Method for determining kernel discriminant loss function for target detection in high-resolution remote sensing images

Abstract

A method for determining a kernel discriminative loss function for target detection in high-resolution remote sensing images belongs to the technical field of remote sensing image detection in deep learning. The present invention addresses the problem that the loss function in existing target detection separates features of each category in the feature space of the original dimension, making it difficult to enhance the nonlinear discriminability of features. The method comprises: for each batch of samples, based on the initialized feature center, sequentially calculating the increment of the feature center of each category relative to the feature center of the previous category to obtain the feature center of each category; mapping the feature center of each category to the Hilbert space, and calculating the square of the distance between the feature centers of each category in the Hilbert space based on the kernel function; calculating the weight term for enhancing inter-class feature separation learning and the weight term for enhancing intra-class feature aggregation learning; and then obtaining a discriminative loss function based on the kernel technique based on the softmax cross entropy loss function. The present invention is used for target detection in high-resolution remote sensing images.

Description

Technical Field

[0001] The present invention relates to a method for determining a kernel discriminant loss function for high-resolution remote sensing image target detection, and belongs to the technical field of remote sensing image detection in deep learning. Background Art

[0002] Very high resolution (VHR) imagery is highly valued in many fields, including disaster management, land planning, urban monitoring, and transportation planning. Object detection in VHR imagery is an important task that has attracted widespread attention.

[0003] Typically, object detection consists of two main tasks: classification and regression. The accuracy of object detection classification depends on the effective extraction of discriminative features. However, the complexity and noisy nature of remote sensing object detection scenarios make it challenging for existing methods to learn discriminative features for practical classification tasks. Therefore, methods for achieving accurate classification in VHR remote sensing imagery still need improvement.

[0004] In recent years, the use of deep learning models for feature extraction in remote sensing imagery has become a growing trend. These deep learning models include convolutional neural networks (CNNs) and Transformers. Applying convolutional neural networks to networks can enhance intra-class consistency and inter-class diversity. However, these methods are not sufficient to extract discriminative features for accurate object classification. In addition, the introduction of the Transformer architecture into the field of computer vision has also achieved promising results. Transformer-based models such as VisionTransformer and Swin Transformer have demonstrated excellent performance in multiple tasks such as image classification and object detection. Despite the success of deep learning models in object detection, the loss functions currently widely used in classification tasks, such as cross-entropy loss and focal loss, cannot fully learn discriminative features. One reason is that these loss functions focus on minimizing the difference between predicted values ​​and actual labels, while ignoring the distribution of inter-class features and intra-class feature representations.

[0005] In order to learn discriminative features, some loss functions map deep features into feature space based on distance metrics, so that features of the same category are close to each other and features of different categories are far away from each other. For example, Center loss based on softmax loss uses the sum of the squared distances between deep features and their feature centers to reduce intra-class distances. VirtualSoftmax enhances the discriminability of learned features by injecting a dynamic virtual negative class into the original softmax. CC-Loss takes into account the relationship between feature distribution and model structure, increasing the inter-class distance and reducing the intra-class distance in the channel dimension. Large margin cosine loss expresses softmax loss as cosine loss and introduces a cosine margin to separate features from different classes.

[0006] However, these loss functions typically only learn discriminative features in the original feature space. This approach struggles to capture the complex nonlinear relationships inherent in the data and is therefore suboptimal for separating features from different categories. Separating features within the original feature space makes it difficult to enhance the nonlinear discriminative nature of features. Summary of the Invention

[0007] Aiming at the problem that the loss function in existing target detection separates features of each category in the feature space of the original dimension and is difficult to enhance the nonlinear discriminability of the features, the present invention provides a method for determining the kernel discriminant loss function for target detection in high-resolution remote sensing images.

