Panchromatic method for repaired part of three-dimensional cultural relic based on shadow line method

Abstract

The invention discloses a full-color method for a repaired part of a three-dimensional cultural relic based on a shadow line method, and relates to the technical field of cultural relic protection. According to the method, cultural relic three-dimensional digital modeling is carried out through 3D scanning, denoising and reconstruction algorithms, and point cloud data of a repaired area are extracted; collecting reflectivity curves to construct a color database, and outputting an optimal color matching scheme through a K-M theory and BP neural network hybrid-driven first model through physical mapping and nonlinear correction iteration; extracting native textures and generating shadow line basic parameters through a second model combined by MCCN and a vector field driving algorithm, and outputting a stereoscopic shadow line parameter set after optimization; and constructing a virtual panchromatic repair model, simulating a multi-view effect, and printing a ground color and a shadow line in a layered manner through a micro-jet technology after the test is qualified. According to the method, accurate configuration of colors and shadow lines is achieved through the two models respectively, accurate, effective, simulatable and damage-free cultural relic repair is achieved by combining three-dimensional virtual simulation and micro-jet layered printing, and the method has deep application value.

Description

A panchromatic method for repairing three-dimensional cultural relics based on the shading method Technical Field

[0001] This invention relates to the field of cultural relic protection technology, specifically to a full-color method for repairing three-dimensional cultural relics based on the shading method, which combines three-dimensional digital modeling, artificial intelligence color matching, and micro-spraying additive manufacturing technology. Background Technology

[0002] Three-dimensional cultural relics (such as bronzes, stone carvings, and painted wood carvings) are prone to surface damage and color fading during long-term preservation due to natural weathering and human-caused damage. Repair and full-color restoration are necessary to restore their historical appearance and artistic value. Cultural relic restoration must adhere to the principles of minimal intervention, reversibility, and recognizability. Traditional restoration methods rely heavily on manual operation, and the restoration effect is highly dependent on the operator's experience, resulting in drawbacks such as low color accuracy, inconsistencies between the shadow lines and textures and the original object, and irreversible restoration processes. With the development of digital technology, 3D modeling, optical color matching, and intelligent algorithms have gradually been integrated into the field of cultural relic restoration, leading to a number of digital restoration-related technological achievements.

[0003] Chinese patent (publication number CN119338991A) discloses a digital protection method, system, equipment and medium for three-dimensional reconstruction and restoration of cultural relics. The method generates virtual restoration fragments through three-dimensional reconstruction, realizing virtual splicing and restoration of damaged areas and avoiding secondary damage from physical operations. However, this technology is still at the level of virtual restoration and does not involve the specific implementation of physical full-color restoration. Furthermore, it cannot generate shadow lines and textures that are adapted to three-dimensional curved surfaces. The restoration effect lacks a sense of three-dimensionality and realism, making it difficult to achieve the restoration principle of uniformity from a distance and discernibility up close.

[0004] Chinese patent (publication number CN106469258A) discloses a method for color matching of colored fibers based on the dual-constant Kubelka-Munk theory. The method achieves accurate color matching of colored fibers using the Kubelka-Munk theory. However, this method is applicable to fiber materials and does not take into account the curved surface features of three-dimensional cultural relics. Furthermore, it can only complete the color matching calculation and cannot generate shadow line parameters in a coordinated manner, making it difficult to meet the full-color restoration requirements of the repaired parts of three-dimensional cultural relics.

[0005] In summary, existing patented technologies for cultural relic restoration still have significant shortcomings. Traditional methods rely on manual operation, which has a high probability of human error and insufficient accuracy in color matching and texture restoration. Digital restoration methods mostly remain at the level of virtual modeling and lack a collaborative solution for virtual restoration and physical full color. Optical color matching methods do not take into account the curved surface features of three-dimensional cultural relics and cannot collaboratively generate shadow line parameters, resulting in a lack of three-dimensionality in the restoration effect.

[0006] Therefore, there is an urgent need for a full-color restoration method that combines 3D digital modeling, intelligent color matching, and stereoscopic shadow line optimization. Through the synergy of physical optics theory and intelligent algorithms, this method can accurately restore the color and texture of the repaired parts of three-dimensional cultural relics, while ensuring the reversibility and controllability of the restoration process. This will address the shortcomings of existing technologies and promote the development of cultural relic restoration technology towards digitalization, intelligence, and precision. Summary of the Invention

[0007] To address the aforementioned technical problems, this application discloses a panchromatic method for repairing three-dimensional cultural relics based on the shading method, specifically including:

[0008] Scan the 3D model of the cultural relic, generate a 3D digital model of the cultural relic, and extract point cloud data of the repair area;

[0009] The reflectance curves of multiple reference points on the artifact were collected by a spectrophotometer, and combined with three-dimensional digital modeling, a color database containing pigment composition, concentration gradient and color change patterns under different lighting conditions was constructed.

[0010] Based on the point cloud data of the repaired area, the best color scheme is output through the first model. The first model is a hybrid driving model that is trained based on a color database and constructed using Kubelka-Munk theory and backpropagation BP neural network algorithm.

[0011] Based on the optimal color scheme and reflectance curve data, the stereoscopic shadow line parameters are output through the second model, which is a combined model constructed by the Multi-View Curve Consistency Network (MCCN) algorithm and the vector field driven algorithm.

[0012] Based on the optimal color scheme and three-dimensional shadow line parameters, the repair effect under different perspectives is simulated on a three-dimensional digital model. After verification, the base color and shadow line are printed layer by layer onto the repair area using micro-spraying technology to complete the repair.

[0013] Preferably, generating a 3D digital model of the cultural relic involves: scanning the cultural relic from multiple perspectives using a 3D scanner with a preset precision to obtain point cloud data of the cultural relic, including 3D coordinates. The Gaussian curvature of the surface, the surface normal vector, and the coordinates of the boundary contour of the repaired area;

[0014] Based on the point cloud data of cultural relics, after removing point cloud noise through a bilateral filtering algorithm, the point cloud is registered from multiple perspectives through an iterative nearest point algorithm to obtain a complete point cloud model under a globally unified coordinate system, and a continuous and smooth 3D digital model is generated through a Poisson reconstruction algorithm.

[0015] Based on the complete point cloud model, the boundary of the repair area is identified by calculating the discrete Gaussian curvature, and the point cloud data of the repair area is extracted using the region growing segmentation algorithm.

[0016] Preferably, the optimal color scheme is output through the first model, specifically by: presetting the number of reference points for the reflectance curve sampling. Extract the area surrounding the repair area The reflectance curves of each reference point are normalized and then input into the first model, which includes a physical analysis module and a data analysis module.

