Controlled lengyel-epstein brain image classification method
The brain image classification method constructed using the controlled Lengyel-Epstein equation generates a stable nonlinear decision boundary by utilizing the generalized Hurst exponential feature vector and modulation control term. This solves the problems of low accuracy and poor interpretability in brain tumor MRI image classification under small sample conditions, and achieves high accuracy and robust brain tumor identification.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NANJING UNIV OF INFORMATION SCI & TECH
- Filing Date
- 2026-03-09
- Publication Date
- 2026-05-15
AI Technical Summary
Existing brain tumor MRI image classification techniques suffer from large accuracy fluctuations under small sample sizes, deep learning models are prone to overfitting, traditional models have unstable decision boundaries and lack physical interpretability, making it difficult to meet clinical diagnostic needs.
A brain image classification method is constructed using the controlled Lengyel-Epstein equation. By extracting the generalized Hurst exponent feature vector, a bivariate feature evolution field is constructed. A modulation control term is introduced, and iterative processing is performed using a five-point central difference operator to generate a stable nonlinear decision boundary.
High-accuracy brain tumor identification was achieved under small sample conditions, improving robustness and interpretability. The generated decision boundary can accurately capture the essential correlation between pathological features.
Smart Images
Figure CN121811162B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of brain tumor auxiliary diagnosis and medical image processing technology, specifically to a controlled Lengyel-Epstein brain image classification method. Background Technology
[0002] Magnetic resonance imaging (MRI), as a high-precision medical imaging technology without ionizing radiation, plays an irreplaceable role in fields such as brain tumor diagnosis, screening for neurodegenerative diseases, and organ lesion grading due to its multi-sequence imaging capabilities. Currently, mainstream classification techniques mostly rely on models such as Support Vector Machines (SVM) or Backpropagation Neural Networks (BPNN). However, when dealing with highly distorted feature manifolds (such as the Archimedean spiral distribution), the shape of the decision boundary generated by SVM is limited by the preset kernel function, easily leading to fitting failure in high-density data regions. Deep learning models are extremely dependent on large datasets; in medical diagnostic tasks with fewer than 100 samples, deep learning is prone to overfitting. Statistics show that the accuracy of conventional neural networks in texture recognition of small-sample MRI images fluctuates significantly, often between 75% and 85%, and their decision logic exhibits "black box" characteristics, lacking physical interpretability and failing to meet the safety requirements of clinical medicine for diagnostic traceability. Furthermore, while existing reaction-diffusion kinetic equations possess the ability to reveal the intrinsic structure of feature space, traditional models such as the original Lengyel-Epstein equation are essentially designed to simulate continuously evolving patterns and lack an externally enforced convergence mechanism. This results in the classification boundary being in a non-steady-state oscillation, unable to converge to a definite decision surface. Therefore, how to construct a recognition scheme that can accurately decouple complex nonlinear manifolds and possess stable physical convergence performance for multifractal features such as the generalized Hurst exponent in MRI images is a critical technical bottleneck that urgently needs to be overcome in the field of intelligent medical diagnosis. Summary of the Invention
[0003] The purpose of this invention is to address the shortcomings of existing technologies by proposing a controlled Lengyel-Epstein brain image classification method.
[0004] This invention discloses a controlled Lengyel-Epstein brain image classification method, comprising the following steps:
[0005] Step 1: Obtain the brain MRI image to be identified, preprocess the brain MRI image to be identified, and obtain the preprocessed image;
[0006] Step 2: Extract the nonlinear indices of the preprocessed image as feature vectors, and then normalize the feature vectors and map them to a two-dimensional or three-dimensional computational region. ;
[0007] Step 3: In the calculation area A bivariate feature evolution field is constructed internally, with one variable set as a uniformly distributed constant background and the other variable mapped to the initial potential field according to the initial label of the sample.
[0008] Step 4: Based on the initial data of the bivariate feature evolution field, construct an image classification task model for the brain MRI dataset and obtain the nonlinear evolution instruction set for the image classification task of the brain MRI dataset.
[0009] Step 5: Apply the nonlinear evolution instruction set to the computational domain. The potential energy components of the eigenvector are iteratively processed.
[0010] Step 6: Monitor the time evolution residuals of the potential energy components of the feature vector in the bivariate feature evolution field in real time, calculate the sum of the absolute differences of the potential energy components of all grid points in the evolution field in two adjacent iteration time steps, stop the iteration when the sum of the absolute differences of the potential energy components enters the steady state and the rate of change is lower than the preset threshold, extract the final steady-state polarity distribution of the potential energy components of the feature vector as the processing result, and realize the classification of brain MRI images.
