A sparsely labeled remote sensing image target detection method based on graph combinatorial optimization

Abstract

The present invention discloses a sparsely labeled remote sensing image target detection method based on graph combination optimization, which belongs to the technical field of remote sensing image target detection; a sparsely labeled remote sensing image data set is constructed, and a rotation target detector is pre-trained using limited labeled data. In the training stage, a student network is used to infer a prediction set, a teacher network generates a candidate pseudo-label set, and a global object graph is constructed. Based on an appropriate objective function, a graph neural network is used to parameterize a probability distribution and map it to a desired solution. The objective function is minimized according to Monte Carlo sampling and Markov inequality, thereby optimizing the graph neural network and obtaining an optimal pseudo-label subset. Finally, the detector is continuously updated and optimized using an increased supervisory signal. The present invention adopts the above method to select an optimal pseudo-label subset based on the combination optimization of the graph neural network, which can effectively utilize limited label data, thereby improving the performance of sparsely labeled remote sensing image target detection.

Description

Technical Field

[0001] The present invention relates to the technical field of remote sensing image target detection, and in particular to a sparsely labeled remote sensing image target detection method based on graph combination optimization. Background Art

[0002] The application of deep neural networks has enabled rapid development of computer vision methods such as object detection in recent years, leading to their widespread application across various fields. With their powerful learning and representation capabilities, deep neural networks can effectively extract features and patterns from image data, enabling accurate object detection and recognition. However, these deep learning methods typically require large amounts of labeled data to guide the model's learning process during training and optimization. The collection and annotation of large-scale labeled data requires not only significant human resources but also specialized knowledge and skills. Furthermore, the annotation process can be subjective and contain inconsistent labels, which can negatively impact model training and performance.

[0003] Especially for remote sensing image target detection, which has the characteristics of numerous targets and complex scenes, this increases the demand for large-scale labeled data and limits the application and development of large-scale remote sensing image target detection methods.

[0004] Therefore, a sparsely labeled remote sensing image object detection method based on graph combinatorial optimization is provided. Summary of the Invention

[0005] The purpose of the present invention is to provide a sparsely labeled remote sensing image target detection method based on graph combinatorial optimization. By utilizing limited label data to train a rotation target detection model and selecting the optimal pseudo-label subset through a combinatorial optimization algorithm of a graph neural network, useful supervision data is increased, the annotation cost is reduced, and the limitation of pseudo-label quality is effectively alleviated, thereby improving the sparsely labeled remote sensing image target detection performance and providing a more flexible and feasible solution for remote sensing image analysis and application.

[0006] To achieve the above objectives, the present invention provides a sparsely labeled remote sensing image target detection method based on graph combination optimization, comprising the following steps:

[0007] S1: Establish a dataset. Construct a sparsely labeled remote sensing image dataset. In each image in the dataset, only some targets are clearly labeled, and the rest are not labeled. In each category in each image, at least one target is labeled. The dataset formula is as follows:

[0008]

[0009] In the above formula, N represents the number of images in the dataset, L i and U idenote the number of labeled instances and the number of unlabeled instances in the i-th image, respectively, and x i ,y i ,b i Represent the image patch, class label, and bounding box of the instance in the i-th image respectively;

[0010] S2: Pre-training the rotation object detector Θ using the data set established in step S1, extracting image features, learning the initial weights of the model, and initializing the model to obtain a pre-trained rotation object detector;

[0011] S3: Use the pre-trained rotation target detector to generate the student network Θ s and the teacher network Θ t , load the pre-training parameters;

[0012] S4: After weak enhancement α(x i ) and strong enhancement Α(x i ) is input to the student network Θ s and the teacher network Θ t Inference is performed in the student network Θ s For inference, we get the prediction set P, the teacher network Θ t Used for reasoning to obtain the candidate pseudo-label set U;

[0013] S5: Construct the candidate pseudo-label set U in step S4 into a global object graph as the input of the graph neural network, represent each pseudo-label sample as a node in the graph, and the edge represents the relationship or similarity between the samples;

[0014] S6: Use a graph neural network to map node feature vectors to probability distributions, sample the probability distributions to obtain subgraphs, and the subgraphs form the final pseudo-label subsets;

[0015] S7: Define an objective function to measure the quality of the pseudo-label subset, minimize the objective function using the gradient descent algorithm, and train the graph neural network model;

[0016] S8: For each image, the pseudo-label subset output by the graph neural network is combined with the original limited true labels, the predicted probability output by the teacher network is used as the weight of the pseudo-label, and the weighted object detection loss function is calculated for the training of the student network;

[0017] S9: Update the teacher network and the student network. After using the gradient descent optimization algorithm to update the parameters of the student network, the teacher network is updated by using the exponential moving average of the student network.