[0017] Based on reflectance curve data, the physical analysis module establishes a physical mapping relationship between pigment concentration and reflectance using the Kubelka-Munk theory, and outputs preliminary color matching parameters.

[0018] Based on the initial color matching parameters, the data analysis module uses a BP neural network to correct nonlinear factors that are difficult to describe by physical theory, and outputs the optimal color matching scheme.

[0019] Preferably, the physical analysis module specifically retrieves the optical parameters of candidate pigments from the color database, including absorption coefficients. and scattering coefficient Based on the preset initial concentration, calculate the overall concentration of the mixed pigment layer. The theoretical reflectivity is calculated using the KM double constant formula, which is:

[0020]

[0021] in, For the pigment layer at wavelength Reflectivity at that location wavelength The absorption coefficient of the pigment. wavelength The scattering coefficient of the pigment at that location;

[0022] The formula for superimposing optical parameters when mixing multiple pigments is:

[0023]

[0024] in, Comprehensive when mixing multiple pigments value, For the first The concentration ratio of the pigments, , For the first The absorption coefficient and scattering coefficient of the pigment, The total number of pigments used in color matching.

[0025] Preferably, the data analysis module includes:

[0026] The BP neural network model of the data analysis module is trained based on the color database. It employs a three-layer BP network. The input layer receives the theoretical reflectance output from the physical analysis module, the hidden layer processes the nonlinear mapping using a Sigmoid activation function, and the output layer outputs the degree of fit between the theoretical color matching value and the artifact. The formula is as follows:

[0027]

[0028] in, For the degree of fit of theoretical parameters, The true reflectance of cultural relics in the color database. The input is the theoretical value for the color scheme;

[0029] Calculate the color matching parameter correction amount based on the theoretical parameter fit. Adjust the parameter amount The color matching parameters were regenerated by substituting them into the physical analysis module, and the process was iterated repeatedly until the theoretical parameters were found to be a good match. ,in The optimal color scheme is output after terminating the iteration by setting a pre-defined theoretical parameter fit threshold.

[0030] Preferably, the stereoscopic shadow line parameters are output through the second model, specifically: the point cloud data of the repair area and the best color scheme in the three-dimensional digital modeling of the cultural relic are normalized, spliced ​​and merged and input into the second model;

[0031] Based on the input data, the original texture features of the cultural relics are extracted by the Multi-View Curve Consistency Network (MCCN) algorithm, and the basic parameters of the shadow lines are output.

[0032] Based on the basic parameters of the shadow lines, the surface adaptation optimization and stereo correction are performed through the vector field driven algorithm, and the stereo shadow line parameters adapted to the three-dimensional surface of the cultural relics are output.

[0033] Based on the stereoscopic ray parameters, after global consistency verification and fine-tuning, the optimal set of stereoscopic ray parameters is output.

[0034] Preferably, the original texture features of cultural relics are extracted by the Multi-View Curve Consistency Network (MCCN) algorithm. Specifically, based on the three-dimensional digital model of the cultural relics, the original texture area of ​​the undamaged body of the cultural relics is sampled from multiple perspectives to collect the texture curves of the cultural relics under different observation perspectives and form a multi-view texture curve dataset.

[0035] Using the point cloud data of the repaired area as the matching basis, the best matching degree between the surface of the repaired area and the original texture of the cultural relic is calculated through curve feature clustering and topological consistency matching of the MCCN algorithm. The most suitable original texture curve is selected as the benchmark texture curve, and the formula is as follows:

[0036]

[0037] in, To match the original baseline texture curve of the cultural relic, The number of sampled views of the cultural relic. For the first Texture curves of cultural relics collected from various perspectives. To repair the reference texture curve of the curved area, For dot product operation, For vector modulo operation, To obtain the maximum value Variable operations;

[0038] Based on the baseline texture curve and combined with the three-dimensional surface features of the repair area, the basic parameter set of the shadow line is output.

[0039] Preferably, surface adaptation optimization and stereo correction are performed using a vector field-driven algorithm, specifically as follows:

[0040] The "planarized shadow line basic parameters" output by the MCCN algorithm are transformed into stereoscopic shadow line parameters adapted to the three-dimensional curved surface of the cultural relic. The basic parameters are then subjected to direction smoothing, density adaptation, tilt angle correction, and length adjustment. Direction smoothing is based on the surface normal vector and tangent direction of the repaired area. Vector projection correction is applied to the basic shadow line direction so that the shadow line direction closely matches the surface tangent direction in areas with greater curvature. The formula is as follows:

[0041]

[0042] in, For the optimized 3D ray direction, The basic shadow line direction output by MCCN. To repair the vertices of the region The direction of the tangent to the curved surface, This is the direction correction factor. As vertices The absolute value of Gaussian curvature;

[0043] Density adaptation is based on the Gaussian curvature of the repaired area, applying a gradient adjustment to the base shadow line density. Areas with larger absolute curvature have denser shadow line densities, while areas with gentler curvature have sparser shadow line densities. The formula is:

[0044]

[0045] in, To optimize the 3D ray density, The base line density output by MCCN, The maximum Gaussian curvature value of the repaired region. This refers to the density gradient coefficient;

[0046] The tilt angle correction involves optimizing the vector angle of the basic shadow line by combining the light and dark characteristics of the artifact's reflectivity curve data. This ensures that the shadow line tilt angle forms a fixed optimal angle with the light reflection direction of the artifact's surface, matching the color transition of the color scheme. The formula is:

[0047]

[0048] in, For the optimized 3D shadow line tilt angle, The base tilt angle output by MCCN For the measured reflectance curve data of the repair area, This represents the average reflectance. For maximum reflectivity, This is the tilt correction factor;

[0049] The length adjustment is based on the boundary contour and surface curvature of the repair area, and the length of the base hatching is adaptively trimmed so that the hatching is shorter in areas with greater curvature. The formula is as follows:

[0050]

[0051]

[0052] in, For the target shadow length, As the reference length, This is a length correction factor. The target shadow width, As the base width, The optimal reflectance value for the best color scheme;

[0053] Based on the corrected parameter values, the optimal set of stereoscopic ray parameters is output. .

[0054] Preferably, the repair effect is simulated from different perspectives in 3D digital modeling, specifically as follows:

[0055] The optimal color scheme and 3D illustrative parameters are precisely mapped onto the mesh surface of the repair area in the 3D digital model of the cultural relic, forming a virtual illustrative layer. The formula is as follows:

[0056]

[0057] in, Vertices in the virtual model The brightness value of the shadow line color at that location. The background brightness value corresponding to the optimal color scheme. The inclination angle of the 3D ray ray parameters. This refers to the contrast coefficient of the shadow lines;

[0058] A virtual base color layer and a virtual shadow layer are overlaid to construct a virtual full-color restoration model.