[0011] Furthermore, the preprocessing includes grayscale normalization, determination of regions of interest, and image enhancement.
[0012] Furthermore, the preprocessed image nonlinearity index mentioned in step 2 is the generalized Hurst exponent index, which is obtained through... First wave function The derivation yields the following calculation formula:
[0013]
[0014] in, For the analytical scale, For the image feature sequence in the th Detrended variance within each segment The total number of segments after the sequence is divided;
[0015] Through power law relationship Determine different orders The generalized Hurst exponent And select index pairs as feature vectors to characterize the texture properties of brain images.
[0016] Further, step 4 involves constructing an image classification task model for the brain MRI dataset based on the initial data of the bivariate feature evolution field, and obtaining a nonlinear evolution instruction set for the brain MRI image classification task, including the following steps:
[0017] Step 401: Based on the initial data of the bivariate feature evolution field, construct a dynamic model customized for the image classification task of the brain MRI dataset. The dynamic model is a nonlinear evolution system based on the improved Lengyel-Epstein equation, and the calculation formula is as follows:
[0018]
[0019] in, The background field component of the eigenvector. The potential energy components of the eigenvector; For the Laplace operator; This is the global time scaling factor. The ratio of diffusion coefficients, The reaction rate constant is... These are the components of the initial potential energy field. The guiding strength coefficient;
[0020] Step 402: Combine the topological distribution characteristics of the generalized Hurst exponent extracted from the brain MRI dataset to parameterize the dynamic model and obtain a set of nonlinear evolution instructions constrained by prior labels.
[0021] Furthermore, the iterative processing of the potential energy components of the feature vector in step 5 is as follows: the potential energy components of the feature vector are processed by a five-point central difference operator in the computational region. The pathological polarity between adjacent grids is iteratively processed;
[0022] The discrete iterative recursive formula is:
[0023]
[0024] in, and Representing grid points exist and The potential energy component values of the eigenvector at each iteration time; This represents the iteration time step. This is the global time scaling factor; The ratio of diffusion coefficients; The grid space step size; It is the reaction rate constant; For grid points exist Background field components at each iteration time; The guiding strength coefficient; To map to grid points The initial potential energy component values of the initial label mapping.
[0025] Furthermore, the iteration time step satisfies stability constraints: .
[0026] The beneficial effects of the technical solution of this invention are as follows: The controlled Lengyel-Epstein brain image classification method proposed in this application first acquires the brain MRI image to be identified, extracts the generalized Hurst exponent index reflecting the polyfractal texture characteristics of the image, and maps it to a high-dimensional feature manifold space; then, an improved LE dynamics system is constructed by introducing a modulation control term based on the initial label information. This method transforms the classification problem into a steady-state evolution problem of a controlled physical field. It utilizes a five-point finite difference discretization scheme and an explicit Euler iterative algorithm to guide the system's evolution from discrete feature states to continuous and stable nonlinear decision boundaries. When processing brain pathology images with complex tissue textures, even with a limited number of labeled samples, the nonlinear decision boundaries generated by this algorithm can accurately capture the essential correlations between pathological features, significantly improving the accuracy of brain tumor identification and demonstrating high robustness and interpretability. Attached Figure Description
[0027] Figure 1 This is a flowchart of the method disclosed in this invention.
[0028] Figure 2 This is a schematic diagram of brain MRI image classification using the method disclosed in this invention. Detailed Implementation
[0029] To make the objectives and technical solutions 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, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the described embodiments of this application without creative effort are within the scope of protection of this application.
[0030] like Figure 1 As shown, this invention discloses a controlled Lengyel-Epstein brain image classification method, comprising the following steps:
[0031] Step 1: Obtain the brain MRI image to be identified, preprocess the brain MRI image to be identified, and obtain the preprocessed image.
[0032] This embodiment utilizes the Harvard Medical School (AANLIB) brain imaging database. A total of 50 image samples were selected, including 25 images of normal brain tissue from healthy subjects as healthy controls, and 25 contrast-enhanced MRI images from patients with gliomas as pathological samples. All images were uniformly adjusted to a resolution of 256×256 pixels, suitable for automatic brain image classification and segmentation research.
