## 5 Metrics
### Metrics for Pixel-Wise Cell Segmentation  
Many different metrics are adopted in the literature to evaluate the performance of (cell) segmentation algorithms. The most frequently used is the one adopted for the CTC [22], generally denoted as **SEG**. Given the ground truth cell segmentation \(GT\) and the corresponding segmentation \(S\) computed with any segmentation algorithm, the Jaccard similarity index, also known as Intersection over Union (IoU), evaluates the degree of overlap between the true and the computed results and is defined as  
\[\text{IoU}(GT,S)=\frac{|GT\cap S|}{|GT\cup S|}, \tag{1}\]  
where \(|\cdot|\) indicates the cardinality of a set (i.e., the number of pixels) and \(\cap\) and \(\cup\) indicate the set intersection and union, respectively. This metric [63] is sometimes equivalently expressed in terms of the number of true positive pixels \(TP\) (\(TP=|GT\cap S|\)), false negative pixels \(FN\) (\(FN=GT-S\)), and false positive pixels \(FP\) (\(FP=S-GT\)) as  
\[\text{IoU}(GT,S)=\frac{TP}{FN+TP+FP}.\]  
The SEG metric adopted in the CTC for a particular video is then computed as the mean IuO over all the GT cells of the video. It should be observed that, although many authors refer to this metric as SEG [72; 93], others just refer to it as AP [45; 46; 74; 75; 88]. Further metrics frequently adopted [23; 25; 63] include  
* the **Recall**, also known as Sensitivity or True Positive Rate, \[\text{Recall}=\frac{TP}{TP+FN},\] (2)  
\begin{table}
\begin{tabular}{l l l l l l} \hline
**Name** & **[Ref]** & **Content** & **Link** & **\# Imgs** & **\# Cells/Tracks** & **\# Cell Lines** \\ \hline CTC & [22] & PhC, DIC, BF & [[http://www.celltrackingchallenge.net](http://www.celltrackingchallenge.net)]([http://www.celltrackingchallenge.net](http://www.celltrackingchallenge.net)) 1 & 213 & 1980/2944 & 5 \\ CTMC & [90] & DIC & [[https://wc.ischochoal.utexas.edu/ctmc/](https://wc.ischochoal.utexas.edu/ctmc/)]([https://wc.ischochoal.utexas.edu/ctmc/](https://wc.ischochoal.utexas.edu/ctmc/)) 2 & 80,389 & 1,097,2233 /1616 & 14 \\ [PERSON] et al. & [91] & PhC & [[https://osf.io/ysaq2/](https://osf.io/ysaq2/)]([https://osf.io/ysaq2/](https://osf.io/ysaq2/)) 1 & 19134 & NA 4 /2011 & 1 \\ Usigaci & [63] & PhC & [[https://github.com/ElsevierSoftwareX/SOFTX_2018_1581](https://github.com/ElsevierSoftwareX/SOFTX_2018_1581)]([https://github.com/ElsevierSoftwareX/SOFTX_2018_1581](https://github.com/ElsevierSoftwareX/SOFTX_2018_1581)) & 37 & 2641/105 & 1 \\ \hline \end{tabular}  
* 1 Accessed on 30 August 2022. 2 Unavailable at the time of writing. 3 Only bounding boxes are provided. 4 Only centroids are provided.  
that gives the percentage of detected true positive pixels as compared to the total number of true positive pixels in the ground truth;
* the **Precision**, also known as Positive Prediction, \[\text{Precision}=\frac{TP}{TP+FP},\] (3) that gives the percentage of detected true positive pixels as compared to the total number of pixels detected by the algorithm, providing an indication on the degree of exactness of the algorithm in identifying only relevant pixels;
* the **F-score**, also known as F-measure or Figure of Merit, \[\text{F}_{1}=\frac{2\cdot\text{Recall}\cdot\text{Precision}}{\text{Recall}+ \text{Precision}}=\frac{2\cdot TP}{2\cdot TP+FP+FN},\] (4) that is the weighted harmonic mean of Precision and Recall. All the above metrics assume values in [0,1] and higher values indicate better results.