# Research on the Correlation Filter Tracking Model Based on the Deep-Prunned Feature Network
## 3 Methods
### Online Updating of Deep-Pruned Feature Network with Alternative Kernels  
In the actual tracking process, interference factors such as occlusion, illumination changes, target scaling, and background switching can affect the ability of the deep-pruned feature network to accurately characterize the tracked target features. This leads to target drift and tracking accuracy degradation. In severe cases, it can lead to tracking failure. To solve this problem, first, the adaptive capacity of the feature network is monitored in real-time during the tracking process. When the adaptive ability of the feature network is detected to decline, the feature network is updated online to improve its adaptive capacity to changes in the tracking scene. _SSIM_[35] (structural similarity index) is a metric that measures the structural similarity of two images. It considers the blurred variation of structural information of images in human perception and measures the similarity of images in terms of brightness, contrast,and structure, respectively. SSIM has global statistical distribution characteristics, which are suitable for a wide range of interference factors and are also consistent with human visual habits. Therefore, we use SSIM as a measure to discriminate whether the adaptive ability of the feature network decreases during the tracking process. To discriminate the adaptive ability of the feature network in the tracking process, the position of the target in frame \(t-1\) is assumed to be \((x_{t-1},y_{t-1})\), and the predicted position of the target in frame \(t\) is \((x_{t},y_{t})\). The rectangular boxes \(S_{t-1}\) and \(S_{t}\) of the same size are the initial target boxes centered at \((x_{t-1},y_{t-1})\) and \((x_{t},y_{t})\) constructed in frame \(t-1\) and frame \(t\), respectively. The _SSIM_ of S\({}_{t-1}\) and S\({}_{t}\) is calculated using Equation (20) [35] as:  
\[SSIM(S_{t-1},S_{t})=\frac{\left(2\mu_{S_{t-1}}\mu_{S_{t}}+C_{1}\right)\left( \sigma_{S_{t-1}S_{t}}+C_{2}\right)}{\left(\mu_{S_{t-1}}^{2}+\mu_{S_{t}}^{2}+C_ {1}\right)\left(\sigma_{S_{t-1}}^{2}+\sigma_{S_{t}}^{2}+C_{2}\right)} \tag{20}\]  
where \(\mu_{S_{t-1}}\) and \(\mu_{S_{t}}\) represent the means of \(S_{t-1}\) and \(S_{t}\), respectively. \(\sigma_{S_{t-1}}\) and \(\sigma_{S_{t}}\) represent the standard deviations of \(S_{t-1}\) and \(S_{t}\), respectively. \(\sigma_{S_{t-1}S_{t}}\) represents the covariances of \(S_{t-1}\) and \(S_{t}\). \(C_{1}\), \(C_{2}\) are constants. The similarity between \(S_{t-1}\) and \(S_{t}\) is judged based on the result of Equation (20) and the pre-defined target frame similarity threshold \(TFSTH\). When _SSIM_ is larger than \(TFSTH\), \(S_{t-1}\) and \(S_{t}\) are considered similar, and the feature network has strong adaptability and does not need to be updated; when _SSIM_ is less than \(TFSTH\), it is considered that \(S_{t-1}\) and \(S_{t}\) are low in similarity, the adaptive capacity of the feature network decreases, and the feature network needs to be updated. The updating process of the feature network is as follows. 1. The desired gaussian response map, denoted as \(DGRM\), is constructed by centering on the target location of the frame \(tth\) predicted by frame \(t-1 th\), and the \(DGRM\) is used as Ground Truth. 2. The convolutional kernel parameters of the pre-pruned feature network are used as the initial values of the updating process, denoted as \(Kernel_{ij}(t-1)\), \((\text{j}=1,2,\ldots,\)\(PPCKN_{i})\). 3. Using the \(tth\) frame as input, feature extraction is performed with the pre-pruned feature network, and the output features are correlated with the filter to generate the output response; i.e., Response. The error between Response and \(DGRM\) is calculated by the loss function defined in Equation (21), and the convolutional kernel parameters are updated once based on Equations (1)-(4). The \(jth\) convolutional kernel in layer \(i\) of the updated pre-pruned feature network is denoted as \(Kernel_{ij}(t)\). \[Loss=\|Response-DGRM\|^{2} \tag{21}\]
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