A graph regularization slow feature analysis method for infrared nondestructive testing data

Abstract

This invention discloses a graph regularized slow feature analysis method for infrared nondestructive testing data, comprising: acquiring an infrared image sequence and preprocessing the infrared image sequence; subsequently, constructing a pixel-level graph Laplacian matrix using a block-parallel strategy, calculating pixel adjacency relationships within local image blocks based on bilateral weights of spatial distance and temperature similarity, and merging them to generate a global sparse adjacency matrix through a maximum value fusion strategy in overlapping regions; constructing a joint objective function that fuses temporal slowness constraints and spatial smoothness constraints, and optimizing the solution using an adaptive dual whitening and matrix trace ratio dynamic adjustment strategy; finally, solving the objective function to extract slow feature components and reconstructing the infrared image. This invention overcomes the computational bottleneck of high-dimensional thermal imaging data through an efficient computational strategy, and utilizes a physically-aware graph regularized slow feature analysis algorithm to achieve feature decoupling of multiple types of defects under spatiotemporal constraints, significantly enhancing the thermal feature edges and signal-to-noise ratio of defects.

Description

Technical Field

[0001] This invention belongs to the field of infrared nondestructive testing and image processing technology. More specifically, this invention relates to a graph regularization slow feature analysis method for infrared nondestructive testing data. Background Technology

[0002] During long-term service, spacecraft in orbit face continuous exposure to a synergistic effect of various extreme environmental loads, including alternating extreme temperatures, high-energy particle radiation, micrometeoroid impacts, and space debris collisions. This can easily lead to complex damage of various types, such as matrix cracking, fiber breakage, delamination, and debonding. These damages are often characterized by multi-scale distribution, complex and varied morphologies, and high concealment. Furthermore, different damage types exhibit significant differences in their development patterns, severity, and maintenance strategies, posing a significant threat to the safety of spacecraft in orbit. Therefore, based on the development of advanced non-contact damage detection technologies, further decoupling of complex damage and accurate identification and classification of damage types have profound engineering significance for ensuring the safe operation and life assessment of spacecraft.

[0003] Currently, infrared thermal imaging defect detection technology is widely used in the defect detection of composite materials and metal materials due to its advantages such as non-contact operation, wide detection coverage, rapid response, and result visualization. Depending on whether an external heat source is required during the detection process, infrared thermal imaging defect detection technology can be divided into active thermal imaging and passive thermal imaging. In the field of defect detection, active thermal imaging is typically used. During active heating, the presence of defects alters the heat flow conduction within the specimen, thus creating a detectable temperature difference field on the specimen surface. The infrared thermal imager records the changes in the surface temperature field over time, generating an infrared image sequence containing rich spatiotemporal information. Different types of defects have different depths, sizes, and thermophysical properties, resulting in varying thermal response characteristics in the infrared image sequence. Furthermore, the acquired raw infrared image sequence usually contains a large amount of heating noise and blurring caused by thermal diffusion, making defect identification difficult. Therefore, it is necessary to use data processing techniques to process the infrared image sequence data.

[0004] Currently, the mainstream infrared image sequence processing algorithms mainly include Principal Component Thermometry (PCT) and Thermal Signal Reconstruction (TSR). PCT, based on principal component analysis, unfolds each frame of the image into a vector, then concatenates them into a two-dimensional temperature matrix according to the frame number, and uses the principle of maximizing statistical variance to separate features. Although this method can effectively improve the signal-to-noise ratio of defects, it relies excessively on global statistical characteristics, ignoring the crucial spatiotemporal evolution information contained in the infrared image sequence. TSR, on the other hand, is a pixel-by-pixel temporal analysis method that reconstructs the image by performing low-order polynomial fitting and differentiation operations on the temperature-time curve in the logarithmic domain. While TSR possesses significant temporal smoothing and denoising capabilities, its pixel-by-pixel independent computation completely severs the spatial correlation between pixels and their neighbors.

[0005] Slow Feature Analysis (SFA), as an unsupervised learning algorithm, can extract the slowest-changing essential features from high-dimensional time-series data. Infrared image sequences can essentially be viewed as combinations of temperature-time curves of a number of pixels, and therefore SFA can also be applied to them. However, directly applying it to high-resolution infrared images faces two major challenges: firstly, the curse of dimensionality, and secondly, the computational complexity. N × N ( N First, the covariance matrix in the dimension of (number of pixels) requires huge memory overhead and computing resources; second, it destroys the spatial structure. Similar to PCT, the traditional SFA vectorization process destroys the original two-dimensional topological structure, causing the extracted features to lose key spatial manifold properties.

