Quebec Mathematical Sciences Colloquium

November 24, 2006 from 16:00 to 18:00 (Montreal/Miami time) On location

The integral geometry of random sets

Colloquium presented by Jonathan Taylor (Université de Montréal)

In various scientific fields from astro- and high energy physics to neuroimaging, researchers observe entire images or functions rather than single observations. The integral geometric properties, notably the Euler characteristic of the level/excursion sets of these functions, typically modelled as Gaussian random fields, have found some interesting applications in these domains. In this talk, I will describe some of the statistical applications of the (average) integral geometric properties of these random sets, particularly their Lipschitz-Killing curvature measures. Two aspects I will focus on our: i) using the Euler characterstic of the excursion at high level to approximate excursion probabilities and ii) a class of non-Gaussian random fields (but built up of Gaussians) and its relation to the classical Kinematic Fundamental Formulae of integral geometry.


CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, Salle / Room 6214