[0033] In the data preprocessing stage, the image screening and processing standards are set as follows: First, the original brain MRI images to be identified are subjected to grayscale standardization to eliminate brightness differences between different scanning batches; second, the region of interest (ROI) is determined using the Otsu method or manual delineation to remove non-brain tissue backgrounds such as the skull; finally, the contrast of tissue texture is improved through image enhancement techniques.
[0034] Step 2: Extract the nonlinear indices of the preprocessed image as feature vectors, and then normalize the feature vectors and map them to a two-dimensional or three-dimensional computational region. .
[0035] Image nonlinearity is used to calculate the generalized Hurst index (GHI), which reflects the polyfractal texture characteristics of brain MRI images, as a vector characterizing the pathological features of the signal.
[0036] The generalized Hurst index is obtained through... First wave function The calculation is obtained using the following formula:
[0037]
[0038] in, For analytical scale For the image feature sequence in the th Detrended variance within each segment The total number of segments after the sequence is divided;
[0039] Through power law relationship Determine different orders The generalized Hurst exponent And select indicators for This serves as a feature vector characterizing the texture properties of brain images. In this embodiment, the index pair with the strongest discriminative ability is selected. As a feature vector, this term eliminates sequence length interference through denominator normalization, and is used to quantify the differences in fractal features between normal brain tissue and tumor tissue in spatial texture description.
[0040] After feature extraction is completed, the obtained feature vectors are linearly mapped to a predefined computational region. This invention provides two spatial mapping schemes: two-dimensional and three-dimensional. Specific embodiments are as follows:
[0041] In one embodiment, the computation region is a two-dimensional space: the index pairs Linear mapping to two-dimensional mesh computational domain The specific mapping rules and parameter settings are based on the following:
[0042] (1) Coordinate matching method: Establish a linear transformation formula between feature values and grid index, i.e., grid horizontal coordinate index y-axis index ,in This represents the grid space step size. In this embodiment, the two-dimensional grid size is set to [value missing]. This scale is based on the compactness setting of small sample feature distribution, aiming to maintain high spatial resolution while ensuring real-time evolutionary iteration.
[0043] (2) Set the grid space step size This value is based on the calculation area. The span and grid size are determined by the formula. The calculation yielded the result.
[0044] In another embodiment, the computation region is three-dimensional space: an index reflecting the global information entropy of the image is introduced as a third feature dimension and mapped to a three-dimensional grid region. This embodiment sets the grid size to [size missing]. The rationale for this scale is that the number of nodes in three-dimensional space increases exponentially with increasing dimension. The node size is optimized to ensure spatial resolution while minimizing the computational cost of explicit finite difference iteration. The three-dimensional spatial step size is uniformly set to... , used to define the physical spacing of feature diffusion in a broader, higher-dimensional space.
[0045] Regardless of the dimensionality scheme used, if multiple feature points are mapped to the same grid point, the mean assignment method is used, that is, the diagnostic labels of all samples at that location are taken. or The average value of the topological distribution is used. The initial topological distribution generated in this step provides the basic feature input for subsequent evolutionary field construction.
[0046] Step 3: In the calculation area A bivariate feature evolution field is constructed internally, with one variable set as a uniformly distributed constant background and the other variable mapped to the initial potential field based on the initial label of the sample.
[0047] Set the grid size to Grid space step size . Variable Set as a constant background image with uniform distribution In the calculation process of this embodiment, the background field component... Its spatiotemporal distribution remains constant and does not participate in the dynamic evolution process that iterates with time steps (i.e., The aim is to provide the system with an isotropic reference physical environment to eliminate non-uniform disturbances in the background space, thereby highlighting the potential energy components. Convergence characteristics guided by modulation control terms.
[0048] For samples containing known diagnostic labels, construct initial potential field components. : Assign grid points to image samples in a brain MRI dataset clinically labeled "tumor / glioma". (Representing the negative polarity diagnostic center), the grid points of the "health control" are assigned values. (Representing the positive polarity diagnostic center), the remaining unmarked areas are set as This step aims to automatically find the optimal locations between different categories of feature points within the feature space by simulating the diffusion process of physicochemical reactions, forming a stable "isolation zone" (i.e., classification boundary). Specifically, this "isolation zone" refers to the interaction between feature points simulated through the coupling diffusion of the u-field and v-field, promoting the aggregation of similar features and the separation of dissimilar features, thereby constructing physical isolation between the feature distribution areas of different pathological states. The initial bivariate field and potential energy component distribution constitute the physical starting state for the subsequent evolution of the controlled dynamic model.
