# Integration of the 3D Environment for UAV Onboard Visual Object Tracking
## 4 Dataset and Evaluation Metrics
### Evaluation Metrics  
Similar to long-term tracking, the tracked object can disappear and reappear. Thus, no manual reinitialization is done when the tracker loses the object. To measure the performance, we utilize common long-term metrics--tracking precision \(Pr\), tracking recall \(Re\), and tracking F1-score \(F(\tau_{\theta})\)--at a given \(\tau_{\theta}\), introduced in [62] and used in [2, 6].  
Let \(G_{t}\) be the ground truth object bounding box, and \(A_{t}\) the bounding box estimation given by the tracker at frame \(t\). Further, let \(\theta_{t}\) denote the prediction confidence, which in our case, is the maximal score given by the tracker regarding its confidence on the presence of the object in the current frame \(t\). If the object is partially/fully occluded, we set \(G_{t}=0\); and similarly, if the trackers predicts an object with a confidence \(\theta_{t}\) below \(\tau_{\theta}\), we set \(A_{t}=0\). Furthermore, let \(n_{g}\) denote the number of frames with \(G_{t}\
eq 0\), where \(t_{g}\in N_{g}=\{1,...,n_{g}\}\), \(n_{p}\) is the number of frames with \(A_{t}\
eq 0\), and \(G_{t}\
eq 0\) with \(t_{p}\in N_{p}=\{1,...,n_{p}\}\). Lastly, \(\Omega(A_{t}(\theta_{t}),G_{t})\) describes the intersection-over-union (IoU) between \(G_{t}\) and \(A_{t}\).  
\[Pr(\tau_{\theta})=\frac{1}{|N_{p}|}\sum_{t_{p}\in N_{p}}\Omega(A_{t_{p}}(\theta _{t_{p}}),G_{t_{p}}), \tag{7}\]  
\[Re(\tau_{\theta})=\frac{1}{|N_{g}|}\sum_{t_{g}\in N_{g}}\Omega(A_{t_{g}}(\theta _{t_{g}}),G_{t_{g}}), \tag{8}\]  
\[\mathcal{F}(\tau_{\theta})=\frac{2 Pr(\tau_{\theta})Re(\tau_{\theta})}{Pr(\tau _{\theta})+Re(\tau_{\theta})}. \tag{9}\]  
The combination of tracking precision \(Pr(\tau_{\theta})\) and tracking recall \(Re(\tau_{\theta})\) as a single score is defined as the tracking F1-score \(\mathcal{F}(\tau_{\theta})\)[62]. Similarly to the long term challenges presented in [2, 6], the final tracking F1-score is used to rank the different tracking algorithms.  
The evaluation protocol is as follows: the trackers are evaluated on all objects present in the AU-AIR-Track. The annotated first frame of the object is used to initialize the tracker. From there, the tracker outputs a prediction bounding box for every subsequent frame where the object is annotated--even during occlusions, no reset is allowed. Tracking precision, tracking recall, and tracking F1-score are computed accordingly to Equations (7)-(9). To avoid statistical errors caused by the classification component of the visual tracker, which describes the appearance of the object through learned weights, we run an evaluation of every tracker five times on both sequences  
Figure 14: The probability distribution of ground-truth bounding boxes over the total sequence length for sequence 0 (**left**) and sequence 1 (**right**) from AU-AIR-Track.  
Figure 15: Filtered point cloud for both sequences composing the dataset. Left is a reconstruction of sequence 0 and right of sequence 1.  
of the AU-AIR-Track. For every evaluation \(e\) and for every object \(i\) present in a sequence, we take the maximum tracking F1-score for that object \(f_{\text{max}i}^{e}\). Considering the maximum tracking F1-score, regardless of \(\tau_{\theta}\), allows us to examine how the tracker would work without human intervention.  
For computing the final F1-score \(f_{\text{final}}\) of a tracker on a sequence of AU-AIR-Track: (1) we average maximum tracking F1-scores \(f_{\text{max}i}^{e}\) extracted from different evaluations \(e\) for the same object \(i\); then, (2) we average all \(f_{\text{max}i}^{e}\) belonging to the same sequence. Equation (10) describes how we computed \(f_{\text{final}}\). Let \(i\) denote the index of the object, with \(i\in I=\{1,...,n\}\); and let \(e\) describe the index for an evaluation, where \(e\in E=\{1,...,m\}\). In our case, we performed five evaluations for each tracker on the AU-AIR-Track.  
\[f_{\text{final}}=\frac{1}{|I||E|}\sum_{i\in I}\sum_{e\in E}f_{\text{max}i}^{e}. \tag{10}\]