In recent years，the rapid advancement of infrared detection and imaging technology has led to an expanding application scope for infrared images^［1］. Infrared detection technology，characterized as a passive detection technique，offers advantages such as long-range detection，high concealment and robust all-weather capabilities^［2］. Recognition of infrared targets，as a crucial component of infrared detection imaging systems，is paramount for enhancing system performance and expanding application domains. Presently，deep learning models demonstrate remarkable performance in visual recognition tasks such as image classification； however，this significant performance heavily relies on the utilization of large quantities of labeled image data for training^［3］. Nevertheless，due to factors such as the high cost and military sensitivity of infrared equipment，acquiring samples of airborne infrared targets poses significant challenges. For certain rare aircraft models，sample data may be limited to only tens or even units^［4］，implying that even with the adoption of methods such as data augmentation or transfer learning，serious overfitting issues can easily arise.

In contrast，the human visual system has the remarkable ability to rapidly form cognitive frameworks for new entities based on a few examples^［5］. This capability enables humans to leverage prior knowledge and experience to quickly learn new tasks without the need for extensive data and time. Inspired by this，methods for few-shot learning to have emerged. The goal of few-shot learning is to design and train models capable of identifying new classes with only a few of annotated examples，akin to the human visual system. Currently，few-shot learning mainly encompasses meta-learning，transfer learning，and metric learning^［6］. Meta-learning involves training a meta-learner across various classification tasks to extract generalizable knowledge. Transfer learning assumes shared knowledge between a source domain and a target domain，pre-training the model on a large amount of source data，and then fine-tuning it on the target domain to adapt to its data distribution. Metric learning aims to learn a discriminate distance metric，ensuring that samples from different classes have a large distance in the embedding space，while the distance between samples from the same class is minimized as much as possible.

Infrared images possess unique characteristics，such as low contrast and low signal-to-noise ratio. Moreover，apart from the target objects，infrared images may also contain various background interference，such as buildings and clouds. Therefore，designing a network model that can focus more on the target objects in infrared images under the constraint of extremely limited samples is crucial for our research. Recent advancements in few-shot learning have seen widespread application of meta-learning and transfer learning. Chen^［2］ and Jin^［4］ have employed meta-learning and improved relation networks techniques for infrared aircraft classification. They leverage the metric learning capability of relation networks and the rapid adaptation ability of meta-learning to enhance the accuracy of infrared airborne target classification. However，these methods often independently extract features from the support set and query samples，which can lead to less discriminative feature representations. Specifically，the meta-learning methods，while capable of rapidly adapting from the support set to the query set，lacks modeling of the semantic correlation between the support and query samples，failing to fully utilize the discriminative information shared across the two sets. Moreover，relation network method emphasizes modeling the relationship between support and query samples，but still extracts features from the two sets independently，unable to fully leverage their inherent semantic association，thereby limiting the robustness and accuracy of recognition. Consequently，these approaches might overlook critical inter-sample relationships，particularly in the context of infrared images where distinguishing between the target and background is more challenging due to lower contrast and resolution. It is noteworthy that infrared images are single-channel images lacking color information and have strong spatial correlation； thus，geometric structures and texture details become crucial features for infrared image recognition. However，existing few-shot learning methods for infrared images have not explicitly focused on these aspects.

In the task of few shot classification，test images in the query set come from novel classes，making it challenging for the extracted features to focus on the target objects^［7］. For instance，in a test image containing multiple objects，the extracted features may only focus on objects from seen classes with a large number of labels in the training set，while ignoring target objects from unseen classes^［8］. Kang et al^［9］. proposed relation embeddings based on self-correlation representation and cross-correlation attention to model features within images and between images，effectively alleviating the aforementioned issue. However，their proposed self-correlation representation module primarily focuses on channel-wise correlations within images，overlooking spatial correlations. However，for infrared images，emphasizing spatial correlations of the image might be more valuable than channel autocorrelation because it can reflect local structures and texture information within the image.

We propose a few-shot infrared aircraft classification method based on cross-correlation networks，which integrates two crucial attention modules and is trained in an end-to-end manner. Firstly，by utilizing the parameter-free self-attention module（SAM），we extract the intra-correlation within each image to acquire feature representations in both spatial and channel dimensions. Subsequently，the cross-attention module（CA） is employed to generate cross-attention between support and query images，thereby enhancing the model's generalization capability. By efficiently fusing features within and between images with minimal parameters，the model reduces computational complexity. In contrast to current models for few-shot infrared aircraft classification，our approach enhances the focus on the infrared imagery’s geometric and textural details. It achieves this by establishing a semantic connection between the feature sets of the support and query samples，thereby improving the model’s ability to accurately identify target objects. The proposed model receives robust support and validation from classification experiments and ablation studies，all achieved without the introduction of excessive parameters.

