A method for image segmentation and parameter automatic measurement of corneal endothelial cells

Abstract

The application introduces a kind of image segmentation and parameter automatic measurement method for corneal endothelial cells. The application relates to the fields of medical image analysis, artificial intelligence, machine vision, etc., and can be used for diagnosis and monitoring of ophthalmic diseases. Through data preprocessing, data enhancement, image segmentation, region of interest extraction, frequency domain analysis, binarization, cell region extraction, reverse positioning and parameter calculation, etc., the automatic segmentation and parameter measurement of corneal endothelial cell images are realized. The method uses advanced deep learning technology, improves the segmentation accuracy and processing speed, and provides strong technical support for the diagnosis, monitoring and treatment effect evaluation of corneal diseases. The application can significantly reduce the work burden of medical personnel, improve the efficiency and quality of overall medical service, and has broad application prospect and social value.

Description

Technical Field

[0001] This invention relates to the fields of medical image analysis, artificial intelligence, and machine vision, and is a method for image segmentation and automatic parameter measurement of corneal endothelial cells. Background Technology

[0002] In ophthalmological research, the structure and function of corneal endothelial cells have always been a focus of attention. These cells, with their unique hexagonal arrangement, are crucial for maintaining corneal transparency and overall physiological function. They are responsible for keeping the corneal surface smooth, ensuring that light transmission is not interfered with by scattering or absorption, thereby preventing blurred vision or blindness. Furthermore, they regulate the ion and water balance of the cornea through pumping, maintaining an appropriate hydration state, and synthesize important biomolecules such as antimicrobial peptides and adhesion proteins, providing immune protection for the cornea. Therefore, the integrity and functional state of corneal endothelial cells are key factors in maintaining corneal transparency and physiological health.

[0003] As we age, the density of corneal endothelial cells naturally decreases and they cease to proliferate. Once lost, they cannot regenerate, and their decreased density and morphological changes are directly related to the decline in corneal function. Against this backdrop, the density and morphological parameters of corneal endothelial cells have become important indicators for assessing corneal health, and are of significant clinical importance for the early diagnosis, disease monitoring, and evaluation of treatment outcomes in corneal diseases. Therefore, accurate segmentation of corneal endothelial cell images forms the technological foundation for achieving this goal.

[0004] However, corneal endothelial cell image segmentation in ophthalmology has traditionally relied on manual or semi-automated techniques, which are inefficient and require a high level of expertise from the operators, limiting their widespread clinical application. Given the prevalence of corneal endothelial lesions in ophthalmology and their potential threat to public health, the search for a rapid and accurate method for corneal endothelial cell image segmentation has become particularly urgent.

[0005] Given the importance of corneal endothelial cells in ophthalmology, and the current technical challenges and clinical needs in corneal endothelial cell image segmentation, this invention aims to provide an innovative and efficient solution. Utilizing advanced deep learning technology, this invention can automatically and accurately perform corneal endothelial cell image segmentation tasks, providing strong technical support for the early diagnosis, progression monitoring, and treatment efficacy evaluation of corneal diseases. This method not only significantly reduces the workload of professionals but also improves segmentation accuracy and processing speed, thereby enhancing the efficiency and quality of overall medical services. Summary of the Invention

[0006] To address the aforementioned issues, this invention proposes a complete architecture comprising a corneal endothelial cell segmentation model and a parameter calculation model. This architecture can be used for clinical analysis of corneal endothelial cells, solving the mathematical modeling problem of acquiring clinical data on corneal endothelial cells. Building upon traditional image segmentation, modules such as ROI extraction and frequency domain analysis are introduced, achieving more accurate cell segmentation and mitigating the problem of unclear cell boundaries in blurred images. By employing a classification algorithm that combines back-localization and support vector machine (SVM) fusion, back-localization acquires data from the original image for more accurate calculation of parameters such as hexagonal cell counts and coefficient of variation. Furthermore, the introduction of SVM into the classifier significantly improves the robustness of the classification results, addressing the low recall rate in corneal endothelial cell shape classification to some extent. This complete development and algorithm implementation process automates the technology, thereby resolving the current imbalance between supply and demand in clinical practice, where doctors have limited diagnostic efficiency while patients have high needs.