[0059] Preferably, the base color and shadow lines are printed layer by layer to the repair area using micro-spraying technology. Specifically, based on a virtual full-color repair model, a physically based lighting rendering engine is used to simulate the repair visual effect under different viewing angles and lighting environments to verify whether the repair effect is natural and coordinated under any conditions. After passing the verification, the best color scheme and three-dimensional shadow line parameters are converted into control instructions for the micro-spraying equipment, and the layer printing path is planned for layer printing and repair.

[0060] Compared with the prior art, the technical solution of this application has the following technical effects:

[0061] This invention uses a first model driven by a hybrid Kubelka-Munk theory and a BP neural network, combined with a color database constructed from the measured reflectance of the artifact itself, to iteratively optimize color matching parameters. This solves the problem of large color discrepancies between traditional manual methods and single optical models, ensuring that the color of the repaired area is highly consistent with the original.

[0062] This invention uses a second model driven by the MCCN algorithm and vector field combination to extract the original texture of cultural relics and optimize the shadow line parameters, so that the shadow lines fit the curvature changes of the three-dimensional surface, thus making up for the shortcomings of existing technologies that cannot generate shadow lines that adapt to complex curved surfaces and lack three-dimensionality in the restoration effect.

[0063] This invention combines three-dimensional virtual simulation verification with micro-spray layer printing, taking into account the reversibility and controllability of the repair process, avoiding secondary damage from manual repair and mold forming, and achieving a WYSIWYG repair effect.

[0064] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the preferred embodiments of this application are described in detail below with reference to the accompanying drawings.

[0065] The above and other objects, advantages and features of this application will become more apparent to those skilled in the art from the following detailed description of specific embodiments in conjunction with the accompanying drawings. Attached Figure Description

[0066] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In all drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0067] Based on the description of the figures and their corresponding technical content in the document, the titles of the figures are as follows:

[0068] Figure 1 is a flowchart of a full-color method for repairing three-dimensional cultural relics based on the shading method;

[0069] Figure 2 is a schematic diagram of the overall structure of a three-dimensional artifact repair method based on the shading method;

[0070] Figure 3 is a first model architecture diagram of a full-color method for repairing three-dimensional cultural relics based on the shading method;

[0071] Figure 4 shows the second model architecture diagram of a full-color method for repairing three-dimensional cultural relics based on the shading method;

[0072] Figure 5 shows the restoration stages of the replica Han Dynasty painted tile in the embodiments of this application.

[0073] Figure 6 is a schematic diagram of the iterative learning parameters of the BN neural network of the first model in the embodiment;

[0074] Figure 7 is a comparison chart of comprehensive indicators for pancolor restoration using this method in the embodiments;

[0075] Figure 8 shows the restoration process of the Tang Dynasty painted human figurine in the embodiment;

[0076] Figure 9 is a comparison chart of restoration data for Tang Dynasty painted human figurines in the embodiments;

[0077] Figure 10 shows the repair process of the severely worn bronze horse in the embodiment;

[0078] Figure 11 is a comparison chart of the repair data of the severely worn bronze horse in the embodiment. Detailed Implementation

[0079] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. In the following description, specific details such as specific configurations and components are provided merely to help fully understand the embodiments of this application. Therefore, those skilled in the art should understand that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. In addition, for clarity and brevity, descriptions of known functions and structures are omitted in the embodiments.

[0080] It should be understood that the phrase "an embodiment" or "this embodiment" throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of this application. Therefore, "an embodiment" or "this embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments.

[0081] Furthermore, reference numerals and / or letters may be repeated in different examples within this application. Such repetition is for the purpose of simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or settings discussed.

[0082] In this article, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can mean: A exists alone, B exists alone, and A and B exist simultaneously. The term " / and" in this article describes another type of relationship between related objects, indicating that two relationships can exist. For example, A / and B can mean: A exists alone, and A and B exist alone. In addition, the character " / " in this article generally indicates that the related objects before and after it are in an "or" relationship.

[0083] In this article, the term "at least one" is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, "at least one of A and B" can mean: A exists alone, A and B exist simultaneously, or B exists alone.

[0084] It should also be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion.

[0085] Example 1 describes a full-color method for repairing three-dimensional cultural relics based on the shading method, as shown in Figure 1. Specifically, it includes:

[0086] Scan the 3D model of the cultural relic, generate a 3D digital model of the cultural relic, and extract point cloud data of the repair area;

[0087] The reflectance curves of multiple reference points on the artifact were collected by a spectrophotometer, and combined with three-dimensional digital modeling, a color database containing pigment composition, concentration gradient and color change patterns under different lighting conditions was constructed.

[0088] Based on the point cloud data of the repaired area, the best color scheme is output through the first model. The first model is a hybrid driving model that is trained based on a color database and constructed using Kubelka-Munk theory and backpropagation BP neural network algorithm.

[0089] Based on the optimal color scheme and reflectance curve data, the stereoscopic shadow line parameters are output through the second model, which is a combined model constructed by the Multi-View Curve Consistency Network (MCCN) algorithm and the vector field driven algorithm.

[0090] Based on the optimal color scheme and three-dimensional shadow line parameters, the repair effect under different perspectives is simulated on a three-dimensional digital model. After verification, the base color and shadow line are printed layer by layer onto the repair area using micro-spraying technology to complete the repair.

[0091] Furthermore, the specific steps for generating a 3D digital model of a cultural relic are as follows: the cultural relic is scanned from multiple perspectives using a 3D scanner with a preset precision to obtain point cloud data of the cultural relic;

[0092] Based on the point cloud data of cultural relics, after removing point cloud noise through a bilateral filtering algorithm, the point cloud is registered from multiple perspectives through an iterative nearest point algorithm to obtain a complete point cloud model under a globally unified coordinate system, and a continuous and smooth 3D digital model is generated through a Poisson reconstruction algorithm.

[0093] Based on the complete point cloud model, the boundary of the repair area is identified by calculating the discrete Gaussian curvature, and the point cloud data of the repair area is extracted using the region growing segmentation algorithm.

