## 2 The Proposed Method
### Gaussian Heat Map Sample Production  
As can be seen from Figure 3, in the infrared video sequence image, the bird target presents the phenomenon that the central area is the brightest and the brightness gradually becomes darker as it expands outward, and this case is just consistent with the distribution of the Gaussian model. Inspired by this observation, aiming at the problem that it is difficult to distinguish individual birds in the gathering and the overlapping regions; the Gaussian heat map sample annotations are automatically generated for the manually selected bird targets. By using a size-adaptive two-dimensional Gaussian kernel, the ground truth Gaussian heat map can be quickly and automatically generated for multiple targets in a  
Figure 2: The original image and the target detection results, (**a**) original image; (**b**) target detection results of TVF algorithm; (**c**) enlarged target detection results of TVF algorithm.  
given candidate target area. For m-th candidate target image block C\({}_{\text{m}}\) screened by the TVF algorithm, all birds existing in the scene are firstly artificially labeled with a set of Z\({}_{\text{m}}\) rectangle boxes R\({}_{\text{m}}^{\text{obj}}=\{\text{R}_{\text{m}}^{\text{Z}}\}_{1\leq z\leq_{ \text{Z}_{\text{m}}}}\), which corresponding center point set and maximum side length set are \(\text{P}_{\text{m}}^{\text{obj}}=\{\text{P}_{\text{m}}^{\text{Z}}\}_{1\leq z \leq_{\text{Z}_{\text{m}}}}\) and \(\text{L}_{\text{m}}^{\text{obj}}=\{\text{L}_{\text{m}}^{\text{z}}\}_{1\leq z \leq_{\text{Z}_{\text{m}}}}\), respectively. The generation process of the ground truth of the Gaussian heat map is as follows: given a candidate target dense region C\({}_{\text{m}}\) screened by the TVF algorithm, after manually selecting bounding boxes for all targets, the Gaussian heat map D\({}_{\text{m}}^{\text{gt}}\) of image patch C\({}_{\text{m}}\) is automatically realized by assigning the corresponding Gaussian value within each target box and assigning zero outside all the bounding boxes. In other words, for any pixel p in the image block C\({}_{\text{m}}\), the bounding box where it is located is judged. If it belongs to a certain box R\({}_{\text{m}}^{\text{z}}\), the true value of its Gaussian heat map is calculated using the Gaussian kernel function \(\mathbb{N}(\text{p}-\mu,\ \sigma)\) by its distance from the center point P\({}_{\text{m}}^{\text{z}}\) and side length L\({}_{\text{m}}^{\text{z}}\) as  
\[\text{D}_{\text{m}}^{\text{gt}}(\text{p})=\mathbb{N}(\text{p}-\mu,\ \sigma)= \mathbb{N}\left(\text{p}-\text{P}_{\text{m}}^{\text{z}},\ \frac{\text{L}_{\text{m}}^{\text{z}}}{2}\right) \tag{5}\]  
Here, \(\mathbb{N}(\text{p}-\mu,\ \sigma)\) denotes the Gaussian kernel function, \(\mu\) and \(\sigma\) represent the mean and the standard deviation of the normal distribution.  
Figure 3 shows the process of generating Gaussian heat maps of the targets in the image of the bird gathering or overlapping region. It can be seen from Figure 3 that the edges of targets in the original image are blurred and the boundaries between them are unclear, resulting in a partial overlap between the manually selected rectangular boxes. However, after Gaussian heat map processing, each target is not only complete but also clearly distinguishable from each other, which proves the effectiveness of the proposed Gaussian heat map sample labeling method to a certain extent.