Cell location and counting method based on manifold regression network and its application
By introducing a regression network model of manifold regularization in cell counting and localization algorithms, the density map is calculated using the cell nuclear point label, and the nonlinear structure of cells is described through the Graplace matrix, the existing algorithm is solved in processing complex cells. The problem of morphology and relying on manual annotation achieves high-precision cell localization and counting and model generalization.
Patent Information
- Application Number
- CN202111059720.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-09-10
- Publication Date
- 2025-02-14
- Estimated Expiration
- 2041-09-10
AI Technical Summary
Existing cell counting and localization algorithms are not effective in dealing with crowded and diverse cell morphology, and rely on precise manual annotation and large-scale networks, which are prone to overfitting.
Using a regression network model based on manifold regularization, the density map is calculated through cell nuclear point labels, the U-Net regression network is constructed, and the manifold regular term is introduced, and the local nonlinear structure of cells is described using the map Laplace matrix to improve the model generalization ability.
It realizes accurate positioning and counting of morphological complex cells without relying on precise manual annotation, which reduces the labeling cost, improves the generalization and positioning accuracy of the model, and avoids overfitting.
Smart Images
Figure CN113889233B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a cell positioning and counting method based on a manifold regression network, and belongs to the technical field of medical image processing. Background Art
[0002] Cell counting plays an important role in disease diagnosis and biomedical research. For the diagnosis and treatment of cancer, the Tumor Proportion Score (TPS) is an important indicator. In order to estimate the TPS, pathologists need to approximately count the positive and negative cancer cells in the histopathological sections. In addition, pathologists may also need to mark some typical cancer cells to increase the reliability of diagnosis, and these tasks are usually time-consuming and tedious. With the emergence of digital biomedical image processing and powerful machine learning tools represented by deep learning, counting and positioning have gradually become computer-implemented and have achieved high accuracy.
[0003] There are two main problems in cell counting and localization in biomedical image analysis. First, the distribution of cells may be too crowded, making it difficult to identify and count cells. Second, cells from different tissues, especially tumor cells, show a variety of colors and morphological structures. In stained tumor sections, some cancer cells are round or oval, while others are elongated. Tumor cells also show different staining levels due to negative or positive staining.
[0004] To solve these problems, traditional cell counting and localization are mostly based on more mature numerical regression and target detection methods, and the models are improved according to specific tasks and different types of biomedical datasets. These cell localization and counting algorithms can be divided into two categories: detection-based methods and regression-based methods. Although these algorithms can achieve good results, they have the following limitations: (1) For crowded and irregular cell counting, unsupervised methods without any human expert guidance perform poorly; (2) The performance of supervised detection methods depends on the number and accuracy of labels, which requires certain pathological knowledge and clinical experience of the annotator, increasing the manpower and time cost of the labeling work; (3) Methods based on cell number regression cannot locate cells and require additional localization models, which are costly in model design and calculation; (4) Supervised detection and regression methods usually rely on large-scale networks and are prone to overfitting. Summary of the invention
[0005] The purpose of the present invention is to provide a regression network model based on manifold regularization, which can effectively locate and count cells with complex morphology by only using cell nucleus point labels, saving the manpower and time cost of labeling work, while ensuring the accuracy of positioning and counting, improving the generalization of the model and avoiding overfitting.