[0007] To achieve the above objectives, the present invention employs the following technical means:

[0008] A method for image segmentation and automatic parameter measurement of corneal endothelial cells includes the following steps:

[0009] Step 1: Data preprocessing: The original image is cropped from the existing medical images and contains several standard hexagonal corneal endothelial cells and abnormal corneal endothelial cells. The original image is then subjected to homomorphic filtering and normalized.

[0010] Step 2, Data Augmentation: Perform affine transformation on the image obtained after Step 1 to augment the dataset. The data augmentation methods include random horizontal / vertical flipping, random rotation, and edge sharpening.

[0011] Step 3, Image Segmentation: The preprocessed image obtained in Step 2 is fed into the Attention U-Net neural network model based on U-Net and attention mechanism to obtain the probability map of cell segmentation;

[0012] Step 4, ROI Extraction: The probability map obtained from image segmentation in Step 3 is fed into the Dense U-Net neural network model based on U-Net and Dense Net structures to extract the region of interest;

[0013] Step 5, Frequency Domain Analysis: Perform frequency domain analysis on the output probability map obtained in Step 3 to estimate the variance of the Gaussian filter and obtain the Gaussian filter.

[0014] Step 6, Binarization: Filter the image using the Gaussian filter calculated in Step 5, and combine it with the watershed algorithm to binarize the image to obtain a binary image of cell edges;

[0015] Step 7, Cell Region Extraction: Perform connected component analysis on the binary graph of cell edges obtained in Step 6, and combine it with the ROI graph obtained in Step 4 to obtain the cell segmentation map of the ROI region;

[0016] Step 8, Reverse Localization and Hexagonal Cell Classification: Using the cell segmentation map obtained in Step 7, extract the complete cell structure and reverse localize it, cropping the position of the corresponding cell in the original image for that region. For the cells contained in this small region, feed them into a lightweight neural network classifier, ResNet18-SVM, to complete feature extraction and classification. This neural network classifier consists of a ResNet18 model and a Support Vector Machine (SVM) feature classifier. The former extracts features from the cell image, while the latter classifies the extracted features to determine the category of each corneal endothelial cell, obtaining the classification result.

[0017] Step 9, Parameter Calculation: Using the classification results of each corneal endothelial cell in Step 8, statistically analyze the cell characteristics and calculate the hexagonal proportion coefficient, endothelial cell density, and coefficient of variation of the clinical data.

[0018] In the above technical solution, the specific algorithm for performing homomorphic filtering on the original image is as follows:

[0019] Step a1. Take the logarithm of the original image to obtain the logarithmic result;

[0020] Step a2. Perform a Fourier transform on the result of step a1 to obtain the frequency domain image result;

[0021] Step a3. Filter the result from step a2 using filter H(u,v):

[0022]

[0023] In the formula, D 2 (u,v) represents the distance function of the result in step a2, γ H =1.5, γ L =0.6, c=5, D0=10;

[0024] Step a4. Perform an inverse Fourier transform on the result from step a3 to obtain the time-domain result;

[0025] Step a5. Perform an exponential transformation on the result from step a4 to obtain the filtered image.

[0026] In the above technical solution, the normalization process for the filtered image is specifically calculated using the following formula:

[0027]

[0028] In the formula, I(i,j) and N(i,j) represent the gray values ​​of the original image and the transformed image, respectively, and min and max represent the minimum and maximum gray values ​​of the original image, respectively.

[0029] In the above technical solution, in step 3,

[0030] The Attention U-Net model is used for cell segmentation, ultimately resulting in a cell probability map.

[0031] The Attention U-Net network is used to segment the input corneal endothelial image. The U-Net model consists of an encoder and a decoder.

[0032] The core algorithm of the encoder is convolution operation, which can generate high-level features of the image step by step;

[0033] The core algorithm of the decoder is an interpolation algorithm, which gradually fuses the generated high-level features with the features of the previous layer to reconstruct the segmentation result;

[0034] The encoder and decoder use an identity mapping to connect features of the same dimension. Attention U-Net builds upon this by introducing an attention gate module. The attention gate module calculates the importance of each pixel between the encoder and decoder, retaining more features from pixels with higher importance, thus allowing the network to focus more on regions of interest. The calculation formula is as follows:

[0035]

[0036] In the formula To obtain image features after the attention gate, For image features in the decoder, g i For the image features in the corresponding encoder; The corresponding weights, σ(·) activation function, Sigmoid, ψ T For convolution calculation, b g b ψ This refers to the relevant biases during matrix computation.

