Résumé
Some geometrical and topological features of the excursions of smooth random fields will be presented, such as their expected Lipschitz-Killing curvatures. The concerned random fields will be Gaussian or Gaussian based, but also shot-noise fields will be considered. Based on these features, one can statistically infer some informations on the underlying random field, in particular statistical tests (of Gaussianity, or of isotropy) and parameters estimations. A special focus on the two-dimensional case will be payed as it is the natural framework for image analysis.
