## 2 Proposed MOT Method
### Similarity Distance Measurement  
Similarity distance is a metric to measure whether the trajectory and the detection belong to the same object. The smaller the metric is, the more likely they are the same, and vice versa. In this paper, we establish the similarity distance measurement equation from two aspects. On one hand, in terms of appearance features, although we can get discriminative pedestrian appearance features through our proposed network, it is still difficult for us to correlate and match two identical objects in different frames which are far apart from each other. Therefore, we set up a feature buffer space for each trajectory to store the appearance features of the detections that it has been associated with. When measuring the similarity distance between a trajectory and detection, our method loads all of the trajectory appearance features from its buffer, and calculates the distance between each feature and the detection features. Then, it uses the minimum of the above distance as the similarity distance. In this paper, the appearance features extracted by our CNN has been already normalized, that is, their L2 norm is equal to 1. Then we use the square of Euclidean distance as the similarity distance measurement of appearance features, and define the following equation:  
\[A_{app}(k_{t}^{i},d_{t}^{j})=\min\biggl{(}(feat_{t}^{i}-feat_{t}^{j})(feat_{t }^{i}-feat_{t}^{j})^{T}\biggl{|}feat_{t}^{i}\in G^{i}\biggr{)} \tag{3}\]  
where \(feat_{t}^{i}\) represents the appearance feature of i-th trajectory and \(feat_{t}^{j}\) represents the appearance feature of i-th detection. \(G^{i}\) represents the features buffer of i-th trajectory. In terms of motion characteristics, we introduce the Kalman filter prediction method to assist our algorithm since it is suitable for linear systems, in which the object states obey Gaussian distribution. Meanwhile, many pedestrians move in a linear mode in real scenes, enabling the Kalman filter to predict the uncertain object state more easily. Specifically, we define the measurement space of a trajectory state or a detection as \((x,y,w,h,v_{x},v_{y},v_{w},v_{h})\), respectively representing the horizontal and vertical coordinates, width and height, as well as the corresponding velocities of the center point of the trajectory bounding box. In our paper, we use the square of Mahalanobis distance as the measurement standard of motion feature similarity distance, and define the following equation:  
\[A_{mot}(k_{t}^{i},d_{t}^{j})=(X_{t}^{i}-Y_{t}^{j})S^{i-1}(X_{t}^{i}-Y_{t}^{j}) \tag{4}\]  
Figure 4: Region segmentation. The size of the Global part is \(128\times 64\). The size of the sub-blocks of Local Cross and Local Horizontal are \(64\times 32\) and \(32\times 64\), respectively. where \(X_{t}^{i}\) and \(S^{i-1}\) represent the projection of i-th trajectory state in the measurement space and the covariance matrix of i-th trajectory state in frame t, respectively. \(Y_{t}^{j}\) represents the measurement space of j-th detection in frame t. In the initial measurement space of a detection, the first four element values are obtained from the prior detector, while the last four element values are initialized to zero. When a track is not associated with any detection, we use the constant velocity linear motion model of the Kalman filter to predict the measurement space of the track directly without correction. Otherwise, when a track is associated with any detection, we update the measurement space of the track according to the detection. Note that when the track state changes from Confirmed to other states, due to occlusion or other reasons, the uncertainty of the track during this period is increased according to the characteristic of the Kalman filter, which may result in a smaller distance between the track and detections, thus we introduce the threshold function as follows.