicators that can distinguish between real data and algorithm-derived data, making it difficult to meet the needs of high-precision academic research and display.

[0004] Therefore, how to achieve precise decoupling between weathering noise and decorative features, and how to realize logical completion of incomplete decorative features and credibility assessment of restoration quality based on semantic knowledge graphs, have become urgent technical problems to be solved. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method for extracting and digitally restoring ancient artifact patterns based on point cloud models. Specifically, the technical solution of this invention includes:

[0006] The original point cloud data of the ancient artifacts is obtained, the Laplace-Beltramian operator of the original point cloud data is constructed, and the eigenvalues ​​and eigenfunctions of the operator are calculated. The original point cloud data is then mapped to the manifold frequency domain.

[0007] The point cloud signal in the frequency domain of the manifold is decomposed using a spectral bandpass filter to separate the base geometry layer, the texture feature layer, and the weathering noise layer. The weathering noise layer is discarded and the texture feature layer is enhanced.

[0008] Ridge detection is performed on the enhanced pattern feature layer to extract the topological skeleton of the incomplete pattern, and the topological skeleton is mapped into a graph structure containing nodes and edges. The cantilever nodes in the graph structure are identified as breakpoints.

[0009] A pre-defined ancient decorative pattern knowledge graph library is introduced, the topological similarity between the topological skeleton and the standard template in the library is calculated, and a non-rigid registration algorithm is used to deform the standard template to fit the topological skeleton, generating a deformation guidance field containing a three-dimensional spatial displacement vector.

[0010] The deformation guidance field is used to perform Poisson fusion on the missing regions of the original point cloud data to generate a restored high-precision model. Based on the difference between the generated data and the original data, a restored confidence heatmap data containing point-by-point confidence values ​​is generated, forming a digital restoration closed loop.

[0011] Preferably, the decomposition of point cloud signals in the frequency domain of a manifold using a spectral domain bandpass filter includes:

[0012] Based on the spectral analysis characteristics of the Laplace-Beltrami operator, a first eigenvalue threshold and a second eigenvalue threshold are set, wherein the second eigenvalue threshold is greater than the first eigenvalue threshold;

[0013] Low-frequency signals with eigenvalues ​​less than the first eigenvalue threshold are identified as the base geometric layer characterizing the overall shape of the object;

[0014] The mid-frequency signal with eigenvalues ​​between the first eigenvalue threshold and the second eigenvalue threshold is identified as a texture feature layer characterizing the undulations of a shallow relief pattern, the texture feature layer containing a continuous geometric manifold structure;

[0015] High-frequency signals with eigenvalues ​​greater than the second eigenvalue threshold are identified as weathering noise layers characterizing surface erosion and random pits;

[0016] The signal intensity of the texture feature layer is amplified by the enhancement algorithm, while the interference from the base geometry layer and the weathering noise layer is suppressed.

[0017] Preferably, ridge line detection is performed on the enhanced pattern feature layer to extract the topological skeleton of the incomplete pattern, and the topological skeleton is mapped to a graph structure, including:

[0018] Calculate the principal curvature direction on the decorative feature layer, extract local maxima along the direction of maximum principal curvature, and connect the local maxima to form discontinuous skeleton segments;

[0019] Construct a graph structure containing nodes and edges, where nodes represent the endpoints of skeleton fragments and edges represent the geometric paths of skeleton fragments;

[0020] Calculate the tangential direction vector at the endpoints of each skeleton segment;

[0021] Based on the geodesic distance between the endpoints of each skeleton segment and the cosine of the angle between the tangential direction vectors, the potential connection paths between the broken skeleton segments are predicted, forming a complete decorative topology network.

[0022] Preferably, deforming the standard template using a non-rigid registration algorithm to fit the topological skeleton includes:

[0023] Retrieve parameterized vector templates that match the style of the pattern topology network from the ancient pattern knowledge graph database;

[0024] Calculate the chamfer distance between the topological skeleton and the parameterized vector template, and use it as a metric for geometric fit.

[0025] Construct an energy functional, which includes a data term and a smoothing term, wherein the data term constrains the template to move toward the observed skeleton, and the smoothing term constrains the continuity of the template deformation;

[0026] Minimize the energy functional, solve for the deformation parameters, and drive the parameterized vector template to undergo non-rigid deformation, so that it covers the topological skeleton while maintaining its own topological integrity.

[0027] Preferably, the deformation guiding field performs Poisson fusion on the missing regions of the original point cloud data to generate the data, including:

[0028] The deformed parameterized vector template is transformed into a gradient field constraint in three-dimensional space;

[0029] A Poisson equation is constructed in the missing region of the original point cloud data, and the gradient field constraint is used as the boundary condition and guiding field of the Poisson equation.

[0030] Solve the Poisson equation to reconstruct the surface mesh of the missing region, so that the newly generated mesh is tangentially continuous with the original point cloud data at the boundary and conforms to the geometric trend of the standard template in the internal region;

[0031] The reconstructed surface mesh is then fused into the base geometry layer to generate a complete, high-precision 3D model.

[0032] Preferably, generating a restored confidence heatmap based on the difference between the generated data and the original data includes:

[0033] The nearest neighbor distance from each point on the surface of the restored high-precision model to the original point cloud data is calculated and defined as the geometric residual.

[0034] For the region generated by Poisson fusion, the local deformation modulus of the deformation guiding field at the corresponding position is calculated, and the normalized value is used as an index of inference uncertainty.

[0035] A point-by-point restoration confidence score is generated by combining the reciprocal of the geometric residual with the negative correlation value of the inference uncertainty index using a weighted summation method.

[0036] The restoration confidence score is mapped to RGB color encoding and superimposed on the surface of the high-precision model to generate a restoration confidence heatmap that intuitively marks the original data area and the algorithm-generated area.

