## 1 Introduction  
Microscopy is a fundamental research pillar enabling scientists to discover the structures and dynamics of cells and subcellular components. Most of these components are _phase objects_, which means they are transparent and colorless and cannot be visualized under a light microscope. To overcome this limit, a solution consists in staining the components with dyes, also known as _fluorophores_ or _fluorochromes_. Such molecules absorb short-wavelength light, generally UV, and emit fluorescence light at a longer wavelength. This mechanism represents the basic premise of _fluorescence microscopy techniques_, and the fluorescence images show the specimen bright on a dark background. The staining techniques use different dyes to point out a specific cellular component. Then, the same specimen can appear with a red, blue, or green color and appearance, as depicted in Figure 1a,b. As the molecular genetic methodologies and tools advance, the fluorescence techniques become more specific and can be applied to a larger set of different model organisms [1; 2]. However, to ensure high-quality images, they require laborious and expensive sample preparation. Furthermore, the dyes reduce their luminance over time due to a light-induced degradation process called _photobleading_[3]. Finally, fluorescent techniques are invasive and interfere with the biological processes causing phototoxicity. On the contrary, _Label-free Imaging (LU)_ techniques can visualize many cellular structures simultaneously with minimal sample preparation, phototoxicity, and no photobleaching, making them particularly suitable for live-cell imaging. Thus, LI provides measurements complementary to fluorescence imaging for several biological studies. Based on optical principles, these techniques measure the light phase change (i.e., the refractive index) passing through the specimen and converting it into intensity modulations producing _qualitative_ phase contrast images, as exemplified in Figure 1c (the phase change information contained in LI images is non-linearly coupled with its luminance intensity and cannot be retrieved quantitatively. An image produced by LI techniques is a map of path-length shifts associated with the specimen, containing information about both the thickness and refractive index of its structure; for further details and explanations, see [4]). Among the traditional techniques to phase change imaging, there are _Phase Contrast_ (PhC) [5] and _Differential Image Contrast_ (DIC) [6] based on the phase gradient method and differential interference contrast, respectively, to measure the refractive index. Another LI technique very similar to DIC is the _Hoffman Modulation Contrast_ (HMC) [7]. Due to intrinsic limitations of the numerical conversion methods, phase contrast images contain artifacts [8] (i.e., bright halo surrounding cell contours) and the \"shade-off effect\", which produces low contrast inside the cells with an intensity very similar to the background. Although several methods have been developed to overcome these artifacts, automatic image processing of label-free images is still challenging, especially the segmentation task for separating cells from the background. Unlike the previous techniques, quantitative LI provides higher contrast and reduces artifacts. Among them, _Quantitative Phase Imaging_ (QPI) techniques refer to the microscopes showing phase quantitative information. Details concerning QPI techniques can be found in [10]. A further alternative to noninvasive techniques is Bright-Field (BF) microscopy. It represents the most straightforward configuration for the light microscope, which is not only cheaper but also does not require sample preparation [11]. BF images provide information about the cellular organization, and they are preferred to visualize specimens with low contrast from the background (unlike in fluorescence) or with low resolution and magnification visualization of thin cellular components (unlike in phase contrast).