# Research on the Correlation Filter Tracking Model Based on the Deep-Prunned Feature Network
## 3 Methods
### Optimal Determination of Global Tracking Pruning Rate Based on Tracking Response Contribution  
As shown in Figure 3, the deep feature network is initially pruned to obtain a pre-pruned feature network with \(PPCKN_{CL}\) convolutional kernels and corresponding \(PPCKN_{CL}\) feature maps \(F_{CL,l}\) (or feature channels), where \(l=1,2,\ldots,PPCKN_{CL}\). The correlation tracking filter (which has \(PPCKN_{CL}\) filter channels) is applied to \(PPCKN_{CL}\) feature maps \(F_{CL,l}\) and outputs \(PPCKN_{CL}\) responses \(g_{l}\) of size \(M\times N\). The \(PPCKN_{CL}\) responses are linearly overlapped to form the total response of the tracking model and the total response is approximated as a two-dimensional gaussian response [3]. The peak of the total response is the predicted position of the tracked target. Since the statistical distribution of each filter channel response and its peak point are different, the contribution of different filter channel responses to the total response of the tracked target is not the same. It is assumed that \((x,y)\) denotes the peak point of the total 2-D gaussian response, i.e., the mean of the 2-D gaussian response, and \(\sigma_{\rm x}\) and \(\sigma_{\rm y}\) are the variances of the 2-D gaussian response. According to the properties of the 2-D gaussian distribution function, about 95.5% of the data are concentrated in a rectangular box centered at \((x,y)\) with a length of \(2\times 2.58\sigma_{\rm x}\), and a width of \(2\times 2.58\sigma_{\rm y}\)[3; 31]. Since the total output response is a superposition of the responses of all single filter channels, the larger the proportion of single filter channel responses that fall within this rectangle, the greater the contribution of the filter channel to the total response is considered. The contribution \(CR^{l}\) of a single filter channel \(g_{l}\) can be obtained from Equations (5)-(7) [3]:  
\[CR^{l}=\frac{rectangle_{box}}{Whole_{size}}^{l} \tag{5}\]  
\[rectangle_{box}}^{l}=\sum_{i}\sum_{j}{\cal F}^{-1}(g_{l}(i,j))\]  
\[ie({\rm x}-2.58\sigma_{\rm x},x+2.58\sigma_{\rm x}),je(y-2.58\sigma_{\rm y},y+2.58\sigma_{\rm y})\]  
\[Whole_{size}}^{l}=\sum_{i=1}^{M}\sum_{j=1}^{N}{\cal F}^{-1}(g_{l}(i,j)) \tag{7}\]  
where \({\rm M}\geq 2\sigma_{\rm x}\), \({\rm N}\geq 2\sigma_{\rm y}\); \({\cal F}^{-1}\) is the inverse Fourier transform; \(rectangle_{box}}^{l}\) is the sum of the sample values of the output response of the filter channel \(g_{l}\) that fall into the rectangular box, and \(Whole_{size}}^{l}\) is the sum of all the sample values of the output response of the filter channel \(g_{l}\), \(l=1,2,\ldots,\ldots,\)\(PPCKN_{CL}\). Figure 3: Optimal determination of global tracking pruning rate based on tracking response contribution. (# indicates the \(ith\) picture in the video sequence). Based on \(CR^{l}\), the \(PPCKN_{CL}\) filter channels of the filter are sorted according to \(CR^{l}\). For the sorted filter channels, a contribution ratio threshold (CRTH) is defined under the precondition that the tracking accuracy is satisfied. When \(CR^{l}\geq CRTH\), the corresponding filter channel is retained (the number of retained filter channels is denoted by \(RFCN_{CL}\) (remain feature channel number)). When \(CR^{l}<CRTH\), the corresponding filter channel is removed (the number of removed filter channels is \(PPCKN_{CL}-RFCN_{CL}\)) to maximize the tracking speed. Since the number of channels in the filter is equal to the number of channels in the last layer of the feature network, this also means that the number of channels that should be retained in the last layer of the feature network is represented by \(RFCN_{CL}\), while the number of channels that should be removed is \(PPCKN_{CL}-RFCN_{CL}\).