Local Measures Distribution For The Estimation Of The Elongation Ratio Of The Typical Grain In Homogeneous Boolean Models

We introduce a particular localization of the Minkowski functionals to characterize and discriminate different random spatial structures. The aim of this paper is to present a method estimating the typical grain elongation ratio in a homogeneous Boolean model. The use of this method is demonstrated on a range of Boolean models of rectangles featuring fixed and random elongation ratio. An optimization algorithm is performed to determine the elongation ratio which maximize the likelihood function of the probability density associated with the local perimeter measure. Therefore, the elongation ratio of the typical grain can be deduced.