Historical defective fresco digital restoration system based on AI

Abstract

The invention discloses an AI-based historical defective fresco digital restoration system, and relates to the technical field of AI restoration, a two-channel filter and a U-Net network are adopted to extract a fresco damage boundary, and edge detection is enhanced in combination with manual labeling; calculating a multi-scale Hurst index, and constructing a matrix quantization fractal feature change rule; dynamically generating a probabilistic grammar rule set based on the fractal incidence matrix, and defining a state transition probability function of texture growth; recursively executing texture generation driven by grammar rules from boundary points, and introducing random disturbance attenuating along with depth to simulate a stroke natural form; textures are generated through Laplacian pyramid layered correction, and the phase of a reference image is aligned in a Fourier domain to reserve structural consistency; and solving an affine transformation matrix with unchanged illumination in the transition zone, and globally optimizing color connection between the restoration area and the original wall painting. According to the method, the dynamic grammar rule base is established by analyzing the fractal features of the residual strokes, so that the generated texture follows creation logic, and the visual coherence of a recovery area is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of AI restoration, and particularly relates to an AI-based historical damaged mural digital restoration system. BACKGROUND

[0002] Mural is the crystallization of ancient art, one of the earliest means for humans to record things and express emotions, and exists in churches, tombs, palaces, temples and the like. However, due to the harsh environment, the abrasion of time, and the damage of factors such as wind and rain, and earthquakes, many existing murals are damaged. Mural, as a witness to the long history of mankind, has an indispensable position, so the research on mural restoration is currently a relatively urgent task.

[0003] Traditional mural restoration is usually mainly manual, which not only requires the staff to have solid knowledge of humanities, art, archaeology and the like, but also consumes a large amount of time and has a complex process. In addition, once a mistake occurs in the manual restoration process, irreversible damage will be caused to the cultural relics. Therefore, in order to overcome the above shortcomings, we hope to use AI to replace or assist mural restoration to reduce the complexity of restoration.

[0004] The existing mural digital restoration technology cannot analyze the non-Euclidean fractal laws of the original mural strokes when dealing with large-area structural damage, resulting in structural fracture of the restored texture and the remaining area. These methods rely on isotropic texture expansion mechanism and ignore the dynamic syntax features such as stroke direction and force variation in historical creation, resulting in pseudo-continuity that violates artistic logic, which destroys the visual consistency of the work. In view of the above problems, the following scheme is proposed. SUMMARY

[0005] The purpose of the present application is to provide an AI-based historical damaged mural digital restoration system, which can model the dynamic generation law of strokes by establishing a fractal syntax driven texture growth mechanism, solving the problem of topological fracture between the restored area and the original mural caused by ignoring non-Euclidean structural features in the prior art.

[0006] To solve the above technical problems, the present application is realized by the following technical scheme: The present application is an AI-based historical damaged mural digital restoration system, which comprises an image preprocessing module, a fractal feature analysis module, a syntax rule library construction module, a recursive texture generation module, a multi-scale fusion module and a color optimization module. The image preprocessing module, fractal feature analysis module, syntax rule library construction module, recursive texture generation module, multi-scale fusion module and color optimization module are connected in sequence, and the output end of the image preprocessing module is unidirectionally connected with the color optimization module. The workflow of the restoration system is as follows: Step S1, edge semantic segmentation: adopt a double-channel filter and a U²-Net network to accurately extract mural damage boundaries, and combine artificial annotation masks to enhance edge detection; Step S2, fractal grammar extraction: calculate multi-scale Hurst indexes from residual strokes in the boundaries, and construct a direction-scale correlation matrix to quantify the variation law of fractal features; Step S3, grammar rule library construction: dynamically generate a probabilistic grammar rule set based on the fractal correlation matrix, and define a state transition probability function for texture growth; Step S4, fractal constraint texture growth: recursively execute grammar rule driven texture generation from boundary points, and introduce random perturbations that decay with depth to simulate the natural morphology of strokes; Step S5, multi-scale feature fusion: correct the generated texture through a Laplacian pyramid layer, and align the reference image phase in the Fourier domain to preserve structural consistency; Step S6, color consistency optimization: solve an affine transformation matrix that is invariant to illumination in the transition zone, and globally optimize the color connection between the restored area and the original mural.