[0006] In order to achieve the above object, a technical solution of the present invention is to provide a cell positioning and counting method based on a manifold regression network, characterized in that it includes the following steps:
[0007] Step 1: According to the cell image X i ∈R B×J The point label Y i ∈R 2×Ji Calculate the density map m i ∈R J , where R represents the real number set, the superscript of R represents the dimension of the vector in the real number set, N, B, J and J i are the number of cell images, the number of dimensions, the number of pixels, and the number of point labels in the cell images, respectively. i represents the cell image X i , point label Y i or density map m i number, i = 1, 2, ..., N; for point labels Represents Y i The two-dimensional coordinates of the j-th point in the density map m i The structure is:
[0008]
[0009] In formula (1), is the density map m i elements, j = 1, 2, ..., J, The mean is The normalized two-dimensional Gaussian kernel of , σ is the isotropic covariance matrix, 1 2×2 is the identity matrix;
[0010] Step 2: Build a regression network, including convolutional layer, pooling layer, upsampling layer and skip connection layer, a total of A layers;
[0011] make is the output feature of a certain layer in the regression network, where a=1,2,…,A is the number of layers in the network, D is the number of channels of the current layer feature, and E is the number of pixels in each feature map. is the e-th pixel on the d-th channel in the feature map of the a-th layer, d = 1, 2, ..., D, e = 1, 2, ..., E, then the construction of the regression network includes the following steps:
[0012] Step 2.1: Construct a convolutional layer for feature extraction, which outputs feature Z a Calculated as:
[0013]
[0014] In formula (2), is the output eigenvalue of the a-1th layer, U and V are the length and width of the filter respectively, f active (·) is the activation function, which uses a linear rectification function:
[0015]
[0016] Step 2.2: Construct a downsampling layer to reduce the size of the data space, whose output feature Z a for:
[0017]
[0018] In formula (4), f pool (·) is the maximum pooling operation;
[0019] Step 2.3: Construct an upsampling layer for restoring the image size, whose output feature Z a for:
[0020]
[0021] In formula (5), f upsample (·) is the upsampling operation;
[0022] Step 2.4: Construct a residual connection layer to supplement high-resolution information, whose output feature Z a for:
[0023] Z a =f skip (f upsample (Z a-1 ),Z a-n ) (6)
[0024] In formula (6), Z a-n It is the input of the pooling layer, and its length, width and number of dimensions are the same as Z a-1 Same, f skip (·) is Z a-n With Z a-1 The merging operation on the spatial dimension, namely Z a ∈R 2B×J ;
[0025] Step 2.5, construct the objective function:
[0026]
[0027] In formula (7), m i For the regression network to the cell image X i Density plot of predictions;
[0028] Step 3: Introduce the manifold regularization term Ω(·) into equation (7), including the following steps:
[0029] Step 3.1: The density map m i With the predicted density map m i Divide into subgraphs, the operation is as follows:
[0030]
[0031] In formula (8), For sub-image operation, h i p and From the density map m i With the predicted density map m i The subgraph selected on and at the same time and Where p = 1, 2, ..., P, P is the number of vertices in the density graph;
[0032] Step 3.2: Construct graph G i = {V i ,E i ,W i}, where V i 、E i and They are defined as graph G i The vertex set, edge set and weight set of ; Represents weight, q=1,2,…,P; calculation subgraph The Euclidean distances to other subgraphs of the density graph are sorted from small to large, and the vertex set consists of the first k vertices with the subgraph Adjacent self-density map composition; weight The calculation method is as follows:
[0033]
[0034] Step 3.3: Construct the manifold regularization term Ω(H i ):
[0035]
[0036] Let the normalized graph Laplacian matrix be L i =D i -1 / 2 (D i -W i )D i -1 / 2 , where D i It is a diagonal matrix, and the values on its diagonal are the weight sets W i The sum of the elements in each column or row in , which makes equation (10) equivalent to:
[0037]
[0038] Step 3.4: Based on equation (7) and equation (11), the objective function is reconstructed as:
[0039]
[0040] In formula (12), λ is a preset constant used to control the manifold regularization term For the original loss function the intensity of punishment;
[0041] Step 3.5, using the adaptive moment estimation optimizer to reversely update the network parameters of the regression network;
[0042] Step 4: Post-processing of the density map, including the following steps:
[0043] Step 4.1. Calculate the i-th cell image X i The predicted cell number C i :
[0044]
[0045] Step 4.2: Convert the density map into a pseudo-color image, set a set of thresholds r for the red, green, and blue channels, extract the pixels within the threshold-limited area, divide it into several 8-connected areas, and obtain the coordinates of the center point of each connected area. These are the predicted location coordinates of the cell.