[0049] Step 4: In this step, using the initial data of the bivariate feature evolution field generated in Step 3, an image classification task model for the brain MRI dataset is constructed, and a nonlinear evolution instruction set for the brain MRI image classification task is obtained. The specific operation process is as follows:
[0050] Step 401: Using the initial data of the bivariate feature evolution field generated in Step 3, construct a dynamic model customized for the image classification task of the brain MRI dataset. The dynamic model is a nonlinear evolution system based on the Lengyel-Epstein equation, and the calculation formula is as follows:
[0051]
[0052] in, The background field component of the feature vector represents the background activity of brain image features in the spatial distribution; The potential energy component of the generalized Hurst exponent of the feature vector, i.e. the diagnostic discriminant component, has a steady-state polarity that directly determines the classification result. This is the Laplacian operator, responsible for the physical diffusion of feature information between grids; The reaction rate constant is... The diffusion coefficient ratio is used to coordinate the smoothness of the classification boundary; This is the global time scaling factor; The initial potential field components generated in step 3, which include the brain image feature vectors containing clinical prior labels. This is the guiding strength coefficient.
[0053] In this step, unlike the original Lengyel-Epstein (LE) equations, a modulation control term is embedded through custom logic. The original LE equation calculation formula is as follows:
[0054]
[0055] in, This represents the activator ingress rate.
[0056] The original Leyne-Leyne equation is mainly used in physical chemistry to simulate the continuously oscillating and dynamically evolving "Turing patterns," whose boundaries drift continuously over time, failing to meet the technical requirements of "deterministic and stable classification boundaries" in brain imaging diagnosis. By introducing modulation control terms... A physical traction mechanism was established for each feature point with a known clinical label. The parameters included... To guide the intensity coefficient, the improved technique essentially involves applying a linear restoring force during the evolution process, causing the field variables to... The initial diagnostic facts always influence the spread. The strong constraints force the system to converge from the dynamic pattern oscillation state to the physical steady state, solving the problems of easy divergence and unstable discriminant surface in small sample image recognition models.
[0057] Step 402: Combine the topological distribution characteristics of the generalized Hurst exponent extracted from the brain MRI dataset to parameterize the dynamic model and obtain a set of nonlinear evolution instructions constrained by prior labels.
[0058] The specific operation involves: targeting the Harvard Medical School (AANLIB) brain image dataset... The topological characteristics within the space are precisely configured using engineering experience and stability testing to accurately configure the model's internal parameters: In this embodiment, the guiding strength coefficient is set. Configure the entry rate parameters Reaction rate constant diffusion coefficient ratio and global time scaling factor .
[0059] The specific values of the above parameters are based on the following: First, because the generalized Hurst exponent features of small sample MRI images are more densely distributed in space, the guiding intensity coefficient... Set as The aim is to provide moderate traction to balance the smoothing effect of the diffusion term and prevent overfitting fluctuations at the boundary under constraints of very few samples; secondly, the parameters and The proportional configuration ensures that the nonlinear response term can effectively capture the curvature changes of brain tissue texture; finally, the diffusion coefficient is compared to To ensure that diagnostic information is available Isotropic extension within the manifold space, with a small global time scaling factor. It helps to accurately search for the equilibrium point with the lowest physical energy within a space of subtle features.
[0060] High strength This ensured a high degree of fidelity of the decision boundary to the original pathology label; parameters Nonlinear terms of control This process is responsible for capturing the distorted topology in the high-dimensional feature space. Through this operation, a set of constrained nonlinear evolution instructions is obtained.
[0061] Step 5: Apply the nonlinear evolution instruction set obtained in Step 4 to the computational domain Ω, and apply it to the generalized Hurst exponent index. The potential energy components are iteratively processed so that the normal potential energy representing health and the pathological potential energy representing tumor form an isolation zone in the originally overlapping feature area.
[0062] The specific steps are as follows:
[0063] First, set the iteration time step. Seconds. The iteration time step is based on the von Neumann stability constraint and satisfies... This setting is designed to ensure that the feature vectors of brain images do not diverge numerically during the diffusion and evolution process, thus maintaining the stability of the diagnostic logic.