[0006] Therefore, it is urgent to construct a physical perception graph regularized slow feature analysis method based on existing infrared image sequence processing techniques. This method should effectively integrate multi-dimensional information such as temporal evolution and spatial manifold, and fully utilize its spatiotemporal constraint complementarity to improve feature decoupling performance. This method needs to integrate a complete process including large-scale block graph construction, adaptive dual whitening, physical perception bilateral weighting, and dynamic spatiotemporal joint optimization to overcome the curse of computational dimensionality and spatial topological deficiencies of traditional algorithms. This will enable high signal-to-noise ratio and high-resolution imaging of weak defects, meeting the urgent need for accurate identification of complex defects in infrared nondestructive testing engineering. Summary of the Invention

[0007] One object of the present invention is to solve at least the above-mentioned problems and / or defects, and to provide at least the advantages described below.

[0008] To achieve these and other advantages according to the present invention, the present invention provides a graph regularization slow feature analysis method for infrared nondestructive testing data, comprising: S1: Acquire the original infrared image sequence X of the object under test using an infrared thermal imager. t×H×W and for Xt×H×W Preprocessing is performed, in which t The time dimension of the frame sequence H For height, W Width; S2: Constructing a global pixel-level graph Laplacian matrix L based on a block-parallel strategy. N×N Establish topological relationships between pixels; S3: Combining the temporal slowness constraint of slow feature analysis with the spatial smoothness constraint of graph Laplacian, construct a spatiotemporal joint optimization objective function; and solve the spatiotemporal joint optimization objective function to extract the slow feature components that reflect the thermal response characteristics of defects and their corresponding spatial projection matrices. S4: Reconstruct the image sequence using the slow feature components and spatial projection matrix to extract defect features from the thermal image.

[0009] Preferably, in S1, for X t×H×W Preprocessing specifically includes: Image sequence vectorization, converting single-frame thermal images X H×W The spatial dimension is flattened into a one-dimensional vector, while preserving the temporal dimension of the frame sequence. t Without changing the temperature matrix, we obtain the two-dimensional temperature matrix X. t×N , N = H × W ; In terms of time dimension, the time temperature of each pixel minus its mean. m with standard deviation σ The standardized temperature matrix is ​​obtained. .

[0010] Preferably, in step S2, the step of constructing the global pixel-level graph Laplacian matrix specifically includes: Select a single frame of raw infrared image X H×W It is then divided into several local sub-blocks with overlapping regions; The pixel adjacency weights within each sub-block are calculated using a two-sided weighting method based on spatial distance and temperature similarity. w ij The calculation formula is as follows: In the above formula, x i x j A vector representing the spatial coordinates of a pixel; T i , T j This indicates the temperature value of a pixel in the reference frame; σ S The spatial attenuation coefficient controls the geometric locality of the plot connections; σT The temperature sensitivity coefficient represents the ability to control heat diffusion across temperature boundaries. Max pooling is used to handle weight conflicts in overlapping regions, merging local adjacency matrices into a global sparse adjacency matrix A. N×N ; Calculate the global sparse adjacency matrix A N×N The row sums are used to construct the angle matrix D. N×N Using the angle matrix D N×N For the global sparse adjacency matrix A N×N Regularization is performed to obtain the regularized graph Laplacian matrix L. r : L r =ID -1 / 2 AD -1 / 2 In the above formula, I is the identity matrix.