[0046] Another technical solution of the present invention is to provide an application of the above-mentioned cell positioning and counting method based on manifold regression network, characterized in that it includes the following steps:
[0047] a) Input cell image X i ∈R B×J , click label Hyperparameter preset values σ, A, D, U, V, k, λ, r, and number of iterations t;
[0048] b) Calculate the density map m by formula (1) i ;
[0049] c) If t≠0, then the cell image X i Input the network, from equation (2) to equation (7), we get m i ; Otherwise, go to step g);
[0050] d) Obtain the subgraph from formula (8) and
[0051] e) Calculate the objective function using equation (12) and use the Adam optimizer to reversely update the network parameters;
[0052] f) Let t = t + 1, and go to step c);
[0053] g) Calculate C by formula (13) i , and calculate the cell coordinates Output the result.
[0054] The present invention is characterized in that:
[0055] 1) This paper proposes a manifold regularized regression model for cell counting and localization, which combines the advantages of deep learning and manifold learning, uses U-Net as the main body of the regression network, and uses the density map m generated by point labels. i As supervisory information, the present invention also introduces a manifold regularization term Ω(·) based on the graph Laplacian matrix to improve the generalization ability of the model and avoid overfitting.
[0056] 2) The regression network selects U-Net as the basic structure, and the residual connection between the contraction layer and the expansion layer fuses the features of different scales, supplements the missing information for the output features of the upsampling layer, and ensures the accuracy of positioning and regression.
[0057] 3) The density map m i It can accurately describe the complex cell locations and their spatial distribution in biomedical images. Therefore, it only needs point labels of cell nuclei to count and locate cells, without relying on precise manual annotations (such as cell nucleus / membrane contours) or requiring additional detection or segmentation methods.
[0058] 4) The manifold regularization term Ω(·) is used to represent the inherent characteristics of cells and express the nonlinear structure of cells. It enables the present invention to have good feature expression ability, is robust to the diversity and complexity of cell shapes and colors, improves regression accuracy, and enhances the generalization ability of the network.
[0059] 5) Thanks to the constraint of the manifold regularization term Ω(·) on the loss function, the present invention has good convergence.
[0060] Due to the adoption of the above technical solution, the present invention has the following advantages and positive effects compared with the prior art:
[0061] 1) The present invention simultaneously counts and locates cells in an end-to-end manner, and the density map used can simultaneously express the number and spatial distribution of cells. The constructed regression U-Net network can combine the density map and connect the contraction and expansion stages through residual connections to achieve synchronization of counting and positioning.
[0062] 2) The present invention combines the advantages of deep learning and manifold learning. It learns the multi-scale features of images through deep learning and uses manifold regularization terms to describe the local nonlinear structure of cells, thereby improving the robustness of the model, being able to effectively identify complex and changeable cell shapes and colors, improving positioning and counting accuracy, and enhancing the generalization ability of the network.
[0063] 3) The present invention is a practical solution to the problem of counting and positioning biological or medical cell images. Counting and positioning can be achieved using only cell point labels, without relying on precise manual labels, effectively saving labeling costs. Positioning and counting experiments were conducted on a widely used simulated fluorescent staining bacterial image set and real lung squamous cell carcinoma sections to verify the feasibility, effectiveness and convergence of the model. BRIEF DESCRIPTION OF THE DRAWINGS
[0064] Figure 1 is a flow chart of the present invention;
[0065] Figure 2 The structural diagram of the backbone regression network;
[0066] FIG3(a) is a simulated microscopic fluorescent staining bacterial image; FIG3(b) is a real density map; FIG3(c) is an estimated density map generated by MRNet of the present invention; FIG3(d) is an estimated density map of a comparison algorithm, which is an estimated density map of U-Net using mean square error (MSE) as a loss function, referred to as U-Net (MSE) for short;
[0067] Figure 4 is the convergence curve of MRNet of the present invention;
[0068] FIG5(a) is a box plot of the mean absolute error (MAE) of cell counts of MRNet of the present invention, the comparison algorithm U-Net (MSE), and U-Net (MESA) using the maximum-excess-over-subarrays (MESA) loss function on real PD-L1-stained lung squamous cell carcinoma pathological sections; FIG5(b) is a box plot of the MSE of the three algorithms;
[0069] Figure 6 This is the cell localization result of MRNet of the present invention on PD-L1 stained lung squamous cell carcinoma pathological sections. DETAILED DESCRIPTION
[0070] The present invention will be further described below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms fall within the scope limited by the appended claims of the application equally.
