Direct parameter estimation for generalised balanced power diagrams

The statistical characterisation and synthetic reproduction of a polycrystalline material's microstructure is assisted by mathematically representing its morphology by a tessellation model. The generalised balanced power diagram (GBPD) is a tessellation model that was shown in previous studies to accurately reproduce the microstructure morphology of various materials by closely matching micrographs obtained through electron microscopy. These studies employed costly optimisation procedures to determine the best-fit model parameters, limiting the scalability of the model. In this work, it is shown that setting the tessellation cell parameters to values such that the shape moments of the corresponding grains are matched results in a quality of fit that is commensurate with optimisation procedures. This fitting approach decouples the interaction among grains when fitting the tessellation parameters and, most notably, provides analytical, closed-form expressions for all the model parameters. The performance of this parameter fitting approach is demonstrated on multiple micrographs of various materials, and it compares similarly to the performance of optimisation procedures reported in recently published literature. As the fitted parameter values are obtained through trivial computations, this approach enables extensive scalability of the GBPD model such that it can be used to represent extremely large characterisation data sets.