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.

Other Information: 

10th Anniversary Speaker Series 2006