[0071] The present invention discloses a cell positioning and counting method based on a manifold regression network, comprising the following steps: calculating a density map according to cell point labels of a biomedical image; constructing a regression network according to cell counting and positioning tasks; constructing a manifold regularization term based on the sub-graph morphological features of the density map and the estimated density map; and optimizing the network using an Adam optimizer until the network reaches stable convergence. The unlabeled cell image is predicted, the number of cells is calculated according to the estimated density map of the network, and the position coordinates are obtained.
[0072] The present invention specifically comprises the following steps:
[0073] Step 1: According to the cell image X i ∈R B×J Point labels Calculate the density map m i ∈R J , where R represents the real number set, the superscript of R represents the dimension of the vector in the real number set, N, B, J and J i are the number of cell images, the number of dimensions, the number of pixels, and the number of point labels in the cell images, respectively. i represents the cell image X i , point label Y i or density map m i Number, i = 1, 2, ..., N. Cell image X i Generally, it is a true color image, so B = 3. in Represents Y i The two-dimensional coordinates of the j-th point in the density map m i The structure is:
[0074]
[0075] In formula (1), is the density map m i elements, j = 1, 2, ..., J, The mean is The normalized two-dimensional Gaussian kernel of , σ is the isotropic covariance matrix, 1 2×2 is the identity matrix.
[0076] Step 2: Construct a regression network, including convolutional layers, pooling layers, upsampling layers, and skip connection layers, a total of A layers. is the output feature of a certain layer in the regression network, where a=1,2,…,A is the number of layers in the network, D is the number of channels of the current layer feature, and E is the number of pixels in each feature map. is the e-th pixel on the d-th channel in the feature map of the a-th layer, d = 1, 2, …, D, e = 1, 2, …, E.
[0077] The construction of the regression network includes the following steps:
[0078] Step 2.1: Construct a convolutional layer for feature extraction, which outputs feature Z a Calculated as:
[0079]
[0080] In formula (2), is the output eigenvalue of the a-1th layer, U and V are the length and width of the filter respectively, f active (·) is the activation function, where the linear rectified function (Rectified Linear Unit, ReLU) is used:
[0081]
[0082] Step 2.2: Construct a downsampling layer to reduce the size of the data space, whose output feature Z a for:
[0083]
[0084] In formula (4), f pool (·) is the maximum pooling operation;
[0085] Step 2.3: Construct an upsampling layer for restoring the image size, whose output feature Z a for:
[0086]
[0087] In formula (5), f upsample (·) is the upsampling operation;
[0088] Step 2.4: Construct a residual connection layer to supplement high-resolution information, whose output feature Z a for:
[0089] Z a =f skip (f upsample (Z a-1 ),Z a-n ) (6)
[0090] In formula (6), Z a-nIt is the input of the pooling layer, and its length, width and number of dimensions are the same as Z a-1 Same, f skip (·) is Z a-n With Z a-1 The merging operation on the spatial dimension, namely Z a ∈R 2B×J ;
[0091] Step 2.5, construct the objective function:
[0092]
[0093] In formula (7), m i For the regression network to the cell image X i Density plot of predictions.