[0037] Preferably, this method further includes:

[0038] Preset recovery confidence threshold;

[0039] If the lowest score region in the restoration confidence heatmap is higher than the restoration confidence threshold, the restoration result is deemed valid and the digital model is directly output.

[0040] If the lowest score region in the restored confidence heatmap is lower than the restored confidence threshold, the low confidence region is marked, triggering a manual interactive correction process that allows the user to adjust the deformation parameters of the parameterized vector template until the score meets the requirements.

[0041] Preferably, this method also includes an auxiliary dating analysis step based on deformation parameters:

[0042] Extract the template deformation parameters generated by the non-rigid registration algorithm. The deformation parameters include scaling factor, deviatoric strain tensor and local curvature change.

[0043] Frequency domain analysis was performed on the deformation parameters, and the mean values ​​of the scaling factor and the modulus of the deviator strain tensor were calculated as tension sensitivity indicators. The variance of the local curvature change was calculated as a regularity indicator.

[0044] The tension index and regularity index are compared with the pre-stored age-index mapping table in the historical age database to output the potential dating range of ancient artifacts.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] 1. This invention utilizes the Laplace-Beltramie operator to map point cloud data to the manifold frequency domain, and constructs a spectral bandpass filter through a set eigenvalue threshold to separate the signal into a base geometry layer, a texture feature layer, and a weathering noise layer. This technique effectively solves the problem of signal aliasing between weathering erosion noise and weak bas-relief features in the spatial frequency domain in existing technologies. It can remove weathering noise of the same scale as the texture while completely preserving micron-level texture details, significantly improving the signal-to-noise ratio and feature fidelity of data preprocessing.

[0047] 2. This invention introduces an ancient decorative pattern knowledge graph database and uses a non-rigid registration algorithm to fit a standard parameterized vector template with a fragmented topological skeleton. This method overcomes the limitations of traditional geometric interpolation repair, which lacks semantic and logical support. It can make evidence-based logical deductions on broken or missing patterns based on archaeological knowledge, avoiding meaningless filling generated by purely geometric algorithms. This ensures that the restored patterns conform to the original historical appearance in terms of topological structure and artistic style, and improves the academic value of the restoration results.

[0048] 3. This invention proposes a reconstruction confidence heatmap generation technique, which generates point-by-point confidence scores by comprehensively calculating the geometric residuals and the local deformation modulus of the deformation-guided field. This effect fills the gap in the existing technology for the lack of quantitative indicators that distinguish between real data and algorithm-induced data. It can intuitively show researchers the reliable and speculative areas of the reconstruction results, providing transparent and rigorous data support for subsequent archaeological research and effectively preventing misleading results caused by over-reconstruction.

[0049] 4. This invention makes full use of the intermediate data generated during the non-rigid registration process, extracts deformation parameters such as scaling factors and deviatoric strain tensors for frequency domain analysis, and quantitatively calculates the tension and regularity indices that reflect the style of the artifact's lines. This enables the technical solution not only to complete the visual restoration of the three-dimensional model, but also to output auxiliary dating suggestions through comparison of mathematical features with historical chronology databases, thus elevating digital preservation work from simple geometric reconstruction to the level of quantitative archaeological analysis. Attached Figure Description

[0050] The present invention will be further explained below with reference to the accompanying drawings and embodiments:

[0051] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0053] Example 1:

[0054] Please see Figure 1 A method for extracting and digitally restoring ancient artifact patterns based on point cloud models, comprising:

[0055] Obtain the original point cloud data of ancient artifacts, construct the Laplace-Beltramian operator of the original point cloud data, calculate the eigenvalues ​​and eigenfunctions of the operator, and map the original point cloud data to the manifold frequency domain;

[0056] The point cloud signal in the frequency domain of the manifold is decomposed using a spectral bandpass filter to separate the base geometry layer, the texture feature layer, and the weathering noise layer. The weathering noise layer is discarded and the texture feature layer is enhanced.

[0057] Ridge detection is performed on the enhanced pattern feature layer to extract the topological skeleton of the incomplete pattern, and the topological skeleton is mapped into a graph structure containing nodes and edges. The cantilever nodes in the graph structure are identified as breakpoints.

[0058] A pre-defined ancient decorative pattern knowledge graph library is introduced, the topological similarity between the topological skeleton and the standard template in the library is calculated, and the standard template is deformed to fit the topological skeleton using a non-rigid registration algorithm to generate a deformation guidance field containing three-dimensional spatial displacement vectors.

[0059] By using a deformation-guided field to perform Poisson fusion on the missing regions of the original point cloud data, a high-precision restored model is generated. Based on the difference between the generated data and the original data, a restored confidence heatmap data containing point-by-point confidence values ​​is generated, forming a digital restoration closed loop.

[0060] This embodiment details the overall execution flow of a point cloud model-based method for extracting and digitally restoring ancient artifact decorations. This method aims to address the challenges of existing technologies in processing severely weathered and incomplete ancient artifacts, which cannot retain subtle relief features while removing noise and lack semantic-based completion capabilities. The system acquires the original point cloud data of the ancient artifact using a high-precision 3D scanner, such as a structured light scanner, and constructs a Laplace-Beltramm operator. This operator, defined on a Riemannian manifold, serves as a mathematical tool for extracting the geometric frequency features of the artifact's surface and is calculated from discrete point cloud data using the cotangent weighting method.

[0061] The system calculates the eigenvalue sequence and corresponding eigenfunctions of the operator. These eigenfunctions constitute orthogonal bases on the manifold. The coordinate signals of the original point cloud data are projected onto these bases, thereby completing the process of mapping spatial geometric information to the frequency domain of the manifold. In the frequency domain of the manifold, the point cloud signal is decomposed using a spectral bandpass filter to separate the base geometric layer representing the macroscopic shape of the object, the decorative feature layer representing the shallow relief pattern, and the weathering noise layer representing surface erosion and random pits.

