## 1 Introduction
By integrating feature enhancement and feature fusion into the conventional structure of the SSD [20], a single shot object detection method named FFESSD [27] achieves a better performance in fuzzy target detection. However, for existing small objects that are dense and overlapping in the scene, the detection performance of both algorithms is not ideal. Because of its powerful modeling ability, the method based on CNN [14] has achieved promising results in general target detection. However, the existing CNN [14] based methods cannot be directly applied to infrared small targets because the weak texture and the low contrast will lead to loss of the target in the deep layer. Since U-Net [29] can realize multi-scale feature fusion by connecting the down-sampled feature maps with the up-sampled feature maps of the same scale for enhancing the descriptive power of features, many improved algorithms based on U-Net [29] have been proposed for small infrared target detection [30; 31; 32]. A lightweight convolution neural network, called TBC-Net [30], is proposed for infrared small target detection. TBC-Net consists of a target extraction module (TEM) and a semantic constraint module (SCM), which are used to extract small targets from infrared images and to classify the extracted target images during the training, respectively. By integrating the global and the local dilated residual convolution blocks into the U-Net [29], the residual learning CNN model DRU-Net (dilated residual U-Net) [31] is initially employed to predict the residual image (i.e., background, clutter, and noise) rather than clean images. Once the residual image is estimated, the targets are obtained by subtracting the residual image from the input image. However, the performance of DRU-Net [31] suffers from multiple targets flocking together or overlapping each other. To handle this problem of pooling layers could lead to the loss of targets in deep layers, a dense nested attention network (DNA-Net) [32] is designed to maintain the infrared small targets in deep layers with the repeated fusion and enhancement of high-level and low-level features. Although many density estimation schemes [33; 34] have been proposed to solve the crowd counting problem, these counting-by-density-estimation approaches focus on measuring the number of people per unit area on the ground but compromises accurate detection of a single individual. Our work is inspired by the density learning that is exploited for crowd counting. However, the density map corresponding to the training sample is calculated by summing all the 2D Gaussian kernels centered at every body's location. Different from them, we use a size-adaptive Gaussian kernel instead of the sum of multiple Gaussian kernels to generate the ground truth of each bird. The advantage of this is that it not only makes use of the brightness distribution characteristics of infrared bird target similar to Gaussian kernel but also facilitates the extraction of individual birds from crowded populations. To solve the problem of pooling layers in the network could lead to the loss of targets in deep layers so we propose a model that incorporates the max-no-pooling convolution blocks into the U-Net. The introduction of the max-no-pooling convolution blocks can enhance the salience of bird targets. Furthermore, \(1\times 1\) convolution is employed to improve calculation speed. In summary, the main contributions of this paper are listed as follows. 1. We propose a two-stage flying bird detection method in infrared video, which consists of the pre-processing and deep learning method. The former is used for background separation, and the latter is used for re-detection of overlapping targets;
2. We propose a method for generating ground truth of bird targets, which can be automatically generated by using a size-adaptive Gaussian kernel;
3. We propose a novel Gaussian heatmap perception network (GHPNet) to predict individual birds in highly crowded and occluded scenes;
4.