[0094] Step 3: Introduce the manifold regularization term Ω(·) into equation (7), including the following steps:
[0095] Step 3.1: The density map m i With the predicted density map m i Divide into subgraphs, the operation is as follows:
[0096]
[0097] In formula (8), For sub-image operation, h i p and From the density map m i With the predicted density map m i The subgraph selected on and at the same time and Where p = 1, 2, ..., P, P is the number of vertices in the density graph;
[0098] Step 3.2: Construct graph G i = {V i ,E i ,W i}, where V i 、E i and They are defined as graph G i The vertex set, edge set and weight set of ; Represents weight, q=1,2,…,P. Computation subgraph The Euclidean distances to other subgraphs of the density graph are sorted from small to large, and the vertex set consists of the first k vertices with the subgraph The adjacent self-density map is composed of weights. The calculation method is as follows:
[0099]
[0100] Step 3.3: Construct the manifold regularization term Ω(H i ):
[0101]
[0102] Let the normalized graph Laplacian matrix be L i =D i -1 / 2 (D i -W i )D i -1 / 2 , where D i It is a diagonal matrix, and the values on its diagonal are the weight sets W i The sum of the elements in each column or row in . Equation (10) is equivalent to:
[0103]
[0104] Step 3.4: Based on equation (7) and equation (11), the objective function is reconstructed as:
[0105]
[0106] In formula (12), λ is a preset constant used to control the manifold regularization term For the original loss function the intensity of punishment;
[0107] Step 3.5: Use the Adaptive Moment Estimation (Adam) optimizer to reversely update the network parameters of the regression network.
[0108] Step 4: Post-processing of the density map, including the following steps:
[0109] Step 4.1. Calculate the i-th cell image X i The predicted cell number C i :
[0110]
[0111] Step 4.2: Convert the density map into a pseudo-color image, set a set of thresholds r for the red, green, and blue channels, extract the pixels within the threshold-limited area, divide it into several 8-connected areas, and obtain the coordinates of the center point of each connected area. These are the predicted location coordinates of the cell.
[0112] In summary, the algorithm implemented by the present invention is recorded as a manifold regression network (Manifold-Constrained Regression Network, MRNet), and its specific steps are summarized as follows:
[0113] a) Input cell image X i ∈R B×J , click label Hyperparameter preset values σ, A, D, U, V, k, λ, r, and number of iterations t;
[0114] b) Calculate the density map m by formula (1) i ;
[0115] c) If t≠0, then the cell image X i Input the network, from equation (2) to equation (7), we get m i ; Otherwise, go to step g);
[0116] d) Obtain the subgraph from formula (8) and
[0117] e) Calculate the objective function using equation (12) and use the Adam optimizer to reversely update the network parameters;
[0118] f) Let t = t + 1, and go to step c);
[0119] g) Calculate C by formula (13) i , and calculate the cell coordinates Output the result.
[0120] Simulated fluorescent staining bacteria image experiment
[0121] The simulated fluorescent stained bacterial images were generated by using the SIMCEP software package in the MATLAB environment. Each image is 256×256 in size and contains 171±64 cells, where 171 is the mean number of cells and 64 is the variance. Several images were randomly selected from the first 100 images as the training set, the remaining samples were used as the validation set, and the last 100 images were used as the test set. Figure 3(a) shows an example of a simulated fluorescent stained bacterial image.
[0122] The backbone regression network structure used by MRNet in the present invention is composed of Figure 2 Description, the main parameters are set as follows: σ = 3, k = 8, λ = 0.1, and the number of iterations t = 100. The hardware environment for running all algorithms is Intel (R) Xeon (R) E3 CPU 3.00GHz (quad-core) 32GB memory, the software platform is Windows 7, MATLAB R2016b, Spyder3.2.4, and Pytorch programming is used.
[0123] Experiment 1 Verification of cell positioning and counting effects
[0124] The evaluation of the algorithm effect mainly includes the following two methods: (a) calculating the MAE of the true density map and the estimated density map; (b) visually comparing the visualization results of the true density map and the estimated density map.