[0008] The present invention provides a method for determining a kernel discriminant loss function for high-resolution remote sensing image target detection, which is obtained based on a softmax cross entropy loss function and includes:

[0009] For each batch of samples, based on the initialized feature center, the increment of the feature center of each category relative to the feature center of the previous category is calculated in turn to obtain the feature center of each category;

[0010] Map the feature center of each category to the Hilbert space, and calculate the square distance between the feature centers of each category in the Hilbert space based on the kernel function;

[0011] The squared distances of all feature centers are summed and normalized to obtain the weight term for enhanced inter-class feature separation learning of the softmax cross entropy loss function;

[0012] Then, the kernel function is used to calculate the proximity between the features of each category sample and the feature center of the corresponding category, and the weight term of the enhanced intra-category feature aggregation learning of the softmax cross entropy loss function is obtained;

[0013] Based on the weight term of enhanced inter-class feature separation learning, the weight term of enhanced intra-class feature aggregation learning and the softmax cross entropy loss function, a discriminant loss function based on kernel techniques is obtained for target detection in high-resolution remote sensing images.

[0014] According to the kernel discriminant loss function determination method for high-resolution remote sensing image target detection of the present invention, the increment of the feature center of each category relative to the feature center of the previous category is calculated as follows:

[0015]

[0016] Where t represents the batch of samples, It represents the increment of the feature center of the i-th category sample in the t-th batch of samples relative to the feature center of the previous category, s ti Indicates the total number of rows of deep features of the i-th class sample in the t-th batch of samples, y k represents the sample label, d(y k =i) is the first discriminant function, which outputs 1 when the condition is met, otherwise it outputs 0; Indicates that the sample label is y k The j-th row of deep features.

[0017] According to the method for determining the kernel discriminant loss function for high-resolution remote sensing image target detection of the present invention, the feature center of each category is calculated as follows:

[0018]

[0019] In the formula is the characteristic center of the i-th type of sample in the t-th batch of samples, w i For intermediate variables:

[0020]

[0021] According to the method for determining the kernel discriminant loss function for high-resolution remote sensing image target detection of the present invention, the feature center of a category is set to x, and the mapping function mapped to the Hilbert space is The feature center of the other category is x′, and the mapping function to the Hilbert space is Calculate the square of the distance between two feature centers mapped to the Hilbert space using the mapping function:

[0022]

[0023] The Gaussian kernel function k(x, x′) is used to solve formula (4). The Gaussian kernel function k(x, x′) is:

[0024]

[0025] Where σ is the parameter of the kernel function, which is a constant; Taylor represents Taylor expansion;

[0026] In the formula For intermediate variables:

[0027]

[0028] Solving formula (4) yields the square of the distance between the two feature centers in the Hilbert space:

[0029]

[0030] According to the kernel discriminant loss function determination method for high-resolution remote sensing image target detection of the present invention, the weight term of enhanced inter-class feature separation learning is expressed as T inter :

[0031]

[0032] Where c represents the total number of sample categories, x i Represents the feature center of the i-th class sample in each batch of samples.

[0033] According to the kernel discriminant loss function determination method for high-resolution remote sensing image target detection of the present invention, the weight term of enhanced intra-class feature aggregation learning is expressed as T intra :

[0034]

[0035] Where k represents the kth sample in the i-th class, b represents the total number of samples in the i-th class, δ(r) is the second discriminant function, if the current sample belongs to the i-th class, then the output is 1, otherwise the output is 0;

[0036] L() means reducing the dimension of the features in the brackets. Represents the characteristics of the kth sample in the i-th class sample, k max is the maximum value of the kernel function, k min is the minimum value of the kernel function.

[0037] According to the kernel discriminant loss function determination method for high-resolution remote sensing image target detection of the present invention, the discriminant loss function based on the kernel technique is expressed as L cls :

[0038]

[0039] Where L softmax is the softmax cross entropy loss function.

[0040] Beneficial effects of the present invention: The method of the present invention uses kernel techniques to effectively learn discriminative features, which can be used in target detection to effectively improve the accuracy of target detection.

[0041] The method of the present invention uses the Mercer kernel to perform calculations in low dimensions, but the actual effect is manifested in high dimensions. It can complete the transformation of features from low dimensions to high dimensions without excessive computational effort. To further learn discriminative features, the method of the present invention maps the feature center of each category to Hilbert space and calculates the L2 distance between the center of each category in Hilbert space. At the same time, to make the feature close to the feature center of the corresponding category, a kernel function is used to calculate the similarity between the feature and its corresponding feature center, thereby obtaining a discriminant loss function based on the kernel technique.