[0037] In the above technical solution, the Dense U-Net model is used to extract the region of interest (ROI).

[0038] The Dense U-Net network is used to extract the Region of Interest (ROI) from the input corneal endothelial image segmentation map. Dense U-Net introduces a dense connection mechanism on the basis of U-Net, which connects the output of all previous convolutional layers to the input of the current layer in each convolutional block, so that subsequent layers can make fuller use of the previous feature information, thereby improving the performance of the network.

[0039] In the above technical solution, step 5 uses frequency domain analysis to estimate the variance of the Gaussian filter. The specific implementation algorithm is as follows:

[0040] Step b1. Perform a two-dimensional discrete Fourier transform on the probability graph to obtain the image F(f,θ);

[0041] Step b2. Perform peak enhancement and dilation reconstruction on the image F from step b1: First, define the image H0(f,θ) based on the input image F(f,θ), as follows:

[0042]

[0043] Then for H t The expansion process is performed iteratively for (t = 0, 1, 2, ...) until a steady state is reached, as shown in the following formula:

[0044]

[0045] In the formula, ⊕ represents the expansion operation, and B is the expansion structuring element;

[0046] Step b3. Calculate the one-dimensional radial value of the result in step b2, that is, calculate the angular average of the two-dimensional Fourier transform value of the image in polar coordinates, as shown in the following formula:

[0047]

[0048] In the formula, F(f,θ) is the Fourier transform of the image in polar coordinates;

[0049] Step b4. Fit the peak value using a Gaussian function; the mean value is the estimated characteristic frequency f. * The Gaussian function formula is as follows:

[0050]

[0051] In the formula, g is the fitting function, f is the spatial frequency, a and b are constants, μ and σ are the mean and standard deviation of the Gaussian distribution, respectively, and c is the offset.

[0052] Step a5. Utilize the characteristic frequency f from step a4 * To estimate the filter variance σ1, this method takes k... σ =0.20:

[0053]

[0054] In the above technical solution, step 7, the extraction of the cell region, is specifically implemented using the following algorithm:

[0055] Step c1. Invert the binary image of the cell edge to obtain an inverted image in which the cell body is white and the cell edge is black;

[0056] Step c2. Perform an opening operation to denoise the reversed graph from step c1;

[0057] Step c3. Perform connected component labeling on the result graph from step c2, and mark each cell in the image;

[0058] Step c4. Combine the results from step c3 with the ROI image obtained in step 4 to obtain a cell segmentation image.

[0059] In the above technical solution, step 8, the reverse localization and hexagonal cell classification, is specifically implemented using the following algorithm:

[0060] Step d1. For the cell segmentation map in step 7, perform connected component labeling and mark each cell in the image;

[0061] Step d2. Using the position of the single cell in step d1, extract the cell at the corresponding position in the original image;

[0062] Step d3. The cell images extracted in step d2 are fed into the ResNet18 neural network for feature extraction;

[0063] Step d4. The features extracted in step d3 are fed into a support vector machine (SVM) for feature classification to determine whether they are hexagonal cells.

[0064] In the above technical solution, the ResNet18-SVM neural network classifier is used to classify corneal endothelial cells with high accuracy. The support vector machine (SVM) is introduced into the model for feature classification, which greatly improves the classification accuracy and robustness of image data.

[0065] Because the present invention employs the above-mentioned technical means, it has the following beneficial effects:

[0066] 1. Regarding the preprocessing of membrane endothelial cell images, this invention employs homomorphic filtering and normalization to preprocess the images, effectively alleviating the image illumination imbalance, enhancing image contrast, and making the images easier to segment.

[0067] 2. In terms of model design, while ensuring appropriate model complexity, this invention uses the AttentionUnet network for cell segmentation. This network introduces an attention mechanism to focus more on the regions of interest, improving segmentation performance and robustness. The Dense U-Net network is used for ROI extraction. Concatenating the outputs of previous layers with the outputs of the current layer can reduce gradient vanishing and improve feature utilization.

[0068] 3. Regarding image binarization, this invention employs a frequency domain analysis-watershed algorithm binarization method, which greatly compensates for the defects of weak edges and yields a more refined binarization method.