[0018] Preferably, in step S2, the process of obtaining the pre-trained rotation object detector is as follows: using standard cross entropy classification loss and SmoothL1 regression loss, utilizing the features of the last fully connected layer of the detector, and maintaining a set of class-level prototypes through a momentum update method, the formula is as follows:

[0019]

[0020] The above formula is the prior knowledge of the pseudo-label screening process. The specific update formula is as follows:

[0021]

[0022] in It is extracted through the basic ROI module The feature of the last fully connected layer has a dimension of d. Belonging to category c, μ is the momentum coefficient set to 0.9.

[0023] Preferably, in step S4, the post-processing process of the teacher network inference candidate pseudo-label set U is as follows: setting a removal threshold, and removing pseudo-labels whose intersection over union (IoU) with the true label is greater than the removal threshold from the candidate pseudo-label set.

[0024] Preferably, in step S5, the specific process of constructing the global object graph is as follows: using the suggestions generated by the region generation network RPN and their geometric distribution, the object graph is represented by a four-tuple G = (V, E, X, A), where V represents a node set, X is an attribute or feature matrix of the node, and E represents a set of edges. is the adjacency matrix.

[0025] Preferably, in step S6, the specific process of generating the pseudo label subset is as follows: for each node v i , update its eigenvector, the formula is as follows:

[0026]

[0027] In the above formula, Represents node v i The feature vector in the tth round iteration, σ represents the nonlinear activation function (such as ReLU), W (t) is the trainable parameter matrix of the tth iteration shared by all nodes, f agg (·) represents the aggregation function defined on adjacent nodes, the operator represents matrix connection;

[0028] The graph neural network uses a fully connected layer to transform each node v i The eigenvector x i Mapped to probability pi , parameterize the distribution D = W (G), and obtain the subgraphs S ~ D by sampling the distribution to obtain the final pseudo-label subset, that is, according to the Bernoulli random variable p i To determine the node v i choice.

[0029] Preferably, the process of defining the objective function in step S7 is as follows:

[0030] The subgraph obtained by sampling is S, and the optimal subgraph S is obtained by minimizing the objective function. * , which is expressed as follows:

[0031]

[0032] In the above formula, Ω represents the feasible domain, and the evaluation function includes three indicators: average information entropy, confidence gap, and class similarity measure. The formula is as follows:

[0033]

[0034] In the above formula, H(·) represents the average information entropy, M(·) represents the confidence gap, which is the difference between the maximum confidence value and the second largest confidence value, and Q(·) represents the class similarity measure. The specific formula is as follows:

[0035]

[0036]

[0037]

[0038] In the above formula, cos(·) represents cosine similarity, and I(·) represents indicator function;

[0039] set up S~D, so that f evaluation (S; G) < ε converts the objective function into the expected form, and the formula of the proxy objective function is: min E S～D [f evaluation (S; G)], calculate this expected value, estimate the quality of the objective function on the pseudo-label subset, use the Monte Carlo sampling method for random sampling, and through multiple random sampling and calculation of the average, obtain the approximate optimal solution formula of the objective function as follows:

[0040]

[0041] According to Markov's inequality, for a non-negative random variable X and any positive number a, there is the following inequality:

[0042] P(X≥a)≤E(X) / a

[0043] In the above formula, P(X≥a) represents the probability that the random variable X is greater than or equal to a, and E(X) represents the expected value of the random variable X, indicating that the probability that a non-negative random variable X is greater than or equal to a positive number a does not exceed its expected value E[X] divided by a;

[0044] When optimizing the approximate optimal solution of the objective function, let a = E S～D [f evaluation (S; G)] / (1-b), the formula is as follows:

[0045] P(f evaluation (S; G) ≥ E S～D [f evaluation (S; G)] / (1-b))≤1-b

[0046] In the above formula, by training the graph neural network, the proxy function is minimized so that the expected value satisfies the formula The optimized formula is as follows:

[0047]

[0048] The above formula indicates that there is an optimal pseudo-label subset.