[0042] Under the constraints of the discriminant loss function based on the kernel technique obtained by the method of the present invention, the target detection model can learn more discriminative features, which helps to find a better hyperplane in the classification task and improve the classification ability of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a flow chart of the method for determining the kernel discriminant loss function for high-resolution remote sensing image target detection according to the present invention;

[0044] Figure 2 This is a visual comparison of the detection results of target detection using the method of the present invention and cross-entropy loss on the DOTA dataset;

[0045] Figure 3 This is a visualization comparison of the detection results of target detection using the method of the present invention and cross-entropy loss on the RSOD dataset. DETAILED DESCRIPTION

[0046] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0047] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0048] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0049] Specific implementation method 1. Combination Figure 1As shown, the present invention provides a method for determining a kernel discriminant loss function for high-resolution remote sensing image target detection, which is obtained based on the softmax cross entropy loss function, including:

[0050] For each batch of samples, based on the initialized feature center, the increment of the feature center of each category relative to the feature center of the previous category is calculated in turn to obtain the feature center of each category;

[0051] Map the feature center of each category to the Hilbert space, and calculate the square distance between the feature centers of each category in the Hilbert space based on the kernel function;

[0052] The squared distances of all feature centers are summed and normalized to obtain the weight term for enhanced inter-class feature separation learning of the softmax cross entropy loss function;

[0053] Then, the kernel function is used to calculate the proximity between the features of each category sample and the feature center of the corresponding category, and the weight term of the enhanced intra-category feature aggregation learning of the softmax cross entropy loss function is obtained;

[0054] Based on the weight term of enhanced inter-class feature separation learning, the weight term of enhanced intra-class feature aggregation learning and the softmax cross entropy loss function, a discriminant loss function based on kernel techniques is obtained for target detection in high-resolution remote sensing images.

[0055] Kernel functions are widely used in SVM (support vector machines) to solve the linear inseparable problem of actual data. The main method to separate linear inseparable data is to map features to a high-dimensional feature space and find a suitable partitioning hyperplane to separate samples of each category. Using the Mercer kernel to perform calculations in low dimensions, the actual effect is reflected in high dimensions, and the transformation of features from low dimensions to high dimensions can be completed without too much calculation. In order to further learn discriminative features, this embodiment proposes a discriminant loss function (KD Loss) based on kernel techniques. KD Loss maps the feature center of each category to the Hilbert space and calculates the L2 distance between the centers of each category in the Hilbert space. The greater the distance, the smaller the KD Loss, and the farther the distance between the centers of each category. At the same time, in order to make the features close to the feature center of the corresponding category, inspired by Center loss, the kernel function is used to calculate the similarity between the feature and its corresponding feature center. This embodiment realizes an attempt to use kernel techniques for nonlinear category separation.

[0056] Softmax cross-entropy loss (softmax cross entropy loss function), which combines softmax and cross-entropy loss, is often used in multi-classification tasks. The classic form of softmax cross-entropy loss is shown below:

[0057]

[0058] Where m is the total number of samples in the current batch, n is the total number of sample categories in the current batch, and w J ∈R d is the weight vector of category J, y J is the label of category J, w yI For label y J The weight vector, x I ∈R d Indicates that it belongs to category y I The I-th depth feature, d represents the feature dimension, b J is the deviation term of category J;

[0059] Although softmax cross-entropy loss can learn features that separate different categories to a certain extent, these features are scattered within the category.

[0060] Center loss and softmax cross-entropy loss are weighted together and used together as supervision for learning discriminative features. This can promote features of the same category to move closer to the feature center of their corresponding category, thereby reducing the distance between classes. Center loss randomly generates a feature center for each category in the network. This center is updated once for the current category after each iteration during the training process. After obtaining the feature center of each category, Center loss calculates the square of the Euclidean distance between the deep feature and the feature center of its corresponding category:

[0061]

[0062] Where c yI Representative category y I The feature center of .