[0011] Preferably, in step S3, the spatiotemporal joint optimization objective function is... J ( ω The expression represents the weighted sum of the time-slow variable and the spatial smoothing term; solving the spatiotemporal joint optimization objective function aims to find a projection direction. ω This minimizes the rate of change of the projected signal over time and the difference within its spatial neighborhood, i.e., minimizes... J ( ω ); In the above formula, The time derivative matrix, β L is the space regularization coefficient. r The regularized graph Laplacian matrix is ​​used. In the same whitening space, the optimization constraints of the spatiotemporal joint optimization objective function are transformed into an eigenvalue problem of the mixture matrix. The mixture matrix consists of the covariance matrix of the time derivative matrix and the regularized graph Laplacian matrix. The specific steps for solving the eigenvalues ​​of the mixture matrix are as follows: According to the standardized temperature matrix Frame count t and pixels N The ratio between them is used to adaptively select to perform dual whitening processing in the time sample space or the spatial feature space to obtain the whitening transformation matrix Q. Based on the normalized temperature matrix Construct a time derivative matrix characterizing the temperature change over time. Subsequently, the time derivative matrix is ​​transformed using the whitening transformation matrix Q. Map to the whitening space and calculate the covariance matrix C. diff_white ; The regularized Graph Laplacian matrix L is obtained by applying the whitening transformation matrix Q. r Mapping to whitening space yields L white And introduce a space regularization coefficient. β The target mixing matrix M in the whitening space is obtained as follows: M=C diff_white + β L white Perform singular value decomposition or eigenvalue decomposition on the target mixing matrix in the whitening space, and sort the eigenvalues ​​from smallest to largest. The sorted eigenvalues ​​are { V 1, V 2,…, V t The corresponding eigenvectors are arranged in order to form an eigenvector matrix U; the whitening transformation matrix Q is multiplied by the eigenvector matrix U to obtain the spatial projection matrix Z that maps the original infrared image space to the slow eigenspace; the normalized temperature matrix is ​​then... Perform matrix multiplication with the spatial projection matrix Z to obtain the slow eigencomponent S.

[0012] Preferably, the spatiotemporal joint optimization objective function is... J ( ω The regularization parameter used to balance the time slowness constraint and the spatial smoothness constraint is adaptively determined; its calculation is based on the ratio of the energy trace of the time derivative matrix to the energy trace of the graph Laplacian matrix.

[0013] Preferably, in step S4, the generalized inverse matrix of the spatial projection matrix Z is calculated; the selected slow eigencomponent S is... i Multiplying by the generalized inverse matrix yields the reconstructed infrared image sequence, where 0 ≤ i ≤ t .

[0014] The present invention has at least the following beneficial effects: Firstly, when dealing with high-dimensional matrix data processing, this invention introduces a block-based parallel graph construction and dual whitening strategy. The block strategy avoids memory overflow caused by constructing a fully connected dense matrix through local computation and maximum value fusion; the dual whitening strategy utilizes the characteristics of infrared image sequences—"few frames, many pixels"—to transfer feature decomposition to a low-dimensional sample space. The combination of these two approaches overcomes the computational bottleneck of high-resolution image manifold learning.

[0015] Secondly, it significantly enhances the sharpness of defect edges and the signal-to-noise ratio. This invention constructs a graph Laplacian matrix based on bilateral weights of spatial distance and temperature similarity. This matrix incorporates thermodynamic physical constraints, enabling the graph structure to sense temperature gradients. During feature extraction, the algorithm automatically severs strong connections between defects and the background, thereby preserving sharp defect edges in the projection matrix and reconstructed image, while simultaneously using graph regularization to smooth background noise.

[0016] Third, it achieves automatic decoupling and parameter adaptation of thermal response characteristics of different types of defects. By fusing time-slowly varying characteristics (SFA) and spatial manifold structure (graphical Laplace matrix), this invention can effectively separate defect signals exhibiting different thermal response modes. Simultaneously, the parameter adaptation mechanism based on matrix trace ratio eliminates the blindness of manually adjusting regularization parameters, improving the robustness and engineering applicability of the method.

[0017] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0018] Figure 1 This is a schematic diagram illustrating the specific implementation process of the graph regularization slow feature analysis method for infrared nondestructive testing data according to the present invention. Figure 2 This is a schematic diagram illustrating the block segmentation strategy and overlapping principle in an embodiment of the present invention; Figure 3 This is the projection matrix corresponding to the first three slow feature components in this embodiment of the invention; Figure 4 These are the original infrared images of the specimen in this embodiment of the invention and the reconstructed thermal images corresponding to the first three slow feature components. Detailed Implementation

[0019] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.

