## 1 Introduction
On the other hand, other works have used models where the graphite nodules are not considered as holes, but as ideal spheres of graphite, with the aim of making a thermoelastic formulation of the internal structure of graphite nodules to verify the elastic behavior of a DCI by means of an FEA [PERSON] et al. (2013). At this point, the works that are mentioned above have only used geometric models where nodules are considered as holes or ideal spheres. To represent how spherical graphite nodules are within a DCI, there is an index called _Circular Shape Factor_ (_CSF_), it has been shown that graphite nodules within a DCI have a _CSF_ value that varies between 0.9 and 1 [PERSON] et al. (2014), where a value of 1 would represent a completely spherical nodule or in two dimensions a perfect circle. Therefore, all of the works that have used idealized models have considered their nodules or holes with a _CSF_ value of 1, such consideration is impossible in the real morphologies, and also, as already mentioned, has significant effects on the mechanical behavior. On the other hand, there are the works that have developed models that try to fit or approach to the real geometry of the DCIs. For instance, the work of [PERSON] et al. [PERSON] et al. (2013), where they predicted [PERSON]'s effective modulus and [PERSON]'s ratio of a DCI based on a multi-scale computational model. The models were generated using image processing techniques to extract the coordinates of the pixels representing the graphite nodules contours, which are used to generate the model for the FEA. They considered a node within each pixel of the contour and then joined each node using straight lines. In this context, there is the work of [PERSON] et al. [PERSON] et al. (2014), which studied the distribution of strains that were produced in a tensile test of a DCI, when comparing finite element simulation and measurements by digital image correlation, in their work they used real micrographs to produce their models. Another work is that of [PERSON] et al. [PERSON] et al. (2016), in which it was developed a methodology for predicting the elastic behavior of a DCI using multi-scale analysis. The procedure combines computational techniques for FEA, micrographic analysis to generate FEA models, and micro-indentation tests to identify the elastic behavior of the different phases of the microstructure. The geometric models were generated employing image processing tools to segment the nodules; the model is estimated by considering a square matrix with square elements whose resolution was 1 \(\upmu\)m, in order to approach the DCIs geometry accurately. However, when the model is represented by square elements, the nodules contours are affected, which also is not realistic. In the methodologies that are followed by the previous works, the image processing is used to extract the graphite nodules contours conserving geometries that are more similar to the real models in comparison with the ideal models, however, when image processing techniques are applied, an error occurs in the extracted contours due to the discretization process at the pixel level, which can affect the real geometry of the DCI. In this sense, it is demonstrated that the variability in the geometry of the generated models has a significant effect on the values of the mechanical properties that were estimated by the application of a FEA, as demonstrated by the works of [PERSON] et al. [17] and [PERSON] et al. [18]. Therefore, it has been concluded, from the various works, that the need to generate geometric models closer to reality, since according to the methodology that was used to generate the models it is possible to obtain different variations in the geometries of the modeled material, and hence a variation in the estimated mechanical properties. As shown in previous works, image processing has been used to obtain realistic models, however, the problem lies at the moment of interpolating to generate the contours of the nodules, and so far, only simple and linear approximations have been reported.