[0069] 4. Regarding hexagonal discrimination, this invention employs a reverse localization-network classification method. Based on the cell segmentation results, the position of the cell in the original image is reversed and classified, reducing the loss of cell information caused by post-processing. By combining ResNet50 and SVM to perform hexagonal discrimination of cells, and combining the powerful feature extraction capability of neural networks and the excellent classification capability of SVM, efficient and high-precision cell classification is achieved.

[0070] 5. Regarding parameter calculation, this invention only calculates the parameters for cells within the ROI image area, reducing the impact of blurred or incomplete cells on the parameter calculation results.

[0071] 6. A fully automated method for image segmentation and parameter measurement of corneal endothelial cells is proposed. In clinical use, only a screenshot of the acquired corneal endothelial cell image is needed. After being fed into a neural network, end-to-end segmentation results can be achieved, and the hexagonality (HEX), endothelial cell density (ECD), and coefficient of variation (CV) of the cells can be displayed simultaneously. The entire process only requires the doctor to send the screenshot from the upper computer of the scanning device into the model inference interface, which has the advantages of convenient testing, fast operation, and accurate results. Attached Figure Description

[0072] Figure 1 This is a flowchart illustrating the corneal endothelial cell images, image segmentation, and automatic parameter measurement involved in this invention.

[0073] Figure 2 This is a structural diagram of the network model (Attention U-Net) used for image segmentation in this invention;

[0074] Figure 3 This is a diagram of the Attention Gate structure of the network model (Attention U-Net) used for image segmentation in this invention;

[0075] Figure 4 This is a diagram of the Dense Block structure of the network model (Dense U-Net) used for ROI extraction in this invention;

[0076] Figure 5This is a schematic diagram showing the results of the binarization method based on frequency domain analysis and watershed algorithm used in this invention;

[0077] Figure 6 This is the cell region labeling process in the present invention;

[0078] Figure 7 This is a structural diagram of the network model (ResNet18-SVM) used for hexagonal cell classification in this invention. Detailed Implementation

[0079] The embodiments of the present invention will be described in detail below. Although the present invention will be described and illustrated in conjunction with some specific embodiments, it should be noted that the present invention is not limited to these embodiments. On the contrary, any modifications or equivalent substitutions made to the present invention should be covered within the scope of the claims of the present invention.

[0080] Furthermore, to better illustrate the present invention, numerous specific details are set forth in the following detailed embodiments. Those skilled in the art will understand that the present invention can be practiced without these specific details.

[0081] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0082] The hardware environment used for algorithm testing is: Intel(R) Xeon(R) CPU E5-1650 v4 @ 3.60GHz GPU NVIDIA TITAN XP, and the runtime environment is Python 3.6 and related extension packages PyTorch.

[0083] The core algorithms of the model are deep convolutional neural networks, homomorphic filtering, frequency domain analysis-watershed, and support vector machines.

[0084] like Figure 1 As shown, a method for image segmentation and automatic parameter measurement of corneal endothelial cells includes the following steps:

[0085] Preprocessing the original image: Homomorphic filtering and normalization are performed on the original image.

[0086] The specific implementation steps of homomorphic filtering are as follows:

[0087] Step a1. Take the logarithm of the original image to obtain the logarithmic result;

[0088] Step a2. Perform a Fourier transform on the result of step a1 to obtain the frequency domain image result;

[0089] Step a3. Design a filter H(u, v) to filter the result in step a2:

[0090]

[0091] In the formula, D(u, v) represents the distance function of the result in step a2, and γ H =1.5, γ L =0.6, c=5, D0=10;

[0092] Step a 4. Perform an inverse Fourier transform on the result of step a 3 to obtain the time-domain result;

[0093] Step a 5. Perform an exponential transformation on the result of step a 4 to obtain the final result.

[0094] The Attention U-Net segmentation network is trained using the preprocessed image, and then the preprocessed image is fed into the Attention U-Net segmentation network for segmentation to obtain the segmentation result image:

[0095] This method expands the dataset by performing operations such as random horizontal / vertical flipping, random rotation, and edge sharpening, thereby improving the model's performance and generalization ability.