[0020] It should be understood that terms such as “having,” “comprising,” and “including” as used herein do not exclude the presence or addition of one or more other elements or combinations thereof. This invention provides a graph-regularized slow feature analysis method for infrared nondestructive testing data, aiming to solve the feature decoupling and computational bottleneck problems in high-resolution infrared image sequence processing during infrared thermal imaging defect detection. For example... Figure 1As shown, the infrared image sequence is first preprocessed, and then a physically-aware global pixel-level Laplacian matrix is ​​constructed using a block-parallel approach and a fusion strategy of maximum values ​​in overlapping regions. A bilateral weighting based on spatial distance and temperature similarity is then used to accurately characterize the spatial structure of thermal flow. Next, by combining adaptive dual whitening and dynamic equilibrium parameters, a joint optimization problem of fusion temporally slow variation and spatial smoothness is constructed and solved. This method overcomes the memory overflow and computational bottlenecks faced by high-resolution infrared data manifold learning. While overcoming the limitations of traditional algorithms in terms of spatiotemporal information fragmentation, it uses physical constraints to forcibly cut off the smooth leakage of defect boundaries, achieving decoupling of thermal response features of different types of defects and significantly improving the signal-to-noise ratio and edge sharpness of weak defects. The specific processing flow of this method includes: S1. Acquire infrared image sequence X of the object under test using an infrared thermal imager. t×H×W Then, it undergoes preprocessing, which mainly includes the following two steps: S11. Image sequence vectorization: First, vectorize the single-frame thermal image X... H×W The spatial dimension is flattened into a one-dimensional vector, and then concatenated into a two-dimensional temperature matrix X according to the time dimension of the frame sequence. t×N , N = H × W In this two-dimensional temperature matrix, row variations represent the temperature change of a single pixel over time, while column variations represent different pixels in the infrared image.

[0021] S12. Matrix Standardization: According to the time dimension (i.e., the temperature time series of each pixel), the time temperature of each pixel is subtracted from its mean. m with standard deviation σ The standardized temperature matrix is ​​obtained. : In the above formula, To prevent division by zero errors, a small constant (e.g., 1×10⁻⁶) -6 ).

[0022] S2. Construct the global pixel-level graph Laplacian matrix L N×N This involves modeling high-resolution infrared images as discrete graph structures on a manifold space to capture the spatiotemporal evolution relationships between pixels. Considering high-resolution images (… H × W The large number of nodes caused by this N × N , N = H × WDirectly constructing the full-pixel Laplacian matrix would face a severe "curse of dimensionality," so a strategy combining block-parallel computation and max pooling is adopted to solve it. The specific steps are as follows: S21. Perform overlapping block segmentation on a single-frame infrared thermal image: Select the original single-frame infrared image X H×W For the global processing domain, the size of the local image patch is set to [value]. B × B To ensure a smooth transition of pixel connectivity at boundaries and eliminate block artifacts during subsequent local adjacency matrix fusion, the overlap step size between adjacent image blocks is set to [value missing]. O Then, the entire image is traversed using a sliding window mechanism, and finally, the image is generated. K A local image patch { P 1, P 2,…, P K}

[0023] S22. For each local image patch P i Construct its internal local adjacency matrix A i To enable the graph structure to perceive temperature distribution and ensure defect edges, a bilateral weighting method based on spatial distance and temperature similarity is used to calculate the pixel adjacency weights within each sub-block. The calculation formula is as follows: In the above formula, x i x j A vector representing the spatial coordinates of a pixel; T i , T j This indicates the temperature value of a pixel in the reference frame; σ S The spatial attenuation coefficient controls the geometric locality of the plot connections; σ T This is a temperature sensitivity coefficient, controlling the ability of heat diffusion across temperature boundaries. Simultaneously, to eliminate redundant connections caused by imaging noise or long-range weak correlations, a dynamic k-nearest neighbor strategy is employed, applying only bilateral weights. w ij Greater than the preset threshold Establish connections between nodes.

[0024] S23, the results obtained from parallel computing K A local adjacency matrix i Map back to the global coordinate system and assemble into a global adjacency matrix A N×N : For the same pixel pair in the overlapping region ( u , vIn cases where weights may be repeatedly calculated across multiple local image patches, a max-pooling strategy is used to handle weight conflicts in overlapping regions. S24. Calculate the graph Laplacian matrix and perform regularization: Calculate A N×N The row sums are used to construct the angle matrix D. N×N Its diagonal elements To prevent numerical instability, isolated nodes ( D ii =0) A small perturbation needs to be added. Then, this perturbation is used to regularize the adjacency matrix, resulting in the regularized graph Laplacian matrix: L r =ID -1 / 2 AD -1 / 2 In the above formula, I is the identity matrix.