[0007] Further, the image preprocessing module is used to extract accurate boundary point sets of mural damage areas, providing a geometric basis for subsequent analysis; The fractal feature analysis module is used to quantify the multi-scale fractal properties of residual strokes, generating a direction-scale correlation feature matrix; The grammar rule library construction module is used to convert fractal features into probabilistic texture growth rules, establishing a dynamic grammar production set; The recursive texture generation module is used to recursively generate multi-scale self-similar texture structures along the boundary normal according to the grammar rules; The multi-scale fusion module is used to fuse texture layers of different scales through frequency domain phase correction, maintaining structural consistency; The color optimization module is used to establish a color mapping model under transition zone constraints, achieving visual consistency between the restored area and the original mural.

[0008] Further, the step S1, edge semantic segmentation specifically includes the following steps: Step S11: input a digital scanned image of a historical mural with dimensions of width height and RGB three channels; Step S12: combine a pre-labeled damage area binary mask by a double-channel edge enhancement filter, the formula is: wherein, Gaussian filter output, The standard deviation of the Gaussian kernel. For image plane coordinates, To input a mural image, A binary mask for manually labeled defective areas. For convolution operators, This is element-wise multiplication; Step S13: Input the filtering result into the U²-Net neural network and calculate the image gradient magnitude. Extract those that meet the conditions pixel set As the boundary of the damage, the edge contour of the missing area is located, where... For gradient operators, It is the L2 norm. The preset threshold; This step uses dual-channel filtering and neural network segmentation to accurately extract structural features and gradient abrupt change points at the damaged boundary, establishing a geometric constraint benchmark for subsequent texture growth and solving the misalignment problem caused by boundary ambiguity.

[0009] Furthermore, step S2, fractal syntax extraction, specifically includes the following steps: Step S21: Extract the remaining brushstroke block within the 5-pixel buffer zone outside the damaged boundary B. The size is 16×16 pixels; Step S22: For each Calculate the multiscale Hurst exponent:

[0010] In the formula, For stroke blocks In scale Hurst exponent For fractal analysis scale, For the k-th local brushstroke image patch, The expected value of the spatial average; Step S23: Establish the direction-scale correlation matrix Quantifying the evolution of the self-similarity of original mural brushstrokes with respect to direction and scale:

[0011] In the formula, The direction-scale correlation matrix, For the m-th direction interval, For the nth scale, As belonging to direction A subset of brushstrokes for The number of strokes, The partial derivative of Hurst index with respect to scale; This step quantifies the multi-scale fractal parameters (Hurst index) of the residual strokes in the boundary buffer, constructs the direction-scale correlation matrix, converts the mural creation rules into calculable mathematical features, and lays the data foundation for the grammar rules.

[0012] Further, the step S3 of constructing the grammar rule library specifically includes the following steps: Step S31: Define a set of grammar productions Each rule is in the form of:

[0013] Wherein, N is the total number of rules in the set of grammar productions, is the th rule, is the current texture growth state symbol, is the direction constraint parameter, are derived sub-symbols, is the core growth probability function; Step S32: Initialize λ according to the R matrix:

[0014] In the formula, is the grammar rule growth probability function, is the probability distribution sharpness coefficient, is the complete mural reference template matrix, is the matrix Frobenius norm; This step generates a set of probabilistic grammar productions based on the fractal correlation matrix, converts physical features into symbolic rules through exponential mapping, realizes the digital encoding of creation logic, and ensures that the texture generation conforms to historical painting techniques.