[0049] Preferably, in step S8, the formula of the loss function for each image is as follows:

[0050]

[0051] In the above formula, N1 represents the number of real labels, N2 represents the number of pseudo labels, and p si and p ti Represent the probability values of the i-th sample predicted by the student model and the teacher model respectively, and denote the regression boxes of the i-th sample predicted by the student model and the teacher model respectively.

[0052] Preferably, in step S9, the updating formula of the teacher network is as follows:

[0053] Θ t =βΘ t +(1-β)Θ s

[0054] In the above formula, β is the moving average factor.

[0055] Therefore, the present invention adopts a sparse labeling remote sensing image target detection method based on graph combination optimization using the above method, which has the following advantages:

[0056] (1) In the present invention, in step S5, the candidate pseudo-label set is constructed into a global object graph, the context object information is recursively diffused through the graph neural network, and the edges are constructed using relative Euclidean distance and feature similarity. This can effectively mine the rich high-order relationships in the local area, comprehensively capture the relationships between objects, better understand the object distribution and semantic information in the graph, and screen high-quality pseudo-labels;

[0057] (2) In the present invention, in step S7, the objective function is based on three factors: the average information entropy measures the diversity and uncertainty of the targets in the pseudo-label subset, the confidence gap measures the degree of certainty of the targets in the pseudo-label subset, and the class similarity metric measures the similarity and distribution between the targets and the class centers in the pseudo-label subset, which can more comprehensively measure the quality of the pseudo-label subset;

[0058] (3) In the present invention, in step S7, the Markov inequality and Monte Carlo sampling method are used to transform the discrete problem into a continuous problem, which can better search for the optimal solution and overcome the challenge of the huge solution space in traditional combinatorial optimization problems;

[0059] (4) In step S8, by using the predicted probability of the teacher network as the pseudo-label loss weight, the student network can pay more attention to the pseudo-label samples with high confidence and ignore the pseudo-label samples with low confidence, which helps the student network to better utilize the credible pseudo-label data and improve the accuracy of target detection.

[0060] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 This is a flow chart of the overall structure of a sparsely labeled remote sensing image target detection method based on graph combination optimization in the present invention. DETAILED DESCRIPTION

[0062] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. The specific model specifications need to be selected and determined based on the actual specifications of the device, etc. The specific selection calculation method adopts the existing technology in this field, so it will not be described in detail.

[0063] Example

[0064] like Figure 1 As shown, the sparse labeling remote sensing image target detection method based on graph combination optimization of the present invention includes the following steps:

[0065] S1: Establish a dataset. Construct a sparsely labeled remote sensing image dataset. In each image in the dataset, only a small number of targets are clearly labeled, and the rest are not labeled. In addition, each category in each image has at least one target labeled. The dataset formula is as follows:

[0066]

[0067] In the above formula, N represents the number of images in the dataset, L i and U i denote the number of labeled instances and the number of unlabeled instances in the i-th image, respectively, and x i ,y i ,b i Represent the image patch, class label, and bounding box of the instance in the i-th image respectively;

[0068] S2: Use the limited labeled data in the dataset constructed in step S1 to pre-train the rotation object detector Θ to extract image features, learn the initial weights of the model, and initialize the model. Standard cross-entropy classification loss and SmoothL1 regression loss are used. Due to the sparsity of labels in the dataset, the impact of false negatives on the model is reduced by suppressing background loss. The loss weight is set to 0.3. Using the features of the last fully connected layer of the detector, a set of class-level prototypes are maintained by momentum updating. The formula is as follows:

[0069]

[0070] The above formula is the prior knowledge of the pseudo-label screening process. The specific update formula is as follows:

[0071]

[0072] in It is extracted through the basic ROI module The feature of the last fully connected layer has a dimension of d. Belonging to category c, μ is the momentum coefficient set to 0.9, and the rotation target detector Θ includes two-stage ReDet, Orientedr-cnn and one-stage S2A-Net, etc.