[0062] Based on this, the system executes a denoising and enhancement strategy, directly discarding the spectral coefficients of the weathering noise layer and enhancing the spectral coefficients of the pattern feature layer, while keeping the base geometry layer unchanged. The point cloud is reconstructed through inverse transformation to obtain a denoised and pattern-sharpened intermediate model. Ridge detection is performed on the enhanced pattern feature layer, the center line of the pattern ridge is extracted as the topological skeleton, and it is mapped as a graph structure containing nodes and edges. The nodes with a degree of 1 in the graph structure are identified as cantilever nodes, i.e., the breakpoints at the pattern fractures.

[0063] A pre-defined ancient decorative pattern knowledge graph library is introduced. The topological similarity between the extracted topological skeleton and the standard template in the library is calculated. The best matching template is selected, and a non-rigid registration algorithm is used to elastically deform the standard template in three-dimensional space, so that it naturally extends and covers the missing area while overlapping the existing skeleton, generating a deformation guidance field. The deformation guidance field is used as a gradient constraint to perform Poisson fusion on the missing area of ​​the original point cloud data. Based on the geometric difference between the generated data and the original data, a restoration confidence heatmap is generated to clearly distinguish between the original real data and the algorithm inference data.

[0064] This embodiment solves the problem of geometric signal aliasing by constructing a manifold frequency domain and utilizing the characteristics of the Laplace-Beltramie operator. It can effectively remove weathering noise of the same scale while preserving the micron-level bas-relief patterns. Combined with the deformation guidance of the knowledge graph, it realizes logical completion based on archaeological semantics, avoids the meaningless filling generated by traditional geometric interpolation, and significantly improves the academic value and aesthetic appeal of the restoration results.

[0065] Example 2:

[0066] Decomposing point cloud signals in the frequency domain of a manifold using a spectral bandpass filter includes:

[0067] Based on the spectral analysis characteristics of the Laplace-Beltrami operator, a first eigenvalue threshold and a second eigenvalue threshold are set, wherein the second eigenvalue threshold is greater than the first eigenvalue threshold;

[0068] Low-frequency signals with eigenvalues ​​less than the first eigenvalue threshold are identified as the base geometric layer characterizing the overall shape of the object;

[0069] The mid-frequency signal with eigenvalues ​​between the first eigenvalue threshold and the second eigenvalue threshold is identified as a texture feature layer characterizing the undulations of the bas-relief pattern. The texture feature layer contains a continuous geometric manifold structure.

[0070] High-frequency signals with eigenvalues ​​greater than the second eigenvalue threshold are identified as weathering noise layers characterizing surface erosion and random pits;

[0071] The signal intensity of the texture feature layer is amplified by the enhancement algorithm, while the interference from the base geometry layer and the weathering noise layer is suppressed.

[0072] This embodiment provides a detailed explanation of the decomposition logic of the spectral domain bandpass filter. In manifold frequency domain analysis, the magnitude of the eigenvalues ​​directly corresponds to the degree of drastic change in geometric features. Based on the spectral analysis characteristics of the Laplace-Beltramm operator, the system sets a first eigenvalue threshold and a second eigenvalue threshold, which constitute the frequency domain cutoff point.

[0073] The system identifies low-frequency signals with eigenvalues ​​less than a first eigenvalue threshold as the substrate geometric layer, corresponding to the physical carrier of the object, with a smooth surface. Mid-frequency signals with eigenvalues ​​between the first and second eigenvalue thresholds are identified as the decorative feature layer, specifically referring to the shallow relief structure carved by ancient craftsmen, containing continuous geometric manifold structures. Furthermore, high-frequency signals with eigenvalues ​​greater than the second eigenvalue threshold are identified as the weathering noise layer, characterized by surface erosion and random pits, exhibiting extremely rapid spatial changes and lacking semantic regularity. Based on this, the system defines enhanced spectral coefficients using an enhancement algorithm. To meet the requirement of suppressing substrate interference in the embodiment, the formula is modified as follows:

[0074]

[0075] in, The original point cloud signal derived from LBO decomposition is in the th... The projection coefficients on each characteristic function have the physical meaning of the original spectral components; : Derived from the preset base suppression coefficient, the value range is usually from 0.0 to 0.3. The physical meaning is to suppress the signal intensity of the macroscopic curved surface of the object as the base layer when extracting decorative features, so as to prevent it from covering the weak relief signal. This value is preset by the user based on the degree of wear of the pattern. Its physical meaning is the pattern enhancement factor, and the value range is usually from 1.2 to 2.0. : Derived from a value set based on experience with the size of the object, its physical meaning is the first characteristic threshold that distinguishes the base from the decoration; : Derived from a value set empirically based on the fineness of the pattern, its physical meaning is the second feature threshold that distinguishes the pattern from noise; : Derived from LBO calculation results, the physical meaning is the first The system reconstructs the point cloud signal based on the calculated enhancement spectral coefficients, thus completing the separation and enhancement of the signal layer.

[0076] This embodiment achieves ternary decoupling of shape, decoration, and noise through explicit frequency domain threshold division; in particular, it introduces a suppression coefficient. The forced zeroing strategy can physically reduce the interference of substrate curvature and weathering pits on subsequent ridge line detection; at the same time, the multiplier amplification of the mid-frequency band makes the originally blurred edges of the patterns due to wear clear and sharp, providing high-quality input data for subsequent topology extraction, and verifying the robustness of this technical solution in processing objects with different degrees of wear.