[0015] Further, the step S4 of fractal constraint texture growth specifically includes the following steps: Step S41: Starting from the boundary point , along the normal direction of the point , start the texture generation process; Step S42: Using a recursive growth mechanism, start from the initial depth and advance to the maximum depth , and perform the following operations at each depth level:

[0016] Wherein, is a random disturbance function consistent with the characteristics of mural materials:

[0017] wherein, is the recursion depth generated texture, is the syntax rule library the jth rule in the library, is the lambda-based rule selection operator, is the morphological dilation operation; is the Gaussian distribution, is the perturbation direction angle, is the uniform distribution; is the perturbation intensity, decaying with depth d as ; This step recursively performs syntax-driven texture generation along the boundary normal, simulates natural stroke variation through a random perturbation operator, and controls structural stability with a depth decay mechanism to realize self-similar structure reconstruction in large-area missing regions.

[0018] Further, the step S5 of multi-scale feature fusion specifically comprises the following steps: Step S51: generating a texture pyramid wherein is the down-sampling rate of the texture layer; Step S52: cross-layer correction in the Laplacian pyramid space: Fourier transforming the generated texture of each layer to obtain a frequency domain representation, retaining its amplitude information but replacing it with the phase spectrum of the lossless reference block , and realizing inverse transform reconstruction of phase alignment through the formula ; wherein, is the corrected texture of the lth layer, is the Fourier transform, is the inverse Fourier transform, is the element-wise multiplication, is the complex phase angle, is the imaginary unit, is the down-sampled version of the lossless area reference block; Step S53: up-sampling the corrected texture of each layer to the original resolution, and outputting the final restoration result through a weighted fusion formula , ensuring the cross-scale consistency of micro-texture and macro-structure; wherein, is the up-sampling operator; This step performs cross-layer frequency domain correction on the generated texture in the Laplacian pyramid space, maintains edge consistency by using reference block phase constraints, and eliminates scale breakage through upsampling fusion to ensure visual coherence.

[0019] Furthermore, step S6, color consistency optimization, specifically includes the following steps: Step S61: Establish a 3-pixel wide transition band inside and outside the damaged boundary B. ; Step S62: By minimizing the color difference between the restored texture and the corresponding pixels of the original mural within the transition band, and simultaneously applying a regularization term to control the smoothness of the mapping, an optimization objective function is constructed, and the optimal color mapping matrix is ​​obtained by solving this function. The optimization objective function is: In the formula, Let be the 3×3 affine transformation matrix to be solved. For the transition zone pixel set, To restore the image at the pixel level RGB color values ​​at that location This represents the RGB color value at pixel q in the original input image. These are the pixel coordinates within the transition zone. It is the L2 norm. For matrix The L1 norm of the gradient, The regularization coefficient is used. Step S63: Obtain the optimal color mapping matrix It applies to the entire defective area and outputs the final restored image; This step solves for the illumination-invariant affine transformation matrix in the transition zone, and constrains the color gradient abrupt change through L1 regularization, thereby achieving a seamless color gradation transition between the generated area and the original mural, which conforms to the spectral characteristics of mineral pigments.

[0020] The present invention has the following beneficial effects: 1. This invention establishes a dynamic grammar rule base by analyzing the fractal features of the remaining brushstrokes, so that the generated textures follow the original creation logic of the mural; by extracting the multi-scale Hurst index and the direction-scale correlation matrix, the self-similarity law of the brushstrokes is quantified; recursive growth transforms the non-Euclidean fractal features into symbolic generation rules, ensuring that the new textures naturally extend with the surrounding traces in terms of topological structure; this process achieves cross-scale structural consistency from microscopic brushstrokes to macroscopic patterns, improving the visual coherence of the restored area.

[0021] 2, The growth process driven by the fractal grammar embeds the material physical property constraint, which effectively avoids the "digital sense" distortion of the synthesized texture; in the random disturbance term, by introducing an attenuation random field consistent with the distribution characteristics of mural pigment particles, the generated brush strokes present the irregular deposition characteristics of natural mineral pigments; the multi-scale fusion mechanism uses the Laplacian pyramid to perform phase correction in the frequency domain space, preserving the porous medium optical properties of the original mural substrate; the embedding of physical mechanisms makes the restoration results closer to the material properties of the cultural relics in the micro-texture layer, providing reliable basis for subsequent protection research.