[0073] S3: Use the pre-trained rotation target detector to generate the student network Θ s and the teacher network Θ t , load the pre-trained parameters;

[0074] S4: After weak enhancement α(x i ) and strong enhancement Α(x i) is input to the student network Θ s and the teacher network Θ t Inference is performed in the student network Θ s For inference, we get the prediction set P, the teacher network Θ t Used for reasoning to obtain the candidate pseudo-label set U;

[0075] S5: Construct the candidate pseudo-label set U in step S4 into a global object graph as the input of the graph neural network, represent each pseudo-label sample as a node in the graph, and the edge represents the relationship or similarity between the samples;

[0076] For each image, a global object graph can be constructed to represent these candidate pseudo-labels, that is, the proposals generated by the region generation network RPN and their geometric distribution. The object graph can be represented by a four-tuple G = (V, E, X, A), where:

[0077] V represents a node set, each node corresponds to a candidate pseudo label, expressed as V = {v1,v2,...,v n}, i.e. V|=n, which represents the number of nodes / candidate pseudo-labels;

[0078] X is the attribute or feature matrix of the node, which represents the feature information of each node. Through the deep convolutional neural network, an attribute and feature description can be extracted for each candidate pseudo label. In form, it can be expressed as, Where F(·) is a multi-scale feature extractor through a basic ROI module, representing the last layer of fully connected layer features, and d is the length of the descriptor (i.e. the dimension of the feature attribute). The feature vectors of all nodes are stacked row by row to form a feature matrix x i Represents the i-th row or node v of the feature matrix i Attributes;

[0079] E represents a set of edges, which is used to represent the relationship or connection between nodes. It is composed of connected edges, and the construction of these edges depends on spatial location, semantic information, scale, feature representation or other factors. For example, we can determine the node v i and v j Is there an edge between them? The following formula is used:

[0080]

[0081] Where i and j represent the indices of the graph nodes, N k (v i ) represents the node v in Euclidean space i The first k nearest neighbors of i ) represents node v iThat is, if the node v j Belongs to the i-th node v i The first k nearest neighbors of , and they have the same category, set e ij =1, otherwise e ij = 0. Of course, other information can also be incorporated into the edge construction. All pairs of nodes with edge connections form an edge set E = {(v i ,v j )|e ij =1,v i ,v j ∈V};

[0082] Is the adjacency matrix, which represents the connection relationship between nodes. When the weight of the adjacency matrix is not considered, if the node v i With node v j If there is an edge between them, then A[i,j]=1, otherwise A[i,j]=0. When similarity is used as the weight of the adjacency matrix, the adjacency matrix can be expressed as, A[i,j]=sim(v i ,v j )*e ij , where sim(v i ,v j ) represents node v i With node v j The cosine similarity between nodes is calculated based on the characteristics or attributes of the nodes and is used to measure the similarity between nodes. In addition to cosine similarity, other similarity measurement methods can also be used, such as correlation coefficient. Choose the appropriate similarity calculation method based on the specific scenario and needs;

[0083] S6: Use a graph neural network to map node feature vectors to probability distributions, sample the probability distributions to obtain subgraphs, and the subgraphs form the final pseudo-label subsets;

[0084] A graph neural network is used on the constructed graph G to aggregate and diffuse context information. For each node v i , update its feature vector h i (usually represented as hidden state): in, Represents node v i The feature vector in the tth round iteration, σ represents the nonlinear activation function (such as ReLU), W (t) is the trainable parameter matrix of the tth iteration shared by all nodes, f agg (·) represents the aggregation function defined on adjacent nodes, the operator This update process can better combine the feature vector of the current node and the aggregated neighbor feature vector to obtain the new node feature vector Aggregation functions are used to aggregate the feature vectors of nodes to obtain the neighbor information of nodes. Common aggregation functions include summation, averaging, and maximum pooling. Graph neural networks use a fully connected layer to aggregate the feature vectors of each node v i The eigenvector x i Mapped to probability p i To simply parameterize the distribution D = W (G), and obtain the final pseudo-label subset by sampling the distribution to obtain subgraphs S ~ D, that is, according to the Bernoulli random variable p i To determine the node v i choice;

[0085] S7: Define an objective function to measure the quality of the pseudo-label subset. The subgraph obtained by sampling is S. Minimizing the objective function yields the optimal subgraph S. * , the formula is as follows:

[0086]

[0087] In the above formula, Ω represents the feasible domain, and the evaluation function includes three indicators: average information entropy, confidence gap, and class similarity measure. The formula is as follows:

[0088]

[0089] In the above formula, H(·) represents the average information entropy, which measures the diversity and uncertainty of the targets in the pseudo-label subset; M(·) represents the confidence gap, which is the difference between the maximum confidence value and the second largest confidence value, and measures the degree of certainty of the targets in the pseudo-label subset; Q(·) represents the class similarity metric, which measures the similarity and distribution between the targets and the class centers in the pseudo-label subset. The specific formula is as follows:

[0090]

[0091]

[0092]