[0077] Example 3:

[0078] Ridge detection is performed on the enhanced pattern feature layer to extract the topological skeleton of the incomplete pattern, and the topological skeleton is mapped to a graph structure including:

[0079] Calculate the principal curvature direction on the decorative feature layer, extract local maxima along the direction of maximum principal curvature, and connect the local maxima to form discontinuous skeleton segments;

[0080] Construct a graph structure containing nodes and edges, where nodes represent the endpoints of skeleton fragments and edges represent the geometric paths of skeleton fragments;

[0081] Calculate the tangential direction vector at the endpoints of each skeleton segment;

[0082] Based on the geodesic distance between the endpoints of each skeleton segment and the cosine of the angle between the tangential direction vectors, the potential connection paths between the broken skeleton segments are predicted, forming a complete decorative topology network.

[0083] This embodiment provides a detailed explanation of the process of ridge detection and graph structure mapping in the decorative feature layer. On the enhanced decorative feature layer, the system calculates the maximum principal curvature of each vertex and its corresponding direction of maximum principal curvature. In response to the local maximum value of the second derivative along the direction of maximum principal curvature at any point, and the maximum principal curvature being greater than a preset significance threshold, the system determines that the point is located on the ridge and connects these points to form a discontinuous skeleton segment.

[0084] A graph structure containing nodes and edges is constructed, where nodes represent the endpoints of skeleton segments and edges represent the geometric paths of skeleton segments. To repair the broken patterns caused by wear, the system calculates the tangential direction vector at the endpoints of each skeleton segment and normalizes it to ensure that the vector magnitude is 1. Based on the geodesic distance between the endpoints of each skeleton segment and the cosine of the angle between the unit tangential direction vectors, the connection cost between two breakpoints is calculated. To address the inconsistency in dimensions caused by the distance term having length dimensions while the angle term is dimensionless, this embodiment introduces a feature scale parameter to normalize the distance. The formula is modified as follows:

[0085]

[0086] in, : Derived from real-time calculation, its physical meaning is the connection cost between two breakpoints; Derived from the calculation results of Dijkstra's algorithm or the thermal kernel method, its physical meaning is the geodesic distance between the endpoints of the manifold surface; Derived from preset feature scale parameters, its physical meaning is the average side length or sampling resolution of the object's point cloud, and it has the dimension of length. This is used to make geodesic distance dimensionless, so as to eliminate the problem of inconsistent dimensions on the left and right sides of the formula;

[0087] Derived from the geometric analysis of the skeleton and normalized, its physical meaning is the unit tangential direction vector at the endpoint of the skeleton segment, ensuring that the dot product value is within the range of [-1,1], representing the extension trend of the pattern; Derived from preset parameters, its physical meaning is distance weight and angle weight, used to balance spatial proximity and directional consistency;

[0088] In response to a connection cost less than a preset connection threshold, the system determines that a potential connection path exists between the two breakpoints and automatically generates a smooth curve that meets the tangential constraints using a cubic Hermitian spline interpolation algorithm; specifically, given the positions of the two breakpoints... and its tangential vector The generated connection curve satisfy:

[0089]

[0090] in, These are normalization parameters; the algorithm ensures that the generated curves have [normalization parameters] at the connection points. Continuity, thus forming a smooth and complete decorative topological network;

[0091] This embodiment utilizes the principal curvature characteristics in differential geometry to accurately locate the center line of the pattern, and creatively introduces a composite criterion of geodesic distance and tangential consistency to predict the connection of discontinuities. By explicitly specifying the cubic Hermitian spline interpolation operator, the randomness problem of curve generation is solved, enabling the algorithm not only to identify existing patterns, but also to infer the direction of the broken parts based on the geometric trend, effectively repairing the discontinuity of patterns caused by weathering, and providing a topologically complete structural foundation for subsequent template matching.

[0092] Example 4:

[0093] The non-rigid registration algorithm is used to deform the standard template to fit the topological skeleton, including:

[0094] Retrieve parameterized vector templates that match the style of the pattern topology network from the ancient pattern knowledge graph database;

[0095] Calculate the chamfer distance between the topological skeleton and the parameterized vector template, and use it as a metric for geometric fit.

[0096] Construct an energy functional, which includes a data term and a smoothing term. The data term constrains the template to conform to the observed skeleton, while the smoothing term constrains the continuity of the template deformation.

[0097] Minimize the energy functional, solve for the deformation parameters, and drive the parameterized vector template to undergo non-rigid deformation, so that it covers the topological skeleton while maintaining its own topological integrity.

[0098] This embodiment provides a detailed explanation of the non-rigid registration algorithm; this step aims to normalize and complete the observed incomplete skeleton using prior knowledge of standard templates; the system performs topological similarity calculation and template retrieval steps: to overcome the lack of semantic association in the single visual bag-of-words model, the ancient ornamentation knowledge graph library in this embodiment uses an entity-relationship-entity semantic structure to store data, specifically in the following form: ;

[0099] This includes not only geometric feature indexes but also archaeological semantic tags, such as date, region, and technique. During the retrieval phase, the system uses the Graph Edit Distance (GED) algorithm to calculate the observation topology skeleton. With standard templates in the library Topological similarity; the graph edit distance (GED) is calculated based on the following basic operation cost definition: the cost of node insertion or deletion. Set as a constant The cost of inserting or deleting. Set as a constant The node replacement cost is defined as:

[0100]

[0101] in, For node degree, The weight coefficients are used; the edge replacement cost is defined as:

[0102]

[0103] The cost is calculated based on the difference in the angle between the edge tangent vectors; the minimum edit path cost is obtained using the A* algorithm as the final GED value; a feature histogram is constructed using the Bag-of-Features model; a point-by-point fast point feature histogram is generated for all templates in the ancient decorative patterns knowledge graph database; and the K-Means clustering algorithm is used to generate a feature histogram containing... Cluster centers, for example , a visual dictionary;

[0104] For the current observed skeleton and candidate template, map the FPFH features of all its points to the nearest visual dictionary center, count the frequency of each center, and generate... 3D feature histogram vector; calculate Bach distance as style matching degree;