[0022] 3, The application deeply encodes the artistic creation rules of a specific era / painting school in the construction process of the dynamic grammar rule library, so that the restoration result conforms to the historical context style; the production rule set initializes the growth probability function through the direction-scale correlation matrix, learns and stores the style fingerprints such as the strength of the creator's brush and the turning angle; the color optimization is based on the affine transformation model established by the transition zone to transfer the natural fading mode of mineral pigments in the illumination invariant space; such design not only reconstructs the visual form, but also maintains the spatiotemporal authenticity of artistic evolution at the brushstroke dynamics level through quantitative artistic creation grammar.

[0023] Of course, implementing any product of the present application does not necessarily require all the advantages described above. BRIEF DESCRIPTION OF DRAWINGS

[0024] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the description of the embodiments. Obviously, the drawings in the following description only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0025] Figure 1 The system structure schematic diagram of the AI-based historical damaged mural digital restoration system of the present application; Figure 2 The flowchart of the AI-based historical damaged mural digital restoration system of the present application. DETAILED DESCRIPTION

[0026] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0027] Please refer to Figure 1As shown, the application is an AI-based historical defect wall painting digital restoration system, which comprises an image preprocessing module, a fractal feature analysis module, a grammar rule library construction module, a recursive texture generation module, a multi-scale fusion module and a color optimization module. The image preprocessing module, fractal feature analysis module, grammar rule library construction module, recursive texture generation module, multi-scale fusion module and color optimization module are connected in sequence, and the output end of the image preprocessing module is unidirectionally connected with the color optimization module. The image preprocessing module is used to extract the accurate boundary point set of the wall painting defect area, and provide a geometric basis for subsequent analysis. The fractal feature analysis module is used to quantify the multi-scale fractal characteristics of the remaining brush strokes, and generate a direction-scale correlation feature matrix. The grammar rule library construction module is used to convert the fractal features into probabilistic texture growth rules, and establish a dynamic grammar production set. The recursive texture generation module is used to recursively generate multi-scale self-similar texture structures along the boundary normal according to the grammar rules. The multi-scale fusion module is used to fuse texture layers of different scales through frequency domain phase correction, and maintain structural consistency. The color optimization module is used to establish a color mapping model under the constraint of the transition zone, and realize the visual consistency of the restored area and the original wall painting.

[0028] Please refer to Figure 2 As shown, the workflow of the restoration system is as follows: Step S1, edge semantic segmentation: adopt a double-channel filter and U²-Net network to accurately extract the wall painting damage boundary, and combine artificial labeled mask to enhance edge detection, specifically: Step S11: input the digital scanned image of the historical wall painting , the dimension of which is width , height and RGB three channels; Step S12: combine the artificial pre-labeled defect area binary mask , and process it through a double-channel edge enhancement filter, the formula of which is: In the formula, is the Gaussian filter output, is the standard deviation of the Gaussian kernel, is the image plane coordinate, is the input wall painting image, is the artificial labeled defect area binary mask, is the convolution operator, is the element-wise multiplication; Step S13: input the filtered result into the U²-Net neural network, and calculate the image gradient amplitude Extract those that meet the conditions pixel set As the boundary of the damage, the edge contour of the missing area is located, where... For gradient operators, It is the L2 norm. This is a preset threshold.

[0029] Step S2, Fractal Syntax Extraction: Calculate the multi-scale Hurst exponent from the remaining brushstrokes at the boundary, and construct a direction-scale correlation matrix to quantify the variation law of fractal features. Specifically: Step S21: Extract the remaining brushstroke block within the 5-pixel buffer zone outside the damaged boundary B. The size is 16×16 pixels; Step S22: For each Calculate the multiscale Hurst exponent:

[0030] In the formula, For stroke blocks In scale Hurst exponent For fractal analysis scale, For the k-th local brushstroke image patch, The expected value of the spatial average; Step S23: Establish the direction-scale correlation matrix Quantifying the evolution of the self-similarity of original mural brushstrokes with respect to direction and scale:

[0031] In the formula, The direction-scale correlation matrix, For the m-th direction interval, For the nth scale, As belonging to direction A subset of brushstrokes for Number of strokes in the middle This is the partial derivative of the Hurst exponent with respect to scale.

