## 3 Methods
### The Process of the ADMTCF
#### 3.1.4 The Mechanism of Multi-Template with Adaptive Size Change for the Process of Tracking  
The mechanism of multi-template with adaptive size change for the process of tracking is the comprehensive use of the above two key points. ADMTCF selects the template image most similar to the current target as the tracking feature in each image frame to track. After selecting the most similar template image, the adaptive size of the template is dynamically changed to conform to the actual scale of the object. After dynamically adjusting the template's size, the ADMTCF calculates the response. We follow [PERSON] et al. to calculate the response value of the correlation filter [36]. The response is calculated as Equations (4)-(7) [36]. The \(z_{1}\) and \(z_{2}\) are the input images. The \(w\) is the parameter matrix of the regression model. The \(f(z)\) is the response value. The position with the highest response value in the image is the predicted position of the object. ADMTCF selects the template which is the most similar to the object and then performs adaptive size changes to improve the tracking accuracy. \[z_{1}=\varphi(x_{1}),z_{2}=\varphi(x_{2}) \tag{4}\]  
\[w=\sum a_{i}\varphi(x_{i}),\ a=[a_{1},a_{2},a_{3}\dots,a_{n}]^{T} \tag{5}\]  
\[\varphi^{T}(x)\varphi(x\prime){=}\ k(x,x\prime) \tag{6}\]  
\[f(z)=w^{T}z=\sum_{j=1}^{n}a_{i}k(z,x_{i}) \tag{7}\]  
We go through all steps of ADMTCF and describe as below. We take different strategies depending on the total number of templates. We calculate the similarity according to Equations (1)-(3). If the total number of templates is 0, then we make three settings. Firstly, we set the No. 1 template as the target in the first frame. Secondly, we set the current template as the No. 1 template. Thirdly, the ADMTCF uses the No. 1 template to calculate the response according to Equations (4)-(7) and obtains the next frame of the image. If the total number of templates is equal to 1, we calculate the similarity by using the No. 1 template and the current adaptive adjustment template, respectively. If the current adaptive adjustment template changes size to obtain greater similarity than the No. 1 template's similarity and the similarity difference is greater than the threshold, we make three operations. Firstly, we add a new No. 1 template. Secondly, we set the image of the original No. 1 template to the No. 2 template. Thirdly, we set the current template as the No. 1 template to calculate the response according to Equations (4)-(7). If not, the algorithm will use the No. 1 template to calculate the response according to Equations (4)-(7) and fetch the next frame of the image. If the total number of templates is equal to 2, we make three operations. Firstly, we use No. 1-2 templates to calculate the similarity in sequence and reorder the templates. Secondly, we set the template with the largest similarity as the No. 1 template. Thirdly, we set the current adaptive adjustment template as the No. 1 template. If the current adaptive adjustment template changes size to obtain a greater similarity than the No. 1 template's similarity and the similarity difference is greater than the threshold, we make three operations. Firstly, we add a new No. 1 template. Secondly, we set the image of the original No. 1 template to the No. 2 template, set the image of the original No. 2 template to the No. 3 template. Thirdly, we set the current template as No. 1 template to calculate the response according to Equations (4)-(7). If not, the algorithm will use the No. 1 template to calculate the response according to Equations (4)-(7) and fetch the next frame of the image. If the total number of templates is equal to 3, we make three operations. Firstly, we use No. 1-3 templates to calculate the similarity in sequence and reorder the templates. Secondly, we set the template with the largest similarity as the No. 1 template. Thirdly, we set the current adaptive adjustment template as the No. 1 template.