[0063] However, Center loss can be ineffective or ineffective for data with widely varying sample types, as the feature centers obtained by taking the squared sum of features are difficult to distinguish. Furthermore, Center loss is primarily targeted at face recognition tasks with a large number of categories and may not be suitable for remote sensing target detection tasks, which have far fewer categories than face recognition.

[0064] In the feature space of the existing method, for categories with large sample differences, the feature center obtained by calculating the sum of squares and averaging the features is not accurate enough. The feature centers of each category may be confused with each other. Therefore, this embodiment enhances the linear separability of deep features in high-dimensional space by mapping the deep feature centers to the Hilbert space and expanding the distance between them. In order to obtain the category center of the deep feature that combines all sample features, first calculate the increment Δx of the feature center of each class of the current batch of samples in each batch i , and then perform weighted average calculation on the feature center increment and the feature center of the previous batch to obtain the feature center of the current batch.

[0065] Furthermore, the increment of the feature center of each category relative to the feature center of the previous category is calculated as follows:

[0066]

[0067] Where t represents the batch of samples, It represents the increment of the feature center of the i-th category sample in the t-th batch of samples relative to the feature center of the previous category, s ti Indicates the total number of rows of deep features of the i-th class sample in the t-th batch of samples, y k represents the sample label, d(y k =i) is the first discriminant function, which outputs 1 when the condition is met, otherwise it outputs 0; Indicates that the sample label is y k The j-th row of deep features.

[0068] In this embodiment, the feature center is iteratively updated based on the current training data and is more closely related to each feature.

[0069] In this embodiment, the feature center of each category is calculated as follows:

[0070]

[0071] In the formula is the characteristic center of the i-th type of sample in the t-th batch of samples, w i For intermediate variables:

[0072]

[0073] After obtaining the feature centers for each category, they are mapped to Hilbert space and introduced with higher or more complex features to find a separating hyperplane that classifies the data as accurately as possible in the high-dimensional feature space. Introducing a high-dimensional feature space enhances the nonlinear discriminative power of features, ultimately improving the model's classification performance. To increase the distance between each feature center, the sum of the squared distances between two feature centers in Hilbert space can be used as a weight in the softmax cross-entropy loss.

[0074] Going further, let the feature center of a category be x, and the mapping function to the Hilbert space is The feature center of the other category is x′, and the mapping function to the Hilbert space is Calculate the square of the distance between two feature centers mapped to the Hilbert space using the mapping function:

[0075]

[0076] It's difficult to find a mapping function when mapping from low-dimensional to high-dimensional space, and calculating the inner product in high-dimensional space is very complex. Therefore, this implementation uses a kernel function to reduce computational complexity, converting the inner product calculation in high-dimensional space into an expression for the inner product in low-dimensional space. This article uses the Gaussian kernel function as an example to explain its calculation principles.

[0077] The Gaussian kernel function k(x, x′) is used to solve formula (4). The Gaussian kernel function k(x, x′) is:

[0078]

[0079] Where σ is the parameter of the kernel function, which is a constant; Taylor represents Taylor expansion;

[0080] In the formula For intermediate variables:

[0081]

[0082] Solve formula (4) to get the sum of the squares of the distances between each two feature centers in the Hilbert space:

[0083]

[0084] Then normalize formula (6) and introduce kernel techniques to reduce the amount of calculation to obtain T inter .

[0085] In this embodiment, the weight term for enhanced inter-class feature separation learning is expressed as T inter :

[0086]

[0087] Where c represents the total number of sample categories, x i Represents the feature center of the i-th class sample in each batch of samples.

[0088] While obtaining clearly separated feature centers of each category, it is also necessary for features of the same category to be close to the corresponding feature centers to achieve accurate classification. In order to enhance the cohesion of features belonging to the same category and reduce the intra-category distance, this embodiment adds a term T about the proximity of each feature point to the corresponding feature center. intra The kernel function is essentially a measure of similarity. The kernel function is used to calculate the proximity between a feature and the feature center of its corresponding category:

[0089] The weight term for enhancing intra-class feature aggregation learning is expressed as T intra :

[0090]

[0091] Where k represents the kth sample in the i-th class, b represents the total number of samples in the i-th class, δ(r) is the second discriminant function, if the current sample belongs to the i-th class, then the output is 1, otherwise the output is 0;

[0092] L() means dimensionality reduction of the features in the brackets. In order to accurately calculate the feature center of each category and include the information of all samples as much as possible, higher-dimensional features are used for calculation. Represents the characteristics of the kth sample in the i-th class sample, K max is the maximum value of the kernel function, K min is the minimum value of the kernel function.