[0105] To address the curse of dimensionality and logical ambiguity issues in multi-objective optimization, the system introduces a comprehensive evaluation function for weighted decision-making, clarifying the calculation logic for the optimal match, as shown in the following formula:

[0106]

[0107] in, : Derived from comprehensive calculation, its physical meaning is the total score of template matching; : Derived from graph edit distance calculation, representing the cost of differences in topological structure; The Bach distance, derived from the feature histogram, represents the probability distribution differences in decorative styles, with a value range of... ; : Derived from preset weights, usually set Prioritize ensuring topological consistency; The coefficient is derived from the adaptive normalization coefficient, and the calculation formula is:

[0108]

[0109] in, To observe the larger value of the number of nodes in the skeleton and the template skeleton, For example, a preset sensitivity constant. This is used to dynamically normalize the GED cost based on the scale of the graph structure, eliminating the bias effect of the complexity of the pattern on the matching score.

[0110] The system sorts the candidate templates based on the score and selects... The highest-ranking template is used as the best matching object, thereby achieving accurate retrieval based on both geometric and semantic constraints;

[0111] After selecting the optimal matching template and initially aligning it to the centroid of the observed skeleton, the system constructs an energy functional containing data terms and smoothing terms to solve for the optimal deformation parameters; for the data terms in the energy functional formula... That is, the chamfer distance has the dimension of length. The sum of squared displacement differences, which is a smoothing term, has the dimension of area. Direct summation would violate the principle of dimensional homogeneity in the formula. This embodiment introduces a characteristic scale factor to perform dimensionless processing on each term. Simultaneously, to address the issue of the smoothing term... The lack of definition leads to the inability to optimize. This embodiment explicitly uses the normalized Dirichlet energy form to constrain the continuity of the deformation field, and the formula is modified as follows:

[0112]

[0113] in, : Derived from the optimization objective setting, its physical meaning is the total energy functional; : Derived from chamfer distance calculation, its physical meaning is data item, constraining points on the template to be as close as possible to the observation skeleton; : Derived from the feature scale calculated during the model preprocessing stage, its physical meaning is the normalized length factor, such as the diagonal length or average side length of the point cloud bounding box, and it has the dimension of length. This is used to eliminate the length dimension of the data terms and to eliminate the area dimension of the smoothing terms in its square form, so that all terms of the formula are dimensionless, satisfying the principle of dimensional homogeneity of physical formulas. : Derived from the deformation parameters to be solved, with the physical meaning of template nodes. and The three-dimensional displacement vector; Derived from a preset constant, its physical meaning is a regularization coefficient, used to balance fitting accuracy and deformation smoothness;

[0114] The system minimizes the energy functional through optimization algorithms, such as the L-BFGS algorithm, and obtains the optimal deformation parameters. The optimal deformation parameters are then used to drive the parameterized vector template to undergo non-rigid deformation, so that it can fill the gaps in the observation data while covering the existing skeleton and utilizing the integrity of the template itself.

[0115] This embodiment solves the problems of semantic completion not being feasible and template selection logic being unclear by constructing a knowledge graph structure containing semantic triples and defining an explicit weighted scoring function. Combined with dimensional correction and an explicitly defined Dirichlet smoothing term, a mathematically complete energy functional is constructed, making the optimization process solvable and convergent, thus realizing an organic combination of data-driven and knowledge-driven approaches.

[0116] Example 5:

[0117] Using a deformation-guided field to perform Poisson fusion on missing regions of the original point cloud data includes:

[0118] The deformed parameterized vector template is transformed into a gradient field constraint in three-dimensional space;

[0119] Poisson equations are constructed in the missing regions of the original point cloud data, and gradient field constraints are used as boundary conditions and guiding fields for the Poisson equations.

[0120] Solve the Poisson equation to reconstruct the surface mesh of the missing region, so that the newly generated mesh is tangentially continuous with the original point cloud data at the boundary and conforms to the geometric trend of the standard template in the internal region;

[0121] The reconstructed surface mesh is then fused into the base geometry layer to generate a complete, high-precision 3D model.

[0122] This embodiment provides a detailed explanation of the Poisson fusion generation process; the system transforms the deformed parameterized vector template into gradient field constraints in three-dimensional space; addressing the physical constraint in the Poisson surface reconstruction algorithm that the guiding field must represent the surface normal vector field rather than the tangential vector, this embodiment introduces a radial field construction operator to correct the geometric logic:

[0123] Construct a voxel mesh in the 3D space surrounding the missing region; for each voxel center point within the mesh... Find the nearest neighbor on the deformed skeleton. And obtain the tangential vector at that skeleton point. And it must be normalized, that is This ensures that the tangential vector used for projection calculations is a unit vector, satisfying the mathematical premise of Schmidt orthogonality; the spatial vector from the skeleton to the voxel is calculated. And by using the Schmidt orthogonalization principle to eliminate the tangential component, a pure radial vector is obtained. :

[0124]

[0125] right Normalization process is performed to obtain The vector Physically, it represents the surface normal vector of the tubular structure centered on the skeleton, thus meeting the input requirements of the Poisson equation;

[0126] A Poisson equation is constructed for the missing regions of the original point cloud data, as shown in the following formula:

[0127]

[0128] in, : It originates from the unknown quantity to be solved, and its physical meaning is to reconstruct the scalar field of the surface, i.e., the indicator function, and its isosurface is the restored surface; The radial normal vector field generated by the above operator is physically a guiding field that indicates that the surface should bulge outwards from the skeleton. Derived from a mathematical definition, its physical meaning is the Laplace operator;

[0129] Boundary conditions are set such that the value of the field to be solved at the boundary is equal to the known geometric information of the original point cloud at the boundary of the missing region; then, the above equations are solved to obtain the scalar field, and isosurfaces are extracted to generate the reconstructed surface mesh; due to the corrected guiding field By accurately reflecting the surface normal information, the Poisson solver can generate tubular or strip geometries that wrap around the skeleton, rather than incorrect cutting planes; this locally reconstructed surface mesh is then fused into the base geometry layer to generate a complete, high-precision 3D model.

