## 3 Method
### Face Appearance Model  
When tracking a person, the face of the target can be observed in many situations, allowing face data to be used for identification. The face data is advantageous for identification compared to the other recognizable information of the body. For example, it is less likely to meet people with similar faces than to meet people with similar fashions. In addition, features are less likely to be mixed because the possibility of occlusion is relatively less than when using the whole body. We propose an appearance model that uses face features to compensate for the problems that arise when using only body features. Figure 4 depicts our proposed face appearance model. Figure 4: Schematic representation of the proposed face appearance model. Our association method aims to associate candidates that are not yet associated after executing that of the baseline tracker. The unassociated detection set is defined as \(D^{missed}=\{d_{1},d_{2},\ldots,d_{missedDets}\}\) and has the detection position \(d\) as an element. The unassociated tracklet set is defined as \(T^{missed}=\{H_{1},H_{2},\ldots,H_{missedTks}\}\) and has a tracklet \(H\) as an element. Since the tracklet has its past trajectories, it is defined as \(H=\left\{h_{1},h_{2},\ldots,h_{historyNum}\right\}\) where \(h\) is the past position as an element. For the extraction of face features, the following definitions are used to detect and embed the candidates' faces. At this time, the embedding is performed only for those whose detected face confidence are greater than or equal to \(\tau^{faceDetect}\) as follows:  
\[b^{face},c^{face}\gets FaceDetector(Crop(x,d)) \tag{9}\]  
\[v\gets FaceEmbeddingModule(Crop(x,b^{face}))\quad\text{if}\quad c^{face} \geq\tau^{faceDetect} \tag{10}\]  
Consequently, the feature vector \(v_{d}\) is obtained from the detection position \(d\), and the feature vector set \(V_{H}\) is obtained from the tracklet \(H\). \(V_{H}\) is defined as \(V_{H}=\left\{v_{h_{p}}|p=1,2,\ldots,featureNum\right\}\) which is a set of feature vectors \(v_{h_{p}}\) from the past position \(h\) of tracklet \(H\). \(featureNum\) denotes the number of face features derived from \(H\), and satisfies \(featureNum\leq historyNum\) since a face may not be detected at a past position. To make the association, the face appearance model needs to calculate the similarity between one detect and one tracklet--that is, the distance between \(v_{d}\) and \(V_{H}\). We propose three distance measurements to consider various environments when calculating the distance. The first distance measurement uses the minimum distance between \(v_{d}\) and \(V_{H}\) as follows:  
\[l_{min}=\underset{p}{min}(\left\|v_{d}-v_{p_{h}}\right\|_{2}). \tag{11}\]  
The second distance measurement uses the average distance between \(v_{d}\) and \(V_{H}\) as follows:  
\[l_{mean}=\frac{1}{featureNum}\sum_{h=1}^{featureNum}(\left\|v_{d}-v_{p_{h}} \right\|_{2}). \tag{12}\]  
The third distance measurement uses the distance between \(v_{d}\) and the most recent vector \(v_{pfeatureNum}\) of \(V_{H}\) as follows:  
\[l_{last}=\left\|v_{d}-v_{p_{featureNum}}\right\|_{2}. \tag{13}\]  
The distance between the detect and the tracklet is measured by selecting the appropriate measurement from the three proposed distance measurements. If the distance is less than the threshold \(\tau^{face}\), it is determined to be the same person and the association can be proceeded. The detailed association procedure is defined with the following Algorithm 1.