# RAMC: A Rotation Adaptive Tracker with Motion Constraint for Satellite Video Single-Object Tracking
## 4 Experimental Details and Analysis
### Experimental Settings
#### 4.1.2 Evaluation Metrics  
To measure the performance of the tracking algorithms, two protocols (success and precision plots) in the online tracking benchmark [50; 51] are used. The success plot displays  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**SVs** & **Frame Size (px)** & **Cropped Region Size (px)** & **GSD (m)** & **Frame Number** & **Target** & **Target Size (px)** & **Rotation** \\ \hline Dubai & 4096 \(\times\) 3072 & 256 \(\times\) 218 & 0.92 & 147 & Car & 15 \(\times\) 7 & \(\surd\) \\ Muharraq & 4096 \(\times\) 2160 & 174 \(\times\) 193 & 0.92 & 500 & Car & 13 \(\times\) 6 & \(\surd\) \\ Hong Kong & 4096 \(\times\) 3720 & 268 \(\times\) 216 & 0.92 & 164 & Car & 14 \(\times\) 7 & \(\surd\) \\ Boston & 4096 \(\times\) 3720 & 215 \(\times\) 300 & 0.92 & 320 & Plane & 36 \(\times\) 33 & \(\surd\) \\ San Diego & 4090 \(\times\) 2160 & 135 \(\times\) 94 & 0.92 & 228 & Car & 13 \(\times\) 6 & – \\ Vancouver & 3840 \(\times\) 2160 & 501 \(\times\) 487 & 0.92 & 405 & Train & 16 \(\times\) 80 & – \\ Minneapolis & 4090 \(\times\) 2160 & 336 \(\times\) 328 & 0.92 & 268 & Car & 24 \(\times\) 7 & – \\ San Francisco & 3840 \(\times\) 2160 & 501 \(\times\) 501 & 1.00 & 500 & Ship & 15 \(\times\) 9 & – \\ \hline \hline \end{tabular}
\end{table}
Table 1: Details of the SV datasets. “px” = pixels.  
Figure 5: The SV datasets used in the experiments. A region marked by a yellow rectangle in each dataset is cropped out, and the tracked object, marked by the green rectangle, is displayed enlarged.  
the percentages of scenarios in which the \(overlap\) between the estimated bounding box \(b_{e}\) and ground truth \(b_{g}\) is larger than the threshold of \(t_{s}\in[0,\ 1]\):  
\[overlap=\frac{\left|b_{g}\cap\ b_{e}\right|}{\left|b_{g}\cup\ b_{e}\right|}, \tag{21}\]  
where \(\cap\) and \(\cup\) denote intersection and union operators, respectively, and \(\mid\cdot\mid\) denotes the number of pixels in the region. The precision plot records the percentage of scenarios in which the center location error (CLE) between the estimated location and ground truth is smaller than the threshold \(t_{p}\in[1,\ 50]\). The area under the curve (AUC) of the success and precision plots is selected to rank all trackers, avoiding unfair comparisons due to specific thresholds. We mainly rank trackers based on the AUC of the success plot because of its representativeness in evaluation [52]. The FPS is used to evaluate tracking speed.  
To narrow the gap between the rotating and axis-aligned bounding boxes in the evaluation, we propose an internal-shrinkage (IS) strategy, as shown in Figure 6.  
Most algorithms receive (initialize) and yield (output) axis-aligned bounding boxes. To optimize the evaluation process, we attempt to initialize and evaluate the algorithms using an external rectangle, as shown in Figure 6. In this way, the initial bounding box contains many backgrounds, and even a small angle deviation may greatly affect the overlap between the estimated external rectangle and the ground truth rectangle, as shown in Figure 6. Considering that the object of SV appears as an ellipse-like distribution pattern, we compute the internal ellipse followed by its external rectangle, as shown in Figure 6. Finally, we use the internal rectangle to initialize trackers that can only receive axis-aligned labels. In this way, the estimated rotating bounding boxes are converted to an external rectangle using the proposed IS strategy for the evaluation.