[0096] For cell image segmentation, this method uses the Attention U-Net neural network model based on U-Net and an attention mechanism to segment the original corneal endothelial cell image. For example... Figure 2 As shown, the Attention U-Net architecture consists of an encoder and a decoder. The encoder generates high-level features of the image, while the decoder reconstructs the segmentation result based on these representations. Between the encoder and decoder, Attention U-Net introduces an attention gate module. Figure 3 As shown, this module can be viewed as a bottleneck structure. Its function is to calculate the importance of each pixel between the encoder and decoder, and to retain more features from pixels with high importance, thus allowing the network to focus more on the region of interest. The specific calculation formula is shown below:

[0097]

[0098] In the formula To obtain image features after the attention gate, For image features in the decoder, g i For the image features in the corresponding encoder; The corresponding weights, σ(·) activation function, Sigmoid, ψ TFor convolution calculation, b g b ψ This refers to the relevant biases during matrix computation.

[0099] The Dense U-Net network for ROI extraction is trained using the segmented images, and then the segmented images are fed into the Dense U-Net network to extract the ROI regions.

[0100] For the extraction of ROI region images, this method uses the Dense U-Net neural network model based on U-Net and Dense Net structures.

[0101] It introduces a dense connection mechanism on top of U-Net to improve the efficiency of feature extraction and information transfer. For example... Figure 4 As shown, Dense Connection refers to connecting the outputs of all preceding convolutional layers to the input of the current layer in each convolutional block, so that subsequent layers can make fuller use of previous feature information, thereby improving the network performance.

[0102] Binarize the segmentation result image to obtain the edge binary image:

[0103] For image binarization, this method uses a frequency domain analysis-watershed algorithm. Because corneal endothelial cells exhibit certain regularity, the Fourier frequency domain image obtained after performing a two-dimensional Fourier transform on the network output probability map will display distinctive concentric rings, such as... Figure 5 As shown on the left. The frequency represented by the radius of this concentric ring is called the characteristic frequency f. * Its relationship with the average cell size is shown in the formula:

[0104]

[0105] We can calculate Figure 5 (Left) The one-dimensional radial values ​​of the image determine the frequency value corresponding to the highest amplitude. The one-dimensional radial values ​​are the angular average F of the two-dimensional Fourier transform values ​​of the image. RM (f), the calculation formula is as follows:

[0106]

[0107] In the formula, F(f,θ) is the Fourier transform of the image in polar coordinates.

[0108] Because corneal endothelial cell images are characterized by low signal-to-noise ratio, low contrast, and low resolution, the peak intensity corresponding to their characteristic frequencies may not be obvious in a one-dimensional radial numerical function image. Therefore, it is possible to first... Figure 5(Left) Dilation reconstruction is performed to enhance the peak value. The enhanced peak value can be fitted to the following Gaussian function using the nonlinear least squares method, and the mean u obtained from the solution is used as the characteristic frequency f. * The estimated value.

[0109]

[0110] In the formula, g is the fitting function, f is the spatial frequency, a and b are constants, μ and σ are the mean and standard deviation of the Gaussian distribution, respectively, and c is the offset.

[0111] After obtaining the characteristic frequencies, the variance σ1 of the Gaussian filter can be estimated using the following formula:

[0112]

[0113] This method takes k. σ =0.20. After filtering the image, the classic watershed algorithm is used to binarize the image, resulting in a binary edge image.

[0114] Cell region labeling is performed by combining edge binary images and ROI region images:

[0115] like Figure 6 As shown, this step includes:

[0116] c1. Invert the obtained binary edge image to obtain image I1;

[0117] c2. Perform an opening operation on the I1 image to remove noise and obtain the I2 image;

[0118] c3. By performing connected component analysis on image I2, we can obtain information about each connected component in the image, that is, information about individual cells (including cell location, size information and area);

[0119] c4. Traverse all connected components and save only cells whose more than 2 / 3 of the pixels are in the ROI image IR to obtain the cell segmentation image;

[0120] By following the steps above, this method can obtain a cell region label map.

[0121] Single cells were extracted by reverse localization using cell region-labeled images and the original image. The ResNe18-SVM classification network was then trained to obtain the single-cell classification results.

[0122] From the cell region labeling map, we can obtain the location of a single cell, reverse locate the cell's position in the original image, and feed it into the classification model for hexagonal discrimination.

[0123] For hexagonal discrimination, we use the ResNet18-SVM network, such as... Figure 7 As shown. Considering the characteristics of hexagonal classification tasks—a large number of images to be processed and a low data dimensionality—this paper uses the lightweight classification model ResNet18 as the basic classifier. The core of the ResNet network structure is the residual module, which superimposes the input onto the output, enabling the neural network to avoid gradient explosion during the learning of differences and to better deepen the network layers.

