# Research on the Correlation Filter Tracking Model Based on the Deep-Prunned Feature Network
## 3 Methods
### Secondary Pruning of Feature Extraction Network Based on Alternative Convolutional Kernels  
The pre-pruned feature network obtained by pre-pruning is used as a feature extraction network for object tracking, which can achieve a certain degree of improvement in tracking speed while ensuring that the loss of accuracy does not affect the overall performance of the model. However, for the tracking system, there is a higher requirement for tracking speed enhancement. To accommodate this requirement, we consider a secondary pruning of the pre-pruned feature network before the start of the tracking process to further improve the tracking speed. To further improve the tracking speed, we performed a secondary pruning on the feature network obtained from the pre-pruning in Section 3.1, based on the global tracking pruning rate (\(GTPR\)). If the pruning strategy of retaining \(KN_{i}=PPCKN_{i}\times GTPR\) important convolutional kernels and removing \(PPCKN_{i}\times 1-GTPR\) non-important convolutional kernels in each layer are directly adopted, the number of convolutional kernels in each layer and the complexity of the feature network can be reduced and improve the tracking speed. However, it is also very likely that removing too many convolutional kernels causes too significant a loss of accuracy in the feature network, which makes it difficult to accurately characterize the target and significantly degrades the tracking accuracy. To compensate for this deficiency, we introduce an alternative convolutional kernel that integrates the joint action of \(PPCKN_{i}\times 1-GTPR\) unimportant convolutional kernels to each layer (except for the first layer, where the unimportant feature maps corresponding to the unimportant convolutional kernels in the first layer are used as the initial values for the iterative solutions of the alternative convolutional kernels in the subsequent layers) of the pre-pruned feature network, while retaining \(KN_{i}=PPCKN_{i}\times GTPR\) important convolutional kernels. The alternative convolutional kernel is used to compensate for the loss of accuracy of the feature network caused by the removal of the \(PPCKN_{i}\times(1-GTPR)\) unimportant convolutional kernels, which improves the feature network's ability to characterize the tracked target, as shown in Figure 4. The iterative solution process for the alternative convolutional kernel in each layer is as follows. The pre-pruned feature network is applied to the first frame of the tracking video sequence, as shown in Figure 5. \(kernel_{Ai}\) is used to denote the operator of the combined action of \(PPCKN_{i}-KN_{i}\) unimportant convolutional kernels (\(kernel_{i,(KN_{i}+1)},kernel_{i,(KN_{i}+2)},\dots,kernel_{i,PPCKN_{i}}\)) in the _ith_ convolutional layer, and it is called the alternative convolutional kernel of these \(PPCKN_{i}-KN_{i}\) unimportant convolutional kernels. Let the feature maps corresponding to these \(PPCKN_{i}-KN_{i}\) unimportant convolutional kernels be \(F_{i,KN_{i}+1},F_{i,KN_{i}+2},\dots,F_{i,PPCKN_{i}}\), then the global pooling \(F_{GAP}^{i}\) corresponding to these \(PPCKN_{i}-KN_{i}\) unimportant feature maps can be obtained from Equation (9). \[F_{GAP}^{i}=GAP\left(\sum F_{i,j}\right) \tag{9}\] \[j\in\left(KN_{i}+1,KN_{i}+2,\dots,PPCKN_{i}\right)\]  
Let the feature map corresponding to the alternative kernel \(kernel_{Ai}\) of the _ith_ convolutional layer (\(i\
eq 1\)) be \(F_{Ai}\), then:  
\[\sum_{j=1}^{PPCKN_{i-1}}Kernel_{Ai}\star F_{(i-1),j}=F_{Ai} \tag{10}\]  
where \"\(\star\)\" denotes the convolution operation. Let \(F_{Ai}=F_{GAP}^{i}\), then the alternative convolutional kernel \(kernel_{Ai}\) is initialized as:  
Figure 4: Definition and initialization of alternative convolutional kernels, and secondary pruning of deep feature extraction network. (# indicates the _ith_ picture in the video sequence). Figure 5: Initialization of the alternative kernels by applying the pre-pruned feature network to the first frame of the tracking video sequence. (# indicates the _ith_ picture in the video sequence). \[