[0094] Furthermore, the specific steps for generating a 3D digital model of a cultural relic are as follows: the cultural relic is scanned from multiple perspectives using a 3D scanner with a preset precision to obtain point cloud data of the cultural relic;

[0095] Based on the point cloud data of cultural relics, after removing point cloud noise through a bilateral filtering algorithm, the point cloud is registered from multiple perspectives through an iterative nearest point algorithm to obtain a complete point cloud model under a globally unified coordinate system, and a continuous and smooth 3D digital model is generated through a Poisson reconstruction algorithm.

[0096] Based on the complete point cloud model, the boundary of the repair area is identified by calculating the discrete Gaussian curvature, and the point cloud data of the repair area is extracted using the region growing segmentation algorithm.

[0097] Furthermore, a structured light 3D scanner (accuracy ≤ 0.05mm) was used to perform a full-range scan of the artifact. Because the artifact's surface may have reflective surfaces or complex textures, multiple overlapping scans were necessary.

[0098] A bilateral filtering algorithm is used to smooth the point cloud. The advantage of this algorithm is that while removing Gaussian noise, it can also preserve the edge features of the repaired area well, avoiding edge blurring;

[0099] Using the ICP algorithm, the rigid body transformation matrix and translation vector between point clouds from different viewpoints are calculated, and all local point clouds are unified to the same world coordinate system to generate a complete point cloud model of cultural relics.

[0100] The registered point cloud is constructed into a triangular mesh model. The discrete Gaussian curvature of each vertex is calculated, a curvature threshold is set, and boundary feature points are identified. The formula is as follows:

[0101]

[0102] in, As vertices Gaussian curvature value at that point, As vertices The mixing area, , As vertices Its first The other two interior angles of the local triangle formed by the neighboring points. This represents the number of neighboring points;

[0103] Using boundary points as seeds, a region growing algorithm is employed to automatically segment and extract a subset of point clouds from the repaired region based on the normal vector consistency criterion.

[0104] Furthermore, the optimal color scheme is output through the first model, specifically: the number of preset reflectance curve sampling reference points. Extract the area surrounding the repair area The reflectance curves of each reference point are normalized and then input into the first model, which includes a physical analysis module and a data analysis module.

[0105] Based on reflectance curve data, the physical analysis module establishes a physical mapping relationship between pigment concentration and reflectance using the Kubelka-Munk theory, and outputs preliminary color matching parameters.

[0106] Based on the initial color matching parameters, the data analysis module uses a BP neural network to correct nonlinear factors that are difficult to describe by physical theory, and outputs the optimal color matching scheme.

[0107] Furthermore, the physical analysis module specifically retrieves the optical parameters of candidate pigments from the color database, including absorption coefficients. and scattering coefficient Based on the preset initial concentration, calculate the overall concentration of the mixed pigment layer. The theoretical reflectivity is calculated using the KM double constant formula, which is:

[0108]

[0109] in, For the pigment layer at wavelength Reflectivity at that location wavelength The absorption coefficient of the pigment. wavelength The scattering coefficient of the pigment at that location;

[0110] The formula for superimposing optical parameters when mixing multiple pigments is:

[0111]

[0112] in, Comprehensive when mixing multiple pigments value, For the first The concentration ratio of the pigments, , For the first The absorption coefficient and scattering coefficient of the pigment, The total number of pigments used in color matching.

[0113] Furthermore, the data analysis module specifically includes:

[0114] The BP neural network model of the data analysis module is trained based on the color database. It employs a three-layer BP network. The input layer receives the theoretical reflectance output from the physical analysis module, the hidden layer processes the nonlinear mapping using a Sigmoid activation function, and the output layer outputs the degree of fit between the theoretical color matching value and the artifact. The formula is as follows:

[0115]

[0116] in, For the degree of fit of theoretical parameters, The true reflectance of cultural relics in the color database. The input is the theoretical value for the color scheme;

[0117] Calculate the color matching parameter correction amount based on the theoretical parameter fit. Adjust the parameter amount Substitute the values ​​into the physical analysis module to regenerate the color matching parameters. The formula is:

[0118]

[0119] in, For the revised color scheme parameters, The old color scheme parameters are from the previous round. To correct the step size coefficient, a value of 0.05 to 0.2 is used to control the magnitude of each correction and avoid overshoot during iteration;

[0120] Iterate repeatedly until the theoretical parameters are in good agreement. ,in The optimal color scheme is output after terminating the iteration by setting a pre-defined theoretical parameter fit threshold.

[0121] Furthermore, the stereoscopic shadow line parameters are output through the second model. Specifically, the point cloud data of the repair area and the best color scheme in the three-dimensional digital modeling of the cultural relic are normalized, spliced ​​and merged and input into the second model.

[0122] Based on the input data, the original texture features of the cultural relics are extracted by the Multi-View Curve Consistency Network (MCCN) algorithm, and the basic parameters of the shadow lines are output.

[0123] Based on the basic parameters of the shadow lines, the surface adaptation optimization and stereo correction are performed through the vector field driven algorithm, and the stereo shadow line parameters adapted to the three-dimensional surface of the cultural relics are output.

[0124] Based on the stereoscopic ray parameters, after global consistency verification and fine-tuning, the optimal set of stereoscopic ray parameters is output.

[0125] Furthermore, the original texture features of cultural relics are extracted through the Multi-View Curve Consistency Network (MCCN) algorithm. Specifically, based on the three-dimensional digital modeling of cultural relics, multi-view curve sampling is performed on the original texture area of ​​the undamaged body of the cultural relics to collect texture curves under different observation angles of the cultural relics and form a multi-view texture curve dataset.

[0126] Using the point cloud data of the repaired area as the matching basis, the best matching degree between the surface of the repaired area and the original texture of the cultural relic is calculated through curve feature clustering and topological consistency matching of the MCCN algorithm. The most suitable original texture curve is selected as the benchmark texture curve, and the formula is as follows:

[0127]

[0128] in, To match the original baseline texture curve of the cultural relic, The number of sampled views of the cultural relic. For the first Texture curves of cultural relics collected from various perspectives. To repair the reference texture curve of the curved area, For dot product operation, For vector modulo operation, To obtain the maximum value Variable operations;

[0129] Based on the baseline texture curve and combined with the 3D surface features of the repaired area, the basic parameter set of the shadow line is output, as follows:

[0130]

[0131] in, In the direction of the base shadow line, Tangent direction Based on the density of the base shadow line, The average length of the baseline texture curve, The linear density constant of the original texture of the cultural relic. Based on the length of the base shadow line, This is the proportionality coefficient. The average radius of curvature of the repaired area. Basic shadow line inclination, For the surface normal vector, Let be the standard illumination direction vector, and let be the tilt angle, which is the angle between the normal vector and the illumination direction. It is an inverse cosine function.

