# Fast and Accurate Visual Tracking with Group Convolution and Pixel-Level Correlation
## 3 Proposed Method
### Pixel to Global Correlation  
Correlation is the most important part of object tracking, which combines template features with search features and then connects them to the output of the classification and regression sub-networks. Unlike depth-wise correlation [3], which correlates template features with search features channel by channel, in this work, we use pixel to global correlation [25], which decomposes template features and correlates every pixel with the search features to obtain a correlated feature map S. This correlation can effectively suppress background interference, improve the target response on the feature map, and further improve the accuracy of the target bounding box.  
The process is shown in Figure 3, where the template features \(Z_{f}\in R^{C\times H_{0}\times W_{0}}\) are first decomposed into spatial feature vectors \(Z_{s}=\left\{Z_{s}^{1},Z_{s}^{2},\ldots,Z_{s}^{n_{z}}\right\}\), \(Z_{s}^{i}\in R^{C\times 1\times 1}\) for each pixel.  
\[n_{z}=H_{0}\times W_{0} \tag{3}\]  
Figure 3: Illustration of pixel to global correlation, where \(Z_{f}\) is the template feature, and \(X_{f}\) is the search feature. (**a**) The template feature is decomposed into feature vectors \(Z_{s}\) and \(Z_{c}\). \(Z_{s}\) converts the template feature into feature vectors according to each pixel position. \(Z_{c}\) converts the template feature maps of each channel into feature vectors. (**b**) Feature vectors \(Z_{s}\) and \(Z_{c}\) are successively correlated with the search feature \(X_{f}\) to obtain features \(S_{1}\) and \(S_{2}\). \(S_{2}\) is the correlation feature map combining the template and search features.  
Figure 2: (**a**) original bottleneck using triple activation function and triple normalization. (**b**) new bottleneck using two activation function and one normalization.  
Similarly, the template features are also converted into channel feature vectors, \(Z_{c}=\left\{Z_{c}^{1},Z_{c}^{2},\ldots,Z_{c}^{c}\right\}\), \(Z_{c}^{i}\in R^{n_{z}\times 1\times 1}\), according to the channel dimension. The search features are first correlated with the spatial feature vectors \(Z_{s}\) to obtain feature map \(S_{1}\) based on Equation (4):  
\[S_{1}=X_{f}*Z_{s}. \tag{4}\]  
Then, feature map \(S_{1}\) is correlated with the channel feature vectors \(X_{f}\) to obtain feature map \(S_{2}\) based on Equation (5):  
\[S_{2}=S_{1}*Z_{c}, \tag{5}\]  
where \(*\) represents the convolution process. Feature map \(S_{2}\) is obtained after both the channel features and spatial features of the template are correlated. Then, the classification and regression sub-networks complete the target prediction.  
Naive correlation [1] and depth-wise correlation [3] use whole template features as kernels to correlate the search features so that the adjacent sliding windows on the feature map produce similar responses, blurring the spatial information. As a refinement method, pixel to global correlation decomposes the template into 1\(*\)1 feature sub-kernels according to the space and channel to correlate the search region, which effectively reduces background interference and further improves the accuracy of the target bounding box, avoiding the blurring of features.