[0032] Step S3, Construction of the Syntax Rule Base: Dynamically generate a probabilistic syntax rule set based on the fractal correlation matrix, and define the state transition probability function for texture growth, specifically as follows: Step S31: Define the set of grammatical production rules Each rule is in the following form:

[0033] in, the total number of rules in the grammar production set, the jth rule, the jth rule, the current texture growth state symbol, the direction constraint parameter, all are derived sub-symbols, the core growth probability function; Step S32: initializing λ according to the R matrix:

[0034] wherein, the grammar rule growth probability function, the probability distribution sharpness coefficient, the complete mural reference template matrix, the matrix Frobenius norm.

[0035] Step S4, fractal constraint texture growth: recursively performing grammar rule driven texture generation from the boundary point, introducing random disturbance with depth decay to simulate the natural form of brush strokes, specifically: Step S41: starting from the boundary point , launching the texture generation process along the normal direction of the point ; Step S42: using a recursive growth mechanism, starting from the initial depth and advancing layer by layer to the maximum depth , performing the following operations at each depth level: wherein, the random disturbance function consistent with the characteristics of mural materials:

[0036] wherein, the recursive depth generated texture, the jth rule in the grammar rule library , the rule selection operator based on λ, the morphological dilation operation; the Gaussian distribution, the disturbance direction angle, the uniform distribution; the disturbance intensity, which decays with depth d .

[0037] Step S5, multi-scale feature fusion: generating texture through Laplacian pyramid layering correction, aligning the reference image phase in the Fourier domain to preserve structural consistency, specifically: Step S51: generating texture pyramid​ ,in downsampling rate Texture layers; Step S52: Perform cross-layer correction in Laplacian pyramid space: generate textures for each layer. Perform a Fourier transform to obtain the frequency domain representation, retain its amplitude information but replace it with a lossless reference block. The phase spectrum, through the formula Achieve phase-aligned inverse transform reconstruction; In the formula, This is the corrected texture of layer l. For Fourier transform, This is the inverse Fourier transform. For element-wise multiplication, To obtain a complex phase angle, The imaginary unit, This is a downsampled version of the lossless region reference block; Step S53: Apply the corrected textures to each layer. Upsampled to the original resolution, then fused using a weighted fusion formula. Output the final restored result to ensure cross-scale consistency between micro-texture and macro-structure; In the formula, This is the upsampling operator.

[0038] Step S6, Color Consistency Optimization: Solve for the illumination-invariant affine transformation matrix in the transition zone, and globally optimize the color connection between the restored area and the original mural. Specifically: Step S61: Establish a 3-pixel wide transition band inside and outside the damaged boundary B. ; Step S62: By minimizing the color difference between the restored texture and the corresponding pixels of the original mural within the transition band, and simultaneously applying a regularization term to control the smoothness of the mapping, an optimization objective function is constructed, and the optimal color mapping matrix is ​​obtained by solving this function. The optimization objective function is:

[0039] In the formula, Let be the 3×3 affine transformation matrix to be solved. For the transition zone pixel set, To restore the image at the pixel level RGB color values ​​at that location This represents the RGB color value at pixel q in the original input image. These are the pixel coordinates within the transition zone. It is the L2 norm. For matrix The L1 norm of the gradient, for the regularization coefficient; Step S63: the optimal color mapping matrix obtained Acting on the entire damaged area, output the final restored image.

