# Target-Aware Feature Bottleneck for Real-Time Visual Tracking
## 3 Proposed Method
### Overview of the Baseline Tracking Algorithm
For points \((i,j)\) inside the target box region, the predicted point-wise bounding box regression map \(y_{R}\) represents the four corners of the estimated target bounding box where \(y_{R}^{(i,j)}\in\mathbb{R}^{4}\) regresses the four boundaries, which are the top, bottom, left-, and right-side coordinates given the target box. Afterward, the non-maximum suppression (NMS) operation is performed on the bounding boxes with the highest probability scores to remove overlapping boxes that exceed a given threshold, where the top-\(N\) candidate ROI (region-of-interest) boxes \(\{\hat{b}_{1},\dots,\hat{b}_{N}\}\) can be chosen for the subsequent region classification stage. Given the top-\(N\) ROI boxes from the previous region proposal stage, we refine these predictions to choose a single output bounding box with the highest classification score. First, using the candidate boxes \(\{\hat{b}_{1},\dots,\hat{b}_{N}\}\), the ROIAlign operation is performed as in \(x_{i}=\texttt{ROIAlign}(F_{x},\hat{b}_{i}),i\in\{1,\dots,N\}\) where \(x_{i}\in\mathbb{R}^{s\times s\times c}\) are the spatially pooled candidate feature representations with the same spatial and channel dimensions as the target feature representation \(z\). Afterward, the candidate feature representations \(x_{i}\) are cross-correlated with the target feature representation \(z\) as in  
\[\hat{x}_{i}=x_{i}\otimes z, \tag{3}\]  
where \(\otimes\) is the element-wise product between two tensors of identical dimensions. Then, from the cross-correlated features \(\hat{x}_{i}\in\mathbb{R}^{s\times s\times c}\), the ROI class logits \(y_{D,i}\in\mathbb{R}^{2}\) and box refinement values \(y_{S,i}\in\mathbb{R}^{4}\) are obtained as in  
\[y_{D,i}=f_{D}^{Q}(\hat{x}_{i}),\;y_{S,i}=f_{S}^{Q}(\hat{x}_{i}), \tag{4}\]  
where the branches \(f_{D}^{Q},f_{S}^{Q}\) also consist of convolution, ReLU, and normalization [62] layers. The output class logits are concatenated to summarize the classification scores \(y_{D}=[y_{D,1},\dots,y_{D,N}]^{T}\in\mathbb{R}^{N\times 2}\) to represent all binary logits for the ROIs, where the softmax operation is performed to obtain positive class probabilities and the \(k\)-th ROI \(\hat{b}_{k}\in\mathbb{R}^{4}\) with the maximum probability chosen for further bounding box refinement. Given the ROI \(\hat{b}_{k}=[x_{k}^{c},y_{k}^{c},w_{k},h_{k}]^{T}\), where \(x_{k}^{c},y_{k}^{c}\in\mathbb{R}\) are the horizontal and vertical center coordinates of the box, and \(w_{k},h_{k}\in\mathbb{R}\) are the width and height of the box, respectively, these values are refined using the refinement values \(y_{S,k}=[dx_{k},dy_{k},dw_{k},dh_{k}]^{T}\in\mathbb{R}^{4}\) as in  
\[ \begin{split}&{x_{k}^{c}}^{\prime}=x_{k}^{c}+w_{k}\cdot dx,\;\;\;{y_{k} ^{c}}^{\prime}=y_{k}^{c}+h_{k}\cdot dy,\\ & w_{k}^{c}=w_{k}\cdot\exp{(dw)},\;\;{h_{k}^{\prime}}=h_{k}\cdot \exp{(dh)},\end{split}  \tag{5}\]  
to produce a refined ROI of \(\hat{b}_{k}^{\prime}=[x_{k}^{c},y_{k}^{c},w_{k}^{\prime},h_{k}^{\prime}]^{T}\) which serves as the output of the tracker for a given frame.