## 2 Materials and Methods
### Structure of CenterNet  
The first step of the multi-pedestrian tracking algorithm is to detect pedestrians, so the performance of the detection network directly affects the results of the tracking model. Since the anchor mechanism was proposed, most high-performance detection algorithms are based on anchoring. Although this is effective, the anchor-based detection network is very sensitive to the scale and aspect ratio hyperparameters of the anchor, which requires a lot of time to adjust., In order to ensure a high recall rate, a large number of anchors is required, which will lead to unbalanced positive and negative samples. In recent years, some studies have questioned the need for anchors and proposed a detection network that does not depend on anchors, CenterNet, which frees the network from the dependence on anchors.  
Given that the anchor-based detection network has the problems of a large number of parameters and sensitivity to hyperparameters that directly affect the accuracy and speed of the tracking model, this paper adopts CenterNet, an anchor-free single-stage object detection network that transforms the object detection problem into an object centroid estimation problem, avoiding the introduction of a large number of parameters by pre-setting anchor frames. The local peak of the heatmap corresponds to the center point of the pedestrian being tracked, and the width and height of the pedestrian detection boxes are directly regressed according to the coordinates of the object's center point, which can accurately locate the pedestrian while reducing the number of parameters, providing a good basis for the subsequent tracking module to accurately match the tracking.  
In the process of pedestrian detection with CenterNet, when the \(S_{t}\) frame passes through the detection network, three branches with different dimensions (heatmap, box_size, offset) are obtained, each of which outputs the location of all detected pedestrian centroids: \(\mathbf{heatmap}_{t}=\{\mathbf{c}_{t}^{1},\mathbf{c}_{t}^{2}\dots\mathbf{c}_{t}^{N}\}\); width and height of all pedestrian detection boxes, \(\mathbf{boxsize}_{t}=\{\mathbf{z}_{t}^{1},\mathbf{z}_{t}^{2}\dots\mathbf{z}_{t}^{N}\}\); the offset is used to refine the pedestrian centroids of the heatmap and improve the accuracy of the detection network. The three branches are shown in Figure 1.  
During pedestrian tracking, due to camera angle and other factors, the size of pedestrians on the surveillance video screen varies widely, and the problem of mutual occlusion in tracking often occurs. Usually, detection convolutional neural networks tend to design the network very deep in order to extract more differentiated high-level semantic information about pedestrians, and as the convolutional neural network deepens, the perceptual field becomes larger and larger, which is very unfavorable to detecting small-sized pedestrians. For example, when a pedestrian turns his back to the camera and walks further and further away, the size presented on the screen becomes smaller and smaller; it will be a misseddetection, which directly leads to the interruption of the trajectory in the subsequent tracking process; in dense scenes where pedestrians block each other, the blocked pedestrians have often missed detection, which leads to ID switches in the subsequent tracking process when two pedestrians walk in opposite directions to produce blocking. It can be seen that the performance of the front-end detection network directly affects the subsequent tracking results. Therefore, we first improve the detection ability and localization accuracy of small-sized pedestrians by introducing a feature pyramid structure to the CenterNet network to fuse deep and shallow feature maps and then improve the accuracy of mutually occluded pedestrians by increasing the resolution of feature maps to reduce the probability of trajectory interruption and ID switches in the subsequent tracking process.