General framework for testing Poisson-Voronoi assumption for real microstructures

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Modeling microstructures is an interesting problem not just in materials science, but also in mathematics and statistics. The most basic model for steel microstructure is the Poisson-Voronoi diagram. It has mathematically attractive properties and it has been used in the approximation of single-phase steel microstructures. The aim of this article is to develop methods that can be used to test whether a real steel microstructure can be approximated by such a model. Therefore, a general framework for testing the Poisson-Voronoi assumption based on images of two-dimension sections of real metals is set out. Following two different approaches, according to the use or not of periodic boundary conditions, three different model tests are proposed. The first two are based on the coefficient of variation and the cumulative distribution function of the cells area. The third exploits tools from to topological data analysis, such as persistence landscapes.