[0132] Furthermore, the curvature features of the three-dimensional surface are quantitatively calculated. Specifically, the curvature of the three-dimensional surface is calculated vertex by vertex for the point cloud data of the repaired area to obtain the Gaussian curvature and average curvature of each vertex.

[0133] The optimization range of the shading parameters is determined based on the curvature data. The greater the curvature of the area (such as the raised, recessed corners, and broken edges of the relief on cultural relics), the greater the correction range of the shading parameters. In areas with gentle curvature, the shading parameters are not over-corrected to ensure that the shading lines fit the curved surface without distortion.

[0134] Furthermore, surface adaptation optimization and stereo correction are performed using a vector field-driven algorithm, specifically as follows:

[0135] The "planarized shadow line basic parameters" output by the MCCN algorithm are transformed into stereoscopic shadow line parameters adapted to the three-dimensional curved surface of the cultural relic. The basic parameters are then subjected to direction smoothing, density adaptation, tilt angle correction, and length adjustment. Direction smoothing is based on the surface normal vector and tangent direction of the repaired area. Vector projection correction is applied to the basic shadow line direction so that the shadow line direction closely matches the surface tangent direction in areas with greater curvature. The formula is as follows:

[0136]

[0137] in, For the optimized 3D ray direction, The basic shadow line direction output by MCCN. To repair the vertices of the region The direction of the tangent to the curved surface, This is the direction correction factor. As vertices The absolute value of Gaussian curvature;

[0138] Density adaptation is based on the Gaussian curvature of the repaired area, applying a gradient adjustment to the base shadow line density. Areas with larger absolute curvature have denser shadow line densities, while areas with gentler curvature have sparser shadow line densities. The formula is:

[0139]

[0140] in, To optimize the 3D ray density, The base line density output by MCCN, The maximum Gaussian curvature value of the repaired region. This refers to the density gradient coefficient;

[0141] The tilt angle correction involves optimizing the vector angle of the basic shadow line by combining the light and dark characteristics of the artifact's reflectivity curve data. This ensures that the shadow line tilt angle forms a fixed optimal angle with the light reflection direction of the artifact's surface, matching the color transition of the color scheme. The formula is:

[0142]

[0143] in, For the optimized 3D shadow line tilt angle, The base tilt angle output by MCCN For the measured reflectance curve data of the repair area, This represents the average reflectance. For maximum reflectivity, This is the tilt correction factor;

[0144] The length adjustment is based on the boundary contour and surface curvature of the repair area, and the length of the base hatching is adaptively trimmed so that the hatching is shorter in areas with greater curvature. The formula is as follows:

[0145]

[0146]

[0147] in, For the target shadow length, As the reference length, This is a length correction factor. The target shadow width, As the base width, The optimal reflectance value for the best color scheme;

[0148] Based on the corrected parameter values, the optimal set of stereoscopic ray parameters is output. .

[0149] Furthermore, the formula for global parameter consistency verification is:

[0150]

[0151] in, This represents the global deviation rate of the shadow line parameters. To repair the number of vertices in the region, This is a preset global deviation rate threshold.

[0152] Furthermore, the repair effects are simulated from different perspectives using 3D digital modeling, specifically:

[0153] The optimal color scheme and 3D illustrative parameters are precisely mapped onto the mesh surface of the repair area in the 3D digital model of the cultural relic, forming a virtual illustrative layer. The formula is as follows:

[0154]

[0155] in, Vertices in the virtual model The brightness value of the shadow line color at that location. The background brightness value corresponding to the optimal color scheme. The inclination angle of the 3D ray ray parameters. This refers to the contrast coefficient of the shadow lines;

[0156] A virtual base color layer and a virtual shadow layer are overlaid to construct a virtual full-color restoration model.

[0157] Further, the base color and the shadow lines are printed in layers onto the repair area through micro-spraying technology, specifically: based on the virtual full-color restoration model, using a physical-level lighting rendering engine, simulate the restoration visual effects under different observation perspectives and lighting environments, and check whether the restoration effects are natural and harmonious under any conditions. The color consistency test formula is:

[0158]

[0159] Among them, is the CIELab color difference value, which measures the color difference between the repair area and the cultural relic itself. and and are the difference values of the repair area and the cultural relic itself on the brightness axis, red-green axis, and yellow-blue axis respectively. is qualified;

[0160] The texture structure similarity test formula is:

[0161]

[0162] Among them, are the shadow line texture images of the repair area and the original texture images of the cultural relic itself respectively. are the means of the images respectively. and are the variances respectively. is the covariance. and are the minimum constants respectively, to avoid the denominator being 0. When is determined to be qualified in the test, it represents that the texture structures are highly consistent.

[0163] After the test is qualified, convert the best color matching scheme and the three-dimensional shadow line parameters into control instructions for the micro-spraying device, plan the layered printing path, and perform layered printing and restoration.

[0164] This embodiment details a full-color method for the repair of three-dimensional cultural relics based on the shadow line method. Through 3D scanning, denoising, and reconstruction algorithms, three-dimensional digital modeling of the cultural relic is carried out, and the point cloud data of the repair area is extracted; the reflectance curve is collected to construct a color database. Through the first model driven by the combination of the K-M theory and the BP neural network, after physical mapping and non-linear correction iteration, the best color matching scheme is output; furthermore, through the second model combined with the MCCN and vector field driving algorithms, the original texture is extracted, the basic shadow line parameters are generated, and after optimization, a set of three-dimensional shadow line parameters is output; a virtual full-color restoration model is constructed, the multi-perspective effects are simulated, and after passing the test, the base color and the shadow lines are printed in layers through micro-spraying technology.

[0165] Example 2, based on Example 1, details an experiment on the restoration of simulated cultural relics using this method in a controlled environment of a cultural relic conservation laboratory. The experimental environmental parameters were controlled as follows: temperature 23±2℃, humidity 50±5%RH, standard D65 light source, and no direct sunlight. A typical restoration case from the experimental group, a simulated Han Dynasty painted pottery shard, was selected as an example. The specific restoration process is as follows:

[0166] As shown in the photograph of the imitation painted pottery shard in Figure 5(a), the base of the pottery shard to be restored is clay, and the surface painting layer is made of natural mineral pigments, including red clay. Yellow ochre ,white The thickness of the painted layer is 30~40 mm. A 2.5cm x 2.0cm damaged area was artificially created; the repair materials consisted of nano-mineral pigments, reversible resin media, and deionized water.

[0167] Remove surface dust from ceramic shards with a soft brush, place them in an ultrasonic cleaner (deionized water, 120W power, 3min), remove them and place them in a low-temperature drying oven (40℃, 2h) to dry them, to avoid moisture affecting scanning accuracy.

