**Objectifs**: The aim of this course is to give an introduction to usual methods developed in Geostatistics and in Mathematical Morphology to model and to simulate random sets and functions (scalar and multivariate).

These models are useful in many physical situations with heterogeneous media, for which a probabilistic approach is required. We can mention for instance problems of fracture statistics of materials, the composition of permeabilities in porous media, scanning or transmission electron microscopy images (including multispectral images), rough surfaces or multicomponent composites, but also some biological textures. On a more macroscopic scale, these models are used in the case of orebody deposits, of oil reservoirs, and even to simulate some data in astronomy. They also generate textures to be used for image coding and synthesis. The common feature of these random structures is their domain of definition in R3, or even in Rn (with n > 3), which requires the use of more general models than standard Stochastic Processes

**Programme**: The main topics of the course are as follows :

- introduction to the theory of random sets,

- models of random space tesselations, boolean random sets and functions, space-time random sets and functions (dead leaves and alternate sequential models, reaction - diffusion).

The courses detail the construction of models, their main properties, and their use from experimental data by means of examples of application.A large part of the course is based on training by means of software Micromorph developed in CMM.

Structure of the course : Five full days in a single week. Lectures (50 %) and practical training on PC computers (50 %).

**Niveau requis :**Basic knowledge in probability theory and in stochastic processes.

**Modalités d'évaluation :**The students prepare a written project from data obtained on simulations.

**Dernière mise à jour :**mercredi 2 novembre 2011