## 2 Literature
### Cell Tracking  
Object tracking consists in locating and monitoring one or more objects of interest and their behavior over time [21]. The image sequence containing cells can be acquired at specific time intervals using the time-lapse technique. When discussing cell tracking, it is generally assumed that segmentation or detection and classification have been performed.  
Some recent tracking methods are here reviewed. [PERSON] et al. [60] propose a global track linking algorithm, which links into tracks cell outlines generated by a segmentation algorithm. It is a batch algorithm that uses the entire image sequence to decide the links. Starting with the hypothesis that there are no cells in the image sequence, it adds one cell track at a time, in a greedy way, choosing the one maximizing a suitable scoring function, using the Viterbi algorithm. The algorithm can handle cell mitosis, apoptosis, and migration in and out of the imaged area and can also deal with false positives, missed detections, and clusters of jointly segmented cells. It has been tested on BF sequences, but in principle, it can be applied to any type of sequences, given a suitable segmentation algorithm to outline the cells. The algorithm has been implemented in several cell trackers, see for example the Baxter Algorithms package (see Section 3).  
[PERSON] et al. [61] propose **MitosisAnalyser**, a framework for detecting, classifying, and tracking mitotic cells in live-cell phase contrast imaging based on mathematical imaging methods. As pre-processing, denoising by Gaussian filter smoothing is applied, followed by rescaling. In the workflow, each mitosis is detected by using the circular Hough transform. The obtained circular contours are used for initializing the tracking algorithm, which is based on variational methods. Backward tracking is used to establish the beginning of mitosis by detecting a change in the cell morphology. This step is followed by forward tracking until the end of mitosis. The output provides the duration of mitosis and information on cell fates (e.g., number of daughter cells, cell death). The Matlab code is publicly available (see Section 3).  
In [62], [PERSON] et al. propose a Graphics Processing Unit (GPU)-based algorithm for tracking yeast cells in PhC microscopy images in real-time. The tracking by detection approach determines a minimum cost configuration for each couple of frames, given by the solution of a linear programming (LP) problem. The GPU-parallel software based on the simplex method, a common tool for solving LP problems, is obtained by exploiting parallelization strategies to maximize the overall throughput and minimize memory transfers between host and device, thus exploiting data locality. The software is publicly available (see Section 3).  
[PERSON] et al. [63] introduce **Usiigaci**, a semi-automated pipeline to segment, track, and visualize cells in PhC sequences. Segmentation is based on a mask regional convolutional neural network (Mask R-CNN) [64], while the tracking module relies on the Trackpy library [65]. A graphical user interface allows the user to verify the results. The software and annotated data are publicly available (see Sections 3 and 4).  
[PERSON] et al. [42], in the same paper as for segmentation, also propose a graph-based cell tracking algorithm for touching cells in BF microscopy images (BF-C2 DL-HSC and BF-C2 DL-MuSC datasets) from the Cell Tracking Challenge [22]. The adapted tracking algorithm includes a movement estimation in the cost function to re-link tracks with missing segmentation masks over a short sequence of frames. Their algorithm can track all segmented cells in an image sequence and only a subset, e.g., a selection of manually marked cells. Results for cell tracking are evaluated using the TRA and CTB metrics (see Section 5) and are shown to perform very well, with TRA scores of 0.929 and 0.967 for the BF-C2 DL-HSC and BF-C2 DL-MuSC images, respectively.