# Target-Aware Feature Bottleneck for Real-Time Visual Tracking
## 3 Proposed Method
### Incorporation of the Target-Aware Feature Bottleneck Module  
In this section, we describe the detailed operation for our proposed target-aware feature bottleneck module. Our goal is to reduce the channel dimension of the backbone feature representation for efficient and fast subsequent computation, with minimal trade-off in discriminative performance. At the high level, our target-aware feature bottleneck module (TAFM) operates as in  
\[{F_{z}^{\prime}},{F_{x}^{\prime}}=\texttt{TAFM}(F_{z},F_{x},b_{0}), \tag{6}\]  
where the output feature maps are \({F_{z}^{\prime}},{F_{x}^{\prime}}\in\mathbb{R}^{h\times w\times c^{\prime}}\) and the hyperparameter \(c^{\prime}<c\) is chosen for reduced computation. Using lightweight target and search feature maps\(F_{z}^{\prime},F_{x}^{\prime}\), the subsequent region proposal (Equation (2)) and classification and refinement (Equation (4)) can be performed with less FLOPs operation, and the amount of reduced computation can vary depending on the architecture of the prediction heads. Our target-aware bottleneck module processes feature maps \(F_{z},F_{x}\) through three stages, which are the (1) pre-modulation stage, (2) convolution stage, and (3) post-modulation stage. The convolution stage performs a simple point-wise conv operation which reduces the channel size from \(c\) to \(c^{\prime}\), whereas the pre- and post-modulation stages perform channel-wise feature modulation through affine transformation based on the target-aware information extracted from the target feature representation. First, we start from extracting the target-specific information to obtain target-adaptive parameters for feature modulation. To extract the target-specific information, we use the target feature map \(F_{z}\) obtained from the initial frame image \(I_{z}\) and the initial target bounding box \(b_{0}=[x_{0}^{c},y_{0}^{c},w_{0},h_{0}]^{T}\) with the box center coordinates \((x_{0}^{c},y_{0}^{c})\), width \(w_{0}\), and height \(h_{0}\). We obtain a spatially pooled target _context_ representation \(z^{\prime}\in\mathbb{R}^{s^{\prime}\times s^{\prime}\times c}\) as in  
\[z^{\prime}=\texttt{ROIAlign}(F_{z},{b_{0}}^{\prime}), \tag{7}\]  
where \({b_{0}}^{\prime}\) is the dilated initial target bounding box \({b_{0}}^{\prime}=[x_{0}^{c},y_{0}^{c},\gamma_{c}w_{0},\gamma_{c}h_{0}]^{T}\), and \(\gamma_{c}\geq 1\) is the hyperparameter for controlling the amount of context information to be included around the target object. Subsequently, from the pooled feature map \(z^{\prime}\), the feature modulation parameters for target-adaptive affine transformation are obtained using the target-aware parameter generator as in  
\[ \begin{split}\alpha_{z}^{p},\beta_{z}^{p},\alpha_{z}^{q},\beta_ {z}^{q}&=h_{z}(z^{\prime})\\ \alpha_{x}^{p},\beta_{x}^{p},\alpha_{x}^{q},\beta_{x}^{q}& =h_{x}(z^{\prime}),\end{split}  \tag{8}\]  
where all the output parameters are \(\alpha_{z}^{p},\beta_{z}^{p},\alpha_{z}^{q},\beta_{z}^{q},\alpha_{x}^{p}, \beta_{x}^{p},\alpha_{x}^{q},\beta_{x}^{q}\in\mathbb{R}^{N_{S}}\), and \(N_{g}\) is a hyperparameter for the number of feature groups. The output parameters are used for affine transformation where \(\alpha\): are later used as multipliers, and \(\beta\): are used as biases. The parameters with superscript \(p\) are used in the pre-modulation stage and with superscript \(q\) are used in the post-modulation stage, and the parameters with subscript \(z\) are used to modulate the target feature map \(F_{z}\) and with subscript \(x\) are used to modulate the search feature map \(F_{x}\). For our experiments, we choose the number of feature groups \(N_{g}\ll c^{\prime}<c\) for a reduced number of weights and increased efficiency, where group-wise modulation provides an adequate trade-off between performance and efficiency.