In this section，we provide a detailed introduction to the Cross-Correlation Network（CCNet） proposed in this paper for few-shot infrared aircraft classification. The overall architecture of CCNet is illustrated in Figure 1，comprising the simple parameter-free attention module and cross attention modules. For each pair of support classes and query samples，appropriate feature representations are obtained through the backbone network. Recent works^［10-14］ have utilized self-similarity as an intermediate feature transformation for deep neural networks，demonstrating its crucial role in learning effective representations of semantic correspondences in network learning. In this study，we introduce the SAM module，which learns the structural layout of images by computing the similarity of internal regions within infrared images. On the other hand，to fully exploit the semantic correlations between support and query features，we design the CA module to compute the cross-correlation between two image representations and learn to generate co-attention from it.

Attention mechanisms allocate different weights to the importance of key information contained within channels，thereby enhancing the network's focus on important information. Common attention mechanisms are typically composed of convolutional layers，pooling layers，activation functions，etc.，introducing additional parameters to the network. To improve network performance without increasing computational complexity，we introduce a simple，parameter-free attention mechanism module called SAM^［15］ into CCNet. The general structure and computation of SAM is shown in Figure 2. SAM adopts an idea based on human visual processing，combining feature and spatial attention mechanisms，and designs a "plug-and-play" three-dimensional weight self-attention mechanism^［16］. SAM calculates weights through an energy function，assigning unique weights to each neuron. Without adding any parameters to the original network，the three-dimensional attention weights can be used to quickly infer feature maps in each layer^［17］. Specifically，information-rich neurons typically exhibit significant activation differences from surrounding neurons，and activated neurons may inhibit the activity of surrounding neurons，known as spatial suppression^［18］.

Building upon this，SAM defines an energy function to measure the difference between each feature and other features，thereby evaluating the importance of each feature. The definition of the energy function is as equation（1）：

where $\hat{t}={\omega }_{t}t+b_t$ and $\widehat{x_i}={\omega }_t{x}_i+b_t$，$t$ and $x_i$ represent the target neuron and other neurons within a single channel of input feature $X\in R^{C\times H\times W}$. Here，i denotes the index of spatial dimension，M=H×W represents the number of neurons in that channel，while ω_t and b_t stand for the weight and bias，respectively. As shown in equation（2），this equation admits an optimal closed-form solution，enabling us to obtain the minimal energy expression：

Where and represent the mean and variance of all neurons in the channel，λ is a hyperparameter used for balancing. Equation（2） implies that as the energy decreases，the difference between neuron t and neighboring neurons becomes greater，making it more critical in image processing. Finally，the input features undergo enhancement processing to implement the attention mechanism through equation（3）：

where E represents the grouping of all $e_t^{\mathrm{*}}$ in both channel and spatial dimensions，and ☉ denotes the calculation of the Hadamard product. Adding a sigmoid function aims to constrain excessively large values in E，thereby ensuring the relative importance of each neuron. Therefore，employing the parameter-free self-attention as a three-dimensional weighting module allows for the assignment of unique weights to each neuron，enhancing the attentional importance of each neuron in the feature maps. This three-dimensional weighting mechanism effectively exploits and highlights the structural features and background information within infrared images，facilitating efficient and reliable identification tasks for infrared targets.

In contrast to previous methods that independently extract features from support sets and query samples，we introduce a cross attention module to compute the cross-correlation between support and query images. The CA module enhances the model's focus on the target object by modeling the semantic relevance between class features and query features，thereby improving the efficiency and accuracy of the subsequent matching process. The cross attention module first takes the self-correlation representations of the support set and query samples（$S_q$ and $S_s$） as inputs，then produces the corresponding cross-correlation representations（$C_q$ and $C_s$）. The architecture of the cross attention module，as shown in Figure 3，primarily comprises three operations： cosine similarity computation，convolutional fusion and joint attention calculation. These operations will be introduced separately below.

In order to reduce computational complexity and obtain a more effective feature representation，we first employ a convolutional layer to decrease the channel dimensions of and from to ，resulting in the outputs and . Subsequently，the cross-correlation representation of and is computed using Equation（4）：

where $x$ denotes a spatial location in the feature map，T signifies matrix transposition，and $R(x_q,x_s)\in R^{H\times W\times H\times W}$ represents the four-dimensional cross-correlation tensor. This computation method not only yields a reliable cross-correlation representation but also reduces the computational load.

