The integral geometry of random sets

Jonathan Taylor
University of Montreal

In various scientific fields from astrophysics 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 integral
geometric properties of these random sets, particularly their
Lipschitz-Killing curvature measures. I will focus on describing the
results, and sketching some proofs for a class of non-Gaussian random
fields (but built up of Gaussians) and the relation (the so called
Gaussian Kinematic Formula) between their Lipschitz-Killing curvature
measures and the classical Kinematic Fundamental Formulae of integral geometry.

Audio (MP3 File, Podcast Ready)

Back to Workshop IV: Image Processing for Random Shapes: Applications to Brain Mapping, Geophysics and Astrophysics