[0130] This embodiment corrects the geometric logic error of directly using the skeleton tangent as the Poisson guiding field. By introducing a radial orthogonalization operator, a physically meaningful normal guiding field is successfully constructed. This improvement ensures that the Poisson equation can be solved to obtain a solid model with a sense of volume, realizes a rigorous mathematical transformation from one-dimensional skeleton lines to three-dimensional solid surfaces, and guarantees the geometric realizability of the restoration result.

[0131] Example 6:

[0132] The generated confidence heatmap based on the differences between the generated data and the original data includes:

[0133] The nearest neighbor distance from each point on the surface of the restored high-precision model to the original point cloud data is calculated and defined as the geometric residual.

[0134] For the region generated by Poisson fusion, the local deformation modulus of the deformation guiding field at the corresponding location is calculated, and the normalized modulus is used as an index of inference uncertainty.

[0135] A point-by-point restoration confidence score is generated by combining the reciprocal of the geometric residual with the negative correlation value of the derivation uncertainty index using a weighted summation method.

[0136] The restoration confidence score is mapped to RGB color encoding and superimposed on the surface of a high-precision model to generate a restoration confidence heatmap that intuitively marks the original data area and the algorithm-generated area.

[0137] This embodiment provides a detailed explanation of the process of generating the restoration confidence heatmap; in order to quantify the reliability of the restoration results, this embodiment defines a restoration confidence score;

[0138] The nearest neighbor distance from each point on the surface of the restored model to the original point cloud data is calculated and defined as the geometric residual. For areas where the original data exists, this value is close to 0, and for missing areas, this value is larger.

[0139] For the region generated by Poisson fusion, the local deformation modulus of the deformation guiding field at that location is calculated. If the template in a certain region deforms drastically, it indicates a lack of data constraints and high uncertainty in the deduction. This modulus is then normalized and used as the deduction uncertainty index. Strictly following the calculation logic described in the implementation example, a weighted summation method is used, combining the reciprocal of the geometric residual with the negative correlation value of the deduction uncertainty index, to generate a point-by-point restoration confidence score. To address the issue that the reciprocal of the geometric residual has the dimension of the reciprocal of length while the deduction uncertainty index is dimensionless, a normalized reference length is introduced, and the formula is modified as follows:

[0140]

[0141] in, The score is derived from the calculation results and its physical meaning is the restoration confidence score. The higher the score, the higher the confidence level. : Derived from geometric calculations, its physical meaning is geometric residual; Derived from the overall scale calculation of the model, its physical meaning is a normalized reference length, such as the length of the diagonal of the model's bounding box, and it has the dimension of length. This is used to convert geometric residuals into dimensionless relative errors, ensuring dimensional balance in the formula; Derived from deformation field analysis, its physical meaning is a normalized inference uncertainty index with values ​​ranging from 0 to 1; : This is derived from a preset minimum value to prevent the denominator from being 0; The score is derived from a preset weighting coefficient and is used to linearly combine two evaluation dimensions. The score is mapped to RGB color encoding, for example, green for high confidence and red for low confidence, and then superimposed on the surface of a high-precision model to generate a restored confidence heatmap.

[0142] This embodiment provides a quantitative method for objectively evaluating the quality of restoration. The heat map intuitively shows archaeologists which areas are authentic, which are guesses from algorithms, and whether the basis for the guesses is sufficient. This not only ensures the rigor of digital archives, but also provides transparent data support for subsequent academic research, avoiding the misleading effects of over-restoration.

[0143] Example 7:

[0144] The method also includes:

[0145] Preset recovery confidence threshold;

[0146] If the lowest score region in the restoration confidence heatmap is higher than the restoration confidence threshold, the restoration result is deemed valid and the digital model is directly output.

[0147] If the lowest-scoring region in the restored confidence heatmap is below the restored confidence threshold, the low-confidence region is marked, triggering a manual interactive correction process that allows users to adjust the deformation parameters of the parameterized vector template until the score meets the requirements.

[0148] This embodiment adds a human-computer interaction correction process to the method; the system presets a recovery confidence threshold, for example, 0.6;

[0149] After generating the heatmap, the system automatically scans the entire map and obtains the values ​​of the lowest-scoring regions. If the lowest-scoring region in the restoration confidence heatmap is higher than the restoration confidence threshold, the system determines the restoration result is valid and directly outputs the digital model. Conversely, if the lowest-scoring region is lower than the restoration confidence threshold, the system marks the low-confidence region and pauses output, while simultaneously triggering a human-interactive interface. During this period, the system allows expert users to manually adjust the key control points of the parametric vector template or modify the deformation rigidity parameters. After user adjustments, the system reruns the registration and fusion steps until the new score meets the requirements.

[0150] This embodiment introduces a closed-loop feedback mechanism for threshold determination, ensuring the baseline quality of the restoration results. In particular, for extreme incomplete cases that are difficult for the algorithm to handle, experts are allowed to intervene for fine-tuning, reflecting the collaborative concept of AI assistance plus expert oversight, which greatly improves the robustness and practicality of the system in complex archaeological scenarios.

[0151] Example 8:

[0152] This method also includes an auxiliary dating analysis step based on deformation parameters:

[0153] Extract the template deformation parameters generated by the non-rigid registration algorithm. The deformation parameters include scaling factor, deviatoric strain tensor and local curvature change.

[0154] Frequency domain analysis was performed on the deformation parameters, and the scaling factor and the mean modulus of the deviator strain tensor were calculated as the tension sensitivity index, while the variance of the local curvature change was calculated as the regularity index.

