Now, we turn our attention to the step in the analysis workflow that we call segmentation. If you remember, we come from the stage of reconstruction which have given us a three-dimensional volume representing our sample. This three-dimensional volume consists of boxes with three-dimensional pixels, you could say, small volume elements, where each element has a gray value, you could say, that represents the contrast of that volume as it appears through, for example, the absorption mechanism that we discussed earlier on. Now, this 3D volume will often be analyzed by looking at the slices through the volume. Like for example, a very simplified version here, where we just see a slice for war volume with some different domains of various gray levels that are represented here in a very simplified manner. Now, what do we want to do for our further analysis, is we want to divide these domains into some clearly labeled domains that the computer is able to use for the modelling steps, analysis steps, that follows the segmentation steps. The human brain very easily recognize the different domains, just by looking at the gray levels, and our brain is very quick to recognize that which domains have different colors or gray levels. But this is not so straightforward necessarily for the computer. For the very clean noise-free case, it is relatively easy, we can use a thresholding, where we say that everything that is lighter a certain way, level value will be assigned to one domain, one phase, one label, and the ones that are at a lower grade level will be assigned to another level. But if we have, for example, noise, which is very commonly the case for X-ray tomography, this becomes less straightforward. But whatever method we choose, we end up with a situation where we have our domain separated in some way or another into clearly identified labels that we then color. For example, we choose to say all the domains belonging to one phase, we color in blue, and the remaining phase in red, for example. Then, we have our segmented data slice that we can work with in the following analysis steps. The strategy we choose to do our segmentation will in each case, depend on the material in question, and also on the particular questions that we want to answer about our sample. Vedrana Andersen Dahl from DTU Compute will give us more detail about these segmentation strategies. It is important to carefully consider what is it you actually want to achieve with segmenting an image. Segmentation, it means partitioning any image into coherent parts, and often v will be using low level information from the image, for example, intensity, may be texture, maybe boundary. Sometimes, we want to partition image into parts which are semantically meaningful, and that might be a little bit more advanced problem. If we have some knowledge about our sample, which we will often have for materials, for example, we can use that information in our segmentation strategy. In material science, we usually know what our image shows. We usually know which materials we are looking at, and it is very useful to utilize this information. Also, as said, you want to consider how to represent the result of your segmentation. Is it okay to have the results where each pixel of your image is labeled by the segmentation labor, or you want to for example detect some objects in the image? If I should try to summarize what Vedrana just told us in a slightly more visual way, I can use this example here with some balls of equal size and equal color. We can use information we have about this symbol. In this case, that the domains that we are looking for, they have a certain size or radius, and certain shape, sphere, that can help us in identifying these domains uniquely, and assign them to one phase, whereas the space, the porosity you could call it in between the balls will be assigned to the other phase. This can then, of course, be taken to another level. We can add extra information about our our sample by including other material's properties of the domains that can be, here represented by color, or this could for materials case, for example, density or chemistry of the various domains that we use in order to help us labeling the various domains. So we can imagine that our single phase sample is mixed up with other phases in our three-dimensional volume, and we then use again as before we use, first of all, the shape and size of the domains in helping us finding the overall phase of solid, so to speak, with respect to the porosity, but we then further subdivided the solid phase into three different phases according to elements use properties like density or chemistry, here again represented by color. After the segmentation step, we have a representation of our volume with a number of phases, or classes, of domains that we have labeled out, and these have arbitrary shapes and sizes, and this is something that we cannot directly use in our modelling that will be the next step of our analysis. So, we need something to bind the information we have from the segmentation step over to the modelling step. The modelling we are covering here in the course is finite element modelling, and these methods will typically require that you represent your phases, your domains, your volume with a certain regular mesh, as you call it, represented here by a number of triangles that constitute, then the shape we have we want to model, and the finite element modelling expects to be able to represent the volume of the slice in this case through some functionals that represent the physical parameters that we want to model, and these can then be varied at the individual nodes that connect the triangles constituting the mesh. So, this is a necessary step to get from the segmentation to the modeling representations of our analysis.