Appears in collection : 2019 - T1 - WS2 - Statistical Modeling for Shapes and Imaging

We consider three geometrical characteristics for excursion sets for 2D stationary isotropic random fields, known as Lipschitz-Killing curvatures, and closely related to area, perimeter and Euler characteristic of those sets.We propose unbiased estimators for fields satisfying a kinematic formula and compute explicitly these characteristics for several random fields, adopting a weak functional framework. Joint work with Agnès Desolneux (CNRS, CMLA, ENS Paris-Saclay), Elena Di Bernardino (CNAM, Paris), Céline Duval and Anne Estrade (MAP5, Paris).