[0025] S3. Constructing and Solving the Spatiotemporal Joint Optimization Objective Function: Spatiotemporal Joint Optimization Objective Function J ( ω The objective function can be expressed as a weighted sum of a time-slow variable (slow feature analysis constraint) and a spatial smoothing term (graph Laplace regularization). Solving the objective function aims to find a projection direction. ω This minimizes the rate of change of the projected signal over time and its difference within the spatial neighborhood, i.e., minimizes the spatiotemporal joint optimization objective function. J ( ω ): In the above formula, The time derivative matrix, β L is the space regularization coefficient. r Let be the graph Laplacian matrix. In the same whitening space, the optimization constraints of the above spatiotemporal joint optimization function can be transformed into an eigenvalue problem of the mixture matrix (the covariance matrix of the time derivative matrix and the regularized graph Laplacian matrix). The specific solution steps are as follows: S31. Based on the standardized two-dimensional temperature matrix Constructing a whitening space: For high-resolution infrared images, due to the number of pixels... N Maximum (10) 6 (At orders of magnitude higher), the covariance matrix cannot be directly constructed. Therefore, it is necessary to use the standardized temperature matrix. Frame count t and pixels N The ratio relationship between them is adaptively determined by solving the covariance matrix in either the time sample space or the spatial feature space. In the above formula, when N ≥2 t Specifically, for high-dimensional, small-sample cases, a dual-space whitening strategy based on the Gram matrix is ​​adopted; conversely, a dual-space whitening strategy based on the covariance matrix is ​​adopted. Then, the covariance matrix C is eigenvalued and the whitening transformation matrix Q is constructed using the eigenvalues ​​Λ and eigenvectors V.

[0026] S32. Map the covariance matrix of the time derivative matrix and the regularized graph Laplacian matrix to the whitening space: First, based on the normalized temperature matrix... Construct the time derivative matrix : In the above formula, Δ t This is the time interval between frames. Derived from the objective function... J ( ω As can be seen, the time derivative matrix also needs to be solved. The covariance matrix. To avoid the curse of dimension, the time derivative matrix is ​​first transformed using the whitening transformation matrix Q. Map to the whitening space, and then calculate its covariance matrix C. diff_white : The regularized Graph Laplacian matrix L r It also maps to the whitened space: L white =Q T L r Q Finally, a space regularization coefficient is introduced. β Composition of the mixing matrix M: M=C diff_white + β L white S33. Solve the mixture matrix to obtain the slow feature signal and the corresponding projection matrix: Perform singular value decomposition or eigenvalue decomposition on M, and sort the eigenvalues ​​from smallest to largest. The sorted eigenvalues ​​are { V 1, V 2,…, V t-1 The corresponding eigenvectors are arranged in order to form an eigenvector matrix U; Q and U are multiplied to obtain a spatial projection matrix Z that maps the original infrared image space to the slow eigenspace, and the normalized temperature matrix is ​​then used. Matrix multiplication with the spatial projection matrix Z yields the slow eigencomponent S, calculated using the following formulas: Z=Q×U To address the weight imbalance caused by the inconsistency in magnitude between the time-domain and spatial-domain terms, spatial regularization coefficients are used. β The calculation introduces an adaptive adjustment mechanism based on the matrix trace. The energy of the covariance matrix of the time derivative matrix is ​​calculated. E T =Trace(C diff_white The energy of the regularized graph Laplacian matrix E S =Trace(L white Define effective balance parameters. β eff : In the above formula, it is to prevent E S =0 and a tiny amount added.

[0027] S4. Image reconstruction and defect extraction, which consists of the following two steps: S41. Calculate the generalized inverse matrix of the spatial projection matrix Z: Since W∈R K×N (in N Number of pixels K It is the characteristic number, and N >> K Matrix F is typically not a square matrix and does not have a full rank, making direct inversion impossible. Therefore, the Moore-Ponros generalized inverse is used to construct the optimal reconstruction operator F: F = (Z) T Z -1 Z T In the above formula, each row of F represents the spatial response mode of the corresponding slow feature component in the original pixel space.