In the process of fine-grained classification of infrared aircraft，due to the similarity of some target shapes，the cross-correlation tensor may contain unreliable correlations. Therefore，we adopt a convolution matching process to obtain a more reliable cross-correlation representation. Specifically，we use four-dimensional convolution，which enhances the expression ability of target features and improves the accuracy of classification by analyzing the consistency of adjacent matches in the four-dimensional space and achieving geometric matching on the tensor^［9］. As shown in the blue box in the middle of Figure 2，the convolution matching block consists of three 4D convolution layers. Firstly，the first convolution layer is responsible for increasing the number of channels to provide a richer feature representation in subsequent processing. Next，the second convolution layer generates multiple correlation tensors and aggregates them into a four-dimensional correlation tensor，achieving geometric matching of the tensor. Finally，the third convolution layer is responsible for restoring the number of channels. Between these three convolution layers，batch normalization layers and ReLU layers are inserted to enhance the stability of the network and improve the non-linearity of the activation function. This design allows the convolution matching block to effectively handle high-dimensional data，extract complex features，and provide more reliable input for subsequent generation of cross-attention.

After obtaining the reliable cross-correlation tensor，it is necessary to generate the common attention maps $C_s$ and $C_q$ for the support set and query set. Taking the calculation of the query attention map $C_q$ as an example，the calculation method is shown in Equation（5）：

where $x$ represents the position in the feature map，σ is the temperature factor，lower temperature will lead to lower entropy，making the distribution concentrate on a few positions with higher confidence^［8］，H and W represent the height and width of the feature map，and $R(x_q,x_s)$ is the matching score between positions $x_q$ and $x_s$. Therefore，the attention map $C_q(x_q)$ in Equation（5） can be understood as converting the matching score of position $x_q$ on the query image into the average probability of matching with position $x_s$ on the support image. The calculation method of attention map $C_s$ is similar to $C_q$. These co-attention maps improve the accuracy of infrared target classification by adjusting the attention position according to the images provided in the testing phase through the meta-learning cross-correlation pattern.

Unlike many recent few-shot learning methods that adopt a 'pre-training + fine-tuning ' two-stage training scheme，we propose an end-to-end training strategy for CCNet. This strategy jointly trains the designed modules and the backbone network by combining the metric loss $L_{metric}$ and the global classification loss $L_{label}$. In this process，the calculation of $L_{metric}$ is based on the cosine similarity between the query prototype feature vector and the support prototype feature vector. The calculation method of the metric loss is shown in Equation（6）. This design of the metric loss helps guide the model to map the query embedding to the neighboring position of the prototype embedding of the same category：

where $sim()$ denotes the calculation of cosine similarity，${\stackrel{-}{s}}^{(n)}$ and ${\stackrel{-}{q}}^{(n)}$ represent the prototype vectors of the nth category，N indicates the total number of categories，and τ is the temperature factor.

The global classification loss $L_{label}$ is computed using a fully connected layer followed by a softmax function，in order to classify each query sample among all available training categories. The specific calculation method is shown in Equation（7）：

where $w_c^T$ represents the weights of the fully connected layer，$b_c$ represents the corresponding bias，and $\left|c_{train}\right|$ represents the number of training categories. The overall classification loss is defined as：

where λ is the weight that balances the effects of different losses. By optimizing the overall loss L，the network can be trained end-to-end using the gradient descent algorithm.

All experiments were conducted in a hardware environment based on the Intel i7 13700 processor，NVIDIA GTX4080 graphics card，and DDR4 64G memory，as well as a software environment with the Win10 system and Pytorch deep learning framework. During the training phase，we adopted a training strategy based on N-way K-shot meta-tasks. Specifically，in each training cycle，N categories are randomly selected from the training data，and then K labeled samples are selected from each category to construct the support set. Subsequently，a certain number of samples are randomly selected from the other samples of these N categories，and these samples constitute the query set. Finally，the model predicts the category labels of the query samples. In the validation and testing phases，we still use the aforementioned meta-task form for evaluation. It should be noted that the data in the validation set，test set，and training set all come from different categories，which means that .