[0155] By comparing the tension index and regularity index with the pre-stored age-index mapping table in the historical age database, the potential dating range of ancient artifacts is output.

[0156] This embodiment adds an auxiliary dating analysis step to the method; this step is performed after non-rigid registration is completed, and the stylistic characteristics of the object are derived in reverse using deformation parameters; the system extracts the template deformation parameters generated by the algorithm, including scaling factors, deviatoric strain tensors, and local curvature changes; addressing the issue of broken variable calculation paths pointed out in the review, this embodiment supplements the method with calculations from three-dimensional displacement vectors. Derive the complete mathematical mapping relationship of the above physical quantities: Calculate the local deformation gradient tensor based on the mesh discrete gradient operator:

[0157]

[0158] Then, define the scaling factor. The determinant of the deformation gradient:

[0159]

[0160] Used to characterize local volume scaling; defines the deviatoric strain tensor. For the partial tensor component of the Green-Lagrange strain tensor, i.e., first calculate the strain tensor:

[0161]

[0162] Then extract its partial tensor components:

[0163]

[0164] It should be noted here that the deviatoric strain tensor described in the embodiments corresponds to the deviatoric strain tensor in physical implementation. The deviatoric tensor component of the strain tensor is the pure shear deformation component, wherein... The trace operation represents the sum of the elements on the main diagonal of a matrix. It is the identity matrix; because without introducing material property parameters, the force cannot be calculated from geometric displacement alone, this embodiment is modified to a dimensionless strain description.

[0165] Frequency domain analysis of deformation parameters: Specifically, the discrete deformation parameters are expressed along the path length of the topological skeleton. Resampling is performed; given that the topological skeleton is usually a non-linear graph structure containing branches or multiple paths, direct one-dimensional serialization has logical ambiguity. This embodiment explicitly defines the main ridge line extraction rule to achieve the linearization of the graph signal: the system traverses all endpoint pairs in the graph structure, calculates their geodesic distance, and identifies the longest connected path as the main ridge line of the ornament.

[0166] Extract only the deformation parameter nodes located on the main ridge line, and resample the main ridge line at equal intervals: calculate the total geodesic length of the main ridge line. Set the number of sampling points for powers, for example, , with step size Linear interpolation is performed on the curve to obtain... 1, equidistant data points; extract these The deformation parameters at each point are arranged strictly according to the path direction to construct a one-dimensional spatial domain signal sequence. The signal sequence was then transformed to the frequency domain using a Fast Fourier Transform (FFT) to obtain its spectrum. ;

[0167] Tension index is calculated based on frequency domain analysis results. To address the inconsistency between the definition of statistical moments (mean vs. energy) in the overview and implementation methods, and to introduce necessary signal processing steps, this embodiment explicitly employs a frequency domain energy calculation method with low-pass filtering truncation. The system only retains the frequency. The energy of the low-frequency components is calculated using Passevar's theorem, and the formula is modified as follows:

[0168]

[0169] in, Derived from low-frequency truncation analysis in the frequency domain, its physical meaning is a tension index, which accurately reflects the strength and macroscopic exaggeration of the main lines of the decoration, and eliminates the interference of high-frequency weathering noise. : Derived from scaling factor The Fourier transform coefficients of the sequence are only taken as... arrive Part of it; Derived from the partial strain tensor The Fourier transform coefficients of the sequence are taken only from the low-frequency components; Derived from a preset low-frequency cutoff frequency, corresponding to the characteristic scale of the pattern style change, it filters out the high-frequency coefficients corresponding to the tiny pits on the surface.

[0170] Calculate the regularity index; for the regularity index That is, the variance calculation result has the dimension of negative square of length. Compared with the dimensionless tension index also used in dating analysis To address the issue of dimension mismatch, this embodiment introduces a feature scale parameter for dimensionless processing and performs correction before feature combination. The formula is as follows:

[0171]

[0172] in, Derived from statistical calculations and corrected for dimensionlessness, its physical meaning is a regularity index. Under this rigorous definition, the larger the index value, the greater the variance of the curvature change, which means that the geometric trend of the decorative lines fluctuates violently, that is, the more irregular the decoration of the object. Derived from the geometric characteristics of an object, its physical meaning is a reference characteristic length, such as the average radius or maximum span of the object, and it has the dimension of length. Its squared term Used to compensate for curvature variance Dimensions are determined to ensure that regularity indicators are dimensionless. : The variance originates from the local curvature variation; : Derived from the above-mentioned displacement vector field The calculated local curvature change has dimensions. ; Source: The arithmetic mean, i.e. ;

[0173] The calculated dimensionless tension index and dimensionless regularity index are used as a feature vector and compared with the pre-stored age-index mapping table in the historical age database. For example, k-nearest neighbor classification is used to output the potential dating suggestion interval for ancient artifacts.

[0174] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for extracting and digitally restoring ancient artifact patterns based on point cloud models, characterized in that, include: The original point cloud data of the ancient artifacts is obtained, the Laplace-Beltramian operator of the original point cloud data is constructed, and the eigenvalues ​​and eigenfunctions of the operator are calculated. The original point cloud data is then mapped to the manifold frequency domain. The point cloud signal in the frequency domain of the manifold is decomposed using a spectral bandpass filter to separate the base geometry layer, the texture feature layer, and the weathering noise layer. The weathering noise layer is discarded and the texture feature layer is enhanced. Ridge detection is performed on the enhanced pattern feature layer to extract the topological skeleton of the incomplete pattern, and the topological skeleton is mapped into a graph structure containing nodes and edges. The cantilever nodes in the graph structure are identified as breakpoints. A pre-defined ancient decorative pattern knowledge graph library is introduced, the topological similarity between the topological skeleton and the standard template in the library is calculated, and a non-rigid registration algorithm is used to deform the standard template to fit the topological skeleton, generating a deformation guidance field containing a three-dimensional spatial displacement vector. The deformation guidance field is used to perform Poisson fusion on the missing regions of the original point cloud data to generate a restored high-precision model. Based on the difference between the generated data and the original data, a restored confidence heatmap data containing point-by-point confidence values ​​is generated, forming a digital restoration closed loop.

