## 2 Literature  
### Cell Segmentation  
Image segmentation is the main task for producing numerical data from live-cell imaging experiments, thus providing direct insight into the living system from the quantitative cell information [23; 24]. Cell segmentation is the process of splitting a microscopy image into \"segments\", i.e., Regions Of Interest (ROIs), and produces an image where cells are separated from the image background by cell contours or cell labels. Accurate cell segmentations are crucial for many challenges involved in cellular analysis, including but not limited to cell tracking [25], cellular features quantification, proliferation, morphology, migration, interactions, and counting [26; 27; 28; 29]. Several steps are considered in the literature for achieving cell segmentation. Some authors [8; 20; 30] consider crucial to initially perform an image reconstruction step, which produces images with higher contrast between foreground and background, increasing the success of the subsequent image processing tasks. The image formation model in phase contrast microscopy can be studied to reduce artefacts and solve the inverse problem through a regularization approach [8]. Some ML-based methods are reviewed by [PERSON] et al. [20] for PhC and DIC images, while [PERSON] et al. [30] present an overview of how DL-based frameworks solve these inverse problems in optical microscopy. Cell detection (or identification) is also frequently adopted previous to segmentation [20; 22], with the aim of locating the cells in the image (e.g., via bounding boxes, as exemplified in Figure 2a). Some specific types of segmentation are frequently considered for cellular images [20; 31; 32; 33]. Semantic segmentation identifies the object (i.e., the cell) category of each pixel for every known object within an image, as exemplified in Figure 2b. Instance segmentation, instead, identifies the object instance (i.e., the cell with specific features) of each pixel for every known object within an image [34]; an example is given in Figure 2c. It should be observed that the problem of cell instance segmentation is sometimes intended as joint cell detection and segmentation (e.g., see [32]), while other times (e.g., see [20]) instant segmentation is used as a synonym for single cell segmentation. Some of the most recent segmentation algorithms are described in the following. In [23], [PERSON] et al. in the software named **DeepCell** adopt deep convolutional neural networks for cell segmentation for various types of microscopy images (PhC, Fluo, and PhC coupled with images of a fluorescent nuclear marker), also providing hints on design rules in training CNNs for this task (image normalization, data augmentation, hyper-parameter tuning, and segmentation refinement). They also extend the deep convolutional neural networks to perform semantic segmentation (i.e., not only image segmentation but  
Figure 2: Results of different image processing tasks: (**a**) cell detection; (**b**) cell semantic segmentation; (**c**) cell instance segmentation. also cell type prediction). The software and the adopted data are publicly available (see Sections 3 and 4). [PERSON] et al. [25] present **fastER**, a fast and trainable tool for cell segmentation that extracts texture and shape features from candidate regions, estimates their likelihood to be a cell with a support vector machine (SVM) algorithm, and calculates an optimal set of non-overlapping candidate regions using a divide and conquer approach. Candidate regions are chosen as the so-called extremal regions (regions with maximal size containing only pixels whose intensities are no greater than a specific threshold), similarly to CellDetect [35]. For each candidate region, a feature vector is extracted to train the SVM model, including typical shape and intensity information (size, major/minor axis lengths, eccentricity, average intensity inside and in its neighborhood, average and standard deviation gradient, and average heterogeneity) [36].