[0064] Secondly, for each element in the grid that carries The potential energy components of the index pair are subjected to local iterative processing. In this embodiment, a five-point central difference operator is used to process the computational region. The diagnostic polarity between adjacent grids is calculated interactively, and the spatial discretization derivation uses the standard five-point finite difference scheme:
[0065]
[0066] The modulation control term is embedded. The LE equation is transformed into the following discrete iterative recursive formula:
[0067]
[0068] in, and Representing grid points exist and The potential energy component values of the eigenvector at each iteration time; This represents the iteration time step. This is the global time scaling factor; The ratio of diffusion coefficients; The grid space step size; It is the reaction rate constant; For grid points exist Background field activity components at each iteration time; The guiding strength coefficient; To map to grid points The initial potential energy component values of the initial label mapping.
[0069] Nonlinear evolution systems based on the Lengyel-Epstein equations smooth and filter random noise in image data using the Laplacian operator term, while simultaneously utilizing modulation control terms. The generated linear restoring force dynamically searches for the equilibrium point with the lowest physical energy among heterogeneous feature points. As the iterative solution proceeds, the normal potential energy representing health and the pathological potential energy representing tumors spontaneously complete physical isolation in the originally overlapping feature area, ultimately generating a uniformly wide and topologically stable physical "isolation zone" in the feature space. This result effectively corrects the nonlinear manifold distortion caused by differences in tissue texture, and the searched and generated dynamic "isolation zone" and its distribution state provide a physical boundary basis for the final steady-state determination and category identification.
[0070] Step 6: Monitor the time evolution residuals of the potential energy components of the feature vector in the bivariate feature evolution field in real time, calculate the sum of the absolute differences of the potential energy components of all grid points in the evolution field in two adjacent iteration time steps, stop the iteration when the sum of the absolute differences of the potential energy components enters the steady state and the rate of change is lower than the preset threshold, extract the final steady-state polarity distribution of the potential energy components of the feature vector as the processing result, and realize the classification of brain MRI images.
[0071] The specific operational logic is as follows:
[0072] First, monitor the characteristic potential components of the generalized Hurst exponent across the entire field in real time. The time evolution residual is used to calculate the time step of all grid points in the entire field at two adjacent iterations. and The sum of the absolute differences in potential energy In this embodiment, the judgment threshold is set to... Meanwhile, to prevent the system residuals from failing to meet the target for an extended period under extreme data noise interference, leading to infinite iterations, a maximum number of iteration steps is simultaneously set. The upper limit of this iteration is based on the following: multiple tests on the evolution trajectory of image feature vectors for small sample MRI datasets showed that a physical system can overcome the initial unstable period and enter a steady state within 2000 steps. This setting can ensure that the decision boundary is completely solidified and avoid redundant calculations.
[0073] When the sum of the absolute differences in potential energy is satisfied Entering steady state, and below When the iteration stops, the potential energy component is extracted. The final steady-state polarity distribution is taken as the processing result. For example... Figure 2 As shown, the diagnostic logic generated by this result is as follows: In the feature space, Value greater than The grid area (displayed as a positive blue charge distribution) was identified as the healthy control area. Value less than The grid area (displayed as a negative polarity red charge distribution) was identified as a tumor pathological area.
[0074] In this embodiment, the computation and verification experiments of the controlled Lengyel-Epstein brain image classification method were run in a specific hardware and software environment. The hardware platform used a computer equipped with an AMD Ryzen 7 4800H processor and a Radeon Graphics card; the software platform was implemented based on MATLAB R2023a. This environment configuration ensured stable numerical computation accuracy of the improved dynamic equations when performing spatiotemporal dual discretization, supporting the high accuracy performance of this method in clinical medical brain image diagnosis scenarios.
[0075] To further verify the technical advancement of this solution, a comparative experiment was conducted on the test set with traditional mainstream classification methods. The experimental results are shown in Table 1.
[0076] Table 1
[0077] Classification method types Specific classifier algorithm Recognition accuracy Traditional statistical machine learning Support Vector Machine (Linear Kernel SVM) 75.00% Traditional statistical machine learning K-Nearest Neighbors (KNN) 82.50% Deep learning models Backpropagation Neural Network (BPNN) 80.00% Ensemble learning model Random Forest (RF) 82.50% Technical solution of the present invention LE equations embedding modulation control terms μ(v0−v) 95.00%
[0078] As shown in Table 1, the experimental data presented here demonstrate that this method achieves a higher recognition accuracy on the same dataset, significantly outperforming traditional methods. To further eliminate overfitting interference and verify the generalization robustness of this scheme, this embodiment simultaneously performed ten-fold cross-validation. The experiment randomly divided Harvard Medical School brain imaging data into ten equal groups. Through alternating training and validation processes, the average recognition accuracy of this method in ten rounds of rolling experiments reached 95%~100%.