[0028] S42, Select the slow feature component S i Multiplying by the generalized inverse matrix yields the reconstructed infrared image sequence, where 0 ≤ i ≤ t : X recon =S i ×F i Example: To verify the effectiveness of the graph regularization slow feature analysis method for infrared nondestructive testing data proposed in this invention, this example selects a carbon fiber reinforced polymer (CFRP) laminate as the test object (the target plate mainly contains two types of defects: 1. Holes, characterized by their large defect area and deep depth; 2. The pit (characterized by a small defect area and shallow depth) was analyzed using long-pulse infrared thermography (LPT) to obtain experimental data. The acquired raw infrared image sequence contained 99 frames of time-series data, stored in CSV format. Since the raw field of view included non-target areas, the target plate needed to be cropped. After processing, the spatial resolution of the image was normalized to 400×400 pixels. Finally, an infrared image sequence with dimensions of 99×400×400 (frame count × height × width) was obtained, with the acquisition time Δ between two frames being... t It takes 0.1 seconds.

[0029] S1. Image preprocessing and data standardization: This mainly aims to convert the original infrared image sequence into a two-dimensional standardized matrix suitable for algorithm processing, thereby eliminating the influence of the reference temperature on the results while satisfying the constraints of slow feature analysis.

[0030] S11. Call the data reading module to read the cropped infrared image sequence X. 99×400×400 Each frame of the two-dimensional image X 400×400 Expanding into a one-dimensional vector and arranging it according to the frame sequence yields a two-dimensional temperature matrix X. 99×160000 .

[0031] S12. According to the time dimension (i.e., the temperature time series of each pixel), subtract the mean value from the time temperature of each pixel. m with standard deviation σ The standardized temperature matrix is ​​obtained. : In the above formula, To prevent division by zero errors, a small constant (in this embodiment, =1×10 -6 ).

[0032] S2. Construct the global pixel-level graph Laplacian matrix L 160000×160000 Given that the image has as many as 160,000 pixels, a block-parallel strategy is used to construct the sparse graph Laplacian matrix to avoid memory overflow. The specific process is as follows: Figure 2 As shown.

[0033] S21. In this embodiment, the 33rd frame of the original image sequence is selected as the reference frame to calculate the physical connection relationship between pixels. The size of the image sub-block is 50×50 pixels. To ensure a smooth transition of pixel connection relationships at the boundaries and eliminate the block effect during subsequent local adjacency matrix fusion, the overlap step size of adjacent sub-blocks is set to 20 pixels. Then, the entire image is traversed according to the sliding window mechanism, and finally 169 local image blocks are generated { P 1, P 2,…,P 169}

[0034] S22. For each local image patch P i Construct its internal local adjacency matrix A i First, the dynamic k-nearest neighbor algorithm is used to search for the 20 nearest neighbor pixels of each pixel in spatial geometry and construct neighbor pairs. Then, a two-sided weighting method based on spatial distance and temperature similarity is used to calculate the weight of each neighbor pair. The calculation formula is as follows: In the above formula, x i x j A vector representing the spatial coordinates of a pixel; T i , T j Indicates the temperature value of a pixel in the reference frame; spatial attenuation coefficient. σ S Set to 2.0; temperature sensitivity coefficient σ T Set to 1.0. Simultaneously, to eliminate redundant connections caused by imaging noise or long-range weak correlations, a preset threshold is used. =0.1, for weight w ij Nodes with a value greater than a preset threshold are connected, while connections with a value less than the preset threshold are forcibly set to 0.

[0035] S23. The 169 local adjacency matrices A obtained through parallel computation i Map back to the global coordinate system and assemble into a global adjacency matrix A 160000×160000 : For the same pixel pair in the overlapping region ( u , v In cases where weights may be repeatedly calculated across multiple local image patches, a max-pooling strategy is used to handle weight conflicts in overlapping regions. S24. Calculate the graph Laplacian matrix and perform regularization: Calculate A 160000×160000 The row sums are used to construct the angle matrix D. 160000×160000 Its diagonal elements To prevent numerical instability, isolated nodes ( D ii =0) A small perturbation (1×10) needs to be added. -6 Subsequently, it is used to regularize the adjacency matrix, resulting in the regularized graph Laplacian matrix: L r =ID -1 / 2AD -1 / 2 In the above formula, I is the identity matrix.

[0036] S3. Constructing and Solving the Spatiotemporal Joint Optimization Function: This step executes the graph regularized slow feature analysis algorithm, constructs a hybrid matrix combining the temporal slow variable (slow feature analysis constraint) and the spatial smoothing term (graph Laplacian regularization), and solves for the slow feature components. In this embodiment, the first 10 slow feature components are solved. The specific steps are as follows: S31. Based on the standardized two-dimensional temperature matrix Constructing a whitening space: Since the number of pixels is 160,000 and the frame rate is 99, the number of pixels is much greater than twice the frame rate. Therefore, a dual-space whitening strategy based on the Gram matrix is ​​adopted: Then, eigenvalue decomposition is performed on C, and the whitening transformation matrix Q is constructed using the eigenvalues ​​Λ and eigenvectors V.