[0040] One specific application of this embodiment is: Implementation object: repair the lotus pattern of partial damage of a mural, with a damaged area of about 15x20cm; Step S1, high-precision edge semantic segmentation Obtain a digital scanned image of the mural (resolution 2480x3200 pixels), and manually label the damaged area mask ; Apply a double-channel edge enhancement filter:

[0041] Extract the damaged boundary through the U²-Net network , set the gradient threshold (the first 15% quantile of the calculated gradient amplitude), and output the boundary point set ; Step S2, fractal grammar rule extraction Extract the remaining brushstroke block outside the boundary B with a 5-pixel buffer ; Calculate the Hurst index (representing the typical lotus curl pattern) of the brushstroke block :

[0042] Construct a direction-scale correlation matrix (example 45° direction):

[0043] Step S3, dynamic grammar rule library construction Define the lotus pattern grammar rule set (example rules):

[0044] Initialize the growth probability function (β=0.75):

[0045] Step S4, fractal constraint texture growth Select boundary points (normal ) as the growth starting point; Perform three-level recursive growth ( ): First level (d=1):

[0046] Level 2 (d=2):

[0047] Level 3 (d=3):

[0048] Step S5: Multi-scale feature fusion Building a texture pyramid: original scale Generate textures ; Downsampling 2 times Gaussian filtering followed by 2×2 pooling; Downsampling 4 times Secondary pooling; Laplacian spatial correction (with) (For example, a layer)

[0049] in Taken from an adjacent complete lotus pattern; Reconstruction and fusion results: ; Step S6: Color Consistency Optimization Establish a transition zone (3-pixel band inside and outside boundary B); Solve for the color mapping matrix:

[0050] Apply M to the defective area and output the final restored image.