In order to validate the effectiveness of the model proposed in this study，we conducted experiments using two datasets： the miniImageNet^［19］ dataset and the self-constructed infrared target dataset miniInfra^{［2，4，20］}. The miniImageNet dataset is a subset of the ImageNet dataset widely used for few-shot learning and has become the benchmark dataset for few-shot learning. The miniInfra dataset is a self-constructed infrared target dataset sourced from publicly available datasets and self-captured infrared images. Partial examples from both datasets are illustrated in Figure 4. To ensure consistency in our experiments，we resized all images across the datasets to 84x84. Moreover，we employed data augmentation strategies such as random cropping and random flipping for both datasets.

In this study，we employ ResNet12^［21］ as the backbone network，which accepts images of spatial dimensions 84×84 as input and generates the basic representation Z. All training and testing are conducted in the form of tasks. For each N-way K-shot classification task，we test 15 query samples per category within each task. For the miniImageNet dataset，2000 meta-tasks were randomly selected from the test set，and for the miniInfra dataset，500 meta-tasks were randomly selected from the test set. Subsequently，we calculate the average classification accuracy and set the confidence intervals to 95%.

The miniImageNet dataset is composed of 100 categories，each containing 600 images，totaling 60，000 visible light images. Following the partitioning standards of previous literature^［22］，we designate 64，16 and 20 categories as the training，validation and test sets，respectively. We conduct 5-way 1-shot and 5-way 5-shot classification tasks.

During the experiments on the miniImageNet dataset，we use the Stochastic Gradient Descent（SGD） optimizer for 80 epochs of training，each epoch consisting of 300 meta-tasks. The initial learning rate is set to 0.1，and a learning rate decay strategy is adopted. At the 60th and 70th epochs，the learning rate is multiplied by a decay factor of 0.05. In the experiments，the temperature factor τ of the metric loss function is set to 0.2，and the hyperparameter λ for balancing the loss weight is set to 0.25.

Table 1 presents the classification results of CCNet on the miniImageNet dataset. We have selected several mainstream methods in the field of few-shot learning in recent years for comparison，including meta-learning，relation networks，adversarial networks，and self-supervised learning. Our method belongs to metric learning methods which can achieve efficient learning for few-shot image classification without any pre-training process and post-processing operations. Although the backbone network of our model is smaller than that of some other methods^{［25-26，30］}，the experimental results on the miniImageNet dataset show that the performance of our model still surpasses these methods. Unlike existing metric-based methods，which independently extract features from the support set and query set，leading to features scattered on non-target objects，CCNet can highlight the target object area and obtain more distinctive features. Specifically，CCNet first focuses on the target object through SAM，which is then combined with the cross-attention module CA，so that it can learn similar features between images and find the differences between fine-grained images more easily. In terms of inference speed，we evaluated 2000 5-way 5-shot tasks on an NVIDIA RTX 4080 GPU，which took approximately 1.5 minutes.

The miniInfra dataset comprises 33 classes of terrestrial targets and 8 classes of aircraft targets. Terrestrial targets encompass various categories such as buildings，bicycles，pedestrians，cars，animals，and boats，with each class containing 100 to 200 infrared images. The 8 classes of aircraft targets include trainer aircraft，civil aviation aircraft，three types of helicopters（Z-8，Z-9，Z-15），and three types of jet aircraft（J-7，J-8，J-11），with each class containing 40 to 80 images. The granularity of aircraft target classification is finer than that of terrestrial targets.

Given the severe shortage of infrared aircraft data and to validate the model's ability to recognize fine-grained targets，we selected 25 types of ground targets as the training set，8 types of ground targets as the validation set，and finally select 8 types of aircraft targets as the test set. The experiments include two standard few shot classification tasks： 5-way 1-shot and 5-way 5-shot. Considering that there are 8 types of aircraft，we added two specific classification tasks： 8-way 1-shot and 8-way 5-shot to test the model's generalization ability for few shot infrared aircraft in a real environment. Consistent with the experimental setup in the miniImageNet dataset，the experiment still uses the SGD optimizer and adopts a learning rate decay strategy. Since the size of the miniInfra dataset is much smaller than the miniImageNet dataset，to prevent overfitting，in the infrared aircraft classification task，we adjusted the number of training epochs to 20 and set the initial learning rate to 0.01.

We compared the experimental results with the existing infrared aircraft classification methods^［2，4］，and the specific results are shown in Table 2. It is worth noting that our training method is end-to-end and does not require any additional data for pre-training. From the results in the table，it can be seen that under the same conditions without using additional data for pre-training，the accuracy of our model in the four classification tasks is significantly better than the existing two classification methods. Especially in the 8-way 1-shot classification task，the model achieved a performance improvement of more than 3% compared to the previous best method，and also achieved a performance improvement of more than 2% in the 8-way 5-shot classification task. It can also be seen from Table 2 that even when compared with the results of the two methods using miniImageNet for pre-training，the accuracy of our method without pre-training is still higher than that of the methods proposed in Ref. ［2］ and ［4］.