[0037] S32. Map the covariance matrix of the time derivative matrix and the regularized graph Laplacian matrix to the whitening space: First, based on... Construct the time derivative matrix : In the above formula, Δ t The value is 0.1s. Then, the time derivative matrix is ​​mapped to the whitening space using the obtained whitening transformation matrix Q, and its covariance matrix is ​​calculated: The regularized Graph Laplacian matrix L r It also maps to the whitened space: L white =Q T L r Q Spatial regularization coefficient β base The value is 2, and then the matrix trace ratio (in this embodiment, C) is used. diff_white The energy trace is 7.451 × 10⁻⁶. 3 L white The energy trace is 2.718 × 10⁻⁶. 2 Effective balance parameters β eff The value is 5.483. This is then dynamically adjusted. Finally, a hybrid matrix M is formed: M=C diff_white + β eff L white S33. Solve the mixture matrix to obtain the slow feature signal and the corresponding projection matrix: Perform singular value decomposition or eigenvalue decomposition on the matrix, and sort the eigenvalues ​​from smallest to largest. The sorted eigenvalues ​​are { V 1, V 2,…, V 98} Select the eigenvectors corresponding to the first 10 eigenvalues ​​and arrange them in order to form an eigenvector matrix U; perform matrix multiplication between Q and U to obtain the spatial projection matrix Z that maps the original infrared image space to the slow eigenspace, and the standardized two-dimensional temperature matrix. Matrix multiplication with the spatial projection matrix Z yields the slow eigencomponent S, calculated using the following formulas: Z=Q×U Figure 3 The projection matrices (component1, component2, component3) corresponding to the first three slow feature components are shown, where the red areas represent positive weight regions and the blue areas represent negative weight regions. It can be observed that the regions exhibiting positive weights are, in order, the hole region, part of the background, the pit region, and the high-temperature region at the hole edge. The results demonstrate that, under spatiotemporal constraints, decoupling of different types of defects is achieved, proving the effectiveness of the algorithm.

[0038] S4. Image reconstruction is performed using the extracted first 10 slow feature components, which consists of the following two steps: S41, Regarding the first k Each component ( k ∈[0,9]), extract the first digit of the spatial projection matrix Z. k Columns, and calculate their generalized inverse matrix F: F = (Z) T Z -1 Z T S42. Select the slow feature component S k Multiplying by the generalized inverse matrix F yields the reconstructed infrared image sequence, where 0 ≤ k ≤9: X recon =S k ×F k Figure 4 The original thermal image of the specimen and the infrared image reconstructed using the first three slow feature components (component1, component2, component3) are presented. The results show that the edges of various defects are clearer in the reconstructed image than in the original thermal image, and the background heating noise is also significantly reduced.

[0039] The number of devices and processing scale described herein are for the purpose of simplifying the description of the invention. Applications, modifications, and variations of the invention will be readily apparent to those skilled in the art.

[0040] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A method for graph regularization slow feature analysis of infrared nondestructive testing data, characterized in that, include: S1: Acquire the original infrared image sequence X of the object under test using an infrared thermal imager. t×H×W and for X t×H×W Preprocessing is performed, in which t The time dimension of the frame sequence H For height, W Width; S2: Constructing a global pixel-level graph Laplacian matrix L based on a block-parallel strategy. N×N Establish topological relationships between pixels; S3: Combining the temporal slowness constraint of slow feature analysis with the spatial smoothness constraint of graph Laplacian, construct a spatiotemporal joint optimization objective function; and solve the spatiotemporal joint optimization objective function to extract the slow feature components that reflect the thermal response characteristics of defects and their corresponding spatial projection matrices. S4: Reconstruct the image sequence using the slow feature components and spatial projection matrix to extract defect features from the thermal image.

2. The graph regularization slow feature analysis method for infrared nondestructive testing data as described in claim 1, characterized in that, In S1, for X t×H×W Preprocessing specifically includes: Image sequence vectorization, converting single-frame thermal images X H×W The spatial dimension is flattened into a one-dimensional vector, while preserving the temporal dimension of the frame sequence. t Without changing the temperature matrix, we obtain the two-dimensional temperature matrix X. t×N , N = H × W ; In terms of time dimension, the time temperature of each pixel minus its mean. m with standard deviation σ The standardized temperature matrix is ​​obtained. .