[0093] In the above formula, cos(·) represents cosine similarity, and I(·) represents indicator function;

[0094] Since the combinatorial optimization problem is discrete and non-differentiable, the problem can be transformed into S~D, so that f evaluation (S; G) < ε, the objective function is converted into the expected form, and the formula of the proxy objective function is: min E S～D [f evaluation(S; G)], by calculating this expected value, we can approximate the quality of the objective function on the pseudo-label subset. Since there are many possibilities, the Monte Carlo sampling method is usually used for random sampling. By sampling multiple times and averaging, we can get the approximate optimal solution formula of the objective function:

[0095]

[0096] According to Markov's inequality, for a non-negative random variable X and any positive number a, there is the following inequality:

[0097] P(X≥a)≤E(X) / a

[0098] In the above formula, P(X≥a) represents the probability that the random variable X is greater than or equal to a, and E(X) represents the expected value of the random variable X, indicating that the probability that a non-negative random variable X is greater than or equal to a positive number a does not exceed its expected value E[X] divided by a;

[0099] When optimizing the approximate optimal solution of the objective function, let a = E S～D [f evaluation (S; G)] / (1-b), the formula is as follows:

[0100] P(f evaluation (S; G) ≥ E S～D [f evaluation (S; G)] / (1-b))≤1-b

[0101] In the above formula, by training the graph neural network, the proxy function is minimized so that the expected value satisfies the formula The optimized formula is as follows:

[0102]

[0103] When the expected value of the evaluation function is very small, there is an upper limit on the probability that the evaluation function value is greater than a certain minimum value, so there is an optimal pseudo-label subset.

[0104] The graph neural network model is trained by minimizing the objective function through the gradient descent algorithm;

[0105] S8: Combine the pseudo-label subset output by the graph neural network with the original limited real labels. The loss function for each image is as follows:

[0106]

[0107] In the above formula, N1 represents the number of real labels, N2 represents the number of pseudo labels, and p si and p ti Represent the probability values of the i-th sample predicted by the student model and the teacher model respectively, and Represent the regression boxes of the i-th sample predicted by the student model and the teacher model respectively.

[0108] S9: Update the teacher network and the student network. Use the gradient descent optimization algorithm to update the parameters of the student network. Update the teacher network by using the exponential moving average of the student network. The specific update formula is as follows:

[0109] Θ t =βΘ t +(1-β)Θ s

[0110] In the above formula, β is the moving average factor.

[0111] Therefore, the present invention adopts a sparsely labeled remote sensing image target detection method based on graph combinatorial optimization. The optimal pseudo-label subset is selected based on the combinatorial optimization of graph neural networks, which can effectively utilize limited label data, reduce annotation costs, and greatly alleviate the limitations of pseudo-label quality, thereby improving the performance of sparsely labeled remote sensing image target detection.

[0112] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A sparsely labeled remote sensing image target detection method based on graph combinatorial optimization, characterized by: The following steps are involved: S1: Establish a dataset. Construct a sparsely labeled remote sensing image dataset. In each image in the dataset, only some targets are clearly labeled, and the rest are not labeled. In each category in each image, at least one target is labeled. The dataset formula is as follows: In the above formula, Indicates the number of images in the dataset, and Respectively represent The number of labeled instances and the number of unlabeled instances in the image, Respectively represent Image patches, class labels, and bounding boxes of instances in an image; S2: Use the dataset created in step S1 to rotate the target detector Perform pre-training to extract image features, learn the initial weights of the model, and initialize the model to obtain a pre-trained rotation object detector; S3: Generate a student network using the pre-trained rotation target detector and teacher network , load the pre-training parameters; S4: respectively will undergo weak enhancement and strong enhancement The image is input to the student network and teacher network Inference is performed in the student network Used for inference to obtain prediction set , Teacher Network Used for reasoning to obtain candidate pseudo-label sets ; S5: The candidate pseudo-label set in step S4 is Construct a global object graph as the input of the graph neural network, represent each pseudo-label sample as a node in the graph, and the edge represents the relationship or similarity between samples; S6: Use a graph neural network to map node feature vectors to probability distributions, sample the probability distributions to obtain subgraphs, and the subgraphs form the final pseudo-label subsets; S7: Define an objective function to measure the quality of the pseudo-label subset, minimize the objective function using the gradient descent algorithm, and train the graph neural network model; S8: For each image, the pseudo-label subset output by the graph neural network is combined with the original limited true labels, the predicted probability output by the teacher network is used as the weight of the pseudo-label, and the weighted object detection loss function is calculated for the training of the student network; S9: Update the teacher network and the student network. After using the gradient descent optimization algorithm to update the parameters of the student network, the teacher network is updated by using the exponential moving average of the student network.

