Industrial processes involving granular media (population of particles: powders, crystals, fibers, etc.) are numerous and present in various industrial contexts (pharmaceuticals, nuclear, materials, agronomy, etc.). The geometric characterization of such particles has always been an issue, either to improve knowledge or to control the process with online property measurement if possible. For this purpose, the acquisition of 2-D images allows a direct visualization of the projected particles that needs to be exploited. One of the major problems is the superposition of particles, a consequence of the projected view. From such data, advanced image processing and analysis methods can be used to individualize and characterize particles (size, shape, spatial dispersion, etc.). However, these methods are not very effective when the granular medium is dense enough. To overcome this limitation, methods based on random (or stochastic) geometry provide digital twins to model and characterize these images of granular media. Synthetic images of granular media are simulated and statistically fitted to real data. The morphological characterization of the particles is then indirectly accessible. These different advanced methods of image analysis and stochastic geometry therefore provide digital tools for characterizing the morphology of granular media (a task that is generally difficult to perform with conventional methods). Our work should therefore lead to new online characterization tools, based on images processed by new algorithms that provide additional information to traditional methods, including shape factors.