[0125] Using the simulated microscopic fluorescent stained cell image of Figure 3(a), the number of training samples (N) was changed, and multiple independent experiments were conducted under each training condition to examine the mean absolute errors of the MRNet of the present invention and the advanced comparison algorithm U-Net (MSE), the Dens+MESA algorithm based on density map and MESA loss, the M-VOC algorithm based on manifold assumption, and the KM-VOC (RBF) algorithm based on radial basis function (RBF), as shown in Table 1. It can be seen that the MRNet of the present invention can surpass the existing advanced algorithms in most cases, and its counting standard deviation is small, indicating that MRNet has good stability.
[0126] Then, the true density map, the estimated density map of the regression U-Net algorithm U-Net (MSE) using the mean square error as the loss function, and the estimated density map of the MRNet of the present invention are experimentally investigated. The estimated density map of MRNet is plotted in Figure 3(c), which shows a clearer target density contour, while the estimated density area of U-Net (MSE) is usually larger than the true density map.
[0127] Table 1 Counting indicators (mean absolute error and standard deviation) of each algorithm in simulated fluorescent stained bacterial images
[0128]
[0129] Experiment 2 Verification of algorithm convergence
[0130] Figure 4 It shows that the MRNet of the present invention has a good convergence speed. The network starts to converge at the 40th iteration and tends to be stable at the 70th iteration.
[0131] PD-L1 staining lung squamous cell carcinoma pathological section experiment
[0132] The size of the PD-L1 stained lung squamous cell carcinoma pathology images used in this experiment was 1000×1000, with a total of 114 images, which were cut from 20 whole slices. The scanner was KF-PRO-120, with a resolution of 0.2481μm / pixel and a magnification of 40 times. Each image contained 23-647 tumor cells. Figure 6Four samples are given. The experiment selects 80% of the images as training samples and the rest as test samples. In the process of generating density maps, σ=4 is taken. The rest of the settings in this experiment are the same as Fluorescently stained bacterial images Test .
[0133] Experiment 1: Verification of cell counting effect
[0134] The evaluation of the algorithm effect mainly includes the following three methods: (a) calculating the MAE between the true density map and the estimated density map; (b) calculating the MRE between the true density map and the estimated density map; (c) visually comparing the true cell localization results with the predicted cell localization results.
[0135] Figure 5(a) examines the mean absolute errors of U-Net (MSE), U-Net (MESA) and the MRNet of the present invention. Figure 5(b) examines the mean relative errors of the three algorithms. The results show that the MRNet algorithm, which introduces the subgraph-based Laplace manifold regularization term, can achieve higher counting accuracy, which is better than the UNet algorithm using MSE and MESA as loss functions.
[0136] Experiment 2 Verification of cell localization effect
[0137] Figure 6 The localization results of the MRNet method of the present invention on PD-L1 stained lung squamous cell carcinoma pathological sections were examined, and it was confirmed that the present invention can provide relatively accurate localization information while counting, and is a practical and efficient method.
