## 2 Materials and Methods
### Multi-Feature Fusion
\(h_{1},w_{1}\) and \(h_{2},w_{2}\) are the height and width of the object and the object search region. For each layer, we extract the first 30 feature channels in descending order in terms of ratio to train the filter and obtain the convolutional object features per layer, as illustrated in Figure 4b. This paper obtains 3 new features by summing the first 30 features per layer, respectively. Then, a rich information feature can be obtained by summing the features  
Figure 4: Feature visualization of small objects. (**a**) 256 channels’ features. (**b**) first 30 features. Figure 3: Feature visualization of various layers from the VGG-19 Networks. (**a**) Input image. (**b**) Conv2-3 layer features. (**c**) Conv3-4 layer features. (**d**) Conv4-4 layer features. (**e**) Conv5-4 layer features. (**f**) fused image features. of the three layers by utilizing different weights. The fused feature \(Fea_{new}\) is depicted in Figure 3f, and is written as:  
\[Fea_{new}=\xi_{1}Fea_{conv2-3}+\xi_{2}Fea_{conv3-4}+\xi_{3}Fea_{conv4-4} \tag{4}\]  
where \(Fea_{conv2-3}\), \(Fea_{conv3-4}\), \(Fea_{conv4-4}\) denote the depth features extracted by theconv2-3 layer, conv3-4 layer, conv4-4 layer, respectively, and \(\xi_{i}(i=1,2,3)\) is the weighting parameter. This paper builds two independent appearance models by training the correlation filters separately using the fused features \(F_{CNN}\) and HOG features \(F_{HOG}\). The decision power of the response is calculated using Average Peak Correlation Energy (_APCE_). We use the difference between the _APCE_ values of two adjacent frames to decide the validity of the features. The average peak correlation energy (_APCE_) is calculated as:  
\[APCE=\frac{|R_{max}-R_{min}|^{2}}{mean\bigg{(}\sum_{m,n}\bigg{(}R_{(i,j)}-R_{ min}\bigg{)}^{2}\bigg{)}} \tag{5}\]  
where \(R_{max}\) and \(R_{min}\) denote the maximum and minimum values of the feature response, respectively, and \(R(i,j)\) denotes the response value at coordinate \((i,j)\). The decision-making power of different frames is represented by \(\phi\):  
\[\left\{ \begin{array}{l}\phi=\frac{1}{|APC_{t}-APC_{t-1}+\eta|}\ \,\ \ \ \ \ \ if\ APC_{t}= APC_{t-1}\\ \phi=\frac{1}{|APC_{t}-APC_{t-1}|}\ \,\ \ \ if\ APC_{t}\
eq APC_{t-1}\end{array} \right. \tag{6}\]  
where \(APCE_{t}\) and \(APCE_{t-1}\) are the _APCE_ values of the feature response at frame \(t\) and \(t-1\), respectively. The larger the \(\phi\) value, the smaller the regional fluctuation of the adjacent feature responses and the stronger the validity of the corresponding feature. \(\eta\) is set to 0.01 to prevent the denominator from being zero. The weights of the \(F_{HOG}\) and \(F_{CNN}\) are assigned according to the decision-making power. Thus, the weights of \(F_{HOG}\) can be expressed as:  
\[W_{HOG}=\frac{\phi_{F_{HOG}}}{\phi_{F_{HOG}}+\phi_{F_{CNN}}} \tag{7}\]  
where \(\phi_{F_{HOG}}\) and \(\phi_{F_{CNN}}\) denote the decision power values of the \(F_{HOG}\) and \(F_{CNN}\) features, respectively. Thus, the final features response is:  
\[f(z)=W_{HOG}\times f_{HOG}(z)+(1-W_{HOG})\times f_{CNN}(z) \tag{8}\]  
where \(f_{HOG}\) and \(f_{CNN}\) are the feature \(f_{HOG}\) and \(f_{CNN}\) response, respectively.