## 5 Metrics
### Metrics for Cell Tracking  
The metrics most frequently adopted for evaluating cell tracking are those introduced by the Multiple Object Tracking (MOT) [96]. The Multiple Object Tracking Accuracy (**MOTA**) [97] is a MOT tracking metric that represents the object coverage [90], also used for example in [63]. It can be defined as  
\[\text{MOTA}=1-\frac{FN+FP+IDSW}{T},\]  
where \(FN\) is the sum over the entire video of all missed cells (number of ground truth bounding boxes not covered by any computed bounding box), \(FP\) is the sum over the entire video of all false positives (number of bounding boxes not covering any ground truth bounding box), \(IDSW\) is the number of object identities switched from one frame to the next (number of bounding boxes covering a ground truth bounding box from a track different than in the previous frame), and \(T\) is the total number of detections in the ground truth.  
Multiple Object Tracking Precision (**MOTP**) [98] is the average dissimilarity between all correctly assigned detections (true positives) and their ground-truths, defined as  
\[\text{MOTP}=\frac{\sum_{i,i}d_{i,i}}{\sum_{t}c_{t}},\]  
where \(c_{t}\) indicates the number of matches in frame \(t\) and \(d_{i,i}\) is the bonding bob overlap of the detection \(i\) with its ground truth. This MOT tracking metric shows the ability of the tracker to estimate precise object positions, independent of its skill at recognizing object configurations, keeping consistent trajectories, and so forth [97].  
More recently, the MOT challenge introduced another tracking metric, named **IDFI**, that quantifies the object's identity across the frames of a sequence [90] and represents the ratio of the detections that were properly identified over the average number of ground-truth and computed detections [99]. It is an F-score as in Equation (4).  
\[\text{IDF1}=\frac{2*IDTP}{2*IDTP+IDFP+IDFN},\]  
where \(IDTP\), \(IDFP\), and \(IDFN\) indicate the number of true positive, false positive, and false negative IDs, respectively.  
Many other metrics introduced for evaluating MOT challenges could also be applied to the case of cell tracking, such as the Higher Order Tracking Accuracy (HOTA) [100].  
Focusing more specifically on cellular microscopy, the metric adopted in CTC [22] for evaluating cell tracking results is the Tracking Accuracy, denoted as **TRA**, used for example in [72; 90; 93]. It is a normalized weighted distance between the tracking ground truth and the result of the algorithm, with weights chosen to reflect the effort it takes a human curator to manually carry out the edits needed for matching the two. Tracking results are first represented as acyclic oriented graphs providing the cells lineage. Then the difficulty in transforming a computed tracking graph into the corresponding ground truth graph is estimated as  
\[\text{TRA}=1-\frac{\min(\text{AOGM},\text{AOGM}_{0})}{\text{AOGM}_{0}},\]  
where AOGM is the Acyclic Oriented Graph Matching (AOGM) measure [95] and AOGM\({}_{0}\) is the AOGM value required for creating the ground truth graph from scratch. TRA assumes values in [0, 1], with higher values corresponding to better tracking performance. The overall performance for the CTB is calculated as the average of the SEG (see Section 5.1) and TRA metrics:  
\[\text{OP}_{CTB}=\frac{1}{2}(\text{SEG}+\text{TRA}).\]