To delve deeper into the impact of the core modules in CCNet，we conducted a series of ablation experiments on the miniImageNet and miniInfra datasets. These experiments included scenarios where two core modules were missing simultaneously，as well as cases where only one of the modules was used independently. We constructed a baseline model that only contains the backbone network and does not include any additional modules，to evaluate the effectiveness of the core modules in CCNet. We carried out 5-way 1-shot ablation experiments on the miniImageNet and miniInfra datasets. As can be seen from Figure 5，although the training accuracy of CCNet（blue line） is slightly lower than that of the baseline model（red line），the validation accuracy of CCNet（green line） has significantly improved compared to the validation accuracy of the baseline model（purple line）. This result indicates that compared to the baseline model，CCNet has stronger generalization ability when applying the trained model to unseen new categories.

In this study，further ablation experiments are conducted on the 5-way 1-shot tasks of two datasets to individually validate the effectiveness of the SAM module and the CA module. When only the CA module is used，the basic representation Z_q is taken as input； when only the SAM module is used，its output is directly utilized for classification. The results of the ablation experiments are presented in Figure 6. The experimental results demonstrate that both the SAM and CA modules can significantly improve the accuracy of classification compared to the baseline model. The SAM module can generate reliable representation and provide robust support for the classification tasks，while the CA module can further enhance the representations generated by SAM and improve the cross-correlation between images，thus further improving the classification accuracy.

We also present the results of class activation mapping（CAM） feature visualization using our CCNet，encompassing both visible and infrared images，as illustrated in Figure 7. In the CAM visualizations，the regions with warmer colors（e.g.，red，yellow） represent areas in the input image that contribute more significantly to the network's classification decision. In other words，cooler colors（e.g.，blue） indicate areas that the model does not focus on or that have lower importance. Figure 7（a） depicts an image containing both a cat and a dog； however，since our objective is to identify the cat，the CAM visualization in Figure 7（b） clearly highlights the network's focus on the cat's region. In the infrared image shown in Figure 7（c），despite the presence of a complex background with pedestrians and a dog，the network accurately concentrates on the dog，which is the target for classification. Furthermore，for the infrared image of a commercial aircraft against a cloudy background in Figure 7（e），the CAM result in Figure 7（f） demonstrates that the network effectively attends to and emphasizes the aircraft target region.

In this study，we replaced different attention modules in the proposed CCNet network model to compare the accuracy and parameter scale of the proposed modules with existing attention modules. Firstly，we evaluated the self-attention and cross-attention methods based on feature similarity，which focus on the correlation of the image spatial structure features.

As shown in Table 3，the results of the SAM module and the CA module on the two datasets are superior to other attention methods. Specifically，on the miniImageNet dataset，the performance of SAM in the self-attention module is second only to the SE attention module，while on the miniInfra dataset，SAM achieved the best result among the self-attention methods. It is worth noting that compared with the baseline model，SAM does not introduce additional parameters. Among the cross-attention methods，the performance of the CA module and the CCA module is similar，but the CA module introduces fewer parameters.

In this study，we have proposed a few-shot infrared aircraft classification method based on the cross-correlation network，which can effectively solve the classification problem of infrared aircraft when the number of samples is severely insufficient. In the research process，in order to reduce model parameters and specifically target the structural features of infrared aircraft target images，we introduce a parameter-free self-attention mechanism to analyze the self-correlation within images. Meanwhile，we design a cross-attention mechanism to investigate the self-correlation between images，which effectively enhances the model's capability to extract features from infrared images. The experimental results show that our method significantly outperforms existing methods in aerial target classification accuracy on the infrared dataset，with an improvement of up to 3% in classification accuracy for specific tasks. Furthermore，the tests on the public miniImageNet dataset and the ablation experiments further verify the effectiveness and contributions of the proposed modules. The method proposed in this paper not only has broad application potential in aircraft detection，but also has great application value in civilian fields where data is scarce，such as medical. But at the same time in the research tasks of this paper it only involves the single task of aircraft classification. However，in actual application scenarios of the infrared detection system it involves a series of complex tasks such as target detection target recognition and target tracking. Therefore，how to deploy the few-shot model to these actual application scenarios and maintain good performance under multiple tasks will be the focus of the next stage of work.