## 3 Model and Methods
### Correlation-Adaptive Partitioning of Feature Embeddings Module  
Considering the continuity of video sequences and to improve the structural integrity of patches, we propose a CAP module. The specific implementation process is as follows: For the input \(t\)-frame video sequence \(v=\{v_{1}\), \(v_{2}\),..., \(v_{t}\}\), we first use the \(a\)\(\times\)\(a\) sliding window to preprocess each video image to generate patches without superimposed pixels \(v_{a}=\{v_{a1},\,v_{a2},\,\ldots,\,v_{at}\}\), \(v_{au}\in\mathbb{R}^{l\times w\times c}\). We then use the \(b\)\(\times\)\(b\) sliding window to partition the patches of each frame, \(p\) feature embeddings are partitioned from each sliding window and arranged horizontally in turn. As the structure of the two-layer sliding window enlarges the receptive field to a certain extent, we do not set the superposition region in the process of partitioning patches. For any one frame in a video sequence \(v\), \(N\) feature embeddings are generated by the CAP module:  
\[N=\frac{h}{b}\times\frac{w}{b}\times p=H\times W\times p \tag{4}\]  
There are \(s=b\)\(\times\)\(b\) patches in the \(b\)\(\times\)\(b\) sliding window. To determine the integrity of the feature embedding within the sliding window for a patch \(x_{m}\in\mathbb{R}^{c\times 1}\), we take the correlation among patches as the basis for inference. We consider that the strong continuity of the feature information between frames in video sequences can be used to help partition the feature embeddings in the sliding window if all the patches in the sliding window at the same position in the video sequence are taken into account. Therefore, for any one patch \(x_{m}\) in the sliding window of \(v_{au}\), the number of patches for which the correlation is calculated is \(b\)\(\times\)\(b\)\(\times\)\(t\). However, the influence of changes in light intensity and viewing angle, occlusion, and other factors means that there may be a large amount of information redundancy in the video sequence, which will affect the partitioning of feature embedding in the sliding window. Furthermore, the large number of patches distributed along the video sequence increases the computational burden of a network. We solve these two problems by adopting the method of mean operation in the direction of the video sequence. The patch sequence \(v_{a}=\{v_{a1},\,v_{a2},\,\ldots,\,v_{at}\}\) is pooled into a reference patche matrix \(V_{a}\in\mathbb{R}^{h\times w\times c}\). Thus, when calculating the correlation, patches in \(x_{m}\) only successively operate with patches in the sliding window at the same position in \(V_{a}\). This method preserves the feature information of edge and texture structure and reduces the information redundancy in the video sequence. Moreover, the number of patches for computing correlations in the sliding window is reduced from \(b\)\(\times\)\(b\)\(\times\)\(t\) to \(b\)\(\times\)\(b\), which greatly reduces the computational cost of the network. For any patches \(x_{m}\) from the sliding window \(b\)\(\times\)\(b\) in \(v_{au}\), the correlation is calculated as follows:  
\[X_{m}=\sum_{n=1}^{s}\left[\text{ReLU}\left(W_{\text{x}}x_{m}\right)\right]^{ T}\cdot\left[\text{ReLU}\left(W_{\text{y}}y_{n}\right)\right] \tag{5}\]  
where \(y_{n}\) is a patch in the sliding window at the same position in \(V_{a}\); \(W_{\text{x}}\in\mathbb{R}^{(c/e)\times c}\) and \(W_{\text{y}}\)\(\in\mathbb{R}^{(c/e)\times c}\) are two adaptive correlation learning matrices, where \(e\) is the positive integer coefficient of the compressed computation. ReLU is the linear rectification activation function. For any one \(b\)\(\times\)\(b\) sliding window in van, we successively calculate the score of the correlation between patches \(x_{m}\) and \(s\) reference patches as the output result in an accumulative manner. Thus, the correlation calculation result sequence of s patches is \(X=\{X_{1},X_{2},\ldots,X_{s}\}\), \(X_{m}\in\mathbb{R}^{1\times s}\).