# Multiple Object Tracking in Robotic Applications: Trends and Challenges
## 3 Mot Benchmark Datasets and Evaluation Metrics
### Evaluation Metrics  
The most common evaluation metrics are the CLEAR MOT metrics, which were developed by Refs. [22; 23]. Mostly tracked objects (MT) and mostly lost objects (ML) in addition to IDF1 are uses to present the leaderboards in MotChallenges. False Positives (_FP_) is the number of falsely detected objects. false Negatives (_FN_) the number of falsely undetected objects. Fragmentation (Fragm) is the number of times a track gets interrupted. ID Switches (IDSW) is the number of times an ID changes. Multiple Object Tracking Accuracy (_MOTA_) is given by (1), whereas Multiple Object tracking Precision (_MOTP_) is given by (2). Finally, frames per second (Hz) and IDF1 given by (3).  
\[MOTA=1-\frac{(FN+FP+IDSW)}{GT} \tag{1}\]  
Figure 11: Samples of the KITTI dataset including Pointcloud and RGB. Visual odometry trajectory (**top left**), disparity and optical flow map (**top right**), visualized point cloud data [95] (**middle**), and 3D labels (**bottom**).  
Figure 12: Samples of the UA-DETRAC dataset showing variation of illumination in the environment from a static camera.  
where \(GT\) is the total number of ground truth labels.  
\[MOTP=\frac{\sum_{i,j}d_{t,i}}{\sum_{t}c_{t}} \tag{2}\]  
where \(c\) is the number of matches in t frame and d is the correctly overlapping detections and tracks.  
\[IdentificationF1(IDF1)=\frac{1}{\frac{1}{IDF}+\frac{1}{IDR}} \tag{3}\]  
where identification precision is defined by:  
\[IDP=\frac{IDTP}{IDTP+IDFP} \tag{4}\]  
and identification recall is defined by:  
\[IDR=\frac{IDTP}{IDTP+IDFN} \tag{5}\]  
_IDTP_ is the sum of true positives edges weights, _IDFP_ is the sum of false positives edges weights, and _IDFN_ is the sum of false negatives edges weights  
The metrics used for evaluating on the UA_DETRAC dataset utilize the precision recall (PR) for calculating the CLEAR metrics, as introduced in Ref. [96]. In addition to these metrics, the HOTA metric introduced in Ref. [99] is calculated by the formula in (6).  
\[\int_{0<a\leq 1}HOTA_{\alpha} \tag{6}\]  
where  
\[\sqrt{\frac{\sum_{ceTp_{a}}(Ass\_IoU)_{a}(c))}{|TP_{a}|+|FN_{a}|+|FP_{a}|}} \tag{7}\]  
where  
\[Ass\_IoU=\frac{|TPA|}{|TPA|+|FNA|+|FPA|} \tag{8}\]  
where _TPA_, _FNA_, and _FPA_ are the association metrics.  
There has been a recent advancement in the multiple object tracking and segmentation (_MOTS_). This field tackles the issues related to the classic _MOT_ which are associated with the utilization of bounding box detection and tracking such as background noises and loss of the shape features. The MOTS20 Challenge [84] proposed metrics for evaluating methods that tackle this issue. The multi-object tracking and segmentation accuracy (_MOTSA_) is calculated using the formula in (9). Similarly, multi-object tracking and segmentation precision (_MOTSP_) and soft multi-object tracking and segmentation accuracy (_sMOTSA_) are found by the formulas in (10) and (11), respectively.  
\[MOTSA=1-\frac{(|FN|+|FP|+|IDSW|)}{|M|} \tag{9}\]  
where \(M\) is the ground truth masks.  
\[MOTSP=\frac{\tilde{TP}}{|TP|} \tag{10}\]  
where \(\tilde{TP}\) is the soft version true positives (_TP_).  
\[sMOTSA=\frac{\tilde{TP}-|FP|-|IDSW|}{|M|} \tag{11}\]