# Deep Directional Network for Object Tracking
## 3 Direction Deep Network Tracker
### Direction Classification Network  
First, we classify positive samples into 11 categories based on direction information, as shown in Figure 3. Specially, the positive samples are divided into upper-left (\(D_{1}\)), left (\(D_{2}\)), lower-left (\(D_{3}\)), lower (\(D_{4}\)), lower-right (\(D_{5}\)), right (\(D_{6}\)), upper-right (\(D_{7}\)), upper (\(D_{8}\)), small-scale (\(S_{1}\)), large-scale (\(S_{2}\)) and true-sample (T), namely, 11 classes of direction information. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Input** & **Layers** & **Size** & **Number** \\ \hline \(112\times 112\times 3\) & Conv1 & \(7\times 7\) & 96 \\ \(53\times 53\times 96\) & Pool1 & \(3\times 3\) & \\ \(26\times 26\times 96\) & Conv2 & \(5\times 5\) & 256 \\ \(11\times 11\times 256\) & Pool2 & \(3\times 3\) & \\ \(5\times 5\times 256\) & Conv3 & \(3\times 3\) & 512 \\ \(3\times 3\times 512\) & FC4 & \(3\times 3\) & 512 \\ \(1\times 1\times 512\) & FC5 & \(1\times 1\) & 512 \\ \(1\times 1\times 512\) & FC6 & \(1\times 1\) & 11 \\ \(1\times 1\times 512\) & FC7 & \(1\times 1\) & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Architecture of the convolutional embedding function. Figure 2: Architecture of our direction learning network. In Figure 3, \([x_{l},x_{r},y_{u},y_{d}]\) represents the left boundary, the right boundary, the upper boundary, and the lower boundary, respectively, of the direction division. The setting of the boundary is determined by the size of the original target of the sample, as shown in Equations (2) and (3). Assume that the ground truth of the current frame is represented by \(\mathrm{g}_{t}=[x_{t},y_{t},w_{t},h_{t}]\), where \(x_{t}\) denotes the position of object along the x axis, \(y_{t}\) is the position of object along the y axis coordinate, \(w_{t}\) represents the width of the target along the x axis, and \(h_{t}\) is the height of the target along the y-axis. \[x_{i}=\left\{ \begin{array}{ll}x_{t}-\alpha w_{t}&if\ (i=l)\\ x_{t}+\alpha w_{t}&if\ (i=r)\end{array} \right. \tag{2}\]  
\[y_{j}=\left\{ \begin{array}{ll}y_{t}-\alpha h_{t}&if\ (j=u)\\ y_{t}+\alpha h_{t}&if\ (j=d)\end{array} \right. \tag{3}\]  
In Equations (2) and (3), \(\alpha\) is the scaling factor of the limited boundary; its specific value is described in the experimental section. The category of sample shown in Figure 3 will be determined by the limited boundary in Equations (2) and (3). \[c=\rho(\mathrm{g}_{s},[x_{l},x_{r},y_{u},y_{d}],[w_{t},h_{t}]) \tag{4}\]  
Equation (4) describes a mechanism for determining the sample category, where \(\mathrm{g}_{s}=[x_{s},y_{s},w_{s},h_{s}]\) is the positional information of the sample, and \(c\) is the output result of the category the sample belongs to. In the paper, \(\rho\) is the discriminant function. We use the bounding box \([x_{l},x_{r},y_{u},y_{d}]\) and sample location information \(\mathrm{g}_{s}\) to determine the direction category of the sample, and use \([x_{l},x_{r},y_{u},y_{d}]\). \(\mathrm{g}_{s}\) and the target's true width and height \([w_{t},h_{t}]\) to determine the scale variation category of the sample. \[c=\left\{ \begin{array}{ll}D_{1}&if\ (x_{s}\leq x_{l}\ and\ y_{s}\leq y_{u})\\ D_{2}&if\ (x_{s}\leq x_{l}\ and\ y_{u}<y_{s}\leq y_{d})\\ D_{3}&if\ (x_{s}\leq x_{l}\ and\ y_{s}>y_{d})\\ D_{4}&if\ (y_{s}\geq y_{d}\ and\ x_{l}<x_{s}\leq x_{r})\\ D_{5}&if\ (y_{s}\geq y_{d}\ and\ x_{s}>x_{r})\\ D_{6}&if\ (x_{s}\geq x_{l}\ and\ y_{u}\leq y_{s}\leq y_{d})\\ D_{7}&if\ (x_{s}\geq x_{r}\ and\ y_{s}<y_{u})\\ D_{8}&if\ (y_{s}\leq y_{u}\ and\ x_{l}<x_{s}<x_{r})\end{array} \right. \tag{5}\]  
The sampling rule will be introduced in Sections 3.4 and 4. The sample category is determined according to the area corresponding to the sample horizontal and vertical coordinate values, as described in Equation (5). If the sample's horizontal and vertical coordinates are in the area between the limited boundary, we will judge whether the target scale variation exists.