[0093] In formula (8), using kernel function to measure the similarity between features and feature centers can use low-dimensional features to reduce computational complexity. The maximum value K of the kernel function between the current category feature and the feature center is used. max and minimum value K min Perform normalization.

[0094] In this embodiment, T inter and T intra Together they serve as the weights of the softmax cross-entropy loss, which reduces the distance between features of the same category while separating the feature centers. The discriminant loss function based on the kernel technique is expressed as L cls :

[0095]

[0096] Where L softmax is the softmax cross entropy loss function.

[0097] Unlike other losses, KD Loss expands the distance between classes in Hilbert space, finding a linear hyperplane for the feature centers of different classes. While separating feature centers, it also calculates the distance between features, thereby expanding the distance between classes while reducing the distance within classes, thereby improving target classification accuracy. Specific embodiment:

[0099] To verify the effectiveness of our method, we conduct experiments on two popular remote sensing datasets, DOTA and RSOD. The experimental results show that KD Loss brings significant performance improvements compared to the baseline method.

[0100] To compare the effects of KD Loss and similar loss functions, extensive experiments were conducted on Cascade R-CNN using ResNet101 and Faster R-CNN using Swin Transformer. To ensure fairness, these experiments were conducted on the same environment and hyperparameters.

[0101] Table 1 Comparison of the performance of KD Loss and similar loss functions on DOTA

[0102]

[0103] Among them, Faster R-CNN-SW=Faster R-CNN+SwinTransformer, Cascade R-CNN-R101=Cascade R-CNN+ResNet101.

[0104] Table 2 Comparison of the performance of KD Loss and similar loss functions on RSOD

[0105]

[0106] Faster R-CNN-SW=Faster R-CNN+Swin Transformer, Cascade R-CNN-R101=Cascade R-CNN+ResNet101

[0107] Table 3 Verification of T on DOTA inter and T intra Ablation experiment on the contribution of KD Loss

[0108]

[0109] Table 4 Comparison of KD loss and baseline models on different backbone networks on the DOTA dataset

[0110]

[0111] Table 5 Ablation experiments with different kernel functions

[0112]

[0113]

[0114] Table 6 Ablation experiments with different parameters in quadratic rational kernel

[0115]

[0116] As shown in Table 1, for the large-scale aerial remote sensing image DOTA dataset, the accuracy of the method of the present invention is better than the comparison method in most categories, reflecting the beneficial effect of the method of the present invention on improving the target detection performance. It is worth mentioning that on the Cascade R-CNN using ResNet101, the method of the present invention is 2.36% higher than the Center loss. For the RSOD dataset with four categories, KD Loss showed excellent performance on both models. As shown in Table 2, in the Faster R-CNN using Swin Transformer, KD Loss is better than Center loss and cross-entropy loss in the three categories of airplanes, playgrounds and overpasses, and is 4.1% better than cross-entropyloss in mAP50. This is sufficient to prove that the method of the present invention has a significant improvement effect on remote sensing target detection compared with similar methods.

[0117] In order to verify T inter and T intra We conducted rigorous ablation experiments on the contribution of KD Loss. We used Cascade R-CNN combined with ResNet101 backbone network as the baseline model. We used the same training strategy and parameters to compare T on the DOTA dataset. inter and T intra and T inter and T intra Combined with the improvement effect on the benchmark. As shown in Table 3, by adding T intra , helps aggregate features within the same class, improving performance by 1.0%. inter Expanding the feature distance between different classes improves the performance by 1.56%. inter and T intra The combination of produces a positive coupling effect, bringing more positive improvements, resulting in a 1.82% increase in mAP. These ablation experiments demonstrate the effectiveness of the loss function proposed in this paper.