[0168] Using a structured light 3D scanner with a 50mm scanning range, the point cloud data of the ceramic shards was obtained from five preset viewpoints. The data included three-dimensional coordinates (x, y, z), Gaussian curvature of the surface, and normal vectors. Each scan took about 8 minutes and the total number of point clouds was about 1.2 million.

[0169] In Geomagic software, a bilateral filtering algorithm is used to remove noise from the point cloud, and the ICP algorithm is used for registration to generate a complete point cloud model in a globally unified coordinate system. Damaged boundaries are identified based on discrete Gaussian curvature calculation, and the point cloud data of the repair area is extracted using a region growing segmentation algorithm.

[0170] A continuous and smooth 3D digital model is generated using the Poisson reconstruction algorithm, as shown in Figure 5(b). The model has approximately 800,000 triangular facets and a surface roughness Ra≤0.03μm.

[0171] Within the intact area of ​​the pottery shard, 20 reference points were evenly selected within a radius of 1.5 cm centered on the damaged area. Each reference point was vertically illuminated using a portable spectrophotometer with a sampling interval of 10 nm, and a wavelength range of 380~780 nm was scanned. The reflectance curve of each point was collected 3 times, and the average value was taken as the true reflectance of that point.

[0172] The reflectance curves of 20 benchmark points, the pigment components (red earth, yellow ochre, white) of the corresponding areas, the concentration gradient, and the color data under different lighting conditions were integrated and imported into the MATLAB database to form a special color database for cultural relics containing 1200 samples.

[0173] The color database was divided into a training set (840 sets) and a validation set (360 sets) in a 7:3 ratio. The first model's backpropagation (BP) neural network was trained with a three-layer structure: 31 neurons in the input layer (corresponding to 380-780nm wavelengths, with 31 wavelengths spaced 10nm apart), 64 neurons in the hidden layer, and 3 neurons in the output layer (corresponding to three pigment concentrations). The learning rate was 0.01, the maximum number of iterations was 1000, and the fit threshold was 0.985. The goal was to minimize the deviation between the predicted and actual reflectance. The weights and thresholds were optimized using gradient descent, and the training continued until the error on the validation set stabilized.

[0174] The optical parameters of three pigments were retrieved from the color database, yielding K=0.82, S=1.25 for red ochre; K=0.65, S=1.18 for yellow ochre; and K=0.12, S=1.86 for white. An initial concentration vector was then preset. Substituting into the KM hybrid optical parameter superposition formula, the comprehensive result is obtained. Then, the theoretical reflectivity is calculated using the KM double constant formula. .

[0175] Figure 6 shows the iterative process of the BP neural network. The theoretical reflectivity is input into the trained BP neural network, and the initial fit is calculated using the fit formula. The concentration is below a preset threshold; the neural network outputs a concentration correction value. Update the concentration vector as follows Repeat the physical layer and intelligent layer computation process, iterating to the 18th iteration, to determine the fit. ,satisfy The requirement is to stop the iteration and output the optimal color scheme: 75% earth red, 20% yellow ochre, and 5% white. The total iteration time is 12.8 minutes.

[0176] Using the texture of the intact area of ​​the pottery shard as a sample, texture curves are acquired through five preset viewpoints to form a multi-view texture dataset. Using the point cloud data of the repaired area as a matching basis, the optimal matching baseline texture curve is calculated, and the basic parameters of the shadow line are output: basic direction. Basic density , base length , base inclination angle .

[0177] Based on the Gaussian curvature data of the point cloud in the repaired area, the parameters were optimized by substituting them into various correction formulas, resulting in the optimized shadow line direction. Dynamically adjusted with the tangent of the surface, the directional offset of the region of maximum curvature is less than The shadow density at the point of maximum curvature is optimized to... ;inclination scope ; shadow length ,width .

[0178] Calculate the global deviation rate of the optimized shadow line parameters. ,satisfy The requirement is to output the optimal set of stereoscopic ray parameters without further fine-tuning: direction. ,density ,length ,inclination ,width .

[0179] As shown in Figure 5(c), the virtual full-color restoration model is constructed by converting the optimal color scheme into RGB values ​​(R=156, G=87, B=42), mapping them onto the three-dimensional mesh of the repair area to form a virtual base color layer, drawing a virtual shadow layer, and then overlaying them to build the virtual full-color restoration model.

[0180] Under a standard D65 light source, the virtual model was rendered from 0°, 30°, 45°, 60°, and 90° viewing angles. Color and texture data of the repaired area and the main body in the rendered images were extracted and quantitatively verified using the CIEDE2000 color difference value. Texture structure similarity All met the preset inspection standards, and the repair effect was deemed qualified.

[0181] The base color material, prepared based on the optimal color scheme, is loaded into a micro inkjet printer and printed with a base color layer of 25μm thickness. After printing, it is placed in a low-temperature drying oven (40℃, 1h) to dry.

[0182] Based on stereoscopic ray parameters, the injection ray material is assembled, and the printing thickness is determined. The shadow layer was dried to obtain the physical repair sample shown in Figure 5 (d).

[0183] Use a soft-bristled brush to remove surface dust from the sample. Observe the integrity of the repair layer under a stereomicroscope; there should be no missed areas or smudges. The total thickness of the repair layer is [not specified]. It matches the thickness of the original painted layer.

[0184] Based on the overall experimental results, the experimental data are shown in Table 1 below:

[0185] Table 1. Comprehensive indicators for laboratory restoration of typical painted pottery fragments.

[0186] Evaluation Indicators, Experimental Results, Preset Standards: CIEDE2000 Color Difference Value: 0.69ΔE≤1.0; Spectral Reflectance: Overlap: 99.2%≥95%; Color Matching: 0.987≥0.985; Texture Structure Similarity (SSIM): 0.96≥0.95; Shadow Line Direction Adaptation Deviation: 5.1°≤8°; Global Parameter Deviation Rate: 0.032≤0.05; Repair Layer Thickness: 3330~40μm; Path Alignment Error: 1.4μm≤5μm surface

[0187] According to the comparison of comprehensive experimental indicators shown in the table above and Figure 7, the color difference value ΔE of this method is 0.69, reaching a level that is indistinguishable to the naked eye. The spectral reflectance overlap exceeds 99%, significantly improving color matching accuracy. Furthermore, the texture structure similarity (SSIM) value reaches 0.96, avoiding the distortion problem of planar shadow lines on complex curved surfaces and achieving perfect adaptation between texture and three-dimensional curved surfaces. In addition, the repair layer thickness of the micro-spray layer printing is uniform, matching the thickness of the original color painting layer, and the path alignment error is minimized. This achieves high-precision results for the shadow lines.