2. The method for extracting and digitally restoring ancient artifact patterns based on point cloud models according to claim 1, characterized in that, Decomposing point cloud signals in the frequency domain of a manifold using a spectral bandpass filter includes: Based on the spectral analysis characteristics of the Laplace-Beltrami operator, a first eigenvalue threshold and a second eigenvalue threshold are set, wherein the second eigenvalue threshold is greater than the first eigenvalue threshold; Low-frequency signals with eigenvalues ​​less than the first eigenvalue threshold are identified as the base geometric layer characterizing the overall shape of the object; The mid-frequency signal with eigenvalues ​​between the first eigenvalue threshold and the second eigenvalue threshold is identified as a texture feature layer characterizing the undulations of a shallow relief pattern, the texture feature layer containing a continuous geometric manifold structure; High-frequency signals with eigenvalues ​​greater than the second eigenvalue threshold are identified as weathering noise layers characterizing surface erosion and random pits; The signal intensity of the texture feature layer is amplified by the enhancement algorithm, while the interference from the base geometry layer and the weathering noise layer is suppressed.

3. The method for extracting and digitally restoring ancient artifact patterns based on point cloud models according to claim 2, characterized in that, Ridge detection is performed on the enhanced pattern feature layer to extract the topological skeleton of the incomplete pattern, and the topological skeleton is mapped into a graph structure including: Calculate the principal curvature direction on the decorative feature layer, extract local maxima along the direction of maximum principal curvature, and connect the local maxima to form discontinuous skeleton segments; Construct a graph structure containing nodes and edges, where nodes represent the endpoints of skeleton fragments and edges represent the geometric paths of skeleton fragments; Calculate the tangential direction vector at the endpoints of each skeleton segment; Based on the geodesic distance between the endpoints of each skeleton segment and the cosine of the angle between the tangential direction vectors, the potential connection paths between the broken skeleton segments are predicted, forming a complete decorative topology network.

4. The method for extracting and digitally restoring ancient artifact patterns based on a point cloud model according to claim 3, characterized in that, Deforming the standard template using a non-rigid registration algorithm to fit the topological skeleton includes: Retrieve parameterized vector templates that match the style of the pattern topology network from the ancient pattern knowledge graph database; Calculate the chamfer distance between the topological skeleton and the parameterized vector template, and use it as a metric for geometric fit. Construct an energy functional, which includes a data term and a smoothing term, wherein the data term constrains the template to move toward the observed skeleton, and the smoothing term constrains the continuity of the template deformation; Minimize the energy functional, solve for the deformation parameters, and drive the parameterized vector template to undergo non-rigid deformation, so that it covers the topological skeleton while maintaining its own topological integrity.

5. The method for extracting and digitally restoring ancient artifact patterns based on a point cloud model according to claim 4, characterized in that, Using the deformation-guided field to perform Poisson fusion on the missing regions of the original point cloud data includes: The deformed parameterized vector template is transformed into a gradient field constraint in three-dimensional space; A Poisson equation is constructed in the missing region of the original point cloud data, and the gradient field constraint is used as the boundary condition and guiding field of the Poisson equation. Solve the Poisson equation to reconstruct the surface mesh of the missing region, so that the newly generated mesh is tangentially continuous with the original point cloud data at the boundary and conforms to the geometric trend of the standard template in the internal region; The reconstructed surface mesh is then fused into the base geometry layer to generate a complete, high-precision 3D model.

6. The method for extracting and digitally restoring ancient artifact patterns based on a point cloud model according to claim 5, characterized in that, The generated confidence heatmap based on the differences between the generated data and the original data includes: The nearest neighbor distance from each point on the surface of the restored high-precision model to the original point cloud data is calculated and defined as the geometric residual. For the region generated by Poisson fusion, the local deformation modulus of the deformation guiding field at the corresponding position is calculated, and the normalized value is used as an index of inference uncertainty. A point-by-point restoration confidence score is generated by combining the reciprocal of the geometric residual with the negative correlation value of the inference uncertainty index using a weighted summation method. The restoration confidence score is mapped to RGB color encoding and superimposed on the surface of the high-precision model to generate a restoration confidence heatmap that intuitively marks the original data area and the algorithm-generated area.

7. The method for extracting and digitally restoring ancient artifact patterns based on a point cloud model according to claim 6, characterized in that, Also includes: Preset recovery confidence threshold; If the lowest score region in the restoration confidence heatmap is higher than the restoration confidence threshold, the restoration result is deemed valid and the digital model is directly output. If the lowest score region in the restored confidence heatmap is lower than the restored confidence threshold, the low confidence region is marked, triggering a manual interactive correction process that allows the user to adjust the deformation parameters of the parameterized vector template until the score meets the requirements.

8. The method for extracting and digitally restoring ancient artifact patterns based on a point cloud model according to claim 4, characterized in that, It also includes auxiliary dating analysis steps based on deformation parameters: Extract the template deformation parameters generated by the non-rigid registration algorithm. The deformation parameters include scaling factor, deviatoric strain tensor and local curvature change. Frequency domain analysis was performed on the deformation parameters, and the mean values ​​of the scaling factor and the modulus of the deviator strain tensor were calculated as tension sensitivity indicators. The variance of the local curvature change was calculated as a regularity indicator. The tension index and regularity index are compared with the pre-stored age-index mapping table in the historical age database to output the potential dating range of ancient artifacts.

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