[0118] To demonstrate that the proposed method can be applied to different models, extensive experiments were conducted on multiple backbones, including ResNet50, ResNext101, and Swin Transformer. All experiments were conducted on Faster R-CNN with consistent parameter settings. The experimental results are shown in Table 4. As shown in Table 4, the proposed method achieved significant accuracy improvements in mAP, mAP50, and mAP75 for the three different networks. For ResNet50, KD Loss achieved a 1.86% higher mAP, a 1.32% higher mAP50, and a 2.39% higher mAP75 than the baseline model. For ResNext101, KD Loss achieved a 2.95% higher mAP, a 2.18% higher mAP50, and a 4.12% higher mAP75 than the baseline model. For Swin Transformer, KD Loss achieved a 3.23% higher mAP, a 2.05% higher mAP50, and a 4.12% higher mAP75 than the baseline model. Obviously, the method of the present invention shows good accuracy improvement when transplanted to different models.

[0119] To further explore the impact of hyperparameters on KD Loss, we examine the effects of different kernel functions and kernel function parameters on model accuracy. Three kernel functions were selected for comparison: the Gaussian kernel, one of the most commonly used kernel functions; the quadratic rational kernel, which can be used as an alternative to the Gaussian kernel in some cases and can reduce computational overhead; and the Cauchy kernel, which is suitable for high-dimensional data. Table 5 lists the kernel functions used. On the DOTA dataset, the quadratic rational kernel outperformed both the Gaussian and Cauchy kernels. Furthermore, the quadratic rational kernel was computationally cheaper than the other two kernel functions. The parameter σ of the quadratic rational kernel is a hyperparameter that controls the smoothness or roughness of the kernel function, affecting its shape. Smaller σ values ​​result in a sharper kernel shape, better fitting the training data, but can also lead to overfitting. Conversely, larger σ values ​​result in a smoother kernel shape, which can lead to a weaker fit to the training data and potentially underfitting. Table 6 shows the different σ values ​​used in the experiments. Table 6 shows that different σ values ​​have different effects on model performance. As shown in Table 6, the model achieves the highest performance when σ is set to 1.

[0120] To verify the effectiveness of KDloss, comprehensive experiments are also conducted on two public datasets in the remote sensing field.

[0121] DOTA is a large-scale dataset commonly used in remote sensing object detection and is often used to evaluate the accuracy of object detection models. It contains 2,806 images collected from various sensors and platforms and includes 188,282 instances. Image sizes range from 800x800 to 4,000x4,000 pixels. DOTA includes 15 categories: airplane (P), baseball field (BD), bridge (B), ground runway (GTF), small vehicle (SV), large vehicle (LV), ship (S), tennis court (TC), basketball court (BC), storage tank (ST), soccer field (SBF), circular route (RA), harbor (H), swimming pool (SP), and helicopter (HC). DOTA is divided into a training set (1 / 2), a validation set (1 / 6), and a test set (1 / 3). Models are trained on the training and validation sets, and the test results on the test set serve as the basis for model accuracy.

[0122] RSOD is a remote sensing object detection dataset. It contains 976 images, including 4,993 aircraft instances in 446 images, 191 playground instances in 189 images, 180 overpass instances in 176 images, and 1,586 oil drum instances in 165 images. Because RSOD does not explicitly divide training and test sets, in this example, 702 images were arbitrarily selected as the training set, and the remaining 234 images were used as the test set.

[0123] In the experiment, the average precision (AP) is used as the evaluation indicator. First, the precision and recall are introduced:

[0124]

[0125]

[0126] Where Recall represents the recall rate, Precision represents the accuracy; TP, FN, and FP represent the number of true positives, false negatives, and false positives, respectively. AP is the area under the precision-recall curve, and mAP is the average AP of all categories, indicating the overall impact of the model on all categories.