[0188] This embodiment details a full-process restoration experiment conducted under controlled conditions using simulated Han Dynasty painted pottery shards as the restoration object. The experimental results fully demonstrate that this method achieves high-precision color matching through the first model and surface adaptation of three-dimensional shadow lines through the second model. Combined with three-dimensional virtual simulation and micro-spray layered printing, it achieves a WYSIWYG restoration effect, effectively solving the defects of existing technologies such as large color matching deviation, poor shadow line adaptation, and irreversible restoration. It can be widely applied to the full-color restoration of various three-dimensional painted cultural relics.

[0189] Example 3, based on Examples 1 and 2, details the process of restoring a Tang Dynasty painted human figurine using this method in cultural relic restoration work. Figure 8 shows the restoration process of the Tang Dynasty painted human figurine. The figurine is 57cm high, made of pottery, and the surface painted layer contains cinnabar (red), azurite (blue), lead white (white), and ochre (yellow), with a thickness of 25-35 mm. The damaged area is from the right shoulder to the right arm. Using 2% Paraloid B72 ethyl acetate solvent as the reinforcing material and ZB-F600 water-based fluorine and water-soluble epoxy resin B-63 as the reinforcing agent, the optimal color scheme and optimal shading parameters were generated using this method. The restoration results are shown in Table 2 below.

[0190] Table 2. Data on the restoration of Tang Dynasty painted human figurines

[0191] Evaluation Indicators, Experimental Results, Preset Standards: CIEDE2000 Color Difference Value: 0.72 ≤ 1.0; Spectral Reflectance: 99.1% ≥ 95%; Texture Structure Similarity (SSIM): 0.97 ≥ 0.95; Shadow Line Direction Adaptation Deviation: 4.2° ≤ 8° surface

[0192] According to the restoration data of the Tang Dynasty painted human figurine shown in the table above and Figure 9, the restoration results of this method exceeded the preset standards in all aspects, verifying the effectiveness of this method in the restoration of this human figurine.

[0193] Example 4, based on Examples 1 and 2, details the process of restoring a severely worn bronze horse using this method in cultural relic restoration work. Figure 10 shows the restoration process of the severely worn bronze horse. The main wear on this artifact is at the horse's leg joints. This method is used to generate the optimal color scheme and optimal shading parameters. Full-color restoration is then performed using the shading method. The restoration results are shown in Table 3 below.

[0194] Evaluation Indicators, Experimental Results, Preset Standards: CIEDE2000 Color Difference Value: 0.93 ≤ 1.0; Spectral Reflectance: 97.2% ≥ 95%; Texture Structure Similarity (SSIM): 0.95 ≥ 0.95; Shadow Line Direction Adaptation Deviation: 6.3° ≤ 8° surface

[0195] As shown in the table above and Figure 11, the restoration data of the severely worn bronze horse demonstrates that the restoration results of this method exceeded the preset standards in all aspects, verifying that this method still maintains high performance in the restoration of severely worn cultural relics, and proving the versatility and stability of this method.

[0196] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. For those skilled in the art, the present invention can have various modifications and variations. Any changes, modifications, substitutions, integrations, and parameter changes made to these embodiments within the spirit and principles of the present invention, without departing from the principles and spirit of the present invention, through conventional substitutions or to achieve the same function, fall within the scope of protection of the present invention.

Claims

1. A panchromatic method for repairing three-dimensional cultural relics based on the shading method, characterized in that, include: The process involves scanning a 3D model of the cultural relic to generate a 3D digital model and extracting point cloud data from the repair area. A spectrophotometer is used to collect reflectance curves from multiple reference points on the relic. Combined with the 3D digital model, a color database is constructed, containing pigment composition, concentration gradients, and color variation patterns under different lighting conditions. Based on the point cloud data of the repair area, an optimal color scheme is output through a first model, which is a hybrid driving model trained on the color database and constructed using Kubelka-Munk theory and a backpropagation BP neural network algorithm. Based on the optimal color scheme and reflectance curve data, a second model outputs stereoscopic shading parameters. This second model is a combination of the Multi-View Curve Consistency Network (MCCN) algorithm and a vector field driving algorithm. Based on the optimal color scheme and stereoscopic shading parameters, the repair effect under different viewpoints is simulated on the 3D digital model. After verification, the base color and shading are printed layer by layer onto the repair area using inkjet printing technology, completing the repair.

2. The method for full-color restoration of three-dimensional cultural relics based on the shading method according to claim 1, characterized in that, The process of generating a 3D digital model of the cultural relic specifically involves: scanning the cultural relic from multiple perspectives using a 3D scanner with a preset precision to obtain point cloud data of the cultural relic, including 3D coordinates. The Gaussian curvature, surface normal vector, and boundary contour coordinates of the repaired area are obtained. Based on the point cloud data of cultural relics, the point cloud noise is removed by the bilateral filtering algorithm, and the point cloud is registered from multiple perspectives by the iterative nearest point algorithm to obtain a complete point cloud model under the global unified coordinate system. The Poisson reconstruction algorithm is then used to generate a continuous and smooth three-dimensional digital model. Based on the complete point cloud model, the boundary of the repair area is identified by calculating the discrete Gaussian curvature, and the point cloud data of the repair area is extracted using the region growing segmentation algorithm.

3. The method for full-color restoration of three-dimensional cultural relics based on the shading method according to claim 1, characterized in that, The step of outputting the optimal color scheme through the first model specifically involves: presetting the number of reference points for the reflectance curve sampling. Extract the area surrounding the repair area The reflectance curves of each reference point are normalized and then input into the first model, which includes a physical analysis module and a data analysis module. Based on the reflectance curve data, the physical analysis module establishes a physical mapping relationship between pigment concentration and reflectance using the Kubelka-Munk theory and outputs preliminary color matching parameters. Based on the preliminary color matching parameters, the data analysis module corrects nonlinear factors that are difficult to describe by physical theory using a BP neural network and outputs the optimal color matching scheme.

4. The method for full-color restoration of three-dimensional cultural relics based on the shading method according to claim 3, characterized in that, The physical analysis module specifically retrieves the optical parameters of candidate pigments from the color database, including absorption coefficients. and scattering coefficient Based on the preset initial concentration, calculate the overall concentration of the mixed pigment layer. The theoretical reflectivity is calculated using the KM double constant formula, which is: in, For the pigment layer at wavelength Reflectivity at that location wavelength The absorption coefficient of the pigment. wavelength The scattering coefficient of the pigment; the formula for superimposing optical parameters when multiple pigments are mixed is: in, Comprehensive when mixing multiple pigments value, For the first The concentration ratio of the pigments, 、 For the first The absorption coefficient and scattering coefficient of the pigment, The total number of pigments used in color matching.