Claims
1. A cell positioning and counting method based on manifold regression network, characterized in that: The following steps are involved: Step 1: According to the cell image X i ∈R B×J Point labels Calculate the density map m i ∈R J , where R represents the real number set, the superscript of R represents the dimension of the vector in the real number set, N, B, J and J i are the number of cell images, the number of dimensions, the number of pixels, and the number of point labels in the cell images, respectively. i represents the cell image X i , point label Y i or density map m i number, i = 1, 2, ..., N; for point labels Represents Y i The two-dimensional coordinates of the j-th point in the density map m i The structure is: In formula (1), is the density map m i elements, j = 1, 2, ..., J, The mean is The normalized two-dimensional Gaussian kernel of , σ is the isotropic covariance matrix, 1 2×2 is the identity matrix; Step 2: Build a regression network, including convolutional layer, pooling layer, upsampling layer and skip connection layer, a total of A layers; make is the output feature of a certain layer in the regression network, where a=1,2,…,A is the number of layers in the network, D is the number of channels of the current layer feature, and E is the number of pixels in each feature map. is the e-th pixel on the d-th channel in the feature map of the a-th layer, d = 1, 2, ..., D, e = 1, 2, ..., E, then the construction of the regression network includes the following steps: Step 2.1: Construct a convolutional layer for feature extraction, which outputs feature Z a Calculated as: In formula (2), is the output eigenvalue of the a-1th layer, U and V are the length and width of the filter respectively, f active (·) is the activation function, which uses a linear rectification function: Step 2.2: Construct a downsampling layer to reduce the size of the data space, whose output feature Z a for: In formula (4), f pool (·) is the maximum pooling operation; Step 2.3: Construct an upsampling layer for restoring the image size, whose output feature Z a for: In formula (5), f upsample (·) is the upsampling operation; Step 2.4: Construct a residual connection layer to supplement high-resolution information, whose output feature Z a for: Z a =f skip (f upsample (Z a-1 ),Z a-n ) (6) In formula (6), Z a-n It is the input of the pooling layer, and its length, width and number of dimensions are the same as Z a-1 Same, f skip (·) is to convert Z a-n With Z a-1 The merging operation on the spatial dimension, namely Z a ∈R 2B×J ; Step 2.5, construct the objective function: In formula (7), m i For the regression network to the cell image X i Density plot of predictions; Step 3: Introduce the manifold regularization term Ω(·) into equation (7), including the following steps: Step 3.1: The density map m i With the predicted density map m i Divide into subgraphs, the operation is as follows: In formula (8), To perform sub-image operations, and From the density map m i With the predicted density map m i The subgraph selected on and at the same time and Where p = 1, 2, ..., P, P is the number of vertices in the density graph; Step 3.2: construct a graph Gi = {Vi, Ei, Wi}, where V i 、E i and They are defined as graph G i The vertex set, edge set and weight set of ; Represents weight, q=1,2,…,P; calculation subgraph The Euclidean distances to other subgraphs of the density graph are sorted from small to large, and the vertex set consists of the first k vertices with the subgraph Adjacent self-density map composition; weight The calculation method is as follows: Step 3.3: Construct the manifold regularization term Ω(H i ): Let the normalized graph Laplacian matrix be L i =D i -1 / 2 (D i -W i )D i -1 / 2 , where D i It is a diagonal matrix, and the values on its diagonal are the weight sets W i The sum of the elements in each column or row in , which makes equation (10) equivalent to: Step 3.4: Based on equation (7) and equation (11), the objective function is reconstructed as: In formula (12), λ is a preset constant used to control the manifold regularization term For the original loss function the intensity of punishment; Step 3.5, using the adaptive moment estimation optimizer to reversely update the network parameters of the regression network; Step 4: Post-processing of the density map, including the following steps: Step 4.
1. Calculate the i-th cell image X i The predicted cell number C i : Step 4.2: Convert the density map into a pseudo-color image, set a set of thresholds r for the red, green, and blue channels, extract the pixels within the threshold-limited area, divide it into several 8-connected areas, and obtain the coordinates of the center point of each connected area. These are the predicted location coordinates of the cell.
2. A cell positioning and counting method based on manifold regression network as claimed in claim 1, characterized in that: The following steps are involved: a) Input cell image X i ∈R B×J , click label Hyperparameter preset values σ, A, D, U, V, k, λ, r, and number of iterations t; b) Calculate the density map m by formula (1) i ; c) If t≠0, then the cell image X i Input the network, from equation (2) to equation (7), we get m i ; Otherwise, go to step g); d) Obtain the subgraph from formula (8) and e) Calculate the objective function using equation (12) and use the Adam optimizer to reversely update the network parameters; f) Let t = t + 1, and go to step c); g) Calculate C by formula (13) i , and calculate the cell coordinates Output the result.