[0127] The method of the present invention is implemented using MMDetection, a pytorch-based object detection tool library. Due to the large image size of the DOTA dataset and the limitation of GPU memory, the images are segmented into 1024*1024 pixel patches with an overlap of 200 pixels. All experiments are performed using 8 NVIDIA GeForce GTX 1080Ti graphics processors. The model is trained using an SGD optimizer with 0.9 momentum and 0.0001 weight decay. For the RSOD dataset, the initial learning rate is 0.02, and a learning rate warm-up of 0.001 is used in the first 500 iterations. The RSOD dataset is trained with 50 iterations, and the learning rate is linearly decayed by a factor of 10 in the 46th and 48th iterations, respectively. For the DOTA dataset, the hyperparameters and training schedule are kept consistent with the settings of the official benchmark.

[0128] Figure 2 Visualization of the detection results of KD Loss and cross-entropy loss based on Faster R-CNN using Swin Transformer; Figure 3 Visualization of the detection results of KD Loss and cross-entropy loss based on Faster R-CNN using Swin Transformer.

[0129] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It should be understood that many modifications may be made to the illustrative embodiments, and that other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in ways other than those described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be used in conjunction with other described embodiments.

Claims

1. A method for determining the kernel discriminant loss function for high-resolution remote sensing image target detection, based on the softmax cross entropy loss function, characterized by include, For each batch of samples, based on the initialized feature center, the increment of the feature center of each category relative to the feature center of the previous category is calculated in turn to obtain the feature center of each category; Map the feature center of each category to the Hilbert space, and calculate the square distance between the feature centers of each category in the Hilbert space based on the kernel function; The squared distances of all feature centers are summed and normalized to obtain the weight term for enhanced inter-class feature separation learning of the softmax cross entropy loss function; Then, the kernel function is used to calculate the proximity between the features of each category sample and the feature center of the corresponding category, and the weight term of the enhanced intra-category feature aggregation learning of the softmax cross entropy loss function is obtained; Based on the weight term of enhanced inter-class feature separation learning, the weight term of enhanced intra-class feature aggregation learning and the softmax cross entropy loss function, a discriminant loss function based on kernel techniques is obtained for target detection in high-resolution remote sensing images. Assume that the feature center of a category is x, and the mapping function to Hilbert space is The weight term for enhanced inter-class feature separation learning is expressed as T inter : Where c represents the total number of sample categories, x i Represents the characteristic center of the i-th class sample in each batch of samples; The weight term for enhancing intra-class feature aggregation learning is expressed as T intra : Where k represents the kth sample in the i-th class, b represents the total number of samples in the i-th class, δ(r) is the second discriminant function, if the current sample belongs to the i-th class, then the output is 1, otherwise the output is 0; L() means reducing the dimension of the features in the brackets. Represents the characteristics of the kth sample in the i-th class sample, k max is the maximum value of the Gaussian kernel function k(), k min is the minimum value of the Gaussian kernel function k(); The discriminant loss function based on the kernel technique is expressed as L cls : Where L softmax is the softmax cross entropy loss function.

2. The method for determining a kernel discriminant loss function for target detection in high-resolution remote sensing images according to claim 1, wherein: The increment of the feature center of each category relative to the feature center of the previous category is calculated as follows: Where t represents the batch of samples, It represents the increment of the feature center of the i-th category sample in the t-th batch of samples relative to the feature center of the previous category, s ti Indicates the total number of rows of deep features of the i-th class sample in the t-th batch of samples, y k represents the sample label, d(y k =i) is the first discriminant function, which outputs 1 when the condition is met, otherwise it outputs 0; Indicates that the sample label is y k The j-th row of deep features.

3. The method for determining a kernel discriminant loss function for target detection in high-resolution remote sensing images according to claim 2, wherein: The feature center of each category is calculated as: In the formula is the characteristic center of the i-th type of sample in the t-th batch of samples, w i For intermediate variables:

4. The method for determining a kernel discriminant loss function for target detection in high-resolution remote sensing images according to claim 3, wherein: Set the feature center of another category to x′, and the mapping function to Hilbert space is Calculate the square of the distance between two feature centers mapped to the Hilbert space using the mapping function: The Gaussian kernel function k(x, x′) is used to solve formula (4). The Gaussian kernel function k(x, x′) is: Where σ is the parameter of the kernel function, which is a constant; Taylor represents Taylor expansion; In the formula For intermediate variables: Solving formula (4) yields the square of the distance between the two feature centers in the Hilbert space:

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