[0124] The core idea of ​​the SVM algorithm is to achieve maximum margin classification by finding an optimal hyperplane in the feature space. It also utilizes kernel tricks to map nonlinear problems to a high-dimensional space for processing, thereby improving the model's generalization ability and classification performance. In this method, using SVM as the classifier outperforms using a neural network with a Softmax layer as the final classifier. Combined with the powerful feature extraction capabilities of the convolutional layers in ResNet18, it achieves efficient and high-precision cell classification.

[0125] Parameters were calculated using individual cell classification results and cell region labeling maps.

[0126] In this method, clinical parameters of corneal endothelial cell images were calculated to obtain segmented images, including endothelial cell density (ECD), coefficient of variation (CV), and hexagonality (HEX). The calculation formulas are as follows:

[0127]

[0128] Where n represents the total number of cells, S i This represents the area of ​​the i-th cell.

[0129]

[0130] in, S represents the average area of ​​the cells, n represents the total number of cells, and S represents the average area of ​​the cells. i This represents the area of ​​the i-th cell.

[0131]

[0132] Where n hex This represents the number of hexagonal cells, and n represents the total number of cells.

[0133] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements and modifications without departing from the concept of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for image segmentation and automatic parameter measurement of corneal endothelial cells, characterized in that, Includes the following steps: Step 1: Data preprocessing: The original image is cropped from the existing medical images and contains several standard hexagonal corneal endothelial cells and abnormal corneal endothelial cells. The original image is then subjected to homomorphic filtering and normalized. Step 2, Data Augmentation: Perform affine transformation on the image obtained after Step 1 to augment the dataset. The data augmentation methods include random horizontal / vertical flipping, random rotation, and edge sharpening. Step 3, Image Segmentation: The preprocessed image obtained in Step 2 is fed into the Attention U-Net neural network model based on U-Net and attention mechanism to obtain the probability map of cell segmentation; Step 4, ROI Extraction: The probability map obtained from image segmentation in Step 3 is fed into the Dense U-Net neural network model based on U-Net and Dense Net structures to extract the region of interest; Step 5, Frequency Domain Analysis: Perform frequency domain analysis on the output probability map obtained in Step 3 to estimate the variance of the Gaussian filter and obtain the Gaussian filter. Step 6, Binarization: Filter the image using the Gaussian filter calculated in Step 5, and combine it with the watershed algorithm to binarize the image to obtain a binary image of cell edges; Step 7, Cell Region Extraction: Perform connected component analysis on the binary graph of cell edges obtained in Step 6, and combine it with the ROI graph obtained in Step 4 to obtain the cell segmentation map of the ROI region; Step 8, Reverse Localization and Hexagonal Cell Classification: Using the cell segmentation map obtained in Step 7, extract the complete cell structure and reverse localize it, cropping the position of the corresponding cell in the original image. For the cells contained in the region, feed them into the lightweight neural network classifier ResNet18-SVM to complete feature extraction and feature classification. This neural network classifier consists of a ResNet18 model and a feature classifier support vector machine (SVM). The former extracts the features of the cell image, and the latter classifies the extracted features to determine the category of each corneal endothelial cell, thus obtaining the classification result. Step 9, Parameter Calculation: Using the classification results of each corneal endothelial cell in Step 8, statistically analyze the cell characteristics and calculate the hexagonal proportion coefficient, endothelial cell density, and coefficient of variation of clinical data; Step 5 uses frequency domain analysis to estimate the variance of the Gaussian filter. The specific algorithm is as follows: Step b1. Perform a two-dimensional discrete Fourier transform on the probability graph to obtain the image F(f,θ); Step b2. Perform peak enhancement and dilation reconstruction on the image F from step b1: First, define the image H0(f,θ) based on the input image F(f,θ), as follows: Then for H t (t=0,1,2……) Iterative expansion is performed until a steady state is reached, as shown in the following formula: In the formula, ⊕ represents the expansion operation, and B is the expansion structuring element; Step b3. Calculate the one-dimensional radial value of the result in step b2, that is, calculate the angular average of the two-dimensional Fourier transform value of the image in polar coordinates, as shown in the following formula: In the formula, F(f,θ) is the Fourier transform of the image in polar coordinates; Step b4. Fit the peak value using a Gaussian function; the mean value is the estimated characteristic frequency f. * The Gaussian function formula is as follows: In the formula, g is the fitting function, f is the spatial frequency, a and b are constants, μ and σ are the mean and standard deviation of the Gaussian distribution, respectively, and c is the offset; Step a5. Utilize the characteristic frequency f from step a4 * Estimating filter variance This method takes k σ =0.20: 。 2. The method for image segmentation and automatic parameter measurement of corneal endothelial cells according to claim 1, characterized in that, The specific algorithm for performing homomorphic filtering on the original image is as follows: Step a1. Take the logarithm of the original image to obtain the logarithmic result; Step a2. Perform a Fourier transform on the result of step a1 to obtain the frequency domain image result; Step a3. Through the filter The results from step a2 are then filtered: In the formula, The distance function representing the result of step a2. , , , ; Step a4. Perform an inverse Fourier transform on the result from step a3 to obtain the time-domain result; Step a5. Perform an exponential transformation on the result from step a4 to obtain the filtered image.