[0079] like Figure 2 As shown, this processing method is in The index pairs construct a smooth and topologically stable nonlinear "isolation zone" on the complex feature plane. Compared with traditional linear decision boundaries or simple Euclidean distance measures, it can more accurately capture the essential manifold relationships between brain image features, demonstrating extremely strong ability to fit complex manifolds and diagnostic robustness.
[0080] As described above, although the invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the invention itself. Various changes in form and detail may be made without departing from the spirit and scope of the invention as defined in the appended claims.
Claims
1. A controlled Lengyel-Epstein brain image classification method, characterized in that, It includes the following steps: Step 1: Obtain the brain MRI image to be identified, preprocess the brain MRI image to be identified, and obtain the preprocessed image; Step 2: Extract the nonlinear indices of the preprocessed image as feature vectors, and then normalize the feature vectors and map them to a two-dimensional or three-dimensional computational region. ; Step 3: In the calculation area A bivariate feature evolution field is constructed internally, with one variable set as a uniformly distributed constant background and the other variable mapped to the initial potential field according to the initial label of the sample. Step 4: Based on the initial data of the bivariate feature evolution field, construct an image classification task model for the brain MRI dataset and obtain a nonlinear evolution instruction set for the brain MRI image classification task. Step 5: Apply the nonlinear evolution instruction set to the computational domain. The potential energy components of the feature vector are iteratively processed. Step 6: Monitor the time evolution residual of the potential energy component of the feature vector in the bivariate feature evolution field in real time, calculate the sum of the absolute difference of the potential energy component of all grid points in the evolution field in two adjacent iteration time steps, and stop the iteration when the sum of the absolute difference of the potential energy component enters the steady state and the rate of change is lower than the preset threshold. Extract the final steady state polarity distribution of the potential energy component of the feature vector as the processing result to achieve brain MRI image classification. Step 4, based on the initial data of the bivariate feature evolution field, constructs an image classification task model for the brain MRI dataset and obtains a nonlinear evolution instruction set for the brain MRI image classification task, including the following steps: Step 401: Based on the initial data of the bivariate feature evolution field, construct a dynamic model customized for the image classification task of the brain MRI dataset. The dynamic model is a nonlinear evolution system based on the improved Lengyel-Epstein equation, and the calculation formula is as follows: ； in, The background field component of the eigenvector. The potential energy components of the eigenvector; For the Laplace operator; This is the global time scaling factor. The ratio of diffusion coefficients, It is the reaction rate constant; These are the components of the initial potential energy field. The guiding strength coefficient; Step 402: Combine the topological distribution characteristics of the generalized Hurst exponent extracted from the brain MRI dataset to parameterize the dynamic model and obtain a set of nonlinear evolution instructions constrained by prior labels; Step 5 involves iteratively processing the potential energy components of the feature vector by applying a five-point central difference operator to the computational region. The pathological polarity between adjacent grids is iteratively processed; The discrete iterative recursive formula is: ； in, and Representing grid points exist and The potential energy component values of the eigenvector at each iteration time; This represents the iteration time step. This is the global time scaling factor; The ratio of diffusion coefficients; The grid space step size; It is the reaction rate constant; For grid points exist Background field components at each iteration time; The guiding strength coefficient; To map to grid points The initial potential energy component values of the initial label mapping.
2. The controlled Lengyel-Epstein brain image classification method according to claim 1, characterized in that, The preprocessing includes grayscale normalization, region of interest determination, and image enhancement.
3. The controlled Lengyel-Epstein brain image classification method according to claim 1, characterized in that, The nonlinear index of the preprocessed image mentioned in step 2 is the generalized Hurst exponent index, which is obtained by... First wave function The derivation yields the following calculation formula: ； in, For the analytical scale, For the image feature sequence in the th Detrended variance within each segment The total number of segments after the sequence is divided; Through power law relationship Determine different orders The generalized Hurst exponent And select index pairs as feature vectors to characterize the texture properties of brain images.
4. The controlled Lengyel-Epstein brain image classification method according to claim 1, characterized in that, The iteration time step satisfies the stability constraint: .