5. The method for full-color restoration of three-dimensional cultural relics based on the shading method according to claim 3, characterized in that, The data analysis module specifically comprises: a BP neural network model trained based on the color database, employing a three-layer BP network. The input layer receives the theoretical reflectance output from the physical analysis module, the hidden layer processes nonlinear mapping using a Sigmoid activation function, and the output layer outputs the degree of fit between the theoretical color matching value and the artifact, as shown in the formula: in, For the degree of fit of theoretical parameters, The true reflectance of cultural relics in the color database. The input is the theoretical color matching value; based on the fit of the theoretical parameters, the correction amount of the color matching parameters is calculated. Adjust the parameter amount The color matching parameters were regenerated by substituting them into the physical analysis module, and the process was iterated repeatedly until the theoretical parameters were found to be a good match. ,in The optimal color scheme is output after terminating the iteration by setting a pre-defined theoretical parameter fit threshold.

6. The method for full-color restoration of three-dimensional cultural relics based on the shading method according to claim 1, characterized in that, The step of outputting stereoscopic shadow line parameters through the second model specifically involves: normalizing the point cloud data of the repaired area and the optimal color scheme in the 3D digital modeling of the cultural relic, then stitching and merging them and inputting them into the second model; based on the input data, extracting the original texture features of the cultural relic through the Multi-View Curve Consistency Network (MCCN) algorithm, and outputting the basic shadow line parameters; based on the basic shadow line parameters, performing surface adaptation optimization and stereoscopic correction through a vector field-driven algorithm, and outputting stereoscopic shadow line parameters adapted to the 3D curved surface of the cultural relic; based on the stereoscopic shadow line parameters, after global consistency verification and fine-tuning, outputting the optimal set of stereoscopic shadow line parameters.

7. The method for full-color restoration of three-dimensional cultural relics based on the shading method according to claim 6, characterized in that, The extraction of the original texture features of cultural relics using the Multi-View Curve Consistency Network (MCCN) algorithm specifically involves: based on a 3D digital model of the cultural relic, multi-view curve sampling is performed on the original texture area of ​​the undamaged body of the cultural relic to collect texture curves from different viewing angles, forming a multi-view texture curve dataset; using the point cloud data of the repaired area as the matching basis, the best matching degree between the surface of the repaired area and the original texture of the cultural relic is calculated through curve feature clustering and topological consistency matching of the MCCN algorithm, and the most suitable original texture curve is selected as the benchmark texture curve, as shown in the formula: in, To match the original baseline texture curve of the cultural relic, The number of sampled views of the cultural relic. For the first Texture curves of cultural relics collected from various perspectives. To repair the reference texture curve of the curved area, For dot product operation, Modulo operation for vectors, To obtain the maximum value Variable operations; based on the baseline texture curve and combined with the three-dimensional surface features of the repaired area, output the basic parameter set of the shadow line.

8. A method for full-color restoration of three-dimensional cultural relics based on the shading method according to claim 6, characterized in that, The surface adaptation optimization and stereoscopic correction using the vector field-driven algorithm specifically involves: converting the "planarized shadow line basic parameters" output by the MCCN algorithm into stereoscopic shadow line parameters adapted to the three-dimensional curved surface of the cultural relic; and performing direction smoothing, density adaptation, tilt angle correction, and length adjustment on the basic parameters. Direction smoothing is based on the surface normal vector and tangent direction of the repaired area, and vector projection correction is applied to the basic shadow line direction so that the shadow line direction closely matches the surface tangent direction in areas with greater curvature. The formula is as follows: in, For the optimized 3D ray direction, The basic shadow line direction output by MCCN. To repair the vertices of the region The direction of the tangent to the curved surface, This is the direction correction factor. As vertices The absolute value of the Gaussian curvature; density adaptation is based on the Gaussian curvature of the repaired area, and the base shadow line density is adjusted by gradient. Areas with a larger absolute value of curvature have denser shadow line density, while areas with gentler curvature have sparser shadow line density. The formula is: in, To optimize the 3D ray density, The base line density output by MCCN, The maximum Gaussian curvature value of the repaired region. The density gradient coefficient is used; the tilt angle correction is achieved by combining the light and dark characteristics of the reflectivity curve data of the artifact itself, and optimizing the vector angle of the basic shadow line tilt angle so that the shadow line tilt angle forms a fixed optimal angle with the light reflection direction of the artifact surface, matching the color light and dark transition of the color scheme. The formula is: in, For the optimized 3D shadow line tilt angle, The base tilt angle output by MCCN For the measured reflectance curve data of the repair area, This represents the average reflectance. For maximum reflectivity, The tilt angle correction factor is used; the length adjustment is based on the boundary contour and surface curvature of the repair area, and the length of the base hatchline is adaptively trimmed so that the hatchline is shorter in areas with greater curvature. The formula is: in, For the target shadow length, As the reference length, This is a length correction factor. For the target shadow width, As the base width, The optimal reflectance value is obtained for the best color scheme; based on the corrected parameter values, the optimal set of stereoscopic ray parameters is output. 。 9. The method for full-color restoration of three-dimensional cultural relics based on the shading method according to claim 1, characterized in that, The simulation of restoration effects from different perspectives on 3D digital modeling specifically involves: accurately mapping the optimal color scheme and stereoscopic shadow line parameters onto the mesh surface of the repair area in the 3D digital model of the cultural relic, forming a virtual shadow line layer, as shown in the formula: in, Vertices in the virtual model The brightness value of the shadow line color at that location. The background brightness value corresponding to the optimal color scheme. The inclination angle of the 3D ray ray parameters. The contrast coefficient is used to overlay the virtual background layer and the virtual shadow layer to construct a virtual full-color restoration model.

10. A method for full-color restoration of three-dimensional cultural relics based on the shading method according to claim 1, characterized in that, The process of printing the base color and shadow lines in layers to the repair area using micro-spraying technology involves: based on a virtual full-color repair model, using a physically based lighting rendering engine, simulating the repair visual effect under different viewing angles and lighting environments, and verifying whether the repair effect is natural and coordinated under any conditions; after passing the verification, the optimal color scheme and three-dimensional shadow line parameters are converted into control instructions for the micro-spraying equipment, and the layered printing path is planned for layered printing and repair.

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