## 4 Object-Aware Adaptive Convolution Kernel Attention Mechanism
### Object-Aware Convolution Kernel Attention Mechanism
\begin{table}
\begin{tabular}{c l} \hline \hline Input & The First Frame \(I\) of the Video, the Position \(B\) of the Object in the Image. \\ \hline \multirow{3}{*}{Step 1} & Convolution kernel weight \(w\). \\ \cline{2-3}  & Based on the object position \(B\), select the object image \(Z\) from the image \(I\). \\ \cline{2-3}  & Take the location \(B\) as the center, select the image \(X\) in the search area \\ \cline{2-3}  & according to the requirements of the candidate area network. \\ \cline{2-3}  & Get the convolution feature \(\varphi(Z)\) of the object image \(Z\) and the convolution feature \(\varphi(X)\) of the image \(X\) in the search area. \\ \cline{2-3}  & The number of channels of \(\varphi(Z)\) is equal to the number of channels of \(\varphi(X)\), denoted as \(C\). \\ \cline{2-3}  & _for \(i=1\) to \(C\)_ \\ \cline{2-3}  & Select the convolution feature \(\varphi_{i}(Z)\) of the \(i\)-th channel of \(\varphi(Z)\) \\ \cline{2-3} Step 3 & Select the convolution feature \(\varphi_{i}(X)\) of the \(i\)-th channel of \(\varphi(X)\) \\ \cline{2-3}  & \(S_{i}=\varphi_{i}(Z)*\varphi_{i}(X)\) \\ \cline{2-3}  & \(w_{i}=psr(S_{i})\), where \(psr()\) is defined by (2) \\ \cline{2-3}  & _end_ \\ \cline{2-3} Step 4 & \(w=\{w_{i}\ |\ i\in\)[1,\(C\)] \\ \cline{2-3}  & Adjust the range of values in the set \(w\) to [0,4] \\ \cline{2-3} Step 5 & Return the weight of the convolution kernel \(w\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The proposed object-aware convolution kernel attention mechanism framework. where \(\varphi_{i}(Z)\) and \(\varphi_{i}(X)\) represent the \(i\)-th convolution kernel feature of the object image and the search area image, respectively. \(\varphi_{i}(Z)*\varphi_{i}(X)\) denotes the correlation operation of the \(i\)-th convolution kernel feature, which is the response map of the \(i\)-th convolution kernel. Therefore, the final response map after weighting the different convolution kernel response maps is expressed as:  
\[f_{i}(Z,X)=\sum_{i=1}^{N}w_{i}\times(\varphi_{i}(Z)*\varphi_{i}(X)) \tag{5}\]  
where \(w_{i}\) denotes the weight of each convolution kernel response map obtained using the aforementioned attention module and \(\times\) represents the element-wise multiplication of the weight and the corresponding response map. Since in the Siamese network, the correlation operation of the convolution feature is essentially a convolution operation, each element of the response map \(f_{i}(Z,X)\) in the aforementioned formula is expressed as \(f_{i}(Z,X)_{u,v}\). Now,  
\[f_{i}(Z,X)_{u,v}=w_{i}\times\sum_{j,k=(u,v)}^{(u+M,v+M)}\varphi_{i}(Z)_{j,k} \times\varphi_{i}(X)_{j,k} \tag{6}\]  
where \((u,v)\) represents the coordinate of an element in the response map, \((j,k)\) denotes the coordinate of an element in the convolution feature, \(M\) denotes the size of the object template convolution feature, \(\varphi_{i}(Z)_{j,k}\) denotes the element in the object convolution feature, \(\varphi_{i}(X)_{j,k}\) denotes the element in the convolution feature of the search area, and \(\times\) represents multiplication by the element value. Therefore, the aforementioned expression is transformed as follows:  
\[f_{i}(Z,X)_{u,v}=\sum_{j,k=(u,v)}^{(u+M,v+M)}\left(w_{i}\times\varphi_{i}(Z)_{ j,k}\right)\times\varphi_{i}(X)_{j,k} \tag{7}\]  
or  
\[f_{i}(Z,X)_{u,v}=\sum_{j,k=(u,v)}^{(u+M,v+M)}\varphi_{i}(Z)_{j,k}\times\left(w _{i}\times\varphi_{i}(X)_{j,k}\right) \tag{8}\]  
It is evident that (7) is equivalent to the following expression:  
\[f_{i}(Z,X)=\sum_{i=1}^{N}(w_{i}\times\varphi_{i}(Z))*\varphi_{i}(X) \tag{9}\]  
or  
\[f_{i}(Z,X)=\sum_{i=1}^{N}\varphi_{i}(Z)*(w_{i}\times\varphi_{i}(X)) \tag{10}\]  
The aforementioned derivation shows that weighting the response maps of different convolution kernels is equivalent to weighting the features of the object template or the features of the search area. For convenience, we use the method of weighting the object template features to achieve the weighting of the convolution kernel response map.