2. The method for sparsely labeled remote sensing image target detection based on graph combinatorial optimization according to claim 1, characterized in that: In step S2, the process of obtaining the pre-trained rotation object detector is as follows: using the standard cross entropy classification loss and SmoothL1 regression loss, utilizing the features of the last fully connected layer of the detector, and maintaining a set of class-level prototypes through the momentum update method, the formula is as follows: The above formula is the prior knowledge of the pseudo-label screening process. The specific update formula is as follows: in It is extracted through the basic ROI module The feature of the last fully connected layer has a dimension of d. Belongs to category c, The momentum coefficient is set to 0.

9.

3. The method for sparsely labeled remote sensing image target detection based on graph combinatorial optimization according to claim 1, characterized in that: In step S4, the teacher network infers the candidate pseudo label set The post-processing process is as follows: set a removal threshold, and remove pseudo labels whose intersection over union (IoU) with the true label is greater than the removal threshold from the candidate pseudo label set.

4. The method for sparsely labeled remote sensing image target detection based on graph combinatorial optimization according to claim 1, characterized in that: In step S5, the specific process of constructing the global object graph is as follows: the proposals generated by the region generation network RPN and their geometric distribution are used to construct the object graph using a four-tuple. express, Represents a collection of nodes, is the attribute or feature matrix of the node, represents a set of edges, is the adjacency matrix.

5. The method for sparsely labeled remote sensing image target detection based on graph combination optimization according to claim 1, characterized in that: In step S6, the specific generation process of the pseudo label subset is as follows: for each node , update its eigenvector, the formula is as follows: In the above formula, Representation node The feature vector at the tth iteration, represents a nonlinear activation function, is the trainable parameter matrix of the tth iteration shared by all nodes, Represents the aggregation function defined on adjacent nodes, operator represents matrix connection; The graph neural network uses a fully connected layer to connect each node The eigenvector of Mapping to probability , parameterized distribution , a subgraph is obtained by sampling this distribution , to obtain the final pseudo-label subset, that is, according to the Bernoulli random variable To determine the node choice.

6. The method for sparsely labeled remote sensing image target detection based on graph combination optimization according to claim 1, characterized in that: The process of defining the objective function in step S7 is as follows: The subgraph obtained by sampling is , minimize the objective function to obtain the optimal subgraph , which is expressed as follows: In the above formula, Represents the feasible domain. The evaluation function includes three indicators: average information entropy, confidence gap and class similarity metric. The formula is as follows: In the above formula, represents the average information entropy, Represents the confidence gap, the difference between the maximum confidence value and the second largest confidence value, Represents the class similarity measure, and the specific formula is as follows: In the above formula, represents the cosine similarity, represents the indicator function; set up Convert the objective function into the expected form, and the formula of the proxy objective function is: , calculate this expected value, estimate the quality of the objective function on the pseudo-label subset, use the Monte Carlo sampling method for random sampling, and through multiple random sampling and calculation of the average, obtain the approximate optimal solution formula of the objective function as follows: According to Markov's inequality, for a non-negative random variable and any positive number , there are the following inequalities: In the above formula, represents a random variable Greater than or equal to The probability of represents a random variable The expected value of , indicating that the probability that a non-negative random variable X is greater than or equal to a positive number a does not exceed its expected value E[X] divided by a; When optimizing the approximate optimal solution of the objective function, let , the formula is as follows: In the above formula, by training the graph neural network, the proxy function is minimized so that the expected value satisfies the formula , the optimized formula is as follows: The above formula indicates that there is an optimal pseudo-label subset.

7. The method for sparsely labeled remote sensing image target detection based on graph combinatorial optimization according to claim 1, characterized in that: In step S8, the formula for the loss function for each image is as follows: In the above formula, represents the number of true labels, represents the number of pseudo labels, and Represent the probability values of the i-th sample predicted by the student model and the teacher model respectively, and denote the regression boxes of the i-th sample predicted by the student model and the teacher model respectively.

8. The method for sparsely labeled remote sensing image target detection based on graph combination optimization according to claim 1, characterized in that: In step S9, the updating formula of the teacher network is as follows: In the above formula, is the moving average factor.

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