## The integral geometry of random sets

- Date: 09/28/2006

John Taylor (University of Montreal)

University of Calgary

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 statistical applications of the

(average) integral geometric properties of these random sets. What

makes all calculations possible is the use of the random functions

themselves as Morse functions and the Rice-Kac formula for counting the

average number of zeros of a function. Most of what I describe is joint

work with Robert Adler and Keith Worsley.

10th Anniversary Speaker Series 2006