[0051] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0052] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. An AI-based historical defect wall painting digital restoration system, characterized by, The restoration system comprises an image preprocessing module, a fractal feature analysis module, a syntax rule library construction module, a recursive texture generation module, a multi-scale fusion module and a color optimization module; The image preprocessing module, the fractal feature analysis module, the syntax rule library construction module, the recursive texture generation module, the multi-scale fusion module and the color optimization module are sequentially connected, and the output end of the image preprocessing module is unidirectionally connected with the color optimization module; The working process of the restoration system is as follows: Step S1, edge semantic segmentation: a double-channel filter and a U²-Net network are used to accurately extract the mural damage boundary, and an artificial labeled mask is combined to enhance edge detection; Step S2, fractal syntax extraction: multi-scale Hurst indexes are calculated from the residual strokes in the boundary to construct a direction-scale correlation matrix to quantify the fractal feature variation law; Step S3, syntax rule library construction: a probabilistic syntax rule set is dynamically generated based on the fractal correlation matrix, and a state transition probability function of texture growth is defined; Step S4, fractal constraint texture growth: recursive texture generation driven by syntax rules is performed from the boundary points, and a random disturbance with depth attenuation is introduced to simulate the natural morphology of strokes; Step S5, multi-scale feature fusion: the generated texture is corrected through a Laplacian pyramid layering, and the structure consistency is aligned with the reference image in the Fourier domain; Step S6, color consistency optimization: an affine transformation matrix that is invariant to illumination is solved in the transition zone, and the color connection of the restored area and the original mural is globally optimized. 2.The AI-based historical defect wall painting digital restoration system of claim 1, wherein The image preprocessing module is used to extract the accurate boundary point set of the mural damage area, providing a geometric basis for subsequent analysis; The fractal feature analysis module is used to quantify the multi-scale fractal characteristics of the residual strokes, and generate a direction-scale correlation feature matrix; The syntax rule library construction module is used to convert fractal features into probabilistic texture growth rules, and establish a dynamic syntax production set; The recursive texture generation module is used to recursively generate multi-scale self-similar texture structures along the boundary normal according to the syntax rules; The multi-scale fusion module is used to fuse texture layers of different scales through frequency domain phase correction, and maintain structure consistency; The color optimization module is used to establish a color mapping model under the constraint of the transition zone, and realize the visual consistency of the restored area and the original mural. 3.The AI-based historical defect wall painting digital restoration system of claim 1, wherein The step S1, edge semantic segmentation, specifically comprises the following steps: Step S11: input the digital scanned image of the historical mural; Step S12: combine the pre-labeled binary mask of the damaged area, and process it through a double-channel edge enhancement filter; Step S13: input the filtered result into a U²-Net neural network, calculate the image gradient amplitude, extract the pixel point set meeting the conditions as the damage boundary, and thus locate the edge contour of the damaged area. 4.The AI-based historical defect wall painting digital restoration system of claim 1, wherein The step S2, fractal syntax extraction, specifically comprises the following steps: Step S21: extract residual stroke blocks in a 5-pixel buffer area outside the damage boundary, with a size of 16x16 pixels; Step S22: calculate the multi-scale Hurst index for each extracted residual stroke block, which quantifies the self-similarity feature of the stroke through spatial expectation operation; Step S23: A direction-scale correlation matrix is established, and the matrix element value is the arithmetic mean of the Hurst index derivative of all strokes in the corresponding direction interval at a specific scale, so as to quantify the evolution law of the self-similarity of the original mural strokes with the direction and scale. 5.The AI-based historical defect wall painting digital restoration system of claim 1, wherein The step S3, the syntax rule library construction specifically includes the following steps: Step S31: A set of formal syntax production rules is defined, and each rule is composed of a four-tuple: a starting state symbol, a generated target symbol pair, a growth probability function controlled by direction and scale; Step S32: The direction-scale correlation matrix obtained in step S2 is used to initialize the growth probability function, and the core mechanism is to calculate the difference between the current mural fractal feature matrix and the complete mural reference template matrix, apply an exponential conversion to the difference, introduce a probability distribution sharpness adjustment coefficient, and finally normalize the scale dimension to generate the probability distribution. 6.The AI-based historical defect wall painting digital restoration system of claim 1, wherein The step S4, the fractal constraint texture growth specifically includes the following steps: Step S41: Starting from the damaged boundary point, the normal direction of the point is taken as the initial growth reference; Step S42: A recursive generation mechanism is adopted to gradually advance the texture construction within the preset maximum depth range, and the generation process of each depth level includes the following three core operations: The probability distribution based on the dynamic syntax rule library is screened to apply the selected rule to the texture unit generated in the last step; A directional random disturbance is applied, which conforms to the physical characteristics of the mural, the direction angle of the disturbance is uniformly sampled within the limited interval, and the disturbance amplitude is exponentially attenuated with the increase of the recursive depth; All the texture fragments generated by the rules in the current layer are integrated through morphological dilation operation; This process is executed in a loop until the maximum recursive depth is reached, and finally the texture of the damaged area is output, which is structure self-similar and natural in stroke morphology. 7.The AI-based historical defect wall painting digital restoration system of claim 1, wherein The step S5, the multi-scale feature fusion specifically includes the following steps: Step S51: The generated texture is constructed into a four-layer pyramid structure, and each layer represents a texture version with different resolutions, wherein the bottom layer is the original resolution, and the upper layers are successively down-sampled by a factor of two; Step S52: Cross-layer correction is performed in the Laplacian pyramid space: the frequency domain of each layer of texture is transformed, the phase spectrum information of the reference area corresponding to the resolution layer is extracted, the amplitude spectrum of the generated texture is kept unchanged, and the phase spectrum is replaced with the phase spectrum of the reference area; the corrected frequency domain data is restored to the spatial domain image through inverse transformation; Step S53: The correction results of all levels are up-sampled to the original mural resolution, and are fused into the final output texture by weighted superposition. 8.The AI-based historical defect wall painting digital restoration system according to claim 1, wherein, The step S6, the color consistency optimization specifically includes the following steps: Step S61: A ring-shaped transition area is constructed by expanding 3 pixels in width inward and outward from the damaged boundary line as the center line; Step S62: An optimization objective function is constructed by minimizing the color difference between the restored texture in the transition zone and the corresponding pixels of the original mural, while applying a regularization term to control the smoothness of the mapping, and the optimal color mapping matrix is obtained by solving the function; Step S63: The optimal color mapping matrix is applied to the entire damaged area to output the final restored image.

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