3. The graph regularization slow feature analysis method for infrared nondestructive testing data as described in claim 1, characterized in that, In step S2, the specific steps for constructing the global pixel-level graph Laplacian matrix include: Select a single frame of raw infrared image X H×W It is then divided into several local sub-blocks with overlapping regions; The pixel adjacency weights within each sub-block are calculated using a two-sided weighting method based on spatial distance and temperature similarity. w ij The calculation formula is as follows: In the above formula, x i x j A spatial coordinate vector representing a pixel; T i , T j This indicates the temperature value of a pixel in the reference frame; σ S The spatial attenuation coefficient controls the geometric locality of the plot connections; σ T The temperature sensitivity coefficient represents the ability to control heat diffusion across temperature boundaries. Max pooling is used to handle weight conflicts in overlapping regions, merging local adjacency matrices into a global sparse adjacency matrix A. N×N ; Calculate the global sparse adjacency matrix A N×N The row sums are used to construct the angle matrix D. N×N Using the angle matrix D N×N For the global sparse adjacency matrix A N×N Regularization is performed to obtain the regularized graph Laplacian matrix L. r : L r =I-D -1 / 2 AD -1 / 2 In the above formula, I is the identity matrix.

4. The graph regularization slow feature analysis method for infrared nondestructive testing data as described in claim 1, characterized in that, In S3, the spatiotemporal joint optimization objective function J ( ω The expression is represented as a weighted sum of the time slow variable (slow feature analysis constraint) and the spatial smoothing term (graph Laplace regularization); solving the spatiotemporal joint optimization objective function aims to find a projection direction. ω This minimizes the rate of change of the projected signal over time and the difference within its spatial neighborhood, i.e., minimizes... J ( ω ); In the above formula, The time derivative matrix, β L is the space regularization coefficient. r The regularized graph Laplacian matrix is ​​used. In the same whitening space, the optimization constraints of the spatiotemporal joint optimization objective function are transformed into an eigenvalue problem of the mixture matrix. The mixture matrix consists of the covariance matrix of the time derivative matrix and the regularized graph Laplacian matrix. The specific steps for solving the eigenvalues ​​of the mixture matrix are as follows: According to the standardized temperature matrix Frame count t and pixels N The ratio between them is used to adaptively select to perform dual whitening processing in the time sample space or the spatial feature space to obtain the whitening transformation matrix Q. Based on the normalized temperature matrix Construct a time derivative matrix characterizing the temperature change over time. Subsequently, the time derivative matrix is ​​transformed using the whitening transformation matrix Q. Map to the whitening space and calculate the covariance matrix C. diff_white ; The regularized Graph Laplacian matrix L is obtained by applying the whitening transformation matrix Q. r Mapping to whitening space yields L white And introduce a space regularization coefficient. β The target mixing matrix M in the whitening space is obtained as follows: M=C diff_white + β L white Perform singular value decomposition or eigenvalue decomposition on the target mixing matrix M in the whitening space, and sort the eigenvalues ​​from smallest to largest. The sorted eigenvalues ​​are { V 1, V 2,…, V t The corresponding eigenvectors are arranged in order to form an eigenvector matrix U; the whitening transformation matrix Q is multiplied by the eigenvector matrix U to obtain the spatial projection matrix Z that maps the original infrared image space to the slow eigenspace; the normalized temperature matrix is ​​then... Perform matrix multiplication with the spatial projection matrix Z to obtain the slow eigencomponent S.

5. The graph regularization slow feature analysis method for infrared nondestructive testing data as described in claim 4, characterized in that, The spatiotemporal joint optimization objective function J ( ω The regularization parameter used to balance the temporal slowness constraint and the spatial smoothness constraint is adaptively determined in the model. The calculation is based on the ratio of the energy trace of the time derivative matrix to the energy trace of the graph Laplace matrix.

6. The graph regularization slow feature analysis method for infrared nondestructive testing data as described in claim 4, characterized in that, In step S4, the generalized inverse matrix of the spatial projection matrix Z is calculated; the selected slow eigencomponent S is then... i Multiplying by the generalized inverse matrix yields the reconstructed infrared image sequence, where 0 ≤ i ≤ t .

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