3. The method for image segmentation and automatic parameter measurement of corneal endothelial cells according to claim 2, characterized in that, The filtered image is then normalized using the following formula: In the formula, and represents the grayscale value of the original image and the grayscale value of the transformed image, respectively. min and max represent the minimum and maximum grayscale values ​​of the original image, respectively.

4. The method for image segmentation and automatic parameter measurement of corneal endothelial cells according to claim 1, characterized in that, In step 3, Cell segmentation is performed using the Attention U-Net model, resulting in a cell probability map: The Attention U-Net network is used to segment the input corneal endothelial image. The U-Net model consists of an encoder and a decoder. The core algorithm of the encoder is convolution operation, which can generate high-level features of the image step by step; The core algorithm of the decoder is an interpolation algorithm, which gradually fuses the generated high-level features with the features of the previous layer to reconstruct the segmentation result; The encoder and decoder use an identity mapping to connect features of the same dimension. Attention U-Net builds upon this by introducing an attention gate module. The attention gate module calculates the importance of each pixel between the encoder and decoder, retaining more features from pixels with higher importance, thus allowing the network to focus more on regions of interest. The calculation formula is as follows: In the formula To obtain image features after the attention gate, For image features in the decoder, For the image features in the corresponding encoder; , The corresponding weights Activation function Sigmoid For convolution calculation, , This refers to the relevant biases during matrix computation.

5. The method for image segmentation and automatic parameter measurement of corneal endothelial cells according to claim 1, characterized in that, The Dense U-Net model is used to extract the region of interest (ROI). The Dense U-Net network is used to extract the Region of Interest (ROI) from the input corneal endothelial image segmentation map. Dense U-Net introduces a dense connection mechanism on the basis of U-Net, which connects the output of all previous convolutional layers to the input of the current layer in each convolutional block, so that subsequent layers can make fuller use of the previous feature information, thereby improving the performance of the network.

6. The method for image segmentation and automatic parameter measurement of corneal endothelial cells according to claim 1, characterized in that, In step 7, the cell region extraction is specifically implemented using the following algorithm: Step c1. Invert the binary image of the cell edge to obtain an inverted image in which the cell body is white and the cell edge is black; Step c2. Perform an opening operation to denoise the reversed graph from step c1; Step c3. Perform connected component labeling on the result graph from step c2, and mark each cell in the image; Step c4. Combine the results from step c3 with the ROI image obtained in step 4 to obtain a cell segmentation image.

7. The method for image segmentation and automatic parameter measurement of corneal endothelial cells according to claim 1, characterized in that, In step 8, the reverse localization and hexagonal cell classification are specifically implemented using the following algorithm: Step d1. For the cell segmentation map in step 7, perform connected component labeling and mark each cell in the image; Step d2. Using the position of the single cell in step d1, extract the cell at the corresponding position in the original image; Step d3. The cell images extracted in step d2 are fed into the ResNet18 neural network for feature extraction; Step d4. The features extracted in step d3 are fed into a support vector machine (SVM) for feature classification to determine whether they are hexagonal cells.

8. The method for image segmentation and automatic parameter measurement of corneal endothelial cells according to claim 1, characterized in that, The model utilizes the ResNet18-SVM neural network classifier to classify corneal endothelial cells with high accuracy, and incorporates a support vector machine (SVM) for feature classification.

Images